22 016 457 a Navigation Compendium. Wised Edition

Home , Alphard, Cupola (ISS module), Dead reckoning, Fortnight, Geographical pole, Nautical almanac

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ID 292 099 22 016 457

TITL! A Navigation Compendium. Wised Edition. INSTITUTION Naval Training Command, Pensacola, Fla.; Naval Training Publications Detachment, Washington, D.C. REPORT WO NAVTRA-10424-A PUB DATE 72 NOTE 207p. AVAILABLE PROMSuperintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20420 (Stock No. 0502-052-4710; no price quoted)

!DRS PRICE NP-$0.75 HC-510.20 PLUS POSTAGE DESCRIPTORS Electronics; Instruction; *Instructional Materials; *Navigation; *Oceanology; Physics; Science Education; Teaching Guides; *Technical Education IDENTIFIERS Navy

ABSTRACT This unit of instruction was prepared for use in navigation study at the Officer Candidate School, the various Naval ROTC Units, and within the fleet. It is considered a naval text. It covers a wide and expanding subject area with brevity. Basic and elementary navigational terms and instruments are presented and described. The use of charts and publications which constitute a source of information which the navigator constantly uses are presented in detail. Such topics as tides and currents, basic and advanced electronic navigation systems, nautical astronomy, time and timepieces, sight reduction and celestial computations are included in +he program. The appendixes include nautical charts, useful physical laws and trigonometric functions, extracts from various publications, and various forms of instruction from navigation workbooks. (!B) A NAVIGATION COMPENDIUM

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Source Lag Used by permission from United 2-1, 3-19, 9-14, 8-118-9, 8-6,9-1 States Naval Institute, Dutton's Navigation and Piloting, 12th Edition, 1969

Sperry Rand Corp, 2-6, 3-5 PREFACE

This Compendium has been prepared for use in Navigatitm study at the Officer Candidate School, the various Naval ROTC Units, and within the fleet. Originally prepared and used by CAPT H. 1i. Moore, USN (rd.) when tin instructor in the grade of LT at the Officer Candidate School, then published as a commercial text, it isnow in a second edition as a naval text.

The matee.al presented is intendett to provide the essentials tothe practice of gation. Accordingly, the Compendium coversa wide and expanding sui)ject area with brevity. This publcation has been prepared for printing by the Naval Training Publicationti Detachment, Washington, D. C,, for the Chiefof Naval Training,

Published by NAVAL TRAINING COMMAND First edition 1966 Revised 1972

UNITED STATES GOVERNNIENT PRINTING 01,11C WASIIIN(T()N, 1). C.: 1972 THE UNITED STATES NAVY

GUARDIAN OF OUR COUNTRY The United States Navy is responsible for maintaining control of the sea and is a ready force on watch at home and overseas, capable of strong action to preserve the peace or of instant offensive action to win in war. It is upon the maintenance of this control that our country's glorious future depends; the United States Navy exists to make it so.

WE SERVE WITH HONOR Tradition, valor, and victory are the Navy's heritage from the past, To these may be added dedication, discipline, and vigilance as the watchwords of the present and the future. At home or on distant stations we serve with pride, confident in the respect of our country, our shipmates, and our families. Our responsibilities sober us; our adversities strengthen us. Service to God and Country is our special privilege. We serve with honor.

THE FUTURE OF THE NAVY The Navy will always employ new weapons, new techniques, and greater power to protect and defend the United States on the sea, under the sea, anti in the air. Now and in the future, control of the sea gives the United States her greatest advantage for the maintenance of peace and for victory in war. Mobility, surprise, dispersal, and offensive power are the keynotes of the new Navy. The roots of the Navy lie in a strong belief in the future, in continued dedication to our tasks, and in reflection on our heritage from the past. Never have our opportunities and our responsibilities been greater.

ii CONTENTS

CHAPTERS AND SECTIONS PAGE

1 INTRODUCTION TO NAVIGATION 101Navigation Defined,...... 1 102 Basic Definitions....swiss's.... 1 103 Direction, a.m... , .... 3 104 Basic Units,, , 3

2 THE COMPASS 4 201Introduction...... 4 202 Magnetism ,...... 4 203Earth's Magnetism , .1...... 4 204Variation and Deviation ,,,,,,, ., 6 205 Compass Designationwit...is.... 6 206 Compass Nomenclature,...... 6 207Limitations..... , 8 208 Compass Error , ...... 9 209 Compass Correction, OOOOOOOOOOOOOOO, 10 210Swinging Ship...... OOOOOOOOO 10 211Practical Compass Adjustment....,,,.,. 10 212 TheGyrocompass...... 11 213Principles of Gyrocompass Operation 11 214 Comparison of Gyrocompass and Magnetic Compass 12 215Gyro Error a 12 216Gyro Systems 14 217The Gyro Repeater i 14 3 NAVIGATIONAL INSTRUMENTS 15

301General 15 302Bearing Taking Devices 15 303Speed Measuring Devices 16 304 Automatic Dead Reckoning Equipment 19 305Short Range Measuring Instruments 20 306Depth Measuring Devices 21 307Electronic Instruments 22 308Celestial Navigation Instruments 23 309Timepieces 24 310Plotting Instruments 25 311. Weather Instruments 27 312Miscellaneous Instruments 28 iii ensidvito arm smoume 10Vd

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T A CHAPTERS AND SECTIONS PAGE

8 BASIC ELECTRONIC NAVIGATION SYSTEMS.. 66 801Gimeral ...... a .66 802MarineRada:monseseese II 66 803Radio Direction Finder esseesseese.s 66 804Radar was .s 67 805Advantages and Limitations ofRadi;r,6 geese67 808Accuracy of Radar . .. eases68 807Radar Fixessees . . sees 68 808Virtual PPI Refleotosoope (VPR) . 6d 809Radar Beacons. . . . 69 810TI__ can _ _ ...... eeeee se69 811Shoran, . 69 812Sonar ,...... sees.e 69 813Loran . . 69 814Theory of Loran-A Operation ,, .,. 70 815Loran-,1 Interference ...... 72 816Advantages and Limitations of Loran-A . . 73 817Loran-A Charts 73 818Loran-A Operation. ,,, 74 819Loran-C 76 820Decoa 76

9 ADVANCED ELECTRONIC NAVIGATION SYSTEMS, 78

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11 TIME 94

1101Introduction 94 1102Time Measurement 94 1103Solar Time 94 1104Time and Arc 97 1105Sidereal Time 97 1106Timepieces 98

V CHAPTERS AND SECTIONS PAGE

12 SIGHT REDUCTION 100

1201Introduction 100 1202Marine Sextant 101 1203 Correcting Sextant Altitudes 103 1204Finding Greenwich Hour Angle and Meridian Angle 106 1205Finding Declination 108 1206 GHA and Declination by Air Almanac 108 1207Solution of the Astronomical Triangle by H.O. 214 109 1208Plotting the Celestial Fix 112 1209Sight Reduction by H.O. 249 113 1210Sight Reduction by MO. 229 114 1211Sight Reduction by H.O. 211 116

13 OTHER CELESTIAL COMPUTATIONS 117

1301Introduction 117 1302Latitude by Meridian Sight 117 1303 Computing Zone Time of Local Apparent Noon (LAN) 119 1304Latitude by Polaris 120 1305Sunrise, Moonrise, and Twilight 122 1306Star Identification' 123 1307 Azimuth of the Sun 127 1308 Azimuth by Polaris 129

14 DUTIES OF THE NAVIGATOR 130

1401Introduction 130 1403Detailed Duties 130 1403Leaving and Entering Port 131 1404Coastal Piloting 133 1405Navigation at Sea. 134 1406Preparation of the Position Report 134 1407Life Boat Navigation 135

APPENDICES 138

INDEX 194

vi CHAPTER 1 INTRODUCTION TO NAVIGATION

101. NAVIGATION DEFINED PILOTING. A near-shore navigation method by which the movements of a ship are directed According to John Hamilton Moore in hisby reference to landmarks, other navigational book The Practical Navigator, as revised byaids, and soundings. Joseph Dessiou and published in London in 1814, "The end and business of Navigation is to in- ELECTRONIC NAVIGATION. A method of struct the mariner how to conduct a ship throughnavigation which employs the use of various the wide and pathless oceans, to the remotestelectronic devices. Electronic navigation differs parts of the world, the safest and shortest way,from piloting primarily in the manner of col- in passages navigable." This definition as ap-lecting information. Procedures involving dis- pearing over a century and a half ago in aplay and evaluation are very similar. manual which was to later have an important American counterpart, The American Practical CELESTIAL NAVIGATION. The determina- Navi ator by Nathaniel Bowditch, remains essen- tion of position by the observation of celestial tial y va id and states the purpose of this com- bodies(sun, moon, planets, and stars). pendium. Nevertheless, navigation as practiced today extends to the air and to outer space. It Navigation may be classified according to is deemed to be both an art and a science. practice as: (1) marine navigation, (2) air navi- With this as a point of departure, a moderngation, and (3) space navigation. The first two definition follows. are basically the same, differing slightlybe- Navigation is the art or science ef. deter-cause of the speed extremes representedby mining the position of a ship or aircraft andaircraft and surface vessels. In aircraft it is of directing that ship or aircraft from one posi- impracticableto strive for marine standards tion to another.It can be regarded as an artof accuracy since it is more import to know uecause its application involves the exercise ofyour approximate present position than your special skills and fine techniques which can be exact position earlier. As airnavigation is perfected only by experience and careful prac-essentially an extension of marine navigation, tice. On the other hand, the subject with equalspace navigation is an extensionof air naviga- validity can be regarded as a science inasmuch tion. Space navigation is developing as required asitis a branch of knowledge dealing with afor the operation of space vehicles. In anticipa- body of facts and truths systematically arrangedtion of interplanetary travel, a body of theory is dnd showing the operation of generallaws. rapidly being expanded and applied to provide Navigation has been practiced for thousands of for navigation in the nearly limitless space of years; however, modern methods date from the the universe, invention of the chronometer, a precision timepiece, in the 18th century. In our discussion we 102. BASIC DEFINITIONS shall find it convenient to divide the subject into four categories as follows: Elementary navigation terms are common to both navigation and geography. The following DEAD RECKONING. A method of navigation are basic: by which the position of a ship is calculated from its last well determined position and its EARTH. The planet with which we are most subsequent direction and rate of progress through familiar. Although it is approximately an oblate the water. spheroid, for navigational purposes we assume

1 A NAVIOATION COMPENDIUM

NORTH POLE

EARTH'S Amp

GREENWICH SHIP'S MERIDIAN GREENWICH MERIDIAN (PRIME)

EQUATOR

SMALL CIRCLE (PARALLEL) SAM

LARGE CIRCLES

SOUTH POLE

65,116(190) Figure 1.1.Earth's coordinate system.

it to be a true sphere about 21,600 nautical miles of every meridian contains the axis ofthe earth. in circumference, (See fig. 1-1.) The poles bisect each meridian; this provides AXIS. The diameter upon which the earth an upper branch and a lower branch. The upper rotates. branch of a meridian is the half betweenthe poles which contains a given position, The lower POLES. The extremitieg of the earth's axis, branchisthe oppositehalf."Meridian"in One is called the north pole (Pn), and theother common usage refers to the upper branch. When the south pole (Ps). the lower branch is spoken of,it must be so GREAT CIRCLE, A circleon the surface specified, of a sphere, the plane of which passes through the center of the sphere. PRIME MERIDIAN, That meridian which passes through the original site of the Royal SMALL CIRCLE. A circleon the surface Observatory in Greenwich, England and is used of a sphere, the plane of which does notpass as the origin or measurement of longitude. It is through the center of the sphere. also referred to as the GREENWICH MERIDIAN. EQUATOR. The great circle on the surface LATITUDE. The angular distance between of the earth which is equidistant from the poles. a position (on the earth) and the equator measured The plane of the equator is perpendicular tothe northward or southward from the equator alonga axis of the earth. meridian and labeled as appropriate, "N"or "S." Latitudemay be abbreviated as "L" or PARALLELS. Small circleson the surface "Lat." of the earth having planes parallel to the plane of the equator and perpendicular to the axis of the LONGITUDE, The angular distance between earth. a position (on the earth) and the prime meridian measured eastward or westward from the prime MERIDIANS. Great circleson the earth's meridian along the arc of the equator to the surface which pass through the poles. The plane meridian of the position, expressed in degrees

2 Chapter 1 INTRODUCTION TO NAVIGATION from 0to180, and labeled as appropriate, RHUMB LINE. A line on the surface of the "E" or "W." Longitude may be abbreviated asearth which makes the same oblique angle with "Long." or with the Greek letter lambda (A).all intersected meridians. 103. DIRECTION 104. BASIC UNITS The direction of a line is the angular inclination of that line to the meridian, measured right DISTANCE, which is the length of a line or clockwise from the north point of the meridianjoining two places on the surfaceof the earth, and expressed in three digits. Direction along ais expressed in nautical miles.One nautical mile meridian itselfis either north (000) or southequals 6,080.2feet and is by definition also (180). With direction defined, we may considerequal to one minute of latitude, or oneminute the following related terms: of arc along any great circle.Dividing the circumference of the earth by thenumber of COURSE, The direction of travel as ordereddegrees in a circle (360), we findthat one degree to the helm for the ship's movement. of arc of a great circle (acircumference) is equaltosixtynauticalmiles.Dividingthis HEADING. The direction a ship points at avalue by the number of minutesin a degree (60), given instant. Heading may differ from course.we conveniently find that oneminute of are of a COURSE MADE GOOD OR TRACK. The great circle is equal to onenautical mile. Thus, direction of a point of arrival from the pointof arc can be convertedto distance, and distance departure. to arc. Distance refers torhumb line distance unless otherwise specified. Theshortest distance BEARING. Thedirection of a terrestrialbetween two points on thesurface of the earth object from an observer. A truebearing isisthe great circle arc connecting them.For measured with reference to the true meridian.navigational convenience, it is common practice A magnetic bearing is measured with referenceto treat the nautical mile as being2000 yards in to the magnetic meridian. A compassbearing is length. measured with referencetothe axis of the SPEED is velocity of travel and is expressed compass card. A relative bearingis measuredin knots. One knot equals one nautical mile per with reference to the fore and aft axisof the hour. ship. Relative bearing plus true heading equals ANGLES are 4.cpressed in degrees and tenths true bearing. All bearings are converted totrueof degrees orin degrees, minutes, and tenths bearings for plotting. of minutes. Example: 349°.6 or 95 °- 14'.7. AZIMUTH. The true direction of a celestial DEPTH is expressed in either feet (P) or body from an observer. fathoms (fm). One fathom is equal to six feet.

3 CHAPTER 2 THE COMPASS

201. INTRODUCTION The intensity is ameasure of the force of attraction and is inversely proportionalto the square The measurement of direction is accomplished of the distance from the pole. A line ofmagnetic by means of the compass, of which thereare twoforce, as mentioned above, isa line connecting types, magnetic and gyro. The former utilizestwo poles along whichan isolated pole would the earth's magnetic field for directive force, move when acted upon by (the earth's) magnet- whilethelatter,as addressed later in this ism. chapter, employs the principles of gyroscopic For the purposes of this discussion,mag- inertia and precession, and the natural phenomenanetism may be thought of as being eitherperma- of the earth's rotation and gravitationalfield. nent or induced, dependingupon the magnetic The magnetic compass,one of the oldest of theproperties of the materials involved navigator's instruments, is of unknown origin. and upon the It manner in which the magnetism is acquired. is believed that the Vikings used itin the The magnetism of materials suchas the high eleventh century. Probably, the first magneticcarbon steel alloys which havea high degree of compass was simply a magnetized needle thrust magnetic retentivity is said to bepermanent as it through a straw, resting in a container ofwater.will continue to bea property of the material The needle was probably magnetizedusing lode-for a long time unless subjectedto extreme heat stone, an iron ore having magnetic qualities.or shock. Today, despite the rising importanceand great Some materials, for example, softiron, which convenience of the gyrocompass, the magnetichave a high degree of permeability,are capable compass retainsits importance because of itsof acquiring magnetism by beingplaced in a simplicity and reliability. A shipmay be sub- magnetic field. The magnetism producedin this jected to electrical power failure, fire, collision, manner is referred to as induced magnetism. grounding, or other hazard, and yet the magneticWhen the influence of the originalmagnetic field compass will usually remain operative. is removed, the induced magnetismdisappears. 202. MAGNETISM 203. EARTH'S MAGNETISM

A magnet is any piece of metalhaving the As a result of its content ofmagnetic mate- property of attracting other pieces of metal. Inrials, the earth has magneticproperties and may its natural state, lodestone or magneticoxide of be treated as a magnet. The magneticpoles are iron, has this property. Ferrous metaland certain located approximately as follows (see fig.2-1): alloys become magnets by being subjectedto the influence of strong magnets. North magnetic pole-74 N; 101 W. In any magnet, thepower of attraction is South magnetic pole-68 S; 144 concentrated at opposite endsor poles. At a E. point about midway between the poles the forceof To avoid confusion when speakingof the action attraction of one pole equals the force of attrac-of poles, colors have been assigned.The earth's tion of the other. The area of influencearound north magnetic pole is designatedas "blue," a magnet is known as a magnetic field; atany and the south magnetic pole isdesignated as given point within this magnetic field the force "red." A law of magnetismstates that unlike of magnetic attraction has both directionand poles attract each other while likepoles repel. intensity. The direction is the inclination ofthe Thus thenorth. seeking pole ofa magnet is line of magnetic force to some given reference.attracted to the earth's north magneticpole and

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is said to be "red" while the south seeking pole meridian;itmust be labeled. east or west. is attacted by the earth'^ south magnetic pole When from the observer'sposition facing north, and is said to be "blue," the magnetic meridian is to the rightor east- The magnetic lines of force which connect the ward, itis labeled east, Under the same cir- magnetic poles may be called magnetic meridians. cumstances, except with the magnetic meridian These meridians are not great circles.Because to theleft or westward,itis labeled west. of the irregular distribution of magnetic material Variation changes with geographiclocality and in the earth, the meridians are irregular, and the may be found on Oceanographic Office Chart 42. planes of the magnetic meridians do not nixes- See figure 2-1. sarily pass through the center of the earth. Mid- way between the magnetic poles a circle called The magnetic compass, being sensitiveto the magnetic equator crosses the magnetic merid- magnetic materials, is affected by ferrous metal ians. within its vicinity (for example the shipupon The earth's magnetism undergoes diurnal, whichitis mounted). This source oferror, annual, and secular changes. Ditwnal changesare which causes the axis of thecompass card to daily changes which are caused by the movement deviate from the magnetic meridian,is called of the magnetic poles in an orbit havinga diam- "deviation." Deviation may be definedas the eter of about 50 miles. Annual ,;hanges simply inclination of the axis of thecompass card to the represent the yearly permanelit change in themagnetic meridian; it is labeled eastor west in earth's magnetic field. Secular changes are those the same manner as variation. The valueof which occur over a great period ofyears. deviation changes with the ship's heading.This If a magnetic needle is freely suspendedin is due to the fact that the ship's inducedmag- both the horizontal and the vertical plane, it will netism varies as the ship changes itsposition seek to align itself with the magnetic meridian relative to the earth's magnetic field. (a magnetic line of force). The vertical angle of inclination with the horizontal plane (planeper- 205. COMPASS DESIGNATION pendicularto force of gravity) made by the magnetic needle is called "dip" and the magnetic needle used to illustrate this vertical angleis The magnetic compasson board ship may called a dip needle. At the magnetic equator, be classified or designated accordingto location dip is 0 degrees; with an increase in magnetic or usage. The magnetic compass located ina latitude, dip increases, reaching 90 degreesat position favorable for taking bearings and used the magnetic poles. in navigation is called the standard (STD)com- The direction and intensity of theearth's pass.The magnetic compass at thesteering magnetic field may be resolved into horizontal station used normally for steering,or as a and vertical components. At the magnetic equi,tor standby when the steering gyro repeaterfails, the horizontal component is of maximum strength is called the steering (STG)compass. Direction and at the magnetic poles the vertical component from either of these instruments mustbe labeled isof maximum strength. A magneticcompass as"per standard compass (PSC)"or "per actually reacts to the horizontal cY nonent of steering compass (PStgC)," for identification. theearth's magneticfieldand tnerefore its A magnetic compass locatedaft at a secondary sensitivity reaches a maximum at the magnetic steering station is called the aftercompass. A equator and decreases with increases in magnetic compass carried in a boat is properly calleda latitude. Dip, which indicates the comparative boat compass. strength of components, may be found by consulting Oceanographic Office Chart number 30, for 206. COMPASS NOMENCLATURE any position on the earth's surface. 204. VARIATION AND DEVIATION The following components makeup a standard 7 1/2 inch Navy compass (7 1/2 inchrefers to Since the magnetic poles do not coincide with diameter as depicted in fig. 2-2): the true poles, and the magnetic meridians do not coincide with the true meridians, th:reare MAGNETS. Four (two in older compasses) two lines of reference differing by a value called cylindricalbundlesof steel wire, with mag- "variation." Variation may be definedas the in- neticproperties,or bar magnets, which are clination of the magnetic meridian to the true attached to the compass card to supply directive

6 Chapter 2 THE COMPASS

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45.595(69) Figure 2-2. U. S. Navy 7 1/2-inch compass. force. Some newer compasses have a circular mark, and the fluid. Part of the bottom may be magnet made of a metallic alloy. transparent (glass) to permit light to shine upward against the compass card. COMPASS CARD. An aluminum disc graduated in degrees from 0 to 360 and also showing FLUID. A liquid surrounding the magnetic cardinal and intercardinal points. North is usually element. By a reduction of weight in accordance indicated by the fleur de lis figure in addition with Archimedes principle of buoyancy, friction to the cardinal point. Being attached to the mag- is reduced making possible closer alignment of nets, the compass card provides a means of the compass needle with the magnetic meridian. reading direction. Any friction present will tend to prevent com- pletealignment withthemagnetic meridian. COMPASS BOWL. A bowl-shaped container In older compasses the liquid may be a mixture of nonmagnetic material (brass) which serves ofethylalcohol and water in approximately to contain the magnetic element, a referenceequal parts. The alcohol serves to lower the

7 A NAVIGATION COMPENDIUM freezing point of the mixture. Newer compasses contain ahighly refined petroleum distillate similar to varsol, which increases stability and efficiency and neither freezes nor becomes more viscous at low temperatures. FLOAT. An aluminum air-filled chamber in the center of the compass card which further reduces weight and friction at the pivot point. EXPANSION BELLOWS. A bellows arrangement in the bottom of the compass bow' which operates to keep the compass bowl completely filledwithliquid,allowing fortemperature changes. A filling screw facilitates Addition of liquid which may become necesso.? notwith- standing the expansion bellows. LUBBERS LINE. A reference mark on the insideof the compass bowl which is aligned with the ship's fore and aft axis, or keel line of the ship. The lubbers line is a referenc,: for the reading of direction from the compass card. The reading of the compass card on the lubbers line at any time is the ship's heading. GIMBALS. The compass bowl has two pivots which fit or rest in a metal ring also having two pivots which rest in the binnacle. This arrangement (gimbals) permits the compass to remain almost horizontal in spite of the motion of the bt ship. An important concept is that, regardless of the movement of the ship, the compass card remains fixed (unless some magnetic material is introduced to cause additional deviation from the magnetic meridian). The ship, the compass 112.7 bowl,andthelubbers line move around the Figure 2-3. Binnacle containing magnetic com- compass card. To the observer as he witnesses pass. this relative motion, it appears that the compass card moves. (b) It is useless at the magnetic poles and is BINNACLE. A nonmagnetic housing (fig. 2-3) sluggish and unreliable in areas near the poles. which supports the magnetic compass and pro- (e) Deviation changes as the ship's magnetic vides a means of inserting corrector magnets propertieschange.The magnetic properties for compass adjustment as explained in art. 211. change with changes in the induced magnetism, The binnacle also contains a light, usually below changesintheship's structure or magnetic the compass bowl,to permit the reading ofcargo. Prolonged periods in dry dock, or along- direction at night. side a dock, the heavy shock of gunfire or of riding out a heavy sea, and the vessel being 207. LIMITATIONS struck bylightning,canalterthemagnetic properties. The following characteristics of the magnetic (d) Deviation changes with heading. The ship compass limit its direction-finding ability: as well as the earth may be considered as a magnet. The effect of the induced magnetism (a)It is sensitive to any magnetic disturb- upon the compass changes with the ship's head- ance. ing.

8 Chapter 2 THE COMPASS SFS' COPY AVAILABLL

(e)It does not point to true north. (f)It requires adjustment annually, and more often if the ship is subjected to such influences as MAtiNt T le COMPASS1AYlp those described in (c) above. AAviNIPS 11 JO 4 t44 bah 140/41, .," . ,../A A. T.'!Attlii..; 208. COMPASS ERROR w Coil Compass error, defined as the inclination of X.05,'' 5'4"I (I .P1 P the axis of the compass card to the true meridian, X ".' 0.PtV may be easily computed since it is the algebraic sum of variation and deviation. Compass error II, 71 Lionel ??Iid (fig. 2-4) must be applied tocompass direction thin to get true direction and must be applied to true 11)41);%%1Abt, 11-'1, ir4 110 '14 114 11% 11 1,%7 direction, with reversal of sign, to arrive at ". . compass direction. Variation is usually found . 1 recorded within the compass rose or direction ) 1,1W 0.(1 : I Hi' Oa 5%.. 2..5% reference of the chart in use, or by eye inter- 9 polationbetween isogoniclinesof variation ',cm: 2.51 I:0;44 printed on the more recent editions of charts. 00:5:4 ;II 1.(7): 3.0:.! ,I t Deviation is found by consulting the magnetic 45 :'.''fi 1 .0.4 225 IF 2.5W 2.0W 4 21,05.1: ;3:::::. il N AXIS OF COMPASS 2.5W 2.5r; I: 2.0:.: 3.n.: CARD li 1 ., r. 90 3.,Tri 2..Yr; 273 . P.ci!.'

f VAR, 0W l' -.10W 4 :'1. 1..n: 1, 2.o..4 1.0.v 1 .(),.. 1.0.-:

135 1 .fir4 n.n 315 ' n.,..,:.' n.5-.

II, I 1.04 1.0:, ; o.o 0.0

0.0 1.5:.i. -1. . o.514 nin

,.. X ..,40 S,,,SI 4941i,S

8 4 ,

4 e I;

11.:01:1,0 2-9" X4-, Si x ;, ii ..4...... , x 'Itoir,''; x -ft- 'sr no.;

, . . ? A4 kr usd a 8 Sc..1c9k WA(

69.13 Figure NIagnetic.. compass table.

tahl (tin. .VIIICI1 MAGNETIC provides the devi- MERIDIAN S ation values;or I5 degrees, Of magnetic heading. II the ship has tig equipment

69.138 InSti 11C41, 1 um against magnetic niines, Figure 2-4. --Components of compass error. aseparate Ix:provided on the

9 A NAVIgATION COMPENDIUM magnetic compass table (deviation table) to take Five general techniques in determining devia- into account the effect of the degaussing equip- tion are in current practice, listed as follows: ment when energized. (a) Comparison with gyrocompass, This technique is most common. It is essential that the 209. COMPASS CORRECTION gyro error, if any, be ascertained and applied. (b) Comparison with other magnetic compass with known deviation. Magnetic compass correction requires the (c) Reciprocal bearings from shore. A mag- understanding of the relationship between compass netic compass may be established on shore free error, variation, and deviation. The differencefrom magnetic influence other than the earth's. between compass and magnetic direction is devia- The ship,on various headings, observes the tion. The difference between magnetic and truebearing of a marker near the shore compass. direction is variation. The difference betweenBy some means of communication, the bearing compass and true direction is compass error.of the ship may be received from the shore (See fig. 2-4.) When correcting or working fromstation. The reciprocal of the received bearing magnetic to true or from compass to true, add is compared with the magnetic bearing in order easterly errors and subtract westerly errors. to determine the deviation. When uncorrecting,or working from true to (d) Direction of distant objects. As a ship magnetic or true to compass, subtract easterlyswings to a mooring buoy, a distant object of errors and add westerly errors. Rememberingknown true bearing may be observed. The radius the following hue may help: of the circle of swing must be short in comparison to the distance in order that the true bearing does Can Dead Men Vote Twice At Elections not change while the ship is at the extremes of its swing. A celestial body may be used for this meaning asits azimuth can be precomputed and plotted as a function of time. Compass Deviation Magnetic Variation True (e) Ranges. Any two objects on shore, when in line, provide direction and are referred to Add East as a range. By observing a range with the ship on different headings, compass error is easily For magnetic compass error, one may usedetermined. equally well the rule as later given for gyro error; "Compass least, error east; compass 211. PRACTICAL COMPASS ADJUSTMENT best, error west." For example, if compass direction is 068 and The purpose of compass adjustment isto deviation is 2 E, then magnetic direction is 070. reduceoreliminate deviation. Following ad- If variation is 3 W, then compass error is 1 Wjustment, residual deviation must be measured. and true direction is 067. Before adjustment,ifthe navigator lacks If the sun is found to bear 105 by magneticexperience, he should consult H.O. 226 (Hand- compass at a time which by computation the book of Magnetic Compass AdNstment and Com- azimuth should have been 093 true, then compasspenl.,ation). This handbook contains a wealth of error is 12 W. If the variation is 8 W, then theinformation; not only does it contain the theory deviation must be 4 W. of adjustment, but it contains a check-off list for adjustment and a guide in table form for the placing or movement of correctors. A summary 210. SWINGING SHIP of the order of procedure is as follows: The navigator computes deviation and pre- (a) Place all deck gear in the vicinity of the pares the magnetic compass table by an opera- compass in its normal position. Secure degaussing tion called swinging ship. Briefly, swinging shipcoils. Check the alignment of the lubbers line consists of recording compass bearings on dif-with the ship's fore and aft axis. Check quadrantal ferent headings and of comparing these compassspheresandFlinders bar for residual mag- bearings with true bearings obtained in some netism.The quadrantalspheres are spheres other manner, thus finding compass error. By mounted on thearmsofthebinnacle, applying variation to compass error, deviationTo check them, rotate them in place and note is determined. any effect upon the compass card. The Flinders

10 Chapter 2THE COMPASS

bar is a cylindrical bar in segments, inserted ina Sir Isaac Newton's first law of motion which tube usually located forward of the binnacle, Hold stated that "a body at rest or in motion willre- each segment horizontally near the northor south main at rest or in uniform motion unlesssome point of the compass card. If the compass card de- external force is applied to its" (see Appendix B), viates more than two degrees as a result of resid- has application to gyroscopic inertia. Newton's ual magnetism in the quadrantal spheres or the mathematical explanation of the earth'spreces- Flinders bar, demagnetization of one or both bysion, a conical motion of the earth's axis caused reannealing is appropriate. by the gravitational pull of thesun, set the stage in (b) Place the Flinders bar by computationor the seventeenth century for the development of the estimate. The Flinders bar corrects deviationgyroscope, Newton was followed by other British caused by induction in vertical soft iron. and German scientists whose experiments ad- (c) Place the quadrantal spheres by estimate, vanced the use of a rotor for direction reference. These spheres correct deviation caused by in- B, sed on these advances, the French physicist duction in symmetrically placed soft iron. Foucault demonstrated the earth's rotation using (d) Place the heeling magnet, red endup in a pendulum in 1851, and with a spinning wheel, north magnetic latitude, and lower to bottom of which he named a "gyroscope,"a year later, By tube unless better information is available. This 1908, gyrocompasses had been successfully tested device corrects for errors due to the roll and in the German Navy, and in 1911, Dr. Elmer Sperry pitch of the ship. demonstrated his American model in the battle- (e) Steam on two adjacent cardinal headings ship U.S.S. Delaware. After World War I,gyro- and correct all deviation from permanentmag- compasses gained in usage, although the early netisni using "fore and aft" magnets foreast and concepts of gyrocompass design saw little change west headings and "athwartship" magnets for until mid-century. During the past two decades, north and south headings, gyrocompass design and usage have rapidly ad- (f)Steam on the two remaining cardinal head- vanced. ings. Using athwartship and fore and aft magnets correct half of any remaining deviation resulting 213. PRINCIPLES OFGYROCOMPASS from permanent magnetism. OPERATION (g) Correct theposition of the quadrantal The gyroscope, a rapidly spinning body with spheres by removing all deviation on one intercar- three axes of angular movement, is increasingly dinal heading. Steam on an adjacent intercardinal used bogh for navigational reference and for pro- heading and remove half of the remaining de- viding stabilization data. One axis of the gyroscope vi ation. is the spin axis; the other axes support inner and (h) Record corrector positions andsecure outer gimbals. Gyroscopic inertia tends to keep the binnacle. the gyroscope spinning in the same plane in which (i)Swing ship and record residual deviation. it is started. When a force is applied to the axis of (j)Energize degaussing circuits (if installed). a spinning gyrocompass, the axis rotates 90 °from Repeat swing, record residual deviation andenter the direction in which the force applied. This, values in the magnetic compass table (see figure known as precession,isin accordance with 2 -5). With degaussing circuits energized,the re- Foucault's law which stated that "a spinning body sidual deviation should not differmore than two tends to swing around so as to place its axis par- degrees from that previously recorded. In addition allel to the axis of an impressed force, such that toH.O. 226, the navigator should consult the its direction of rotation is the same as that of the Naval Ships Technical Manual, Chapters 9240 impressed force" (see Appendix B). Thus by the and 9810. application of torques of the proper direction and magnitude, a gyroscope can be made to align its 212. THE GYROCOMPASS axis of rotation with the plane of the meridian, and While the magnetic compass uses the earth's provide direction as a compass. The pull o magnetic field, the gyrocompass uses the earth's gravity provides the necessary torque, keepingth. gravitational field and rotation, and the inherent spinning axis parallel to the meridian, causin properties of a gyroscope knownas gyroscopic precession around a vertical axis ata rate ar inertia and precession, for directive force. The direction which cancels the effect of theearth's gyrocompass, unlike the magnetic compass, is rotation, and causing the spinning axis toremain essentially a modern device, although the basic nearly level when parallel to thr!meridian. Oscil- theory of its operation had early antecedents. The lationsacrossthemeridianarereduced ancient Egyptians understood something ofthe by adampingactiontotheforcepro- earth's rotation on its axis, and of precession. ducing precession. Additionally,more precision 11 A NAVIGATION COMPENDIUM isobtained by compensation of those errorsby change oflatitude,change of speed, and introduced by a shipboard environment. acceleration. Furthermore, after these compen- sations have been made, a small residual error 214. COMPARISON OF GYROCOMPASS is not uncommon. However, the latest models, AND MAGNETIC COMPASS includingthe Mark 19, have automatic speed The gyrocompass has four important ad- and latitude compensating devices. vantages over the magnetic compass, as follows: (f) The gyrocompass should be started four hours prior to getting underway to ensure satis- (a) Thegyrocompassseekstruenorth, factory operation. If it is expected that the ship whereas the magnetic compass seeks the direc-will get underway on short notice, the gyro- tion of the magnetic north pole. compass should be kept running. In an emergency, (b) The gyrocompass is not affected by prox- the gyrocompass can be started and, while slightly imity to the magnetic poles. The magnetic com- less dependable, can generally be used after thirty pass, on the other hand, is rendered useless minutes of operation. near the magnetic poles because the directional In summing up the relative merits of the two force of the earth's magnetic field is almost compasses,it can be said that the magnetic vertical in these areas. compass is the most reliable while the gyro- (c) The gyrocompass is not affected by mag- compass is the most convenient. netic material. It can therefore be located in a well protected place below decks. The magnetic 215. GYRO ERROR compass is very sensitive to nearby magnetic material; hence it must be located topside in a A modern gyrocompass, properly adjusted, relatively unprotected place. Even so, the mag- generally has an error of only a fraction of a netic compass is usually subject to errors duedegree. Occasionally, an error of a degree or to the magnetic properties of the metal in themore may be present. In case of serious mal- ship. function, the error may be as much as 180°. (d) The directional information provided by Itis not a perfect compass, and it requires the gyrocompass can be transmitted electricallyfrequent checking, Usually, and particularly in to remotely located indicators called gyro re-naval ships, the accuracy of the gyrocompass peaters. The magnetic compass is not as readily is checked at least daily when underway. The adaptabletothistype of remote indication.prudent navigator checks his gyrocompass at every practical opportunity. This is done by Limiting features of the gyrocompass include: celestialobservation, by noting a range (two (a) The gyrocompass is a complex mechanical objectsinlineof known true direction), by device and hence is subject to mechanical failure. routine comparison with themagnetic com- The magnetic compass, being a very simple in- pass, and by trial and error as described in strument,isvirtually immune ft.omechanical Chapter 7. failure. The difference between true direction and (b) The gyrocompass is dependent upon andirection by gyrocompass is known as "gyro uninterrupted supply ofelectrical power.In error."Itisclassifiedas"easterly"or various types of emergency, it is not uncommon "westerly." If the compass points to the east for the ship's main electrical power source to of true north, the error is easterly. Conversely, fail, and thus an alternate supply source is re- ifthe compass points to the west of north, quired. The magnetic compass would naturally the error is westerly. To convert gyrocompass be unaffected by a power failure. directiontotruedirection when gyro error (c) The gyrocompass requires the services exists, add easterly and subtract westerly gyro of a skilled technician for maintenance and re-error. To convert true direction to direction by pair. Very littleskillis required to keep the gyrocompass, subtract easterly and add westerly magnetic compass operating properly. gyro error. When the erroris easterly, the (d) The directive force, and hence the ac- gyrocompass reads low, and when westerly gyro curacy, of the gyrocompass decreases at higher error exists, the gyrocompass reads too high. latitudes, particularly above 75°, although newer "Compassleast,erroreast:compass best, precision models such as the Mark 19 have error west." largely overcome this limitation. As an example,if the true bearing of two (e) Older models of the gyrocompass mustobjects in a range is 075 and the gyro bearing be adjusted to compensate for errors caused is076.5,thegyro error is1.5 west. If the

12 Chapter 2THE COMPASS

00#

' 71~Nlymmiwy

fa Q. 0

MASTER COMPASS

COMPASS FAILURE S ANNUNCIATOR Maw

CONTROL CABINET

STATIC POWER SUPPLY

27.169(190) Figure 2-6. Sperry Mark 19 Mod 3C Gyrocompass equipment.

13 A NAVIGATION COMPENDIUM

azimuth of the sun is observed to be 164 when the computed true azimuth is 164.5, the gyro error is 0.5 east. . OIMPAL MOUNT 216. GYRO SYSTEMS Gyrocompass design has seen many improvements since the Mark 1 was introduced after Sperry'sinitialinstallationintheU. S. S. mOVAbt E Diat. Delaware. '1 oday, many destroyers for example, have the Mark 11 Mod 6. The master compass inthis system includes a sensitive element, mercury ballistic, phantom element, spider, binnacle and gimbal rings. The sensitive element is north seeking, and the mercury ballistic uses gravity to make the compass seek north. The phantom elemene consists of parts which support

the sensitive element, which in turn is sup- . ported by the spider. Pivoted gimbals within the binnacle or case support the spider. The Mark 19 Mod 3 (see figure a-6), as MAktcS;14 FoNE- used generally in larger naval ships, 3ontains AP.40-,AF LINE bOx tt Lint Rt.tNE) two gyroscopes which serveasa sensitive 14. element. A meridian gyro aligns its spin axis MOuNr ING Foot with the meridian, and a slave gyro mounted Of 31 on the same support, is oriented east and west. This system identifiesthe true vertical, as well as north, and thus is useful in fire control. 51.131 The Mark 23 Mod 0 is a small gyrocompass Figure 2-7. Gyro repeater. designed for use in smaller ships. It is also used as a second or auxiliary compass in largerreliable,rugged, easy to operate, reasonably vessels. Some features, such as that of sensing small, and relatively inexpensive, gyrocompass. the force of gravity, are similar to those found For the care and overhaul of gyro systems, in the Mark 19. Chapter 9240 of Naval Ships Technical Manual Inthe most recent Sperry gyrocompass, is applicable. the Mark 27, outside gimbal rings are eliminated, and the conventional wire suspension is re- 217. THE GYRO REPEATER placed by flotation in silicone oil. It is accord- While technically a part of the gyro system, ingly smaller and more simplified. Unlike older the gyro repeater (fig. 2-7) can be treated as gyrocompasses, which established the verticala compass.Itconsists of a compass stand, by a pendulous suspension of the instrument,a lubber'sline (reference point aligned with the Mark 27 is designed to use a feature known foreand aft axis of the ship), and compass as "deck-plane azimuth."Thisnew insightcard graduated in 360 degrees. The compass eliminates the need for pendulous suspension.card is driven through a synchro system which Nevertheless, itis compatible with the needsreceives an electrical input from the master of the navigator who uses a coordinate system gyrocompass. which is perpendicular to the vertical. Azimuth A gyro repeater mounted in the pilot house error withthis new design, as cotnpared to in the vicinity of the helm is known as a "steer- azimuth in the horizontal plane, is0° on the ing repeater." If mounted on the wings of the cardinal headings (0°,90°, 180°, and 270°) and bridge or elsewhere forthe convenience of maximum, but acceptable, on the intercardinal taking bearings or azimuths, a gyro repeater headings (45°, 135°, 225°, and 315°). The speed is simply called a "bearing repeater." Other of the wheel, 12,000 rpm, is just half the speedrepeatersinthe gyro system are built into inthe Mark 19, and this alone reduces thethose instruments and devices which require power requirement and the generated heat.The the indication of direction, such as radar, fire advantages of the Mark 27 are that it is a highly control, and automatic dead reckoning equipment.

14 CHAPTER 3 NAVIGATIONAL INSTRUMENTS

30'. CENERAL mounted, enabling thenavigatorto read the bearing or azimuth from the reflectedportion In determining position, andin conducting aof the compass card. For observingazimuths of ship or aircraft fromone position to another,thesun, an additional reflecting mirror and the navigator must utilize certaininstrumentshousing are mounted on the ring, eachmidway in addition to the compass as discussedin thebetween the forward and aftervanes. The sun's preceding Chapter. These usually includebear-rays are reflected by the mirror to the housing ing taking devices whichare used in conjunctionwhere a vertical slit admitsa line of light. This with the compass. Speed, distance,and depthadmitted light passes througha 45 degree re- measuring devices are essential. Plotting tools,flecting prism and is projectedon the compass automatic dead reckoning, relatively sophisti-card from which the azimuth is directlyread. cated electronic navigation equipment,time- In observing both bearingsand azimuths, two pieces, and celestial navigation instrumentsarespirit levels, which are attached,must be used also included. to level the instrument. An azimuthcircle with- Instructions for the care, custody, andre-out the housing and spare mirror iscalled a placement of navigational instrumentsin naval BEARING CIRCLE. ships are contained in Naval Ships Technical A TELESCOPIC ALIDADE (fig. 3-2)is similar ,anual Chapter 9240. to a bearing circle, differing only inhaving a telescope attached to the metal ringin lieu of 302. BEARING TAKING DEVICES the forward and after sightvanes. A reticule within thetelescope, together witha prism, facilitatesthe reading of bearings whilethe Instruments for observing azimuths andbear- telescope lens magnifying power makesdistant ings consist of azimuth circles,bearing circles, objects appear more visible to theobserver. telescopic alidades, self-synchronousalidades, When looking through thetelescope, the bearing and peloruses or dumbcompasses. Their de- may be read, since the appropriate part of the scriptions follow. compass card is reflected by the prism in such An AZIMUTH CIRCLE (fig. 3-1)is a non- a way as to appear in the lower part of the field magnetic metal ring sized to fitupon a 7 1/2 of vision. inch compass bowl or upona gyro repeater. When a ship is yawing badly,it is easy to The inner lip is graduatedin degrees from 0 lose sight of an object usingthe telescopic to 360 in a counterclockwise directionfor thealidade, the field of vision beingvery limited. purpose of taking relative bearings. Two sighting To overcome this handicap,a telescope has been vanes,the forward or far vane containinga mounted on a compass card havingan additional vertical wire, and the afteror near vane con- synchro motor driven by the mastergyrocom- taining a peep sight, facilitate theobservation of pass. Itis possible with this development to bearings and azimuths. Two finger lugsare used set the alidade on a desired truebearing and to position exactly the instrument whilealigning observe an object without having thetelescope the vanes. A hinged reflectorvane mounted at deviate from the desired bearingbecause of the the base and beyond the forwardvane is usedmotion of theship.This instrumentis the for reflecting stars and planets whenobserving SELF-SYNCHRONOUS ALIDADE. See figure3-3. azimuths. Beneath the forwardvane a reflecting The PELORUS (dumb compass)(fig. 3-4) mirror and theextended verticalwire.are consistsofa compass stand, compass bowl

15 A NAVIOATION COMPINDIUM

BESTCopy AVAIMBLE

65.122 Figure 3 -1. Azimuth circle.

(containinglubber's line), and compas card.line; then the relative bearing is addeto the The compass card, which is graduated in 360true heading noted at time of "Mark," to obtain degrees, may be rotated using a knurled knobthe true bearing. For greater convenience, in on the side of the compasshew,. To obtain a modern installations the dumb compass has been true ,bearing using the pelorus and bearingcircle, generally replaced with a gyro repeater. In .7ur- the observer must match the ship's true course rent usage, however, a gyro repeater mounted on the compass card, and thelubber's line onin a "pelorus" stand will be referred to as a the compass bowl, using the knurled knob. After "pelorus." aligning the sight vanes with the object, he should call "Mark" and note the bearing from the 303. SPEED MEASURING DEVICES reflectedportionof the compass card. On "Mark" the helmsman should note the ship's heading. The observer should then apply the Instruments for measuring speedor distance difference between course and heading as a sailed are known as logs, and may beconsidered correction to his bearing, taking care to apply under six general types. the correction in the right direction. Another method is to read the relative bearing from the An old and simple type was theCHIP LOG inner lip of the bearing cirule at the lubber'swhich consisted of a piece of linecontaining

16 Chapter 3NAVIGATIONAL INSTRUMENTS

IMOPTER SCALE TELESCOPE OBJECTIVE PRISM OPERATING -.. BODY FILTER ASSEMBLY r KNOB .---.., 1 I EYEGUARD 1

1 ,.

fit. I -, ...;4 ; , ;,... *7711itLir,,os,tstni Oiliti.WoLv,..Y:Ig:::.,Iti.:;-...;likievib 053'CO'R`k Malt4141*161, ,,v CROSSLINE ILLUMINATOR -- ALTITUDE PRISM ASSEMBLY READ ASSEMBLY

BEARING CIRCLE ASSEMBLY SPIRIT LEVEL

MARK 2, MOD 3

MARK 3, MOO 0

No- e' .131". e

MARK 4, MOD 0

45.39 Figure 3-2. Telescopic alidade. equally spaced knots and terminated by a wood is observed, and as it passes the stem of the ship float. The log was paid out over the stern of athe stop watch is started. As it passes the stern, ship underway. By counting the knots paid outthe stop watch isstopped. From the elapsed over a period of time, and considering the dis- time and the length of the ship, the navigator tancebetweenknots,the navigator computed computes speed. Before stop watches were avail- speed. A more accurate type of chip log consists able, a sandglass was used for time measure- simply of a chip of wood and a timepiece such ment with all forms of chip logs. as a stop watch. While the ship is in motion the chip is thrown into the water forward of the stem More in general use isthe Pitometer or and to leeward. The relative motion of the chip PITO-STATICtype. Pitometer logs (pit logs)

17 A NAVIGATION COMPENDIUM

sIs

45.39(69)8 Figure 3-S.Self-synchronous alidade.

have a three foot pitot tube extending through the hull, which contains two or more orifices, 69.20 one of which measures dynamic pressure and Figure 3-4.Pelorus or "dumb compass." the others static pressure. Through a system of bellows, mercury tubes, electromechanical link- ages, or some combination thereof, the differ-a magnetic field with respect to a conductor, ence between dynamic and static pressure iswill induce a signal voltage that is measurable measured. This difference, being proportionaland transmittible. This voltage varies with the tospeed, is recorded on a master indicatorspeed of the ship, thus providing an accurate capable of transmitting readings to remote sta- indication of speed. Alth xigh pitching and roll- tions. ing of the ship will also provide an incremental output signal, such is rejected by the trans- A log in general use is the IMPELLER TYPE mitter indicator. Underwater Log System in which a water-driven propeller produces an electric impulse which With pito-static and rodmeter types of logs, in turn is used to indicate speed and distanceit is essential that the navigator at all times be traveled. A rodmeter, extending about two feet aware of the ship's increased draft when the pitot through the sea valve, contains the impeller intube (known also as the pit sword) or the rod- its head assembly. The frequency of the alter- meter is lowered. When shallow water, or any nating current generated is amplified and passed endangeringunderwaterobstruction,isap- to a master transmitter indicator, and is directly proached, the pitot tube or rodmeter should be proportional to ship's speed. raised and housed. Also in general use, and of high precision A log less accurate but stillin use, par- and accuracy, is the ELECTROMAGNETIC log. ticularly in small craft,is the TAFFRAIL or Calibrated for speedsJf 0 to 40 knots, it con- PATENT log. 7t consists of a rotator and sinker sists of a rodmeter, which is generally retract- attached to a line paid out astern and connected able through a sea valve, and an induction device to a registering device located on an after rail toproducea signal voltage. Its principle of or taffrail. Towed sufficiently far astern to avoid operation is that any movement of a conductor the wake effect, the rotator turns by the action across a magnetic field, or any movement ofof the water against its spiral fins. Through

18 Chapter 3NAVIGATIONAL INSTRUMENTS the log line, the register, which is calibrated to In addition to the use of logs we may compute indicate miles and tenths of miles run, is driven. the approximate speed knowing engine or shaft The taffrail or patent log should be frequently revolutions per minute (RPM), Within the engine checked for accuracy. Importantly, the log tends room, a counter records either engine turns, to read slightly high in a head sea and slightlyshaft turns, or both. The ratio of engine turns low in a following sea. to shaft turns is the reduction gear ratio and both are directly related to speed since speed An important feature of the logs thus far is dependent upon the turning of the propellers described is that they are intended to measureand the pitch of the propeller blades (constant the speed through the water. Coming into use on most vessels). A ship may run a measured is the Doppler sonar which provides an effective mile (a course of definite length established by means for measuring speed over the bottom. ranges on shore) at various engine or shaft RPM This innovation in speed measurement has a settingsand prepare a graph showing speed great advantage in accuracy, making it particu- vs RPM, with RPM along the ordinate and speed larly useful in piloting and specifically in anchor- in knots along the abscissa. From this graph ing and mooring. It is, however, limited to use a table may be prepared to provide a useful inwater depths of only a few hundred feet.reference for both the officer of the deck and the navigator. An example of the newest log is the Sperry Doppler Sonar Speed Log, Model SRD-301. It uses a pulse system at a frequency of 2 Mega- 304. AUTOMATIC DEAD RECKONING hertz and a single, extremely small, transducer. EQUIPMENT Because of its small size, the transducer is mounted flush with the bottom of the hull. This This equipment consists of a DEAD RECKON- precludes fouling or damage by seaweed or other ING ANALYZER-INDICATOR (DRAI), (fig. 3-6) objects,and makes it unnecessary to install and a DEAD RECKONING TRACER (DRT) (fig. pneumatic or hydraulic retracting mechanisms. 3-7). Since dead reckoning requires the knowl- Digital data outputs provide data to ..adar and edge of the direction and the speed of the ship's other navigation and collision avoidance systems. progress, electrical inputs from the gyro and It has a speed range of 0 to 35 knots. See figurelog are required to supply the DRAI with direc- 3-5. tion and speed respectively. The DRAI resolves DISPLAY UNIT ELECTRONICSUNIT

TRANSCEIVER

TRANSDUCER

TO SHIP'S SUPPLY t7

SEA CHEST djale

190.3 Figure 3-5. Composition of Sperry Doppler Sonar Speed Log SRD-301 System.

19 A NAVIGATION COMPENDIUM

. ti-41110,4. 7.10111111/14,. t.11 TIMekel tt tit)

11 40.147 Figure 3-6.Dead Reckoning Analyzer-Indicator Mark 9 Mod 0. direction and speed into east-west and north-pencil as its position image moves across the south components and sends these componentschart. For a relative plot, used primarily in as inputs to the DRT. On direct reading dials, tactical situations on the high seas, blank plotting the dead reckoned coordinates in latitude andpaper is used. Contacts or targets are plotted longitude are generally given. These dials shouldwith respect to the ship, in addition to a trace be set to conform to the ship's position uponof the ship's path. A type of DRT used largely starting the dead reckoning equipment and reset inantisubmarine warfare shipsis the NC-2 upon fixing the ship's position. While the dialsMod 2 Plotting Table which conveniently pro- are convenient, the DRAI unfortunately cannotjects by spots of light not only the ship's posi- account for current effect. A scale setting for tion but that of certain selected targets. the DRT is selected and made, and this setting together with heading and speed inputs from the 305. SHORT RANGE MEASURING gyro and log respectively, after resolution by INSTRUMENTS the DRAI into N-S and E-W components, enable the DRT to trace the ship's track. (See figure Forrangesof200to10,000yardsthe 3-8.) STADINIE TERisutilized.The trigonometric The DRT may be used to produce either aprinciple employed is that in a rignt triangle, geographical or a relative plot. Foi a geographicalif one knows the length of one leg and the value representation, a Mercator or a polar coordi- of the opposite angle, the length of the other leg nate chart is used, with chart scale fully con- mhy be computed. On an index arm of a sta- sidered. The ship'sprogress is traced withdimeter the height of an object in feet is set;

20 MA11.10Vi. Chapter 3NAVIGATIONAL INSTRUMENTS tOri

*; 1 ir TRACER

RANGE-BEARING LEAD SCREW PROJECTOR ASSEMBLY DRIVE UNIT ASSEMBLY j

PENCIL CARRIAGE ASSEMBLY LAMP 4-- ASSEMBLY

DIAL UNIT ASSEMBLY

CROSS SCREW DRIVE UNIT ASSEMBLY

CROSS SCREW

CHART BOARD

40,61 Figure 3-7. DRT plotting table. this moves an index mirror through a small arc of stadimeter, alike in principle of operation and thus introduces one given value. Through but differing in construction, are the Brandon a sighting telescope, two images of the object sextant type(fig, 3-9) and the Fisk type (fig. of known height may be viewed. A direct image 3-10). appears on the left and a reflected image appears on the right (the reflected image is produced by the index mirror). By moving a mi- 306. DEPTH MEASURING DEVICES crometer drum, the top of the reflected image may be brought into coincidence with the bottom Depth measuring devices may be classified as ofthedirectimage.This movement of the mechanical and electronic. The mechanical type micrometer drum measures the subtended arc is represented by the hand lead; the most com- (the second given value) and automatically solves mon example of an electronic type is the fathom - the triangle for the length of the adjacent leg; eter. from the drum, the range in yards (length of The oldest and most reliable depth finding adjacent leg) may be read directly. Two types device for shallow depths is the HAND LEAD.

21 A NAVIGATION COMPENDIUM

ORAL is the application of tallow or other suitable substance to the indentation in order to sample DIRECTION the bottom for determination of type or com- (HEADING) ORA SPEED position. The DEEP SEA LEAD is a lead weighing from 30 to 50 lbs. attached to about 100 fm of line for deep water sounding. The FA THOME TER (fig. 3-11) or echo sounder is an electronic device which is capable of transmitting a sound signal vertically and of meas- ---tt-- uring thetime between transmission of the L - LOG signal and return of the echo. Since the signal GYRO SCALE- -,- - --DR(-) I --0), I must travel to the bottom and return, the depth I is half of the distance traveled, considering the - -J average speed of sound waves in water, which is about 800 fathoms per second. The navigator must remember that the fathometer sends the signal from the keel and therefore recorded or N-S indicated depths are depths underthe keel. E-W DRT - TRACK Actual depth is equal to the sum of (1) depth under the keel and (2) draft of the ship. More importantly, the navigator must know the depth 190.4 under the lowest projection, usually the sonar Figure 3-8.Schematic of DRAI/DRT. dome in naval ships. The AN/UQN-4, a new precision echo sounder, is the planned successor to the AN/UQN-1 currentlyingeneral use. Reference is made to its use in the New Testa- ment (27th Chapter, Acts of the Apostles). It 307. ELECTRONIC INSTRUMENTS consists of a lead weight (7-14 lb) attached to a 25 fathom line marked as follows: Six electronic instruments or systems contribute materially to navigation; these are the 2 fm 2 strips of leather radio receiver, the radio direction finder, radar, 3 fm 3 strips of leather sonar, loran, and Decca. 5 fm white rag The RADIO RECEIVER provides a method 7 fm red rag of receiving time signals, weather, and hydro- 10 fm leather with hole graphic messages which advise the navigator 13 fm same as 3 fm of changes in navigational aids. 15 fm same as 5 fm 17 fm same as 7 fm A RADIO DIRECTION FINDER (RDF) con- 20 fm line with two knots sists of a receiver and a loop antenna which 25 fm line with one knot is direction sensitive. The bearing of any station which transmits may be ascertained, and if it can The hand lead is heaved by using a pendulumbe identified, a locus of position obtained. Also motion to produce momentum for two complete certain RDF stations, will upon request, re- turns, then let go at such time as to allow theceive a transmission and report the bearing. lead to sink ahead of the chains (station on ship RADAR (an abbreviation of the term "radio from which soundings are taken). The leadsmen detecting and ranging") equipment sends out call out depths referring to definite markingsradio waves in a desired direction and meas- as "By the mark...." and other depth valuesures the time delay between transmission of as "By the deep". Phraseology for fractionsa signal and the receipt of its echo. Using the are"And a half," "And a quarter," or "Atime delay and the speed of travel of radio quarter less" as appropriate; for example, "Andwaves in air, the equipment is capable of indi- ahalf five" (5 1/2 fm) or "A quarter less cating range (distance). four" (3 3/4 fm). The lead line should be meas- SONAR (sonic ranging) equipment, although ured and marked when wet. In the end of the lead developed primarily for underwater dete,:tion, a hollow indentation permits "arming," which fulfillsanavigational purpose by furnishing

22 Chapter 3NAVIGATIONA L INS Tit l!MEN

58.78.1 Figure 3-9. -- Brandon sextant type stadimeter. distances and bearings of underwater objects.master station is associated with three second- Sonar transmits a sound wave in water in anyary stations; all transmit a continuous wave at a desired direction;ifan echo is received,itdifferent frequency, making it possible for hyper- measures the time delay, takes into accountbolic lines or loci of position to be determined. the underwater speed of sound, and then indi- Except for radio receivers, the above elec- cates both the distance and the bearing of the tronicinstruments or sets are described in reflecting object. greater detail in Chapter8. Newer electronic LORAN (an abbreviation of the term "longnavigation systems now coming into use are range navigation") equipment consists of a radiodescribed in Chapter 9. receiver on board ship and pairs of transmitting stations on shore. The radio receiver measures 308. CELESTIAL NAVIGATION the time delay between receipt of signals from INSTRUMENTS individual stations within each station pair; each time delay produces a hyperbolic locus of posi- The primary celestial navigation instrument tion. is the SEXTANT, so named because as originated DECCA isa British electronic navigationit contained a metal frame which represented system in which the distances from transmitters one sixth of a circle. Like the stadimeter (es- aredetermined by phase comparison. Eachpecially the Brandon sextant type), the field of

23 A NAVIGATION COMPENDIUM

SONAR RECtIvEitTPANSMITTER tki".1 aft.

11. 1111 1 4 Aft,

58.78.2 Figure 3-10. Fisk-type stadimeter. vision offered by the sextant provides a direct image on the left and a reflected image on the right. By moving the index arm along the limb of the instrument, an index mirror is rotated through a small angle, a celestial body is brought into coincidence with the horizon, and a vertical angle is measured. The value of this angle may be directly read from the limb and vernier. 62.9 The instrument may also be held 90 degrees to Figure 3-11.AN/UQN-1 fathometer. normal and used to measure horizontal angles by bringing two objects into coincidence. The sextant is described in greater detail in Chapter SHIP'S CLOCKS are ordinary spring-powered 12. clocks set to keep standard or zone time and located within a ship wherever essential. These 309. TIMEPIECES clocks mast be wound, checked, and reset (if necessary) every 6 days. The knowledge of precise time is essential The COMPARING WATCH is a high grade to the computation of longitude. Therefore, since pocket watch which the navigator uses for check- a modern navigator must compute longitude asing the exact time of observation of celestial well as latitude to completely fix his position, bodies.Upon thenavigator's"Mark," when he provides himself with accurate time throughobserving a celestial body, the quartermaster the use of chronometers. Ship's clocks, com-records the time as v..,ad from the comparing paring watches, and stop watches, are also essen- watch. Later the quartermaster compares the tial timepieces. watch with the chronometer and after applying The CHRONOMETER is a high grade clockany watch or chronometer error, provides the mountedin a nonmagnetic case supported bynavigator with either the local zone time or the girnbp.ls and resting in a padded wooden case.Greenwich mean time of the observation. The chronometer is wound daily and frequently The STOP WATCH isuseful in celestial checked by radio time signal; it is initially set navigation, and in piloting for the identification to keep the time of Greenwich, England (Green- of lights. When observing celestial bodies, the wich mean time). Subsequent error is recorded watch is started on the first "Mark." On suc- as checked, without resetting of the chronometer. ceeding "Marks" the time in seconds is recorded.

24 Chapter 3NAVIGATIONAL INSTRUMENTS BEST COPYAVAILABLE

legibly, and lightly to facilitate easy erasure. Art gum erasers are normally used for erasure «t- sincein comparison withIndia red rubber erasers, art gum is less destructive to chart surfaces. The NAVIGATOR'S CASE which contains drawing compass, dividers, and screw driver (for adjusting points) is an essential navigation 4.16 instrument. Dividers are used to measure dis- Figure 3-12. Parallel ruler. tance; the drawing compass is useful for con- structing circles and arcs such as circular lines of position and arcs of visibility. After observation, the stop watch is compared PARALLEL RULERS (fig. 3-12) are simple (ata given instant) with the chronometer anddevices for plotting direction. The rulers con- the chronometer time of the first sight or obser- sist of two parallel bars with cross braces of vationiscomputed. Any chronometer errorequal length which are so attached as to form presentisapplied,providing the Greenwichequal oppositeangles, thus keeping the bars mean timeof thefirst observation. For the parallel. The rulers are laid on the compass rose Greenwich time of subsequent observations, the (direction reference of a chart) with the leading recorded timesin seconds are added to theedge aligning the center of the rose and the Greenwich mean time of the first sight. Time- desired direction on the periphery of the rose. pieces including newer quartz crystal oscillator Holding first one bar and moving the second, then clocks, are described in greater detail in chapter holding the second and moving the first, parallel 11. motion is insured. Lines representing direction may be plotted as desired upon the chart. 310. PLOTTING INSTRUMENTS The ROLLER RULER consists of a rectangular frame with pivot points at two inside extremes The most basic of plotting instruments is holding a hexagonal roller. From any desired thePENCIL; navigators use No. 2 or No. 3position this ruler may be rolled, thus trans- pencils, and keeping all lines short, write labels ferring parallel lines of direction.

.lu 01.1%II %tit I.. I

59.57(190) Figure 3-13. Universal drafting machine.

25 A NAVIGATION COMPENDIUM

and drafting arm, desired angles which represent direction, may be drawn. The UNIVERSAL DRAFTING MACHINE or PARALLEL MOTION PROTRACTOR (fig. 3-13) is a plotting device which is anchored to the chart table and consists of two links and a drafting arm. Between the two links an elbow permits unrestricted movement. Between the out- board link and the drafting arm a metal disc is graduated as a protractor. It permits orientation of the protractor with the chart. A set screw, usually on the inner edge, is loosened when in use, in order to set the drafting arm on any given 29.269(190)X direction,it is tightened before plotting. The Figure 3-14. Three-arm protractor. advantage of the Universal drafting machine over other plotting instruments is speed. A THREE-ARM PROTRACTOR (fig. 3-14) The HOEY POSITION PLOTTER is a celluloid consists of a circular metal or celluloid disc protractor with an attached drafting arm. Thegraduated in degrees with a fixed arm at 000 and protractor has imprinted horizontal and verticaltwo movable arms, attached to the center. After linespermitting alignment with parallels ora sextant observation of twu horizontal angles meridians. After alignment, using the protractordefined by three objects with the observer at

45.52(74) Figure 3-15. Nautical slide rule.

26 Chapter 3NAVIGATIONAL INSTRUMENTS the vertex, the three-arm protractor may be set up to represent the two angleS and the position P\IN1051,1. of the observer. When the three-arm protractor tOri has been thus set and oriented to the objects used for measurement, on the chart, the center of the protractor is the position of the observer. Two right triangles may be used in conjunction with a compass rose as a means for plotting direction. Although not a plotting instrument in a true sense, a useful plotting accessory is the nautical slide rule (fig. 3-15). Composed of plastic, and circular in shape, the nautical slide rule provides a quick solution for problems involving time, speed and distance. It solves the formula D=SxT in which D is distance in miles, S is speed in knots, and T is time in hours. Addi- tionally, it provides distance in both miles and yards,and time both in hours and minutes.

GLASS PANELED COVER FOR BAROMETER CASE

BAROMETER SWINGS UP AND IS 69.87 SECURED IN CASE BY TWO SPRING CLIPS Figure 3-17. Aneroid barometer.

TUBULAR GLASS SHIELD 311. WEATHER INSTRUMENTS

VERNIER AND BAROMETER The basic weather instrument is the BAROM- SCALES ETER which measures atmospheric pressure in termsof inches of mercury. Two types,the VERNIER -"1------.ADJUSTMENT mercurial (fig. 3-16) and the aneroid (fig. 3-17), THUMB SCREW are in use. The mercurial consists of a column of mercury acted upon at the lower surface by GIMBAL SUSPENSION the atmospheric pressure which drives the mer- RING cury up into a vacuum tube calibrated for reading in inches. The aneroid barometer is more complicated mechanically and consists of a metal t BAROMETER cylinderwhichcontractsand expandswith j, HOLDING ATTACHED changes in atmospheric pressure. This change II CLIP THERMOMETER passes over a linkage to an indicator where the pressure, in inches of mercury, may be read. Standard atmospheric pressure is 29.92 inches. LARGE Fluctuations FIXED in pressureareindicationsof CAPACITY weather changes. MERCURY A THERMOWTER is a well known instru- CISTERN ment for determining temperature (also useful in weather prediction), scarcely necessary to be described.Most Navy thermometersare 69.86 calibratedinaccordance with the Fahrenheit Figure 3-16.Mercurial barometer. scale(freezingof water 32 degrees, boiling

27 A NAVIGATION COMPENDIUM point 212). The Centigrade thermometer is gen-the first component (true wind speed) may be erally used in experimental work (freezing point computed. of water 0 degrees, boiling point 100). 312. MISCELLANEOUS INSTRUMENTS The PSYCHROMETER consists of two ther- mometers mounted side by side in a wooden Binoculars and flashlights serve useful pur- case. One conventional type thermometer isposes in the navigation department. Binoculars, called the "dry bulb." The other, called the becauseoftheir magnification, which ranges "wet bulb,"has a small container of waterfrom about 7-power for handheld binoculars to connected to the outside surface of the bulb by20-power for a larger ship mounted type, pro- a wick. The evaporation of water around thevide a means of early sighting and identification wet bulb lowers the temperature, bringing about of navigational aids. The glass lenses used in a lower reading. By comparing the two ther-binoculars are normally treated for reduction mometer readings and consulting a table con-of glare, and additional filters are often avail- tained in The American Practical Navigatorable. Binoculars are delicate instruments and (Bowditch), the relative humidity, which is use- must be handled carefully and cleaned frequently. fulin weather predicting, may be computed.They should never be dropped nor subjected to sharp knocks.For cleaning, only lens paper The ANEMOMETER measures wind velocity. should be used, otherwise the polished surface It consists of a metal cross, having a smallwill be damaged and their usefulness as an sphere at each extremity, which rotates in the optical aid will accordingly be reduced. horizontal plane as a result of wind force. It is The FLASHLIGHT is useful during morning mounted in an exposed location on the mast or and evening twilight observations to provide light yardarm and is equipped with an electricallyfor reading the comparing or stop watch as well operated indicating device which is calibratedas the limb and vernier of the sextant. A red in knots. When underway, the wind speed meas- plastic disc should be inserted in the illuminant ured is that of the apparent wind, which is theend to insure a red light in order not to disturb resultant forceofthefollowing components: thenavigator'snight vision or unnecessarily (1) the true wind and (2) ship's course and speed. illuminate the ship when steaming under wartime Knowing the resultant and the second component, darken-ship conditions.

26 CHAPTER CHARTS AND PUBLICATIONS

401. INTRODUCTION century A.D., made many charts and maps, some of which were used until the time of Charts and publications constitute a source Columbus.Ptolemy,who was unequalledin ofinformation which the navigator constantlyastronomy until Copernicusinthesixteenth uses. A chart or a map is a representation ofcentury, had based his charts on the theory that an area of the earth's surface. For example,the world was round, with a circumference of the early charts devised and used by the natives 18,000 miles as computed by the Greek philoso- of the South Sea islands were merely diagram-pher Posidonius, circa 130 to 51 B.C. It was matic, being constructed of palm leaves and sea unfortunate that Ptolemy based his cartography shells. The sea shells represented islands andon the calculations of Posidonius, inasmuch as the palm fronds represented currents and the a more accurate circumference of 24,000 statute anglesofintersection of ocean swells. Themiles had been calculated in the third century Pacific natives still use their knowledge of these B.C. by another Alexandrian, Eratosthenes. In angles of intersection as a basis for a unique fact,the computation of Eratosthenes was to system of navigation which they successfullyremain as the most accurate until 1669. Im- practice. portantcontributions of Ptolemy included the Thereis a difference between charts and convention of making the top of a chart or map maps. Maps, for the most part, show land areas, to be north in direction, and the listing of im- theirpolitical subdivision, and topography. Aportant places by latitude and longitude. chartservesa navigation purpose;nautical IntheMiddle Ages, using the knowledge charts show water or coastal areas and give a acquired by seamen principally in the Mediter- great deal of hydrographic information whichranean Sea, charts were constructed in Catalonia, isuseful to the navigator. An air navigation known as Porto lan charts. A distinguishing fea- chart may, like a map, portray mostly land, ture of these charts was the depiction of direc- butit will provide the air navigator with ele- tion by thirty-two lines emanating from a point. vations and locations of navigational aids. Usage These lines represented the thirty-two points is the basis for chart and map classification. of a compass, as was then in general usage, A chart projection is a method of represent-a point being the equivalent of 11 1/4 degrees ing a 3-dimensional object on a 2-dimensional (360/32).This depiction of direction was an surface. Cartographers (chart or map makers) antecedent of the modern compass rose. employ various chart projection techniques to construct desired charts. However, it is impos- 403. MERCATOR PROJECTION sible to project a 3-dimensional object upon a 2-dimensional surface without some distortion. Moderncartographyisindebtedtothe The best type of chart projection depends upon Flemish astronomer, geographer, and theologian, the area to be represented and how the chart Gerardus Mercator, who in the sixteenth century is to be used. made a world chart, based upon a cylindrical Publications are separately addressed in art. projection.Essentially,thechart, which has 412. ever since borne his name, is projected by first placing a cylinder around the earth, tangent 402. EARLY CHARTS at the equator. (See fig. 4-1.) Planes are passed through themeridians andprojectedtothe Ptolemy, the Alexandrian astronomer, mathe- cylinder upon which they appear as parallel matician and geographer, who lived in the second lines. Lines are drawn from the center of the

29 A NAVIGATION COMPENDIUM

um...mu* .MM g

-7w1.1111

tchaToa

/-.----

65.117 Figure 4-1.Mercator chart of the world.

earth to the cylinder passing through the parallels; at any latitude,lu of longitude is equal to 60 this locates the parallels on the cylinder. Nextmiles multiplied by the cosine of that latitude, the cylinder is cut lengthwise and flattened out. and the relationship between latitude and longitude The resulting graticule (horizontal and verticalis found by the solution of the trigonometric lines of a chart) is representative of a Mercator equation clt o =d1 /cosyin which d o is the dif- projection, the important difference being thatference in longitude and d1 is the difference in in the latter, parallels are snaced by mathe-latitude, both in arc. Also, p=dtox cosiin matical formulae. In fact, both meridians andwhich p is the length of an arc ofa parallel; parallels are expanded with increased latitude, d io=p x sec IThus, considering the trigono- the expansion being equal to tlu secant of the metric relationship of secants and cosines, itcan latitude. Inasmuch as the secant of 90° is inbe proved that inasmuch as the expansion of finity, a Mercator projection basedupon tangency meridians is dependent upon the secant ofthe with the equator, cannot include the poles. latitude, the separation of meridians is dependent To envision the linear relationship betweenupon the cosine of the latitude. parallels of latitude and meridians on a Mercator The advantage of a Mercatorprojection, also projection, it is helpful to remember that merid- called an orthographic cylindricalprojection, is ians are separated in distance in accordance that it is a conformal chart, showingtrue angles with the cosine of the latitude. At theequator, and true distance. A rhumb line plotsas a straight or latitude 0°, the cosine of the latitude is 1 and line on a Mercator chart. By definition,a rhumb one degree of longitude is equal in distance to line is a line which makes thesame oblique angle one degree of latitude; at the equator, and onlywith all intersected meridians, Ona Mercator at the equator, the longitude scalecan serve as chart meridians are parallel;therefore, any a true distance scale. At latitude 60°, where the transversal fulfills the requirementsof a rhumb cosine is 0.5, one degree of longitude is equal in line. A disadvantage ofa Mercator chart is the distance to one half of one degree of latitude,or distortion at high latitudes, Onthe earth the 30 nautical miles. At the poles,or latitude 90°, meridians actuallyconverge at the poles while the cosine is 0, and the meridians merge. Thus, on the chart they are parallel;a conformal chart

30 Chapter 4CHARTS AND PUBLICATIONS under these conditions can be had by expansioncompass rose.It contains no information on of the meridians. On a Mercator chart, because land, water depth or navigational aids. Being less of the higher latitude, Greenland appears largerexpensive than charts to produce, such sheets than the United States, although it is actuallyare used primarily for economy in plottingceles- much smaller. Despite this distortion in hightial fixes. latitudes, the dete..mining of true distance is not A small area plotting sheet (fig. 4-3) makes prevented. The expansion of the meridians, whichuse of the fact that on a Mercator projection of is related trigonometrically to the latitude, makes a small area, the difference in spacing between areas appear larger, and changes at the same successive parallels of latitude is nearly negli- timethelatitude (distance measuring) scale, gible. It thus approximates a Mercator projec- thus permitting the navigator to measure true tion by using equal spacing between the parallels distance. Since the distortion varies with therepresente,.. The relationship between latitude latitude, whenever measuring distance on a Mer- and longitude is found by solution of the trigono- cator chart of a large area, the navigator setsmetric formula Dlo equals p secLwhere Dlo his dividers to the scale of the mid-latitude of the isthe differencein longitude in arc, and p areain which he is making a measurement. equals the linear distance between two meridians See figure 4-2. measured along an arc of a parallel. Given either thelatitudescale or the longitude scale the 404. PLOTTING SHEETS othernay be computed graphically as follows: A plotting sheet inn incomplete chart with (a) Longitude scale specified. Any uniformly latitudeandlongitudelines, and generally aruled paper may be used. Place the paper with

4-A U

U H

MID LATITUDE

-A

190.5 Figure 4-2. Distance measured at mid-latitude of route on a mercator chart.

31 3 Li 40 50 100- 00E 10' 20' 1 30g IL -. 1 1 I 1 1 1 1 II Ox A %W"r I % .,10I 1 1 or i 1111111111//1/11/ s I I 1 i I /NI i IP% 1 i 350 III 0 j() ZO / 1/ / 1 \\ \\ ASTP SO ////z& ... 1 ..... 1 146,4) ._., ... V 0 1 z .e, .. to 4. , 4N O db 1 i =_- ..-:-.- Z..\ ti 0IR 0 -aN0 I --:"-:- --a - oeu 0 NI 1 rp- . . - _ -= -z-- 40 ---:--. o ea --_ - 1 10 Z. oo * -...4.... --.- "%. al of" 0 S s..,, cb iiii 1 '. ....- 1 0_, .... I , i 0 --,,,. .... t-,,, 1 la 1 , t - 1 1 ...I" 1` 0 s 0 4 % % / / 4 1 L 1 01 Iiiiii 10 Il 11111111161 , I OM a 111100000i 00 1 I I , 1 0 1:1ffi \ \\ \ I \ Figure 4-3. Small area plotting sheet, longitude scale specified. 1 I 65.130(190) Chapter 4CHARTS AND PUBLICATIONS the lines vertical; label meridians as desired. Men ofancient Greece, who founded Greek Construct a perpendicular to the meridians mid- geometry, astronomy and philosophy, in addi- way between the top and bottom of the plotting tiontobeing a navigator and cartographer, sheet. Label this perpendicular as a latitide line circa the sixth century B.C. The value of this making it any desired mid-latitude, At the point projection was little realized until the earth's of intersection of the mid-latitude line and the circumference had been more accurately com- central meridian, construct an angle with the hor- puted,if even then, and its usage appears to zontal equal to the mid-latitude. The length of this have been secondary to the later Portolan and transverse line between two meridians which are Mercator charts. 1 degree apart in longitude, is 60 miles or 1 degree The gnomonic or great circle projection is of latitude. The length of this transverse line be- made by projecting the earth's features from tween two meridians which are 10' apart in longi- itscenter to a plane tangent to its surface; tude is 10 nautical miles or 10' of latitude. Using the center of the plane (point of tangency) marks these measurements, the remaining latitude lines the center of the projected area. The gnomonic may be plotted. projection is advantageous in that great circles (b) Latitude scale specified. Any uniformly (the arcs of which represent the shortest dis- ruled paper may be used. Place the paper with the tance between two points on a spherical surface) lines horizontal and label parallels as desired.plot as straight lines. Known alio as an azimuthal Construct a perpendicular to the parallels, tnidway projection, all directions or azimuths from its between the right and left edges of the sheet.center are true. The chief limitation, neverthe- Label this meridian as the central meridian. U sing less, is that difficulty is encountered in finding as a radius, the distance between themid-latitude both direction and distance. Also, there is some line and an adjacent latitude line, measured alongdistortion which increases with distance from the central meridian, draw a circle with the center the point of tangency. at the point of intersection of the mid-latitude line The gnomonic (great circle) chart (fig. 4-4) and the central meridian. From the center of thisis normally used for planning long voyages since circle construct a line which makes an angle withgreat circle courses are generally shorter than the horizontal equal to the mid-latitude. At therhumb line courses. On a gnomonic chart, the point of intersection of this line and the circle, navigatorplotsthe departure point and the drop a perpendicular to the mid-latitude line.point of destination. These points are then con- The distance between this perpendicular and thenected with a straight line. Route points are central meridian, measured along the mid-latitudemarked each 5 degrees of longitude apart. The line, represents 1 degree of longitude if the lati-coordinates of these points are noted, trans- tude lines are 1 degree apart, and 10' of longitudeferred to a Mercator chart, and connected by if the latitude spacing is 10'. straight lines. These lines in effect, are chords A plotting sheet may also be constructed usingof the great circle course. The ship, in making "meridional parts" as given for each degree andthe voyage, changes to a new course upon reach- minute of latitude in Table 5 of American Practi-ing each route point. Thisis more practical cal Navigator (Bowditch). Meridional parts, ex-than changing course continuously, which would pressed in minutes of equatorial arc, provide abe required if an exact great circle were to be computed expansion of the meridian, based upon followed. the secant of the latitude. Plotting sheets for large areas should be constructed using meridional406. POLAR CHART PROJECTIONS parts. Additionally, and more in use, are position Obviously, because of extreme distortion in plotting sheets printed by the Naval Oceanographichigh latitudes, the ordinary and popular Mer- Office for various latitudes. These ready-madecatorprojectionisunsatisfactoryforpolar plotting sheets have numbered parallels, and un-navigation. There are five general types of pro- numbered meridians which are spaced as appro-jections which may be used. Two of these types priate for the latitude and thus may be numberedare special forms of the Mercator andGnomonic. as convenient for the navigator. The polar gnomonic isa special gnomonic chart projected by placing the plane tangent to 405. GNOMONIC PROJECTION the surface of the earth at the pole. Meridians The gnomonic projection actually predatesare shown as straight lines radiating from the Portolan and Mercator charts. Itis creditedpoles. An interesting concept is that at the north to Thales of Miletus, Chief of the Seven Wisepole all directions are south and at the south

33 A NAVIGATION COMPENDIUM

10' ISO' 155 110 115 110 110 110 110 110' IC' 130

65.118(69)B Figure 4-4.Gnomonic chart. polealldirectionsarenorth. Parallels areto the meridian of Greenwich, and thus passes shown as concentric circles around the pole,through the north pole and southward into the spacing increasing with the distance from thePacific: The direction of this lineis"grid pole. north" and remains as such when technically, The azimuthal equidistant projection is simi- theaircraftis traveling southward from the lar to the polar gnomonic except that parallels pole. Inasmuch as direction never changes, polar are uniformly spaced. The maneuvering board, navigation is greatly simplified. With this grid although used primarilyin solving problems system, as shown in figure 4-5, a "Polar Path in relative motion, is an example of an azimuthalGyro" is used. Built by Bendix Aviation Corpor- equidistant projection. ation, and housed in a sphere the size of an The polar stereographic (azimuthal ortho-orange, this gyro when set in a given direction morphic) projection is made by ;lacing a planewill continue to point in that direction. Addi- tangent to the earth at the pole, and perpendicu-tionally, the gyro may be used to steer an air- lar to the earth's axis. The earth's features craft's automatic pilot. As a check upon position are projected from the opposite pole rather thanfor additional navigational safety, celestial navi- from the center of the earth as in the case of gation procedures may be used. the polar gnomonic projection. The inverse Mercator is useful and preferred 407. CONIC PROJECTIONS by many navigators because it is similar to the ordinary Mercator with which they are already Ptolemy charted the Mediterranean using the familiar. The inverse and the oblique Mercator first known conic projection. Conic type pro- are types of transverse Mercator projections jections in use today are the Lambert Conformal, which are projected by placing the cylinderother conic, and polyconic projections. In all tangent to a great circle on the earth's surfacecases, one or more cones are placed on the other than the equator. the great circleearth'ssurface with the axis of the cone(s) making thepoint of tangency is a meridian, coinciding or in alignment with the axis of the the result is an inverse Mercator. If the pointearth. The area of least distortion is near the of tangency is not a meridian, then an oblique apex of the cone. Mercator will be the result. The Lambert Conformal may be projected A recent innovation of use particularly to air by making the cone not tangent to the earth but navigation in the arctic regions is known as the intersecting the earth through two parallels. polar grid system. It does not allow the con- Like the Mercator, however, it spaces parallels ventional use of the geographical pole to become by computation, relating the separation of paral- an encumbrance. The grid system for the northlels to that of meridians, and thus providing polar region, for example, consists of an over- a conformal chart. It was designed in the Eight- printed chart depicting a grid of parallel lines eenth century by an Alsatian, Johann Lambert. in lieu of meridians. The center line corresponds Itisused primarilyin aeronautical charts.

34 Chapter 4CHARTS AND PUBLICATIONS

POLAR CIRCLE

190.6 Figure 4-5. Polar grid chart. Although all four planes are flying "grid north," the first plane is heading south, the second west, the third east, and the fourth north.

Although conic charts resemble Mercators, 408. CHART SOURCES, IDENTIFICATION direction is less accurate. To obtain best re- AND SCALE sults in measuring direction, the nearest compass rose, or the nearest meridian, should be used.The navigator cannotindiscriminately There are two major chart issuing activities choose any compass rose, parallel, or meridian for U.S. vessels, the Naval Oceanographic Office, as a direction reference. A rhumb line on a and the National Ocean Survey; both are situated Lambert Conformal chart is a curved line. A inWashington,D.C.,and convenientlyhave great circle on a Lambert Conformal chart ap- numerousbranch offices. The Naval Oceano- proximates a straight line. For a long voyage, graphic Office, by its own surveys and through a straight line should be drawn on a Lambert liaisonwithforeign oceanographic agencies, Conformal chart, and the course noted at the prepares and publishes both nautical and aero- intersection of each meridian. For distance, nautical chartsof the high seas and foreign thenearest latitude scale should be utilized. waters. The National Ocean Survey within the

35 A NAVIGATION COMPENDIUM

Department of Commerceprepares and pub- ingeographic sequence. Currently, thereare lishes coastal and harbor charts of the Unitedgaps in the numbering sequence in anticipation States and its possessions, Also, aeronauticalof the issuance of additional large-scale charts. charts of the United States are published by This system of chart identificationwas estab- the National Ocean Survey, which was formerlylished by the Naval Oceanographic Officeon 1 known as the United States Coast and Geodetic March 1971, replacinga system which had been Survey. ,in effect for approximately 140years. To accom- Minor sources for charts include: modate the change in identification numbers, new editions of previously issued charts bear (a) The U.S. Lake Survey Office, Army Engi- the new N.O. numbers in bold type and the former neer District, Detroit, Michigan, for charts of H.O. (Hydrographic Office) numbers in smaller the Great Lakes (less Georgian Bay andCanadianand lighter type. Harbors), Lake Champlain, and the St. Lawrence Charts which show features in large size River above St. Regis and Cornwall,Canada; and with great detail are "large-scale" charts. and "Small-scale" charts show less detail, butcover (b) The Department of the Army, Corps ofa greater area, as they depict more miles per Engineers, Army Map Service, Washington, D.C., inch.Itisimportantto remember that the for topographical maps. larger the scale number, the smaller the scale. A chart is identified by numberas well as 409. CHART PROCUREMENT by source. The numbersare related to geo- AND CORRECTION graphical location and scale. The relationship to geographical area simplifies filing andre- Two types of chart catalogs provide informa- trieving, and permits the orderly arrangement tionforchart ordering, chart coverage, and of charts by portfolio. Charts are numbered withaccounting. Each issuing activity compilesa one to five digits as follows: chart catalog listing chart numbers and titles of charts which they have issued. Thus, the Naval OneOceanographic symbol sheets and flagOceanographic Office publishes N.O. Pub. No. charts (nine non-navigational and non-geographic 1-N,inthe form of a series of pamphlets. charts). Additionally, that office publishesa "Portfolio Chart List," N.O. Pub. 1-PCL, which lists the Two & ThreeCharts of the world'sdeepcharts of major issuing activities and provides oceans dividedin nine areas coinciding withinstructions for their arrangement by portfolio. ocean basins. The first digit indicates area, forN.O. Pub. 1-PCL provides informationas well example, "1" is a North Atlantic chart. The on chart procurement and correction. next one or two digits indicate scale. The scale Charts may be ordered by Navy ships from range of a two digit chart is 1:9,000,000 and Naval Oceanographic Distribution Centers.These smaller; three digits indicate a scale between are located at Philadelphia, Pa., and Clearfield, 1:2,000,000 and 1:9,000,000. See fig. 4-6. Utah, for support of Atlantic and Pacific Fleet ships respectively. DD Form 1149 is used for Four A special series of non-navigational chart requisitions. Priority for delivery should charts, including wall charts, planning charts, be specified. magnetic, time zone and star charts. Scaleis Corrections to charts are promulgated weekly not involved. in Notice to Mariners. The quartermaster main- tains a 5 x 8 card (N1105610/2) for each chart FiveThese charts are most used by navi- carried.This card containsthecharttitle, gators, and range in scale from 1:2,000,000 to chart number, edition number, edition date, and larger. They consist mainly of coastal and harbor the number of the last Notice to Marinerscor- charts.Coastal areasare dividedinto nine rection posted prior to receipt. Colunris:ere regions, with each region having asmany as provided for posting the relerence numivrs of nine sub-regions which are numbered counter- correctionsreceived its weekiyNoticeto clockwise around the continents. See fig. 4-7. Mariners.The navigatorrequire: immediate All five numbers havea geographic meaning. correction of charts which cover a re:1:-, Inc ship The first two digits indicate the generalgeo- is expected to visit. Charts ofremote areas graphic location by region and subregion. The which are not expected to he usedi)r charts final three numbers serve in placing the charts which will not be used untila distant IIt Uri' date

36 ID' 100 1111 140 A. a a a 103' 1410" 100' Dr 10- 40- 40" a- . 1. lio- . . ARCTIC OCEAN , .. ARCTIC OCEAN ,.. SOS, 8 .,/' 0.0* 001770 IOW . LID- . pey. MaSee a -3S--"en)P GREENLAND C: ilisIlilID WPM ID. wan fiami,....%; gm. <- &F/.. e.) 0 .__..:*-- ,711, r- " IC., U. S. S. MSC AM ALAS VA .... "QUM : U. S. S. R I. 747 OW CO YAK. VAUD* - ID (NINA PACIFIC OCEAN NORTH UNITED STATES NORTH ATLANTIC OCEAN it Clmau"..$ 5 103111 41110110 MUMS 5, C3 tc= u- j \ INDIAN . AUSTRALIA COW SOUTH AMERICA 7 OCEAN I-1 nouu. Z..' 1110 tt,-) SOUTH PACIFIC OCEAN 6 SOUTH ATLANTIC OCEAN 2 7 ID .4ci '4,- rz-/". sus ate um 4 at. '00 1/43, 1 9 41, 131 910.3. Mr UM WU - e N WORLD, OCEAN BASINS 10 IC 00 a0. 40 ler Figure 4-6. Wm Id ocean 110basins. 40 OD' We' AtcTica 1 90.7 4c- 7c- O. BEST 70 COPY AVAILABLEa"' I- so- 140 1:0" 140. ISO' 041" VC. REGION 3 ' ARCTIC OCEAN ,,, 110 lar 1:0' *toas- _ 4o _A A a- ARCTIC OCEAN Kt' 1,14:1141 IOWA REGION 3 ,,,,, MINTS MIA UNITED suns 22 REGION REGION 5 REGION 6 OCEAN REGION 7 SOUTH PACIFIC OCEAN SOUTH ATLANTIC23 OCEAN 75 29 REGION 2 SO INDEX OF REGIONS THE SUBREGIONS ANDWORLD Figure 4-7. The world index of regions and subregions. 190.8 BEST COPY AVAILABLE Chapter 4CHARTS AND PUBLICATIONS are not corrected; posting of the correction iswithin the legend the depth unit used and the sufficient for the interim. Prior to using anydatum or reference plane. Fathom curves con- chart,allposted corrections must be made,nect points of equal depth, and, regardless of with card NH05610/2 showing the date correctedwhether soundings are in fathoms or in feet, and the initials of the corrector. This is anthe curves are based vpon soundings in fathoms. efficient way of making chart corrections, since These are commonly shown for depths of 1, 2, one correction may cancel out another. Nay 3,6,tO, and multiples of 10 fathoms. Tide Regulations Art. 0930, requires that every charttables will refer to the datum plane of the chart. used for navigation be corrected before use, The newer chart editions may show bottom con- through the latest information that can be ob-tours in great detail using color. Shoal areas tained, which is applicable to it. Corrections,may be emphasized by the use of different other than temporary, are made with ink; the usecolors or shades. The type of lettering used of red ink, which is not readable under customaryto indicate depth is unimportant; it indicates the red night lights, should be al'oided. Standardactivity which reported the depth. chart symbols are used in making corrections. Eottom types are abbreviated using either capital or lower case lettering. A capital letter 410. CHART ACCURACY indicates composition; a lower case letter, color or texture. A chart is no more accurate than the survey Commonly used nautical chart symbols and upon which itis based. With this in mind the abbreviations appear in Appendix A. navigator is obligated to evaluate probable accuracy. 412. PUBLICATIONS Guides to probable accuracy are as follows: Publications used by the navigator may be SURVEY. Note the recency of survey, theclassified as manuals, navigation tables, al- number of surveys, and the surveying agency.manacs, and chart supplementary publications. Recent surveys, because of better instrumenta- These publications are usually obtained from the tion, are generally superior to those made in the Naval Oceanographic Office, or Naval Oceano- distant past. graphic Distribution Centers, in the same manner as charts, certain manuals and almanacs, ex- COMPLETENESS OF SOUNDINGS. Blank cepted. On board ship they are stowed on the spaces or sparse soundings may indicate annavigator's publication shelf (generally located incomplete survey. above, and in easy reach of, the navigator's chart desk). Corrections to oceanographic publications PRINTING. Plate printed (black and white)are promulgated by the Naval Oceanographic charts have a considerable shrinkage error inOffice weekly; annual supplements are origin- comparison with lithographic (colored) charts. ated by the Naval Oceanograp'll..: Office which summarize the weekly corrections. SCALE. Detailed information cannot be in- a. Some useful manuals used in navigation cluded on a small-scale chart of a large area. include: 411. CHART READING H. 0.-9 American Practical Navigator. Nathaniel Bowditch, near the end of the eighteenth Through chart reading a navigator translates century,discovered numerous errorsin the symbols into a pict'1re. As a qualification for principal navigation text then in use, which was chart reading he must then recognize standard titled, Practical Navigator, a British publication abbreviations and conventions. written by John Hamilton Moore. Bowditch then The lettering distinguishes topographic and published a corrected version with additional hydrographic features. Aiertical lettering is char- information. In 1802 he completely revised his acteristic of land features whicharealways earlier work, included a new method for the above water regardless of tide; leaning letteringdetermination oflongitude,and publishedin is characteristic of hydrographic features suchsimplified formhisnew American Practical as reefs which may be above or below water Navigator. Through updating,ithas remained depending upon the state of the tide. asa most valuable text and reference. The Soundings may be recorded in either fathoms navigational tables whichit contains are par- or feet, but in any case the chart will indicateticularly useful. The copyrilht was purchased

39 A NAVIGATION COMPENDIUM

in 1868 by the Hydrographic Office, the fore- HO-261 The Azimuths of CelestialBodies. runner of the Oceanographic Office, which hasThis volume is similar to H0-260except that published subsequent revised editions. it provides azimuths for bodieswith declination Dutton's Navigation and Piloting. Since1926, of 24° to 70°.It replaced 110-120 which isno when first prepared asa text for midshipmen atlonger in print. the U.S. Naval Academy by Commander Benjamin (2) Tables for computation ofposition Dutton under the title Navigationand Nautical HO -208 Navigation Tables forMariners and Astronomy, this through revision has remainedAviators. (Dreisonstok). as the basic navigation textbook for the U.S. HO-211 Dead Reckoning Altitudeand Azimuth Navy. Published by the U.S.Naval Institute, Tables. (Ageton) Annapolis, Maryland, itwas significantly up- HO-214 Tablesof Computed Altitude and dated in its twelfth edition (1969). Azimuth. This set, developedby the Hydrographic Primer of Navigation, Written byColonel Office, consists of nine volumes,one for each George W. Mixter and initially publishedin 1940, this ten degrees of latitude, and has wideusage, is an excellent navigation textbook.It isfor both the computation of linesof position and basic and non-technical, and thus usefulto theazimuth. beginner. Nonetheless, it is sufficiently thorough HO-218 Astronomical NavigationTables. Con- for the practicing navigator. Publishedby D. sisting of 14 volumes, one for each fivedegrees Van Nostrand Company, Inc. of Princeton,New of latitude from 11° to 69°, andwith solutions for Jersey,ithas been periodically updated, its22 stars, these t. hiesare similar to H0-214, most recent revision (fifth edition) beingpub- but are less accurate inasmuch lished in 1967. as they are designed primarily foruseinairnavigation. Air Navigation. (Department of the AirForce, 110-229 Sight Reduction Tablesfor Marine AF Manual 51-40, Volume I). Thismanual, forNavigation. Prepared througha cooperative effort use in air nav'gation, is basic and precise, andinternationally between the U.S. NavalOceano- provides vital material for bothstudents andgraphic Office, the U.S. Naval Observatory,and air navigators. It is published by the AirTrain-Her Majesty'sNautical Almanac Office, and ing Command, U.S. Air Force, andis sold byconsisting of six volumes, one for each 15°of the Superintendent of Documents, U.S. Govern-latitude, this set will eventually replace H0-214. ment Printing Office, Washington, D.C. HO-249 Sight Reduction Tables forAir Navi- Space Navigation Handbook.(Department ofgation. Prepared cooperativelyas in the case the Navy, NavPers 92988). Publishedby the ofH0-229but earlier,through a combined Chief of Naval Personnel,and based primarilyBritish and American effort, upon the research, teaching, and inventive genius and consisting of of Captain P. V. three volumes, HO-249 is the aircounterpart H. Weems, USN (Ret.), thisof H0-229. Volume Iprovides solutions for text provides in brief forma simplified concept selected stars,VolumeIIprovides complete for the more difficult three-dimensionalnavi- data for latitudes 0° to 39°, and VolumeIII pro- gation in space, together with supportingback- vides complete data for latitudes 40°to 89°. ground information. c. Almanacs have a relatively short but in- b. Navigation tables which provideazimuths teresting background. Astronomical observations of the sun and other bodies,and solutions ofof the Danish astronomer Tycho Brahe in the the astronomical triangle for thedeterminationlate sixteenth century were the basis of Kepler's of position without resort to difficultformulae, laws of motion which in turn became the founda- are as follow: tion of modern astronomy and celestial navigation. The first almanac for mariners was the (1) Azimuth tables British Nautical Almanac which appeared in 1767. H0-66 Arctic Azimuth Tables. Thesetables America entered the field in 1852 when the U.S. provide values for azimuth angles of bodieswith Navy Depot of Charts and Instruments, which a declination of 0° to23°, with declination ofpreceded the Hydrographic Office, publisted the the same name as latitude, forlatitudes of 70°American Ephemeris and Nautical Almanac for to 88°. No longer in print. the year 1855. Since 185b, an American Nautical HO-260 Azimuth Tables. Thesetables com-Almanac hasbeen publishedannually;itis plement 110-66 for latitudes of 0°to 70°, and slinuar to the American I.:ph( meris and Nautical replace HO-71 which was referred toas theAlmanac exceptthatitomits the Ephemeris "red azimuth tables" r.nd which isno longer which is of primary intere.t to astronomers. in print. Thus,theNautical Almanacistheprincipal

40 Chapter 4CHARTS AND PUBLICATIONS

almanac for the use of mariners today, although Notice to Mariners A weekly pamphlet from theAir Almanac, which was of more recentthe Naval Oceanographic Office. Two copies are origin and which was prepared largely for usemailed to each addressee on the N.O. mailing in air navigation,isalso in general use. Al-list unless more are requested. One copy is manacs should be requested either from theused for chart correction and permanent file Superintendent, Naval Observatory, Washington, while the second copy is used for correcting D.C., or in the case of commerical activitiesCoast-Pilots, Sailing Directions, and Light Lists, from the Superintendent of Documents. being cut up as necessary (corrections may be The Nautical Almanac is now prepared jointly "pen and ink" or "cut-out"). by theU.S.Naval Observatory in Washington, Daily Memoranda Single sheets containing D.C. and H.M. Nautical Almanac Office, Royalhydrographic information promulgated if urgent Greenwich Observatory, to meet the require- by radio from the Naval Oceanographic Office ments of the U.S. Navy and the British Admiralty. andlater superseded by Notice to Mariners. Printedseparately and annuallyinthe two Monthly Information Bulletin.This monthly countries, this almanac provides all necessarybulletin from the Naval Oceanographic Office astronomical data for the practice of celestialserves the purpose of updating index catalogs navigation at sea. and the Portfolio Chart List, e. Other: The Air Almanac first appeared as an Ameri- can publication in 1983. It is issued thrice yearly, H0-117 RadioNavigational Aids,in two each edition being prepared for a four-monthvolumes, HO-117A and HO-117B by geographic period. The U.S. Naval Observatory and H.M.location, contains information such as the time Royal Greenwich Observatory cooperate in itsand frequency of hydrographic broadcasts, Naval publication. While useful for both marine and air Observatory radio time signals, distress traffic, navigation,itis primarily used for the latter. radio beacons and dirt.ction-finder stations, loran d. Chartsupplementarypublicationsare coverage and stations, and radio regulations for books used in conjunction with charts and in- territorial waters. clude the following: HO-118 Radio Weather Aids, also in two volumes, HO-118A and HO-118B by geographic Coast Pilots Edited by the National Ocean location,contains information concerning the Survey, a Coast Pilot provides navigational and making of weather reports, codes, report con- general interest information for the coasts of tents, and frequencies, and informs the navigator the United States and its possessions. of available weather broadcasts. Sailing Directions Edited by the Oceano- HO-150 World Port Index is a useful guide graphic Office, Sailing Directions provide navi- containing detailed information concerning spe- gationalandgeneral interest information for cific ports and provides a cross reference of definitegeographic areas beyond thecoasts chartsand publications applicable to a given of the United States and U.S. possessions. port. Tide, Tidal Current Tables, and Tidal Cur- HO-151 Table of Distances Between Ports rent ChartsPrepared by the National Ocean Usefulin voyage planning, HO-151 lists dis- Survey, Tide, Tidal Current Tables and Tidaltances between ports. Current Charts, as discussed in the following HO-220NavigationDictionary Auseful chapter, provide predictions of tidal effect. reference for learning the meaning of various LightListsThe Light List provides de- navigation terms and expressions. scriptive information concerning lights of the H0-226Handbook of Magnetic Compass Ad- coasts of the United States and U.S. possessions justment and Compensation (Spencer and Kucera). infivelistswhich areprinted by the U.S. This useful manual was described in art. 211. Government Printing Office. The Oceanographic HO-2102D Star Finder and Identifier. This Office prepares for foreign waters a List ofdevice, which is most useful in celestial navi- Lights in seven volumes. gation, is described in chapter 13.

41 CHAPTER 5 TIDES AND CURRENTS

501. INTRODUCTION end result is that as the moon transits a meridian, depth increases on both the upper branch and the lower branch of that meridian. Johannes Kepler (1571-1630), a German who succeeded, and was familiar with the work of, 502. TIDE the Danish Astronomer 3rahe, developed three laws of motion which in turn led to the develop- Tide is the vertical rise and fall of the ocean ment of the almanac. In turn, Kepler's laws levelresulting from gravitational force. The (Appendix B) led to the development of threefollowing terms are associated with tide: lawsof gravity and motion by theEnglish mathematician and philosopher Sir Isaac Newton HIGH TIDE.Highest water level normally (1642-1727). From Kepler's laws and his own,reached during a cycle. Newton developed his famous universal law of gravitation (Appendix B) which states that "every LOW TIDE.Lowest water level normally particle of matter attracts every other particlereached during a cycle. with a force that varies directly as the product of their masses and inversely as the square of STAND. A period within the cycle during the distance between them. which the water level appears not to change. Thus, gravitation, the force of attraction between bodies in the universe, depends upon the RANGE. The difference between the height mass of the bodies concerned and their distance of high water (high tide) and the height of low of separation. The moon, a satellite of the earth,water (low tide). Heights are reckoned from a isnear enough and large enough to exert areference plane. sizable pull. The sun also exerts a force, which is inferior to that force exerted by the moon, DATUM PLANE. A reference plane estab- because of the comparative distances. This grav- lished which may or may not be sea level but in itational forceofattraction acts upon everyall cases may be converted to mean sea level. particle within the earth; since different points on the earth are at varying distances from the MEAN LOW WATER. A datum plane based moon, the force of attraction consists of com- upon the average of all low tides. ponents of varying values, depending upon distance. The point on the surface of the earth MEAN LOWER LOW WATER. A datum plane which lies on a line connecting the centers ofbased upon the average of the lower of two low the earth and the moon is acted upon with great tides which occur during a lunar day (a lunar relative force because of the comparatively short day isa time measurement based upon one distance involved. This brings the water (theapparent revolution of the moon about the earth). earth may be considered as a hard core sur- rounded by water) toward the moon, making the MEAN LOW WATER SPRINGS. A datum depth greater. Also the center of the earth isplane based upon the average of extreme low acted upon by a greater force than is a point tides called spring tides. on the side of the earth opposite the moon. For that reason, the center of the core tends to pull In some foreign countries, the datum plane toward the moon making the depth of the watermay not correspond to those listed above. How- on the opposite side of the earth greater. Theever, the tide tables are based upon the datum

42 Chapter 5 TIDES AND CURRENTS

plane of the most detailed local chart, The datumthe nearest minute is given together with tidal plane is an arbitrary value, It must be under-difference, Tidal difference consists ofa time stood that ACTUAL DEPTH OF WATER EQUALScorrection (in hours and minutes) and a height CHARTED DEPTH PLUS HEIGHT OF TIDE, Ifcorrection (in feet), both preceded by eithera the height of tide is a negative value, then theplus or minus sign. There is generallya height actualdepthisless than the charted depth.correction for both high and low water, If the TIDAL CYCLE. Since a high tide occurs atcorrection is omitted for low water height, it two longitudes simultaneously, in one lunar daymay be assumed that the height of low water at (24 hours, 50 minutes) two high tides and twothe subordinate station is the same as the height low tides occur. One high tide and one low tide at the reference station,If for some reason, constitute a tidal cycle which, in time is oneheight differences at a given station would give half a lunar day or 12 hours and 25 minutes,an unsatisfactory prediction, height difference The time difference betweenone high tide and is omitted and ratios for high and/or low water one low tide is approximately 6 hours and 12 1/2 are given, identified by asterisk, To find the minutes (half a tidal cycle). heightsof high and low water using ratios, multiply the heights at the reference station by PRIMING, When the gravitational effect oftheir respective ratios. If a ratio is accompanied the sun leads the moon's effect, causing the time by a correction, multiply the heights of high and of high tide to be earlier than normal,we call low water at the reference station by theratio, the phenomenon "priming of the tide." then apply the correction. Table 2 also provides LAGGING. When the gravitational effect ofthe mean range (difference in height between the sun trails the moon's effect, causing the time mean high water and mean low water), the spring ofhigh tide to be retarded, we speak of the range(average semidiurnal range occurring phenomenon as the "lagging of the tide." semi-monthly as a result of a new or full moon), and the mean tide level (a plane riidway between SPRING TIDE, When thesun and moon are mean low water and mean high water)withrespect actinginconjunction, which occurs when we to chart datum. have either a new or a full moon, high tides are TABLE 3. Table 3 isa convenient means of higher than usual and low tides are lower thaninterpolation which allows for the character- usual. These extremes are called spring tides, istics of the tidal cycle. While tables 1 and 2 NEAP TIDE. When thesun and moon areprovide time and heights of high and low tides, acting in opposition, tidal range is ata minimum the state of the tide may be desired fora given and the tide is called neap tide. time in between. The arguments for entering table 3 are duration of rise or fall of tide, time 503. TIDE TABLES between that desired and the nearest tide, and range. From table 3 we obtain a correction. If Tablesareprepared annually for variousthe nearest tide is high tide, the correction is areas by the National Ocean Survey of the De-subtracted from the height of the high tide; if partment of Commerce, which contain predic-the nearest tide is low tide, the correction is tionsofthestateof the tide. Each volume added to the height of lov, qde. This providesthe consists of the following tables: height of the tide at the desired time. TABLE 1. A list of reference stations for The height of the tide alone does not fully which the tide has been predicted. The time and describe the state of the tide;it is desirable to heights of high and low tides are tabulated forknow whether the tide is rising or falling. If the each day in the year for each of these refer-desired time is preceded bya high tide and is ence stations. Also, theposition of the datumsucceeded by a low tide, the tide is falling. If plane with refere ice to mean sea level is given the desired time is preceded bya low tide and for each reference station. is succeeded by a high tide, the tide is rising. The tide tables as published include three TABLE 2.A list of subordinate stations additionaltablesfortheconvenienceof the for which the tidal differences have been pre- mariner. Table 4 provides the local mean time dicted with respect to a reference station havingof sunrise and sunset. Table 5 providescor- nearly the same tidal cycle. Above groups ofrections for conversion of local mean time to subordinate stations, the reference station for standardtime. Table 6 provides the time of that group islisted. After the name of each moonriseandmoonset as computed for key subordinate station the latitude and longitude toreference stations,

43 A NAVIGATION COMPENDIUM

EXAMPLE 1 (Data from Appendix C): What is the state of the tide at Mayport, Florida on 7 August 1970 at 1320? Reference Station High Tide Height Low Tide Height Mayport, Fla. 1124 4.3 1718 0.6 Duration of fall:1718 - 1124 = 5 hrs., 54 min. Time between desired time and nearest tide (high): 1320 -1124 =1 hr., 56 min. Range of tide: 4.3 - 0.6 = 3.7 ft. Correction (Table 3): 0.9 ft. State: 4.3 - 0.9 = 3.4 ft.The tide is falling.

Data was taken from the tables for the de- (1hr., 56 min.), and (3) range of tide (3.7 ft.). sired data, noting times and heights of the two The correction (0.9) thus obtained was applied nearest tides. Table 3 was entered using the to the height of the nearest tide (4.3 ft.). During arguments (1) duration of fall (5 hrs., 54 min.), the period 1124 to 1718 the tide changes from (2) time interval between high and desired time high to low and therefore must be falling.

EXAMPLE 2 ,'rata from Appendix C):

What is the state of the tide at St. Augustine, Floridaon 4 July 1970 at 0600?

Reference Station High Tide Height Low Tide Height Mayport, Fla. 0848 3.7 0236 0.0 Corrections +14 -0.3 +43 0.() St. Augustine, Fla. 0902 3.4 0310 0.0 Duration of rise: 0902- 0319= 5 hrs., 43 min. Time between desired time and nearest tide (low): 0600-0319=2hrs., 41min. Range of tide: 3.4 - 0.0 = 3.4 ft. Correction (Table 3): 1.6 ft. State: 0.0+1.6 = 1.6 ft. The tide iaising.

The appropriate reference station was found Atlantic North. . .Westward fromCape Verde above the subordinatestationin bold print, in Equatorial Islands andclockwisein Table 2. Subordinate station corrections applied NorthAtlantic to reference station values were also found in Atlantic South. .. .Westward from the African Table 2. Equatorial coast andcounterclockwise in South Atlantic 504. OCEAN CURRENTS Atlantic Betweenthetwo currents Equatorial described above and east- Counter ward from South America to A current is the horizontal flowormovement Africa of water.There are two general types, ocean Gulf Stream Through Straits of Florida, currents and tidal currents. The ocean currents extending northeast result from the effects of the wind above the sea, Greenland Southward alcmg east coast and effects of temperature and salinity differ- of Greenland, thence north- ences within the sea. The following ocean cur- westward and counterclock- rents are most noteworthy: wise in Baffin Bay

44 Chapter 5 TIDES AND CURRENTS

Labrador .Formed from the Greenlandhorizontal movement of water, we speak of the Current and flowing south-conditionas "slack" or "slack water." The ward from Davis Straits a-strengthof the current at any time depends long the Labrador coast, upon both the tidal cycle and the configuration of land. When high tide occurs in a bay havinga Brazil Southwestward and counter-small mouth, a great amount 4 water must flow clockwise in the South Atlan-through the mouth, and therefore a strong cur- tic as a branch of the Atlanticrent may be expected.This current willat EquatorialCurrent,alongleast be strong in comparison with a current South American coast entering a bay having a wide mouth or entrance. Pacific North.. .Westward in North Pacific 506. TIDAL CURRENT TABLES Equatorial Like tide tables, tidal current tables are pre- Pacific South . .Westward and counterclock-pared annually for various areas by the National Equatorial wise in South Pacific Ocean Survey of the Department of Commerce, to provide predictions of the state of the current. Pacific ..Between thetwo currentsEach volume consists of the following tables: Equatorial described above and east- Counter ward in Pacific TABLE 1. A list of reference stations in geographical sequence, for which the current has Japan Stream... .Northeastward off shore ofbeen predicted. For each reference station the Japan; partially a branch oftimes of slack water, maximum current and the the Pacific North Equatorialvelocities of maximum current are tabulated for Current each day of the year. Also, table 1 tabulates flood and ebb direction. Oyashiwo Southeastward between Alas- ka and Siberia,along the TABLE 2. A list of subordinate stations for Siberian coast which the difference between local current and current at a reference station has been predicted. California Southeastward off Califor-Above groups of subordinate stations, theappro- nian shore priate reference station is listed. After the name of each subordinatestation, the latitude and 411114bettralia Southward between Australialongitude to the nearest minute is given. Following fie and New Zealand; a branchthe geographical coordinates, the time difference of the Pacific South Equa-and velocity ratio are tabulated. To find the time torial Current of a current at the subordinate station, apply the Peruvian Northward along west coasttime correction according to sign, to a time of of South America current at the reference station. To find the velocity of the current at any subordinate station, Indian South Counterclockwisein Indianmultiply the velocity at the reference station Equatorial Ocean by the velocity ratio at the subordinate station. Agulhas SouthwardbetweenAfricaAmong rrany current characteristics tabulated and bladagascar are the average velocity of flood andebb currents. TA BLE 3. Table 3 provides a means of inter- 505. TIDAL CURRENTS polation for the state of the current at any time between tabulated times. It is divided into two Tidal currents result from tidal changes; inparts, table 3A and table 313. Table 3A is used order for the tide to rise and fall there mustfor tidal currents while table 3B is used for be some hoilzontal movement of water betweenhydraulic currents such as the man-caused cur- the ocean and the coastal estuaries. During therents found in the Cape Cod Canal and other rise in tide, while the current is standing towardlisted reference stations or referred subordinate the shore, we refer to the current as "flooding."stations. The arguments for entering table 3 are When the current is standing away froni the shore,the interval between slack and maximum current itis "ebbing." When there is no detectableand the interval between slack and desired time.

45 A NAVIGATION COMPENDIUM

Table 3 provides a factor which must be multi-applies to currents, such as those in the Cape plied by the velocity at either the reference or Cod Canal, and at other listed reference stations the subordinate station, depending upon which is or referred subordinate stations. Table 5 pro- under consideration. vides data on rotary tidal currents such as are found at Nantucket Shoals. The state of the current is the velocity in knots, whether it is ebbing or flooding, and the The tidal current tables also contain current direction toward which it flows. diagrams for certain harbors. These diagrams provide a graphic table showing the velocities of The tidal current tables include two additional flood and ebb and times of slack and its strength tabulations which are sometimes useful in the over a considerable length of channel in a tidal prediction of tidal current. Table 4 predicts the waterway. Additionally, the tidal current tables duration of slack water, the period in minutes contain data for estimating the currents which when the velocity varies from zero to 0.5 kts., are wind-driven and the combined effect of tidal in 0.1 kt. increments. It is divided, like Table 3, and wind currents. Certain ocean currents, such into two parts, Tables 4A and 4B. The former as the Guff Stream (in the Tidal Current Tables, applies to normal tidal currents while the latterAtlantic Coast of North America), are described.

EXAMPLE 1 (Data from Appendix D):

What isthe state of the current at St. Johns River Entrance, Florida on 2 March 1970 at 14007

Ma^imum Velocity Reference Station Slack Current (flood/ebb)Direction

St. Johns River Entrance, Fla. 1312 1506 1.2 f. 275(f)

Interval between slack and maximum current: 1506 - 1312 = 1hr., 54 min.

Interval between slack and desired time: 1400 - 1312 = 48 min.

Factor (Table 3): 0.5

Velocity: 1.2 x 0.5 = 0.6 kts.

Direction: The current is flooding. Direction is 275.

Inchoosing current times, as inthetide bracketthedesired timeat the subordinate tables, choose the two times which form the station;afterthetimecorrection hasbeen nearest bracket to the desired time. In some applied,one time must immediately precede problems,particularly where the subordinate thedesired time,an theother must im- station time correction is large, the given time mediately follow it. An easy way to take into is seen to be bracketed by the selected reference accountthe correctionisto add minus cor- station quantities, but when the time correction rections to the desired time, then choose brackets is applied the given time is not bracketed at the at reference station, and conversely subtract plus subordinate station. The bracketing times in tide corrections from the desired time before select- and current subordinate station problems must ing brackets.

46 Chapter 5 TIDES AND CURRENTS

EXAMPLE 2 (Data from Appendix D):

What is the state of the current at Jacksonville,Florida, off Washington Street, on 12 April 1970 at 0720?

Maximum Velocity Reference Station Slack Current (flood/ebb)Direction St. Johns River Entrance, Fla. 0300 0548 1.7 e.

Corrections +220 +250 0.7 (Veloc- 060 (e) ity ratio) Jacksonville, Fla., 0520 0838 1.2 060 (e) off Washington St. Interval between slack and maximum current: 0838- 0520 = 3hrs., 18 mm. Interval between slack and desired time: 0720- 0520 = 2 hrs. Factor (Table 3): 0.8 Velocity: 1.2 x 0.8 = 1.0 kt. Direction: The current is ebbing. Direction is ORO.

Tidal current charts are now available forclosely the axis of the Gulf Stream, the ship's certain major ports or seaways, to be used in speed may be increased without any increase conjunction with the Tidal Current 'Fables. These in engine or shaft RPM. When rounding Florida charts, prepared by the National Ocean Survey, enroute to the Gulf, the mean axis of the stream show hourly directions and velocity of tidal should be avoided in order not to slow the speed currents. To select which chart to use froma of advance; actually, a lesser countercurrent booklet for a given port, determine from the to the Gulf Stream may be experienced in close tidal current tables the time difference between proximity to the Florida Keys, which will be thedesired time and thenearest precedingof assistance. slack water; the chart that agrees mostnearly Tidal currentsaffecta ship considerably withthistime computation should be used.when docking, undocking, and whenever underway in pilot waters. A current may be so strong 507. CONSIDERATION OF TIDE asto prevent a partially disabled ship from AND CURRENT making any headway. The navigator may use both ocean currents and tidal currents to his advantage, and should The navigator must fully consider the state always be fully conscious of the state of the of the tide together with charted depth to insure current and of any expected changes, anticipating that water is kept under the ship's keel. Tidalhow the expected changes, in the state of the ranges may be such as to cause some basinscurrent willaffect the maneuverability of his to dry at low tide even though sufficient water ship. As for reliance upon tidal current data, ispresentforsafenavigationat high tide.. the navigator must expect conditions occasionally Occasionally thetidal range permits crossing otherthan thos' predicted. Storm conditions, of bars which would not otherwise be navigable. man-made currents from lock sluice gatesor Knowledge of ocean currents may be usedspillways, and currents developed in dredging toadvantage, either to speed a voyage or tooperations, among others, tend to reduce the conservefuel.When standing northeastward accuracy of tidal current data available to the throughtheStraitsofFlorida,by following navigator.

47 CHAPTER 6 DEAD RECKONING

601. INTRODUCTION along the course line, to the predicted position 15 minutes in the future. The DIA plot is first Dead reckorp: c-:pr!violz,lv !Ice!) d n prediction of the ship's travel and later a a in I:. ,II: h tnt t :ti. history of the route the ship attempted ofa s::.pis cait Irom the direction :1; follow.The course line may be referred therate ofprogre:,.,s through the water from ,o as a DR track or trackline. the last Nell determined position. The direction and the rate of progress cannot always be meas- When using time and speed to compute dis- ured exactly, and dead reckoning as a method tance in dead reckoning, it is often advantageous may leave much to be desired. However, when touse the three-minute rule. Easily proven, either celestial navigation or pilotingis used the rule merely notes that the distance traveled as a primary means of navigation, dead reckon- inyardsinthree minutes is 100 times the ing provides a check and serves the worthwhile speedinknots. Thus,ifa ship is making a purpose of indicating errors. When other means speed of twenty knots, it will travel 2000 yards, of navigation fail, the navigator must rely upon or one nautical mile, in three minutes. dead reckoning alone. Since the automatic dead A well determined positionis labeled with reckoning equipment is subject to mechanical the time indicated in 4 digits followed by the or electrical failure, the navigator with drafting word "Fix;" for example "0800 Fix." Above instruments, and up to date information con-a course line, the letter "C" is placed, followed cerning the ship's movements, manually con-by the ship's true course in 3 digits, indicating structs the dead reckoned plot. the direction of travel; for example, "C090." Below the course line, the letter "5" followed 602. THE PLOT by the ship's speed in knots indicates the rate of progress and determines the speed of genera- Dead reckoning, as presently accomplished, tion of the trackline;for example, "S12." A is a graphic means of navigation. Decades ago, dead reckoned position is labeled with the time it was accomplished by computation using trig- followedbytheletters"DR"; for example, onometric formulae. A dead reckoning plot (fig. "0900 DR." Symbols as well as labels can be 6-1) originates with a well determined positionused to distinguish a fix from a dead reckoned (a fix or running fix as described in the follow- position. While both are normally indicated as ing chapter). From the fix, a course line repre- a circle around a point, and are distinguished senting theship's course is drawn, using the by the letters "fix" or "DR," some navigators compass rose as a reference. The course line followaformerpractice of indicating a fix is actually a locus of successive DR positions. with a circle and a D11 with an arc connecting Predictedpositions, called DR positions, AIt the course lines, an approximate semi-circle. marked at intervals along the course line. These positions are determined by the speed of the DR positions are usually plotted for each ship, the time interval, and the scale of the hour. Inin-shore navigation the DR should be chart. For example a ship making a speed of plotted more frequently, perhaps as oftenas 10knots would travel2 1/2 nautical miles in every3 minutes,but always depending upon 15minutes. On a DR course line,using the circumstances and proximity to danger. At sea chart scale,a navigator would set his divider on a steady course using a small 'wale chart, points 2 1/2 nautical miles apartin order to one DR position plotted each 4 hciirs is con- measure from the Last well determined position, sidered satisfactory.

46 Chapter 6DEAD RECKONING

5 04, 20 S

190.9 Figure 6-1. Dead reckoning plot.

By the dead reckoning plot,the estimated line, terminated by an arrowhead at the fix. This time of arrival (ETA) at a destination is com- line or vector represents current. The direction puted in advance. Similarly, the estimated time of the line (arrow) is the set. The length of the of departure (ETD) from a given point may be linein nautical miles divided by the hours the calculated unlessthe point marks the origincurrent has acted (time interval between last of the voyage in which case it is determined two fixes) is the drift. by operational planning. The navigator consults current tables,the Coast Pilot or Sailing Directionsas appropriate, 603. CURRENT and pilot charts and draws from his ownex- perience to decide what caused an apparentcur- We have previously thought of current as rent.If he decides that the apparent current the horizontal movement of water; at this point represents an actual movement of water which we must defineitfor our future convenience, can be expected to continue for some time, he as the total effect of all forces causing a dis-may use the determined set and drift of the crepancy between predicted and actual positions. current to either compute the course and speed Current when so broadly defined includes t-e essential to making good a desired trackor to horizontalmovementof water, wind effect, predict the resultant track for any given course steering errors, variationsin engine speeds, and speed. The accuracy of such computations andany momentary deviation from the basic depends upon the accuracy of the prediction of course made by the conning officer. the set and drift and whether or notany change Current can be described in terms of two in the value of the current occurs. qualities called set and drift. SET is the direc- To predict the track using (1) course and tion a current acts; DRIFT is the velocity inspeed of the ship and (2)set and drift of the knots of a current. current, represent these basic values by vectors. To derive set and drift (fig. 6-2),a fix is com- The direction and length of the ship's vectorare pared with the DR position for the same time based respectively upon the ship'scourse and by connecting the DR and the fix with a brokenspeed; the direction and length of the current

49 A NAVIGATION COMPENDIUM

hour. When the navigatorprefers the latter representation, and accordingly draws his vectors, then the length of the resultant track is a corresponding multiple of the speed made good. When it is desired to make good a predeter- mined track, the first step is to construct the resultant which represents the desired track. From the termination of the desired track (point of destination), the current vector is drawn as the reciprocal of the set, with the length equal to the drift multipled by the time enroute in hour:..By completing the triangle the ship's vectorisdetermined;to compute the ship's course and speed respectively, determine the direction of the vector, and its length divided by the duration of the voyage in hours. This plot is of great practical use. 58.84C It is no more a safe practice to assume that Figure 6-2. The current effect. a current will adhere to a predicted value than itisto assume that no current exists. The cautious navigator will construct on his chart vector is based upon the current's set and drift.both the DR track based upon course and speed Draw the ship vector for an hour's effect. From and the predicted track taking current into ac- the end of the ship's vector, draw the currentcount. He carefully checks all features between vector for an hour's effect. The resultant, that the two tracks, to detect dangers should the is the line connecting the origin of the plot andcurrent be reduced. He checks features adjacent the terminating end of the current vector, repre- toand beyond each track to detect dangers sents the probable track; by inspection of the should the effect of current either exceed or direction and length of this resultant vectorundergo a reversal in its predicted value. The the navigator predicts course and speed made navigator should assume that the most unfavor- good. The vectors may be drawn in length toable condition of current exists and take appro- represent either an hour or a multiple of anpriate action to insure the safety of his vessel.

50 CHAPTER 7 PILOTING

701. INTRODUCTION landmark in a reciprocal direction. For example, if a lighthouse bears 040, the shipbears 220 from Pilotinghas been previously defined as a thelighthouse. A bearing line of position is method of directing the move.nents of a vessel labeled with the time expressed in four digits by reference to landmarks, other navigational above theline and the bearing in three digits aids, and soundings.It is generally used as a below the line. primary means of navigation when entering or leaving port and in coastal navigation, It may be A special type of bearing is the tangent. When used at sea when the bottom contour makes the a bearing is observed of the right hand edge of aprojection of land, the bearing is a right establishment of a fix by means of sounding tangent. Similarly, a bearing on the left hand possible. In piloting,the navigator (a) obtainsedge of a projection of land as viewed by the warnings of danger, (b) fixes the position fre- observer is aleft tangent. A tangent provides quently and accurately, and (c) determines the an afirmrate line of position if the point of land appropriate navigational action. is sufficiently abrupt to provide a definite point for measurement; itis inaccurate, for example, 702. LINES OF POSITION when the slope is so gradual that the point for Piloting involves the use of lines of position, measurement moves horizontally with the tide. which arelociof a ship's position. A line of A distance arc is a circular line of position. position is determined with reference to a land- When the distance from an observer to a landmark; in order for a landmark to be useful for markisknown, the locus of the observer's this purpose it must be correctly identified, and position is a circle with the landmark as center its position must be shown on the chart which is having a radius equal to the distance. The entire in use. There are three general types of lines circle need not be drawn, since in practice the of position(fig.7-1),(...) ranges, (b) bearings navigator normally knows his position with suf- including tangents, and (c) distance arcs. ficient accuracy as to require only the drawing A shipis on "range" when two landmarks of an arc of a circle. The arc is labeled with are observed to be in line. This range is repre- the time above expressed in four digits and the sented on a chart by means of a straight line, distance belowin nautical miles (and tenths). whichif extended, would pass through the two The distance to a landmark may be measured related charts symbols. This line, labeled withusing radar, the stadimeter, or the sextant in the time expressed in four digits (above the line), conjunction with tables 9 and 10 of the American isa locusof the ship's position. It should be Practical Navigator. notedthatthe word "range" inthis context differs significantly from its use as a synonym of distance. 703. FINES It is preferable to plot true bearings although either true or magnetic bearing may be plotted. A fix(fig.7-2), previously thought of as a Therefore, when the relative bearing of a land- v.ell determined position, may now be defined as mark is observed, it should be converted to true the point of intersection of two or more simul- bearing or direction by the addition of the ship': taneously obtained lines of position. The synthol true heading. Since a bearing indicates thedirec- forafixis a small circle around the point of tion of a terrestrial object from the observer, intersection. Itis labcled for better identifica- in plotting,Li line of position is drawn from the tionw.iththetime expressedin four digits

51 A NAVIGATION COMPENDIUM

69.141 Figure 7-1. Lines of position.

followed by the word "fix." Fixes may beob- error as compared to two lines of position tained using the following combinations of linesseparated by less than 30 degrees of spread. of position: If in both cases a small unknown compass error exists, or if a slight error is made in reading (a) A line of bearing or tangent and a distancethe bearings, the resulting discrepancy will be arc. lessin the case of the fix produced by widely (b) Two or more lines of bearing or tangents. separated lines of position than in that of the fix (c) Two or more distance arcs. obtained from lines of position separated by a (d) Two or more ranges. few degrees. (e) A range and a line of bearing or tangent. If only two landmarks are used, any error in (f) A range and a distance arc. observation or idcialtication may not be apparent. By obtainins three or more lines of position, Since two circles may intersect at two points, each line ci position acts as a check. If all cross two distance arcs used to obtain a fix are some- in a pinpoint or form a small triangle, the fix what undesirable; the navigator in making his may genexally be relied upon. Where three lines choice between two points of intersection may, of posit.on are used, a spread of 60 degrees however, consider an approximate bearing, sound- would result in optimum accuracy. ing, or his DR position. When a distance arc of When a choice of landmarks or other aids cne landmark and a bearing of another are used,exists between permanent structures, such as the navigator may again be faced by the problem lighthouses or other structural and natural fea- of choosing between two points of intersection turesidentifiable ashore orin shallow water, of loci. and less permanent aids such as buoys, the former should be given preference. The fact must be 704. SELECTING LANDMARKS recognized that buoys, while very convenient, may drift from their charted position, because Three considerations in the selecting of land- of weather and sea conditions, or through mari- marks or other aids for use in obtaining lines time accident. of position are: angle of intersection,(b) The navigator oftentimes has no choice of number of objects, and (c) permanency. landmarks, their permanency, number, or spread. Two lines of position crossing at nearly rightIn such cases he must use whatever is available, angles will result in a fix with a small amount of no matter how undesirable. In the evaluation of

52 Chapter 7PILOTING

determine the correct error. If the error assumed

N is improperly identified (east or west), the tri- 4 angle will plot larger. If the error proves to be properly identified but the triangle still exists, LIGHTHOUSE although reduced in size, the navigator should on the second trial, assume a larger error in sf 00 the same direction. 1000 FIX 1000 706. RUNNING FIXES 4.5 088° T It is not always possible for the navigator to ti observe lines of position simultaneously. Some- times only one landmark is available; the navi-

GH NOUSE gator may make frequent observations of the one landmark,or he may, after one observation, lose sight of the available la.' imark only to sight a new navigational aid. During these observations, if the navigator is able to compute distance IN he may easily establish his fix. If not, or if for any reason his data consists of lines of position LIGHT HOUSE obtained at different times, then he may establish a position which only partially takes into account the current. This position is the running fix identified by the same symbol as the fix except that the time labelis followed by the abbreviation "R. Fix." It is better than a DR position but less desirable than a fix. 1500 FI A running fix is established by advancing the first line of position in the direction of travel of 1500 the ship (the course), a distance equal to the 4 MILES nautical miles the ship should have traveled during the interval between the time of the first 58.76: .77 line of position and the time of the second line Figure 7-2. Fixes. of position. The point of intersection of the first line of position as advanced, and the second line of position, is the running fix. The advanced line hisfix,the number of landmarks, their per- of position is labeled with the times of the two manency, and their spread should receive con- lines of position (LOP's) separated by a dash, and sideration. When three lines of position cross the direction, above and below line, respec- forming a triangle, it is difficult to determine tively. See fig. 7-3. whether the triangle is the result of a corn2ass To advance a line of bearing, a tangent, or error or ar 'rroneous line of position. The plotting a range, measure from the point of intersection of four lines of position will usually indicateof the LOP and the DR track line, along the if a line of position is in error. trackline,the distance the ship would have traveled at its given speed. This measurement 705. CHANGE IN COMPASS ERROR provides a point on the DR track line, through which the earlier line of position is re-plotted When lines of position cross to form a small without any change in its direction. (Fig. 7-3A.) triangle, the fix is considered to be the center To advance a distance arc, draw the course of the triangle, a point which is determined byline as a broken line on the chart from the land- eye. If the size of the triangle appears signifi-mark first observed. Along this broken course cant, itis possible that the value of the compass line, measure the distance the ship should have error has changed. traveled, based upon the elapsed time between To compute the new compass error, without observations and the speed of the ship. At the the benefit of a range or azimuth, assume anpoint thus established, reconstruct the earlier error, then by successive trials and assumptions distance arc. (Fig. 7-3B.)

53 A NAVIGATION COMPENDIUM

I 03C 090 0,

A. BEARING LOP ADVANCED B. DISTANCE ARC ADVANCED

1015

090

C. PERPENDICULAR METHOD D. COURSE MADE GOOD METHOD

58.76(190) Figure 7-3.Running fixes.

Iftheship changes course and/or speed respect to the old DR, then it has been advanced between observationstheproblemisnot soparallel to itself a distance and a direction con- simple to solve, and one of the following methods sistentwiththeship's movement during the should be used intervening time. A variation of this method is to construct, instead of a perpendicular, a line PERPENDICULAR METHOD.After two lines of any direction between the first DR and LOP, of position are obtained, plot DR positions cor- This lineisthen duplicated at the second DR responding to the times of the LOPs. From the and the LOP advanced as before, In duplication, earlier DR, drop a perpendicular to the earlier the line from the second DR must ' e of the snit LOP. At the second DR, construct a line having length and direction as the line connecting :.he the same direction and length as the first per- first DR and LOP. (Fig. 7-3C.) pendicular. At the termination of the latter line, construct a line parallel to the original LOP; COURSE MADE GOOD NIETII0D. --As in the thisis the advanced LOP. The intersection of perpendicular method, plot DR positions to initch this advanced LOP and the last observed LOP the time labels of the LOP's. Connect the DR establishesthe running fix. The logic of the positions;theconnectingline represents the perpendicular method isthat since the speed course and distance which the ship should have and course of the ship generates the DR track made good. Advance the firstI.()1a distance; line,if the advanced LOP lies with respect to and direction corresponding to the line connect- the second DR position as it previously lay with ing the two DR positions. (Fig. 7-3D.)

54 Chapter 7 PILOTING

DRAI METHOD. Since the DRAI resolvescourse of the ship and a sight line in the direc- received inputs into components (N or S, E or W)tion of a navigationally useful object is observed the components for a given run may be plottedand noted, together with the time. A second ob- and connected by a line. The hypotenuse of theservation is made and the time noted when the right triangle thus formed represents the direc-angle on the bow is double that of the first tion and distance the first LOP should be ad-observation. At that instant, the distance from vanced. the object is equal to the distance run between observations. 707. SPECIAL CASES The triangle formed by two bearings and the course line is a right isosceles triangle in the A special case of the running fix is the "bow special bow and beam case which we have seen. and beam" situation. (See fig. 7-4.) When the However,it can be easily proved that upon bearing of a landmark diverges 45 degrees fromdoubling the angle on the bow, the triangle thus the ship's heading, it is said to be broad on theformed is also an isosceles triangle, having two bow. When the divergence increases to 90 de-equal sides, although not usually a right triangle. grees,itis on the beam. By noting the time a landmark is broad on the bow and the time it is 708. RUNNING FIX ERRORS on the beam, the distance passed abeam can be computed; the distance abeam will be equal to The running fix may be a well determined the distance run between bow and beam bearings position and is usually considered as such. For which in turn will depend upon the elapsed time this reason, the DR track is normally replotted and the ship's speed. Knowing the distance abeam, using the running fix as a new point of origin. when a beam bearing is observed, makes the However a running fix does not fully account plotting of the running fix quite simple. The truefor current, and the displacement of the running bearing will be the true heading plus or minus fix from the DR is not a true indication of current. 90 degrees depending upon whether the landmark If a head current is expected, extra allowance is abeam to starboard or abeam to port. The should be made for clearance of dangers to be distance run equals the distance abeam becausepassed libeam, because the plot of running fixes 45 and 90 degree angles provide a right isoscelesbased upon any single landmark near the beam triangle with equal sides. will indicate the ship to be farther from that Another special case, which is related to thatdanger than it actually is. If a following current of the bow and beam, is one known as "doublingis experienced, then the opposite condition exists. the angle on the bow." The angle formed by the This occurs because the actual distance made good is less with a head current and greater with a following current than the distance the LOP is advanced based upon dead reckoning. Usually, a limitation of 30 minutes should be imposed on the elapsed time between lines of position in a nulling fix; this however,is not a hard rule because of other considerations. 709. ESTIMATED POSITION DISTANCE ABEAM ( 2 MI.) While it may not be feasible for the navigator to ootain either a fix or a running fix, he may observe such dataastomake possible the plotting of a position more probable than a DR. Such a position is called an estimated position. COURSE Itisidentified as a square with a dot in the center and labeled with the time in four digits KNOWN followed by the letters "EP." RUN If the navigator has computed or knows the (2 MI.) approximate strength of the current, this information may be applied to obtain an EP. At any 58.79 DR position, construct the current vector; the Figure 7-4.Bow and beam bearings. direction of the vector will represent the set and

55 A NAVIGATION COMPENDIUM the length of the vector will depend upon theof travel; a dot is placed approximately three drift and the elapsed time since the last fix. Theinches back of the arrow point as a reference point of termination of this vector is the esti-mark. Fourth, the flimsy paper is placed over mated position. the DR track with the reference dot over the Occasionally in reduced visibility the navi-DR position corresponding to the first recorded gator may sight an aid momentarily and establishsounding and with the arrow in the direction of an EP. An EP may identify a fix or running fixtravel; the contour of the sounding recorded at which, in the judgment of the navigator, has beenthat time is traced and labeled. Fifth, by moving inaccurately obtained, or a fix obtained usingthe sheet in the direction of travel, and with the radio bearings. referencedot over successive DR positions, When a vessel passes over a bottom havingcorresponding contour lines are identified by abrupt changes in depth or irregular contours,sounding and traced.Finally, after three or soundings may be utilized in the establishmentmore contours are plotted, the intersection of of an EP. The navigator directs the recordingcontours may indicate a fix.It should be re- of soundings at regular intervals. If these sound- membered that contour lines because of their ings are obtained using the fathometer then the irregularity may cross at more than one point, draft of the ship is added to all values. His dataand thus several may need to be plotted to re- then consists of depth recorded against time. solve possible ambiguity. The time of the fix A sheet of paper is graduated on one edge withcorresponds tothe timeof the last plotted the space between marks corresponding to the sounding. distance run (as measured on the scale of the chart in use) between the recording of soundings. EXAMPLE: Having notedthe bottom contour These marks are labeled with time and depth. lines on the chart in use, the following soundings The navigator places the sheet on the chart withwere taken and recorded. thelabeled edge of the sheet in the general vicinity of the DR track. He moves the paper Time Sounding laterally in an effort to match the depths on the paper with charted depths (bottom contour). In 000 110 fms. lieu of the use of a sheet of paper on which the 1005 110 fms. edge serves as the DR track, a sheet of flimsy 1007 120 fms. paper with the DR track drawn anywhere on it, 1010 130 fms, may be marked with soundings and used. If 1015 140 fms. successful, the navigator may locate an estimated position by this procedure. Preparation: Whether the navigator considers the DRor the EP as the ship's actual position depends Having recorded the time of crossing of each upon the proximity of danger to each positioncontour, as indicated by sounding, on the chart, with the track extended ahead, whichever posi-place the ship's DR track on the chart and indi- tion and track is nearest r.I9nger should be con- catethe DR positionfor each of the times sidered as the actual position and track in order recorded. (Fig. 7-5.) to provide the widest margin of safety. Take a sheet of flimsy paper, drawa line across the sheet, and place an arrow point on 710. FIXES BY SOUNDING one end of the line to indicate the direction of travel.Placea referencedot approximately A new and rather unique piloting procedure three inches behind the head of the arrow. (Fig. has evolved whereby a fix instead of an EP can 7-6A.) be obtained by soundings. This new procedure is characterized by the use of bottom contour lines Plotting: as lines of position. By this method, it is first necessary to record Step 1 Place the flimsy paper over the chart the time of crossing each bottom contour line,with the dot over the first DR position and the together with the sounding. Second, it is neces- arrow pointing in the direction of travel, Trace sary to indicate on the DR track the DR positions the contour of the sounding recorded at that time for times that such soundings were taken. Third, and label with sounding. (Fig. 7-6A.) on a sheet of flimsy paper a line is drawn with Step 2 Move the flimsy sheet in the direc- an arrow on one end to indicate the directiontion of travel until the dot is over the second DR

56 Chapter 7 PILOTING -=

58.79(190) Figure 7-5. Fix determined by sounding.

position,Tracethecontourofthe soundingon the flimsy paper. Place the last DR time recorded for that time and label with the sound- over the newly obtainuci fix and check the times ing. (Wig. 7-613.) and soundings against the apparent track. (Figs. Step 3 Move the sheet in the direction of 7-61) and 7-5.) travel until the dot is over the third DR position. It may be noted that the position obtained by Trace the contour of the sounding recorded for thisprocedureistechnicallyarunning fix, that time and label with the sounding. Examine rather than a fix. Dependent upon the amount of for possible fix results. (Fig. 7-6C,) elapsed time and the correlation of track and Step 4 Move the sheet in the direction ofsoundings, the position obtained may be con- travel and trace the next sounding as in stepssidered as a fix, a running fix, or an estimated 1 through 3.The position of the fix should be position. apparent. The time of the fix when located will be the recorded time for the sounding last used 711. DANGER BEARINGS AND for fix information. (Fig. 7-6D.) DANGER ANGLES Step 5 Since sounding contours arcnot usually straight lines and can cross in more than Itispossible to keep a ship in sale v,ater oneplace,thepositionmust be checked by withoat frequent fixes through the use of danger placing the DR, with both time and soundings, bearings and danger angles.

57 A NAVIGATION COMPENDIUM

STEP 3

190.10 Figure 7-6. LOP and fix dett.:rrnination by sounding.

5% Chapter 7PILOTING

If a ship must pass a dangerous area such as 712. TACTICAL CHARACTERISTICS unmarked shoal water, draw a circle around IN PILOTING the area on the chart. Check the chart for some prominent landmark in the general direction of Thus far in this discourse upon piloting, the travel (or the reciprocal). Draw a line from the tactical characteristics of the ship have not been landmark tangent to the danger circle and labelconsidered. It has been assumed that course and the line with its direction. This direction is the speed changes would be effected instantaneously. danger bearing on the landmark from which itIn actuality, such is not the case. At sea, when is drawn. With the danger bearing as a line ofat great distance from navigational hazards, such demarcation, the mariner can tell whether he isan assumption can be made, inasmuch as the ship outside or inside of the danger area just by isinno immediate danger, and on a small checking the bearing of the object. /scale chart the tactical characteristics will not ' alter the plot. However, most piloting is accom- Danger angles are of two types, horizontalplished inshore, in close proximity to naviga- and vertical.If two prominent landmarks are tional hazards, Large scale charts enable the available,a horizontal angleist ;eci.If onlynavigatortodepict his position with greater one prominent landmark isavailable then aaccuracy as essential for ensuring safe passage. verticalangleis used; however, this method Accordingly,the largest scale, most detailed requiresthattheheight of the landmark becharts available are used when in restricted or known. In either case the first step is to drawpilot waters, and full allowance is made for the a circle around the danger area on the chart. tactical characteristics of the ship. For a horizontal angle, a circle is constructed Tactical characteristics vary with each ship. passing through the two available prominentTo effect either a course or a speed change landmarks, and tangent to the danger circle. Ifrequires varying amounts of time and space, itis desired to leave the danger area betweendependent upon the ship, the magnitude of the the ship's track and the selected landmarks, thechange, sea and weather conditions. Particularly circle through the landmarks contains the danger in effecting a course change, the ship may be circle;ifitiswis'ledto pass between theexpected to be offset some distance from the danger circle and the prominent landmarks, the planned track unless the turning characteristics danger circle although tangent, will lie outside are considered. Failure to consider such char- thecircle which passes through the selected acteristics can directly contribute to driving the landmarks. To construct two circles tangent to ship into danger. each other, itis necessary to make use of the Tactical data is obtained and recorded for fact that their diameters lie in a straight line.each ship to describe turning characteristics in From the point of tangency of the two circlesterms of "advance" and "transfer" for varying draw two chords, one to each landmark. Theserudder angles, usually every 15°. "Advance" is chords provide an ins,:ribed angle the value ofthe distance gained along the original course which is the danger angle. To leave the dangerextended, and "transfer" is the distance offset area between the track and the selected land-perpendicular to the original course; both are marks, the angle formed by the two landmarksmeasured from the rlint at which the rudder is with the ship's position as a vertex must not be put over. Advance is maximum for a turn of 90°. allowed to become greater than the danger angle. Other related terms include: To pass between the two prominent landmarks andthedanger area, the angle must not be Angle of turn The arc in degrees through allowed to become smaller than the danger angle. which a ship turns. Turning_ circleThe path fullowed by the To use a vertical angle, construct a circle pivot point of a ship turning 360°. tangent to the danger circle, using the landmark Tactical diameterThe distance offset right of known height as the center. The vertical dan- orleft of the original course when a turn of ger angle may be found by entering table 9 of 180' is made. the American Practical Navigator with the radius Final diameterThe distance perpendicular of the tangent circle and the height of the object. totheoriginal course as measured between tangents to the turning circle at 180° and 360° 'l'o pas` between two danger areas, the navi- points in the turn. Essentially, it is the diameter gator computes an upper and a lower limitation oftheturniiigcircle. The final diameter is for the value of the danger angle. always somewhat less than the tactical diameter.

39 A NAVIGATION COMPENDIUM

Standard tactical diameter A prescribed dis- The requirement foranchoring should be tance used by all ships in a formation as aanticip. 'ecl, and except in an emergency situa- tactical diameter for uniformity in maneuvering.tion, de. .,rves detailed preparation. The location Standard rudderThat amount of rudder re-must bestudied,notingthe depth of water, quired for a ship to turn in its standard tactical nature of Lottorn, and the navigational aide use- diameter. ful for act. '.;.u.Illy fixing the position during the approach, upon, and after anchoring. The proxim- Tactical data also includes tables of accelera- ity of navigational hazards, and the proximity of tion and deceleration to accommodate the need channelsorfairways subject to ship traffic, for accurate calculation of a ship's progressshould be considered. The nature or type of along the planned track. bottom is an indication of the holding qualities: In restricted or pilot waters, the need for for example, the anchor will hold better in mud accuracy is generally so great, that advance andor clay than in sand or rock, and will usually transfer must be considered before each course hold better in sand than on a rock bottom. The change. Accordingly, advance and transfer aretype of bottom, depth of water, and anticipated estimated, and at that point on the chart whereweather, should be considered in planning the the course change is to be effected, it is plotted scope of anchor chain, in addition to the proximity in reverse direction. This identifies the point ofotherships, underway orat anchor, and at which the rudder should be put over to effect navigational dangers. the course change in a timely fashion. Addi- A planned track must be prepared to . the tionally, the bearing of a landmark or other aid anchorage,with carefulcot. iderationofall tonavigation,preferably close to the beam, hydrographic features and the draft of the ship. should be noted, as measured from that pointConsideration must be given to the raising of on the plot at which the rudder will be put over. thepit sword or rodmeter, if extended, and of This bearing, termed the "turn bearing," is used the type which can be raised and housed. Wind as one means of ascertaini g the proper time and current must 1-s! considered.It is advan- for making the turn. However, it is always goodtageous to approach the anchorage, when pos- practice to obtain a fix a minute or so beforesible, by heading directly into the current, except the turn, and an additional fix after the turn whenwhen the wind effect exceeds that of the current, the ship is steady on its new course. in which caseitis advantageous to head into In addition to allowing for advance and trans- the wind. Such contributes to greater steering fer in making a turn, the combined effect of wind accuracy, which can be further improved by the and current should be considered. The wind can ship maintaining a steady course for at least be observed, and the current can generally be the last 500 yards to the anchorage. The loca- predicted,as we have seen previously, fromtion of navigational aids should be fully con- tables. Experience in ship handling and knowl- sidered. If wind and current conditions will also edge of local sea and weather conditions are permit approaching the anchorage with the ship most helpful, and provide reason for navigation "on range," which isthe maintaining of two being an art as well as a science. fixed objectsin line with the direction of the line corresponding to heading, then even greater navigational accuracy can hachieved. The navi- 713. PRECISION ANCHORING gator can thereby practically eliminate the citct of compass error on steering. lie can determine For practical convenience, the Oceanographic the ship's progress along the approach track Office publishes anchorage charts of principalmerely by observing ;idplotting one orts. These are merely harbor charts with bearing, filthOUgh the plotting of two s..ich anchorage berths preselected and overprinted as bearings is more desirable. colored circles of various diameters. Anchorage Infurther preparation, the navigat:,i should berths, with centers usually in a straight line, consider the distance from the bridge, where the and with limiting circles usually tangent to those bearings arc to be taken, to the li,1%1/4:-.plpc,it

'mining, are identified by letters anVor whl.11 point the anchor is to ! till ' rs for :simplification of anchorage assignment. known as"bridge-haw:,e d 1:.-4 a nee I' Converted Ior anchorage in an area '1 IliCh SUCil berths to yard:3, al11 rnt.a-oircd along Ow track trzln, t :ire not readily. available, it th prat:11(.1.! anchorage in opposite Wrection the .i!y!.0ain, to specify or locate the anchorage in terms c,f thebridg-e-haw:-t:rit.4t,11101.* th,%! ); ill :x:.o.ing di:-;tance from a prominent landmark. which Will t ht2 sr 11.(' Chapter 7 PILOTING hawseinthe properposition for anchoring,the other arcs are labeled in accordance with assuming that the heading of the ship corresponds theirrepresented range from the anchorage. to the direction of the approach track. Appro- (See fig. 7-7.) priately, the bearings upon anchoring will nor- If turns are to be made in the approach, the mally be observed from the bridge, and when navigator should note and record the "turn bear- plotted should fix the ship's position that distance ings" of suitable navigational aids. The immedi- away from the desired anchorage as is equal to ate availability of turn bearings, together with an the bridge-hawse distance in a direction whichestimate of advance and transfer, will serve the is the reciprocal of heading. Also, the navigator navigator in effecting the turn with accuracy. should strike arcs of range circles, from the Additionally, he will note and record the "drop point established using bridge-hawse distance, bearing," thatis,the bearing of a prominent so that the distance to anchorage can be directly landmark which is approximately perpendicular read fromtheplotwithout resort to directto the approach track. Allowance for the bridge- measurement. Arcs of range circles are usually hawse distance is made in determining the drop drawn, crossing the approach tack, using radii bearing. in 100 yard increments out to 1000 yards, with It is common practice for the navigator, well additional arcs at 1200, 1500, and 2000 yards. prior to anchoring, to inform the Commanding Labeling the point for letting go the anchor as 0, Officer, the Officer of the Deck, and the First

CI80

'TURN BEARING 270° ISHIP'S ADVANCE C240

BRIDGE-HAWSE 15 DISTANCE 12

ANCHORAGE 12 34 5 6 7 8 910

DROP BEARING -150°

O RANGE LIGHT CUPOLA 0 TANK SPIRE

190.11 Figure 7-7. Preparation for precision anchoring.

61 A NAVIGATION COM PNI IUM

Lieutenant of the depth of water, the type ofnot be completely relied upon. Their service is bottom, and the distance and location of shoalchiefly that of warning the navigator of impending water or other navigational hazard in the vicinitydanger. The following are representative types of the planned anchorage. l3efore the approach, (descriptive of the float, which identifies a buoy): the navigator should-show the Commanding Offi- cer and Officer of the Deck the approach track SPAR BUOY. A trimmed log which resem- and inform them of the principal landmarks tobles a stake at a distance. be used, of turn bearings if any, and of the drop bearing. Throughout the approach, the navigator CAN BUOY. A cylindrical steel float. will report the direction and distance to anchorage. NUN BUOY. A steel float the shape of a Itis good seamanship practice under most truncated cone. conditions for the ship's headway to be reduced as it approaches the anchorage, and upon reach- BELL BUOY. A buoy with a skeleton tower ing the drop bearing, in anticipation of which whichholds a bell generally actuated by the propellers are reversed, to let go anchor withmotion of the sea. Some bells are struck by the a small amount of sternway on. This generallyaction of gas compressed in a cylinder. makes it possible to set the anchor without its chain tending under the ship where it may en- GONG BUOY. Similar to a bell buoy but danger such appendages to the underwater bodyequipped with gongs instead of a bell, which make as the sonar transducer. By a careful combina- sounds of different tones. tion of engine orders and the holding or veering of chain, the anchor can usually be safely set. WHISTLE BUOY. Similar to a bell buoy but Upon anchoring, it is necessary to accurately equipped with a whistle (useful in low visibility) fix the position by observing and plotting a round usually actuated by the motion of the sea. Some of bearings. As soon as the anchor is known to buoysareequipped with trumpets which are be holding, the position should again be fixed. sounded mechanically. Additionally, by using a sextant and a three-arm protractor as explained in art. 310, with sextant LIGHTED BUOY. Buoy which carries alight measurement of horizontal angles as observedat the top of the skeleton with either acetylene from the forecastle (at the hawse, when the chaingas or electric batteries for power. A lighted is nearly vertical), an accurate fix can be ob-buoy may for some reason become extinguished tained. This can serve as a check upon the fix and therefore is not completely reliable. based upon bearings observed from the bridge. While at anchor, bearings are taken and re- COMBINATION BUOY. A buoy which com- corded periodically forcomparison with the bines a light signal with a sound signal. Examples established fix as a precaution against dragging. are lighted whistle buoys, lighted bell buoys, Upon getting underway from anchor, the navi- and lighted gong buoys. gatormust commence piloting proof' lures as soon as the heaving in of the anchor chain is RADAR REFLECTOR BUOY. A buoy which commenced. The ship's position must. e accu- supports a screen and makes early detection by rately known, particularly from the time the radar probable. anchor breaks ground. During this crucial period in getting underway from anchor, accurate knowl- Buoys which mark turning points may be edge of the ship's position is necessary as a equipped with a ball, cage, or some other device. precaution against dragging or drifting into shoal Each maritime country has developed, and water or other hazard. in most cases, standardized by law, the colors forits own particular buoyage system. These 714. BUOYAGE systems are described in appropriate Oceano- graphic Office Sailing Directions. The following Buoys are navigational aids which serve as colors represent U.S. buoys and, with the excep- markers. Some are so equipped as to Ix: useful tion of white and yellow, indicate lateral signifi- at night or during periods of reduced visibility: cance: some are not so equipped and hence are useful only in daytime. Buoys are not fixed aids (they RED. Identifies buoys on starboard hand of consist of a float, mooring, and anchor) and can achannelentering from seaward. A rule to

62 Chapter 7-PILOTING

rememberis "31t,. "meaning"Red-Right-to candlepower. The geographic visibility and the Returning," These buoys are usually of any typeheight of a light may be found on the chart, adia- except can, and bear even numbers commencingcent to the light symbol, and in the Li.ahts I,iSt. With2atthe seaward end of a channel. TheyThe higher the light the greater the distance it may carry a red or white light. should be seen; theoretically, the distance a light BLACK. Identifies buoys on the port handshould be seen by an observer at sea level is the 01 a thantiel entering from seaward. These buoyslength of a beam measured from the light to its art usually of any type except nun, and bear oddpoint of tangency with the earth's curved surtace, numbers commencing at the seaward end of theassuming that the light is not restricted by candle- channel with I. They may carry a green or whitepower or brilliancy. light. R1:1)ANI.) BLACK HORIZONTALLY The nominal range is the maximum distance at STR I Identifies an obstruction or junctionwhich a light may be seen in clear weather, which and ma:: !K' passed on either hand. is meteorologically defined as a visibility of ten BLACK AND WHITE VERTICALLYnautical miles. Nominal range is listed for only STiiiPrl). -Identifies a fairway or midchannelthose lights having a computed nominal range of trim which should be passed close aboard. Onlyfive nautical miles or greater. If the geographic white'liithtsarc carried by this type of buoy.range is greater than the listed nominal range, Anchorage. the latter will normally govern. Y1: t,1.t rbk. Quarantine anchorage. The luminous range is the maximum distance a lip1..oie-.;, stikes, and spindles may be erected light may be seen under existing conditions of ,,,Lalow water. Their color is in accord withvisibility. The luminous range is determined from the uuo.tge system but usually also provides aeither the nominal range or the intensity, and the contst with the background. These are fixedexisting conditions of visibility. See Appendix E. landn:.1:ks generally more reliable than buoys. Intensity or candlepower of light given i 6. ap- Rpresntat iv, lighted and unlighted buoys, as proximate and is based upon the International wellas;variousbeacons,areillustratedin Standard Candela. ppe nd 1 N A. The navigator is interested in the radius of 713. LIGHTS visibility of a given light under existent conditions. Thus, the navigator normally determines luminous Lighted aids consist of lightships, lighthouses, range, then computes that limitation imposed by lighted beacons, and lighted buoys. These are the earth's curvature; by comparison, it can read- listed in the light liTt to facilitate identification. ily be seen which limitation is applicable, that Failure to correctly identify a light has often determined by intensity or that imposed by the resulted ill disaster; light identification requires heights of the light and of the observer's platform. corree!ed chai t and publications, and warrants the ',1:7 )1 a stop watch to check the period or Using the luminous range diagram (Appendix cycle. (. naracteristies of lighted buoys are illus- E), either the nominal range or the intensity, and trated in Appendix A. the meteorological visibility, the luminous range Li!....htcolors may be white (V ), red (H), or can be found by inspection. Using the distance of greet-, (6!. If not indicated, the light is assumed visibility of objects at sea (Appendix E), the height to bwhite. of the light, and the navigator's height of eye, the ,:eriod 0: a light is the time in seconds distance a light can be seen as limited by arth's a light requires to complete a cycle, or endure curvature can be computed; values as taken troin :t tit of changes. the table of distance of visibility for each art the two heights are simply added. The radius tit visibility of the light will equal the lesser of these two range limitations, luminous andarth's cur - :s!bility is categorized by three types vatu re, i;eogiaphic, nominal, and luminous. r-graphic visibility (-)f:t light is the nurn- The tipplicahle Light List provides the toights twi o miles a light !nay be seen by an of lights, and as appropriate, the nominal range ,ra he 15 ft. abo%, sea level, under and intensity. The navigator must know I:is own rfect visibility, and without regard height of eye and the meteorological ve,Wility. 63 S44 ,... 4 5 4 A ;71 C _ z ANACAPA 6L AND )t ROSASAN TA I) C

Je 03( g 6 COY,. I, It A 4° rll . . SYSCoss .:. ,:,;...1\ ,xoliitis 7,, . ).1.f ;5701 Pi 044 'RU( ISIFAirey f AY' .. I.5001, 7 u i 355*..l."1.1. 2 ,I, , ? S P5 s-rii". t.-_-=------, ...-- f"7.::---- , .-% 111.:(% r g., it 1--.1 t's...."--' )},: c. SWIt' "ANCEs" ON 5" ---"-..!' .'' ....1 ---""::if cor. IN S ow tA Itti sgAs I i A .0 \`40 \ 2.110" 05n 37,CIA P /44440 rINIO Pi ON PT . 4410 444,1 so .. 174 Figure 7-8. Piloting plot and bearing book. 'S 29: pot E N. Ra :,7 ,..S.011C, 4 'Afr. POP TseN .7.....174(Ass. 1024 A y[ 69.143 Chapter 7 PILOTING

EXAMPLE 1: to determine the meteorological conditionof ViSt- Given: Light,55 feet high, geographic bility, range 13 miles, nominal range 11 miles, intensity 2,000 Candelas. 717. PREDICTING THE SIGHTING Navigator's height of eye, 27 feet; OF A LIGHT visibility 5 miles. To find: Radius of visibility. Having computed the radius of visibility, draw Solution: Enter the luminous range diagram a circle using the computed radius with the light (Appendix E) with (1) either the as center. The point of intersection of this circle nominal range or the intensity; and and the DR track marks the point at which a light (2) the meteorological visibility. should be sighed. This time is computed by dead When both nominal range and in- reckoning; the true bearing is the true direction tensity are given, it is preferable of the light from the point of intersection of the to enter the diagram with intensity. DR track and the circle. Itmay be determined that the luminous range is 7 miles. Since 718. LIGHT SECTORS the navigator is at a greater height than that upon which geographic Shield or colored glass shades may be fitted range is computed (15 feet), heto lights making them obscure in one or more should be able to seethe light at sectors or so that they will appear to be one color least 13 miles away (its geograph- in certain sectors and a different color in other ic range), unless limited by its sectors. These sectors may be located on the intensity. Using the distance of chart by dotted lines and color indications. Such visibilityofobjectsat sea as sectors are described using true direction in three tabulated in Appendix E, the dis- digits for each sector boundary, and the direction tance visible as limited by the givenisas observed from seaward looking earth's curvature is computed as towards the light and clockwise. Many of our lights follows: located along dangerous coastlines such as the height of light, 55 feet -8.5 Florida Keys have red and white sectors; when in height of eye,27 feet -6.0 the white sector the ship is usually in safe water Total- 14.5nautical miles but when in the red sector the ship is inside of a However, since the light is limited by intensity danger bearing and is in danger of running upon and existing visibility, the luminous range is a reef. applicable, and the radius of visibility is 7 miles. EXAMPLE 2: 719. BEARING BOOK Given: Light with same characteristics It is good practice to maintain a small book of asinExample1.Navigator's convenient size for the recording of bearings and height of eye is 10 feet; visibility other desired piloting information, together with is 20 miles. the identity of aids used and the time. Normally, To find: Radius of visibility. the pages of such a record book are ruled so as to Solution: The luminous range based upon provide approximately six vertical columns. Each the diagram, is found to be 16 page, as used, is dated, and the first column on nautical miles. The range, based the left is used for the recordingof time. In other upon theearth'scurvature, is columns, headed individually by the identity of determined as follows: aids, the bearings observed are accurately re- height of light, 55 feet -8.5 corded, horizontally opposite to the recorded height of eye,10 feet -3.6 time. One column may be set aside for recording Total- 12.1nautical miles soundings for correlation with fixes as obtained. Thus, the radius of visibility, in Bearings are true unless otherwise noted. If gyro this case, as limited by the earth's bearings are recorded in lieu of true bearings, curvature,is about 12 nautical they must be so identified, together with the gyro miles. error, if any. Because of the importance of such It should be noted that if the characteristics of a record, as of other records having legal signif- a light and the distance to it upon sighting are icance, erasures are not permissible.(See fig. known, the luminous range diagram may be used 7-8.) 65 CHAPTER 8 BASIC ELECTRONICNAVIGATION SYSTEMS

801. GENERAL 803. RADIO DIRECTION FINDER Electronic navigation is considered hereas a This is an azimuthal instrument, formerly definite division of navigation andone which will called a radio compass, whichupon receipt of a be further developed during the nextfewdecades. As far as basic techniques radio signal can determine the directionof the are concerned, elec- sending station. It is an importantnavigational tronic navigation is an extension of piloting. It aid because of its usefulness in search andrescue, differs from piloting in the methodsby which the or distress operations, and in homing aircraft. data is collected. Generally, the shipboard equipmentconsists of a receiver and two antennas. Oneantenna is Radio, radio direction finder, radar,sonar, a vertical stationary sense antenna, the othera loran and Decca, are examples ofbasic elec-rotatable loop antenna. The latter,in essence, tronic navigation equipment. Radio,as used prin- is the "direction finder." cipally for obtaining time signals, weather,and As the antenna is rotated, itsoutput varies hydrographic information, was briefly mentioned with the angle relative to the directionof the in art. 307. The other basic electronicinstru-received signal. When it is perpendicularto the ments, together with related equipment suchas signal, signal strength is ata minimum or "null." radar beacons and Shoran,are addressed inThe reading is taken at this pointbecause a greater detail in this chapter. ,tore advancedsmall change in the relative direction ofthe electronic navigation systemsare described in signal thus obtained causesa greater change in chapter 9. signal strength than doesan equal change when the signal strength is at ornear the maximum level. 802. MARINE RADIOBEACONS Changes in the signal strengthcan Lc observed and related to bearings whichare read from a dial. Bearingsmay be true or relative, Marine radiobeacons are importantaids to depending upon the equipment. Sincethere are electronic navigation andare described in H.O. two "null" points for each completerevolution 117 Radio Navigational Aids. The letters "RBn" of the antenna, the sensingantenna works in denote their location on a nautical chart.They conjunctionwith the loop antenna to resolvethe are particularly useful in piloting during periods ambiguity. of poor visibility. Transmitting inthe medium Variations of this antennaarrangement exist frequency range, and identified by the dotand in the Automatic Direction Finder (ADF)in which dash arrangement of their transmission,radio- two loops are rigidly mounted in sucha manner beacons may be classified as directional, rota- that one is rotated 90° with respectto the other. tional,and circular. Directional radiobeacons The relative output of the twoantennas is related simply transmit their signals in beamsalong a to the orientation of each withrespect to the fixed bearing. Rotational radiobeaconsrevolve direction of travel of the radiowave. Newer a beam of radio waves in a manner similar toradio direction finders, often small,portable, the revolving beam of light of certain lighthouses. and battery operated, havea ferrite roci coupled Circular radiobeacons, the mostcommon type, inductively to the receiver whichserve:, in lieu send out waves in all directions for shiprecep- of the loop antenna. tion by radio direction finder as describedin Radio bearings may be obtainedfrcIii l'quip- the following article. ment other than the radio direction finck .,ndit 66 Chapter 8BASIC ELECTRONIC NAVIGATION SYSTEMS the source of the signal can be identified, such The centerof the PPI scope represents the bearings may be used to establish or to confirm ship's position. Reflecting objects within range a navigationalposition. As primary sources,appear asshapes upon the scope. Range may however, marine radio beacons and direction be read from the PPI scope either approximately finder stations are regularly provided in many by the use of concentric range circles or more parts of the world. Their position can be deter- accurately by matching a "range bug" with a mined from maritime charts and from HO Pubtarget pip and reading the range from a dial. 117, Radio Navigational Aids. It is of the greatest (See fig. 8-1.) importance in plotting radio bearings to keep in mind the fact that the reciprocal of the bearing 805. ADVANTAGES AND LIMITATIONS represents the direction of the ship from the OF RADAR transmitting source. These bearings are great circle bearings and uver long distances must be The usefulness of radar, a range-bearing de- corrected, prior to plotting on a Mercator chart, vice, is illustrated by the following advantages: by a method described in HO Pub 117, Radio Navigational Aids. (a) Safety in fog pilotingRadar provides an extra pair of eyes when the ship operates in 804. RADAR reduced visibility, and can penetrate darkness and fog in the interest of safety. The word "radar" is an abbreviation for (b) Means of obtaining range and bearing "radio detectionand ranging." Radar equip- This information may be sufficient to establish ment generates a directional radio wave which a fix. travels at thespeed of light and which upon (c) Means for rapidly obtaining fixes The striking anobject,isreflectedback at the radar may easily provide position information same velocity. A radar set is so calibrated that faster than can be obtained through any other the range (distance) of an object can be directly means. The PPI actually provides a continuous read; this is feasible since the equipment is de- fix. signed to compute distance from speed and time (d) Accuracy This depends upon skill of the (the fraction of a second required for the signal operator and the adjustment of the equipment; to travel to an object and return is divided by two). The direction of a generated signal depends upon the direction the antenna is trained; for continuous search in all directions the antenna is S permitted to rotate at uniform speed. I . The principal parts of a radar set and their functions are: (a) TransmitterTransmits electrical energy. (b) NIDdulator Cuts off transmitter periodi- 11. cally to convert signal to pulses. (c) AntennaRadiatessignaland receives A' echo. (d) Receiver Receives echo via antenna. (e) IndicatorIndicates the time interval between pulse transmission and pulse return as a measurement of distance to the reflecting object. Part of the indicator is the cathode ray tube, the face of which is referred to as the "scope." There are two general types of scopes differing I in presentation, the most common of which is the "PPI" or "plan position indicator." It is graduated in degrees for the direct reading of trueandrelative bearings;true directicsnis 190.12X suppliedbyaninput from the gyrocompass. Figure 8-1 Radar PPI presentation.

67 A NAVIGATION COMPENDIUM

however, an accuracy of a few yardsmay be shadows result when the land contour prevents attained. radio waves from striking the entire surface.(A (e) RangeThe range is much greater thansmall hill in the rear of a high hill wouldappear visual range. It depends upon the earth'scurva- in land shadow.) ture, as in the case of the radius of visibility of lights, and upon the characteristics of the set, It is not unusual to detect a high mountain 806. ACCURACY OF RADAR at a range of 150 miles, The calculated distance The accuracy of a radar position may be affect- to the moon was checked by radar, considerably ed by the following: prior to the making of lunar flights. (1)Use as an anticollision deviceThe radar (a) Beam width (bearing accuracy)If visual supplies information about the movements ofbearings are available they should be used in lieu nearby ships. Conning of the ship may beaccom- of radar bearings. plished by reference to the PPIscope. (b) Pulse length (range accu racy binge ac- (g) Storm trackingRadar is useful intrack- curacy is usually greater than Waring accuracy. ing violent storms. (c) Mechanical adjustment. (h) Remote indicationThe PPIscope pres- (d) Ability of the operator. entation may beautomatically indicated at remote locations. (e) False targetsAn example 01a false target is surf which may reflectOu.101:6 and appear as a shore line. The limitations of radararc: (f) Shadows This result of contours ruakos identification difficult as shapes on thescope may (a) Mechanical and electrical characterIt is subject to mechanical and/or electrical fail-not correspond to actual shapes on the chart. ure, 807. RADAR FIXES (b) Minimumandmaximumrange limitations There is a minimum range limitation The following methods, whichare usci in pi- resulting from the echo of signals from nearbyloting, may be employed to establisha radar fix: wave crests. These echoes are called "seare- turn." The radius of the sea return isa few (a) Range andbearingofan object 1 he hundred yards dependingupon the adjustment of accuracy may be improved by the :-.011)stitution the equipment. Nearby objects may be obscured of a visual bearing. by the sea return thus establishinga minimum (b) Two or more bearings lic...cause of lx.'arrange. As previously mentioned, the maximum ing inaccuracy this is nota preferred ineth(x.i. range depends upon the earth's curvature and the (c) Two bearings and a rangeIt ther;tnge characteristics of the set. arc does not pass through the point of inter- (c) Interpretation This is often difficult. Thesection of the bearings, the fix should !x.es- operator should be able to provide navigational tablished as the point on the distance(rangv) information through the recognition of electron arc equidistant from each bearing lih. patterns. There is not always enough information (d) Two or more range arc he- prey ides fur definite scope interpretation. the best fix. Three arcsare better than :\k). (d) Bearing inaccuracyThe radiowaves Two circles may intersectat tAt) liontt- anti Ow:, travel as fan-shaped beams which result inechoes force the navigator to Choose bytweyn pt)-:!-.1- greater in width by several degrees than the angle ble positions. subtended by the reflecting surface. If thebeam (e) Three-arm protractor method )ne 111.ty width in degrees is known, the operatorshould measure bearings of three objects and :-:etiii add half the width to left tangents andsubtract 3-arm protractorastieserilxciin 31U, half the width from right tangents. :trt. (e) Susceptibility to interference Both natu- 808. VIRTUAL PPI REFLECTosCUPE PIQ ral (atmospheric) and artificial (jamming)interference may restrict usefulness ofequipment. The VPR is an attachment Min m i be (1)Necessity for transmissionfrom the usedin ck.snpmetion with thel';'; ;, ship This reduces security by breakingradio radar to fix the position of the shiptfor:t1h,111...,- silence. ly on a navi,,ation chart. Itconsist:: of-1 illat (g) Land shadows andseareturnThese board upon which a navigatitm chart may causeobjectsnot to be detected. Land and a set of reflecting mirrors whi..-II. er%:.

68 Chapter 8 BASIC ELECTRONIC NAVIGATION SYSTEMS reflect the chart upon the PPI scope. The center TACAN is installed in military aircraft, and of the scope represents the position of the in some aircraft carriers as a homing device. ship; therefore,ii the reflected chart image is Itis operated simply by turning on a power matched with the scope, the center of the scope switch, selecting a station, and reading the range marks the ship's position on the chart. VPR and bearing. Maximum range is195 nautical ehart,, must be drawn to a scale which is con- miles,andthusitis a short-range system. si%tent «ith the range scale of the PPI scope. TACAN has been accepted as the primary navi- Sometimes the V PH chart is a grid chart thus gation aid for the Air Route TrafficControl ii-Aingthe operator to read at any time the System. gr Idposition of the ship. The navigator may tran,itt...r this position to a navigation grid chart 811. SHORAN characterized by the same grid system but not neeessarily having the same scale. "Shoran" is an abbrevieim for "short range navigation" and makes use of the principle that t409. RADAlt BEACONS radar ranges are more accurate than radar bearings.Signals from either a ship or aircraft l'wo common radar wacons are "racon"trigger two fixed transmitters which send out and "ramark." RACON, used primarily in air- signals simultaneously. The intersection of two craft, consists of a transmitter and a receivercircles of position on the receiving scope is re- on board the aircraft and a transponder at some presentative of the ship's position. These circles designatedposition. The aircraft transmits a may be drawn on the chart using the transmitters signal, which upon being received by the trans- as centers. Shoran,acircularcloserange ponder, triggers the transponder and sends anavigation system, may give an accuracy as signal back to the aircraft; this returning signal great as 25 feet but can accommodate only one is received upon a scope similar to a PPI scope. ship or aircraft at a time and is limited in range Direction can be determined since the signal by the curvature of the earth. appealsas a radial line of dots and dashes extending from the center of the scope to the 812. SONAR spot which represents the beacon. The periphery of the scopeisgraduated in degrees, so the "Sonar," an abbreviation for "Sound naviga- bearings can by easily read. The length of the tion ranging," operates in principle as the fa- li "c ..letermines range. The dots and dashes, thometer or echo sounder as described in art. id,.ntify the transponder. 306 except thatitradiates a signal which is It ANIABK, designed primarilyformarine generally horizontal rather than vertical. Ac- '.1<1!. isa beacon which transmits signals con- curate ranges on underwater objects may be ob- t,n:;ousk Thesesignals when received, also tained, and inasmuch as the sonar transducer can appe.ir aradialline emanating from the be rotated, reasonably accurate bearings may also center scope graduated to permit the reading be obtained. Using such ranges and bearings, or of d:r: Flie range can not be determined, ranges alone, piloting procedures as also appli- old !here is no coding system for identification. cable to radar are used. In fog or other reduced visibility, the sonar may provide the most ac- >du,l'A AN curateand useful information, particularlyif rock ledges are present. The sonar is also most "TNCAN" is an abbreviation for helpfulindetecting and avoidingice bergs. "tacticalair navigation."It,like radar, is a range-!naring navigation system. Operating in 813. LORAN the ultra high frequency portion of the spectrum, i igned to prow hie a continuous hear "Loran," an abbreviation for "long range ing and (11.-ttanketoa ground station. TACAN navigation," is a hyperbolic navigation system, stations are identified by transmissions in In- developed in the Radiation Laboratories at Mas- ternatr analNfor.ze Code at 35 second intervals. sachusetts Institute of Technology during World TICAN as a system is superior to earlier very War II.It makes use of a cathode ray tube and tit 1 :rw-,,cncv ;)rnni-directional range anddis- electronic circuits to measure the time difference tni.e :!: a-zirIng equipment used in air naviga- between receipt of two signals traveling at the thin :icaus is more accurate and easier to speed of light (about 186,281 miles per second). operate. Loran-A is standard loran. Another type of loran,

69 A NAVIGATION COMPENDIUM

loran-C, is described later in this chapter. In Loran-A equipment aboard ship consists ofa contrast with radar, loran is characterized by: receiver-indicator (fig. 8-2). The receiver picks up and amplifies a signal while the indicator (a) Havingon boarda ship or aircraft a provides a video presentation. The indicator also receiver but not a transmitter (radar both trans- contains a timer by which the navigator canmeas- mits and receives). ure the interval in microseconds between times (b) Measuring the time difference in receiptof receipt of pulse emissions froma given pair of two signals instead of measuring the timere- of stations. quired for an outgoing signal to travel toa reflecting surface and return. Station pairs are identified by frequency (channel),basic pulse recurrence rate, and specific (c) Utilizing low frequencies (1750-1950 kHz pulse recurrence rate. There are four channels in loran-A and 90-110 kHz in loran-C) whileexpressed in kilo Hertz (khz), with frequencies radar utilizes high frequencies. as follows: (d) Requiring ground stations to transmitsig- nals as pulse emissions. Radar requiresno other Channel 1 1950 kHz. Channel 3 1900 kHz. station; it is complete in itself. Channel 2 1850 kHz. Channel 4 1750 kHz.

814. THEORY OF LORAN-A OPERATION There are three basic pulse recurrence rates associated with each channel: Loran-A operating stations (transmitting sta- S Special-20 pulses per second with 50,000 tions)are organized in pairs called "station ms intervals pairs." The station pair consists ofa master or key station and a secondary station; the two sta- L Low 25 pulses per second with 40,000 ms tions, on the average, are located 200 to400 intervals. miles apart. Each station sends out synchronized pulses at regular intervals and the receipt of H High 33 1/3 pulses per second with signals from a station pair bya ship or an air- 30,000 ms intervals. craft makes it possible to read the time difference. The ship's line of position, basedupon one time difference reading, is a hyperbolic line since The interval is the quotient whenone million is such a curve defines all points a constant differ- divided by the number of pulses per second. ence in distance from two fixes points (in this case There are eight station pairs, numbered from from two transmitting stations). Time difference 0 to 7, associated with each basic pulserecur- readings are measured in microseconds;a micro- rence rate, each station pair having a specific second equals one millionth of a second, and is pulse recurrence rate. In thecase of station abbreviated "ins." pair 0, the specific pulse recurrence rate equals the basic pulse recurrence rate. Other station The arc of a great circle which connects pairshave aspecific pulse recurrence rate two stations of a_.-station pair is the baseline.less than the basic pulserecurrence rate and The perpendicular bisector of the baselineis differing by a value equivalent to 100ms times the centerline. Extensions of the baselineare the station pair number. Examples of specific simply called baseline extensions. pulse recurrence rates are as follows: Station Special BPRR Low BPRR High BPRR Pair Interval Interval Interval 0 50,000 ms 40,000 ms 30,000 ms

1 49,900 ms 39,900 ms 29,900 ms 2 49,800 ms 39,800 ms 29,800 ms 3 49,700 ms 39,700 ms 29,700 ms

70 Chapter 8BASIC ELECTRONIC NAVIGATION SYSTEMS

SWEEP TIME DIFF FOCUS DRIFT Co FUNCTION COUNT ER TIMER AND INDICATOR PRR 0* C°

AFC

VC^.. .40 (11 55

DE LAY CRANK

. t BR IL ######## ,,,, ......

CHANNEL R-F SECTION 52 ANIJAM 53 LOCAL DIST.

69.47 Figure 8-2. Loran-A receiver-indicator. Station pairs are identified by number, a letter, In actual op' ration of the transmitting stations, and a number such as "1H2" which signifiesthree delays are introduced at the secondary sta- channel 1, high basic pulse recurrence rate, andtioncalled (1) baseline delay,(2)half pulse station pair No. 2 (specific pulse recurrence rate:recurren-!e rate delay, and (3) coding delay.The 29,800 ms intervals). master s.ation initiates a pulse which travels all The simplest receiver would presentelectronsdirection.(including along the baseline). This in a horizontal line with twopips a distance apartpulse,upon arrival at the secondary station, eual to the time difference.However, receivertriggers the secondary transmitter. The delay scopes are designed havingtwo traces, the upperthus introduced, the baseline delay, depends upon or "A" trace and thelower or "B" trace. The the speed of radio waves (speed of light) and the trace is actually the righthand half of a singledistance traveled, and is equal to the product of trace presentation. By movingthe pipon the lower6.18 ms and the length of the baseline in nautical trace, which is a signalfrom a secondary station,miles; itinsures that the master station signal untilit is directly beneath the signalfrom thewill be received first. Cpon receipt of a master master station on the A trace,we measure thesignal by the secondary station, the half pulse time difference inmicroseconds. recurrence rate delay isintroduced, which is

71 U111=1, A NAVIGATION COMPENDIUM

the specific pulserecurrence rate interval in and 1236 ms (time of travel of signal microseconds divided by two. This from second- insures that ary station to ship), the sum is 4399Ins. Sub- one signal will appear on each trace, since the tracting 2472 ms from 4399ms we find the pre- right half of the actual trace is underneaththe dicted time difference to be 1927 left half and each half is equalto half the pulse ms, which identi- recurrence rate. Last of all, the coding delay fies a hyperbolic line of position, (950 -1000 ms) is introduced; this provides Sometimes a masterstation will be located a mini- between two secondary stationsand will transmit mum reading and insures the operator of beingon two frequencies or recurrencerates in order able to determine which pip is to the righton the to key (control) two secondarystations. This is scope. The coding delay also provides security called "double pulsing." to the system in wartime,as it may be used to ThF. accuracy of loran-A restrict the successfuluse of our loran depends upon a ship's tions, position with respect to the baseline.On the baseline, the greatest accuracy is experienced,as one microsecond may represent only250 yards. Pro- To illustrate the relationshipbetween the time ceeding away from the baseline along difference reading and theobserver's position, the center- it may be helpful to examine line, accuracy gradually decreases.Along the the method by which baseline extension,one microsecond may repre- a time difference readingcan be predicted if thesent as meeh as 10 miles, and ship's position is known.In this example, the a fix obtained in maeter station is 350 miles from this area may be inaccurate. Ifone microsecond the secondary represents more than 2 nautical miles, theloran station. The ship is located 400miles from thecan not be expected to give satisfactory results in master station and 200 miles fromthe secondarynavigation. stition. The coding delay is 1000ms. The signal will travel from the master Two types of wavesare used in loran-A, station to the shipground waves and skywaves. Ground waves in' Yme interval equal to 400 milesx 6.18 ms are those which travel directly from the per ni:le or 2472 ms. At thesame time, the trans- samesignal mitting station to the ship andhave a maximum willtravelalong the baselinerange limitation under average conditions of 700 tothe secondarystation, The period of time which miles. Sky waves reflect fromthe ionosphere elapses during the travel ofa pulse(ionized layers of atmosphere) andarrive after to the secondarystationisdependent upon the length of the baseline and ground waves because of thegreater distance in this case is equal traveled. For identification, thefirst sky wave to 3 ;.0 miles x 6.18 ms per mileor 2163 nis. reflected from the ''E" layer of the Upon the arrival of the masterstation pulse at ionosphere the secondary station, the is known as the "one hop E,"and the second secondary station is as the''two hop E." The first skywave to be actuated, but before transmitting,it introduces first the half pulse reflected from the "1.'" layeraccordingly is the recurrence rate delay and "one hop F" and the secondis the "two hop F. secondly the coding delay. Itis not necessary Sky waves haverange limitations normally of that we know the,.alueof the halfpulse recurrence rate delay because 500 to 1400 miles, Five hundred andseven hundred our scope is so constructed miles mark the lower andupper boundaries of thatthehalf pulse recurrence rate delaydoes not enter into the measurement. the critical range, inside of whichwave identi- Since the trace fication is necessary. In matchingpips, a ground is divided into an Atrace and a13 trace, and the lower pip wave from the secondary station ismatched to is moved underneath the the ground wave from themaster station or a :!;;.,erpip, the chief separationor half pulse firstsky wave is matched toa first sky wave. re..urrc.,nce rate delay cancels itselfout. The Only "one hop En sky :to. >.pin waves are used. Second isnot moved as far as would besky waves are not dependable,and sky waves n,..;:essary if the scope containeda single trace, are not matched with ground waves. See fig, :CIO. this d:stance which it doesnot travel is the 8-3, h p:;i5C recurrence rate delay whichensures pi;) will a, pear on each trace. Thecoding 815, LORAN-A IN'rEi(rEla:Nci: .0..is 1(100 ms and this value-A Ii be measured e tee 1er:in re ..er. At the endof coding delay, Loran-A interference differsrum most other the F. ,! ' Y.% station will transmit, and the time interferencein thatitisvisual, rather than the receipt of this transmissionis audible as in the case of radio andsonar. At- x h.ix ms per mile or 12:16 ms. Adding mospheric interference makes the flowof elec- 7.14 }3.:-;e1;:it delay), 1000 ms (codingdelay), trons uneven on the scolx'; thisinterference is 72 Chapter 8 BASIC ELECTRONIC NAVIGATION SYSTEMS

flillt\\%1111=.=.1.0

GROUND VALE FIRST SKY WAVE SECOND SKY %NAVE

190.13X Figure8-3. Scope appearanceof waves. descriptively called "gross." Radar transm's- (f) Land does not reduce accuracy(of par- sions appear as evenly spaced pips on a loran ticular interest to air navigators). trace; electrical influences and code sending also (g) Fix is independent of accurate time. produce visual interference. Fortunately, most (h) Homing is convenient. interference doesnotimpair scope reading. (i) Radio silence is maintained. Additionalsignals known as spillover and (j) Jamming is difficult. ghost pulses may interiere, Spillover is the term (k) Possible wartime security. used to describe signals received from adjacent frequencies; since some channels are only sepa- Disadvantages or limitations include: rated by 50 kHz it is as poss ..le to receive signals from two stations on a bran receiver as on (a) Possible mechanical or electrical failure. a radio receiver, If a is suspected 4o be (b) Restricted coverage(lack of sites for spillover, the set should be ',.ned to an adjacent transmitter stations, the expense of stations, and channel or frequency. If it is spillover, the signal the need for agreements with foreign states). will come in stronger; if not it will fade, Ghost (c) Identification of signals not always re- pulses may be received from an adjacent basic liable. recurrence rate. Ghost pulses are characterized bv their instability. 817. LORAN -A CHARTS When a loran-A station is out of synchronization the signals either appear and disappear Either loran-A charts (fig, 8-4), which are or appear to shift to the right about 1000 ms then nautical charts over-printed with loran informa- back,atintervals of vpproximately 1 second. tion, or loran-A tables (H.O. Pub. 221) may be Such blinking action warns the operator not to used for co-vert:. g loran-A readings into LOP's takereadings,When thestationsareagain and fixes. Loran-A charts as normally available synchronized, wl.ich usually requires not more of.er a rapid means, and have been made for than a minute, blinking ceases. those areas where loran-A signals are available. Loran-A charts show hyperbolic lines of posi- slt;. .-\;)VANTAGI.:!-: AND LIMITATIONS OF' tion usually for each 20 ms of time difference on large scalecharts and for each 100 ms of time difference on small scale charts. The lines The advantages of loran-A include the fol- emanating from different station pairs are identi- lowing: fiedbytheircolor as well as by a label of rate and ms time difference along each such (a) Speedy fixes (1-5 niirutes). hyperbolic line. Hapidly trained operators (4 days at fleet Charted hyperl:olic lines are for ground wave sc..hools). time differences; if first sky waves are matched, ,c) «cattierdoesnotaffectreliability of then the time difference obtained must be correct- operat ion . ed so as to be comparable to ground wave time (d) 21 hour service. differences. Corrections are found at the inter- (t.,)Long range (1400 miles). sectionsofmeridiansand parallels and are

73 A NAVIGATION COMPENDIUM

00 Ihr I.4 10) IW ' I41' 50. .44 1 6.) I60' 109. I Si' lb, iW 155' Ise li 1V' IM' 150' ntifi,e1.1 rot .., so.,...... ".... or Tel . .19!. .141 "14 ir''''F''."S' rl, ..I7 ri,.. r r... .,""Pr( .J.*."7 "71"1", 1.1.17. .. 1. 1 \ / of.

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69.49 Figure 8 -4.A portion of a loran chart. printed the same color as the rate to which theythen they should be adv2nced or retarded toa apply. Eye interpolation may be.-ieeessary to common time using procedures described in the determine the sky wave correction, when the posi- study of the running fix. If the charted hyperbolic tion of the shipis between tabulated values. lines are fax apart, a self-explanatory linear When obtained, corrections are added or sub- interpolater appearing on loran charts may be tracted according to sign. used to increase the accuracy and lessen the When plotting a loran-A fix, select two hyper- difficui4 of interpolation. bolic linesin the vicinity of the DR position The accuracy of a loran-A fix dependsupon between thevalues of which the actual time the angle of intersection of LOP's, the position difference reading of a station pair lies. Using with respect to the transmitting stations, the eye interpolation and :t straight edge, draw a short synchronization of the station pair, and the opera- line labeling it with the time above and the sta- tor's skillin identifying and matching signals. tion pair number and ms time difference below. Thisis a loran-A line of position. By plotting 816. LORAN-A OPERATION two or more such 1,0P's (a isuming they are The steps in taking and using a loran-A read- obtained in rapid succession) a fix is obtained ing in the AN/UPN-12 and similar sets, are which is represented by a small circle` and the normally as follows: time in four digits followed by the word "fix." (a) Determity from the approximate position If the LOP's are not obbined in rapid succe,-;sion, of the ship, the transmitting station pairs which

74 Chapter 8BASIC ELECTRONIC NAVIGATION SYSTEMS serve the ship's position and the type of signals remainder of the following procedures and leave expected from these transmitting station pairs. the"antijam" switchin the "out" position. (b) Turn on the receiving set by setting the If heavy interference is encountered, leave the power switch to the "standby" position. "AFC" switch off and set "antijam" switch to (c) Allow a warm-up of at least one (1) minute the "in" position. before switching to "power-on." Turn the power (j)Use the "delay" crank in the "coarse" switch to "power on" position. position to place the leading edge of the lower (d) Refer to the Loran-A Charts of the ap- pedestal under the lower (secondary) pulse which proximate geographical location of the ship. Set corresponds to the selected master pulse. the "pulse recurrence rate" (PRE tnd "channel" (k) Set the "sweep function" switch to posi- to correspond to a loran-A transmitting station tion 2. pair determined in Step 1. Set "sweep function" (1)With the "delay" crank in the "fine" switch to one, the AFC sire' ,h to "off" and the position, align the two selected pulses vertically. "time difference" counter t....pproximately11,000 (m) Set the "sweep function" switch to posi- with "delay" crank. tion 3. (e) Adjust the "gain" and "bal" controls to (n) Match the two pulses, using the "delay" equalize signal heights. Set "Local-dist" switch crank (in the "fine" position) "gain" and "bal" to D, I, or L, dependent upon which position will controls. (See fig. 8-5.) obtain best operating conditions. (o) Record the "time difference" counter- (f)Use ''drift," ''gain,'' "bal," and "L-R" reading. controls to locate the desired signals, then turn (p) Repeatsteps d through o, setting the the "drift" control to a point where the signals "PAR" and "channel" switches to the pulse are locked in on the indicator screen. Readjust recurrence rate and channel corresponding to the the "gain" and "bal" controls so that signals others of the loran-A transmitting pairs. are of convenient operating amplitude. (q) Apply necessary corrections to the "dif- (g) Determine ground and sky-wave compo- ference" readings, referring to Loran-A naviga- nents of the signals and decide whether ground tion tables or charts. Take into account the time or sky-wave matching is to be used. of day at which readings were taken, whether (h) Usethe "L-R" switch to position the received signals were strong or weak, and whether upper (master) pulse selected for matching at ground or sky waves were used to match signals. the leading (left) edge of the upper pedestal. Plot lines of position. (i)Set the "AFC" switch to the "on" posi- (r) Obtain loran-A fix, considering the rela- tion.Unlessnoise pulses cause pulse jitter, tive accuracy of the various lines of position leave the "AFC" swit h in this position for the which depend, among other things, on the spacing

70.99(190)X Figure 8 -5.Matching Loran-A signals. A NAVIGATION COMPENDIUM of the lines of position in the geographical area frequency(1(F) channel, There are six basic of the ship. pulse recurrence rates as follows: (s) Compare the loran-A fix with other navigational information, and make the necessary H 33 1/2 pulses/second record entries of the exact location of the ship, L 25 pulses/second (t)Turn the "power" switch to the "stand- S 20 pulses/second by" ( r "off" position. SH 162/3pulses/second SL 121/2pulses/second 819. LORAN-C SS 10 pulses/second Loran-C is a pulsed, hyperbolic, long-range Associated with each basic pulse recurrencerate navigation system, operating on a radio frequency are eight specific pulse recurrence rates. As in of 90-110 kHz,It was developed for greater Loran-A, specific pulse recurrence rates are range and accuracy, and first became opera- separated from the basic pulse recurrence rate tionalin 1957. Because of its lower frequency, by multiples of 100 ms. Station type designators and greater baseline distance (500 to 700 miles consist of one or more letters to indicate the as compared to 200 to 400 miles in Loran-A),basic pulse recurrence rate (H, L, S, SH, SL, reasonable accuracy to 1200 nautical miles for or SS), anumber (0-7) to indicate the specific ground waves and 3000 nautical miles for sky pulse recurrence rate, and letters such as X waves can be attained. Basic principles of opera- or Y to indicate a particular secondary station. tion are similar to those which apply to Loran-A, Ground wave coverage is a function of pro- however,greater convenience of operation is pagation strength, and the strength of signal to provided. noise ratio, Ground waves may extend as far as 2000 nautical miles and are normally reliable to A Loran-C network consists of one master 1200 nautical miles for 300 KW pulse power. and two or more secondary stations. As in First hop-E sky waves extend out to 2300 miles, Loran-A, the signal from the master activates and second hop-E sky waves may reach out to each secondary station, Network arrangements 3400 miles. To be sufficiently stable for use, include (a) the triad, with a master between two complete darkness is usually necessary for re- secondaries; (b) the star or "Y" formation with ceipt of second hop-E sky waves. Accuracy of a master positioned between three secondaries; Loran-C pulse transmissions, as made possible and (c) the square, It should also be noted that by phase comparison and longer baselines, de- a master station may serve as a secondary sta- pends upon atmospheric conditions, noise and in- tion in another network. Loran-C uses a multi- terference. Ground waves are normally accurate pulsed transmission with eight pulses each 1000 to 0.1 percent of the distance traveled. Sky wave ms, except for signals from the master station, accuracy is usually to 3 to 5 miles. which include a ninth pulse for identification. Plotting procedures in Loran-A and Loran-C Pulses are phase-coded, which protects against are similar, A single observation provides read- interference from outside sources and reduces ings which establish lines of positions for all the contamination of ground waves by sky waves. pairs within a network. For maximum accuracy, Loran-C receivers are specially designed; how- Loran-C tables (H.O. Pub. 221 series) may be ever, the system is sufficiently compatible with used. In those circumstances in which modified Loran-A that receivers in the latter system can Loran-A equipment is used, because of elapsed be modified for Loran-C use, except for 12 speci- time between readings, it may be advisable to fic pulse recurrence rates, but with less accuracy. advance or retard certain LOPs using running Phase measurement, which is helpful in station fix procedures. identification and indiscriminationbetween Loran-C provides for (a) electronic naviga- ground waves and sky waves, as well as most tion; (b) systemized long-range time distribution: otheroperationswithLoran-C receivers,is automatic; read-outs are direct. The constant (c) time standardization between widely separated time difference obtained from the reading on receiving locations; and (d) the study of electro- one station pair, as in Loran-A, provides a hy- magnetic wave propagation. perbolic line of position. 820. DECCA A major difference between system:- is that Defect is a low frequency British hyperbolic in Loran-C,all stationi share the same radio radionavigation systemfirst usedin\\

76 Chapter 8 BASIC ELECTRONIC NAVIGATION SYSTENIS

War 11 to guide allied forces to the Normandyun Decca charts showing hyperbolic lines in color beaches. It is highly accurate and reliable, andcorresponding to that of the associated secondary likeotherelectronic systems, its operation,station, The Decca receiver consists of four radio although slightly affected by atmospheric condi-receivers, one for each frequency. By the reading tions, is not precluded by low visibility. In thisof dials called Decometers, the necessary infor- s!,stem, chains are established, with each chainmation for plotting a fix is obtained. consisting of one master z,nd three secondary Decca coverage is available over most of stations. Preferably, the secondary stations areWestern Europe,in parts of the Indian Ocean equally spaced on a circle with a radius of 70including the Persian Gulf, along the coasts of to !-..0 miles and with the ma:ter station at theEastern Canada andthe Northeastern United venter, Decea operates in the 70 to 130 kHz band.States, and along the coast of southern California. Its reliable operational range, accurate to about Secondary stations are identified by the colors150 yards in daytime and 800 yards at night, is purple, red, and green. These, and the master,approxim ttely 250 neles, I)ecca receivers may be transmit a continuous wave at different frequen-carried in aircraft as well as ships. cies. A hyperbolic line of position is determined United States and Canadian rights to the .1),cea by the phase relationship of a secondary signalsystem are held by the Pacific Division of Bendix as compared with the signal of the master. TwoAviation Corporation, which also produces a long- secondaries and a master provide readings fromrange comdanion of Decea called Deetra. [...send which a fix can be obtained. The third secondarytoboth ships and aircraft, Deetra primarily in a chain serves as a check. Fixes are plottedserves transatlantic aviation. CHAPTER 9 ADVANCED ELECTRONIC NAVIGATION SYSTEMS

901. GENERAL 902. RATAN Electronic navigation, essentially an extension Currently undergoing consideration and in of piloting, has been characterized since 1950 limited use is the Radar Television Aid to Navi- by a proliferation of systems. Basic electronic gation, called RATAN. Itis simply an extension navigation devices, as developed and earlier ac- or a refinement to radar navigation making use cepted for general use, were described in Chapter of shore stations, high-definition radar, and UH F 8. This chapter, while not addressing all of the television equipment, to transmit a radar image. many new devices and systems in use today, pro- The receiver, an inexpensive transiEtorized tele- vides basic descriptive data for the newer andvision receiver, provides a display of the shore more sophisticated systems in use. line, channel buoys, lighthouses, other markers, and moving ship traffic. Whereas radar shows a One method of classification of electronic ship as the focal point on a radar scope, RATAN navigation systems, based upon the form of the presents a fixed background with the ship moving line of position or fix obtained, includes fivewithin the pattern. An added feature is a scan types or categories as follows: coverter which stores the radar image and identifies moving objects on the screen. Movingvessels (a) HyperbolicLoran and Decca, and as de- are identified on the scope by their "fading tails," Ecribed in this chapter, Omega and some types of an indication of relative movement, Raydist. RATAN is important because it is anall-weather navigation device and inexpensive, but has the (b) Circular Shoran, and Raydist. disadvantage of being dependent upon a transmit- (c) AzimuthalRadio direction finder, and as ting station ashore. Furthermore, onboard recep- described herein, Consol and Consolan. tion has been poor, and needed frequencies have not yet been allocated. Assuming that reception (d) Range-bearingRadar and Tacan. This can be improved and frequencies allocated, it is includes "Ratan," a limited form of radar navi- being considered as a possible adjunct to Marine gatiun described in this chapter. Traffic System Installations. (e) Motion sensingAs describedherein, Satellite Navigation (NAVSAT), Inertial Naviga- tion, and Acoustic Doppler. 903. R.A.YDIST A second and equally as valid a method of Raydist, through precise tracking of CA' trans- classificationis based upon range, as follows: mitters, is useful in navigation, surveying, and other position plotting. Itis used extensively by (a) Short-range Radar (including Ratan) and the National Ocean Survey, commercial organiza- Shoran. tions such as those engaged in offshore oil ex- ploration, and foreign governments . An early form (b) Mid-range Raydist. of Raydist, Type E was used for tracking the (c) Long-range Radio direction finder, first U.S. satellites. Decca, and Loran, and as described in this chap- Raydist is considered here as a mid-range ter, Consol, Consolan, Omega, Satellite Naviga- navigation system.It employs radio distance tion (NAVSAT), Inertial Navigation and Acoustic measuring to produce either circular or hype' Doppler. bolic lines of position; however, types of Ray(

78 Chapter 9ADVANCED ELECTRONIC NAVIGATION SYSTEMS earlier used to produce the latter are now gradu- with energy of the proper phase and amplitude, ally being replaced by circular distance meas-thus generating the field pattern. The receiver uringforms which are non-saturable and have isequipped with an omnidirectional antenna. greater potential for accuracy. An example of Consol stations are located in Western Europe, the newer form is the Type N. ranging from southern Spain to the Soviet Arctic. In operation, Raydist requires two CW transmitters on a baseline, with a separation of as much as 100 miles. Operating frequencies are 'n 906. CONSOLAN the1.6to5 mHz range, permitting effecthe transmission beyond line of sight range. Depend- Consolan is an American version of Consol, ing upon power, ranges up to 200 miles may be and accordingly is a long-range, azimuthal navi- reached. Stations differ by about 400 cycles per gation system. In contrast with Consol, Consolan second, which permits phase comparison at other uses two transmitting antennas rather than three. locations. An accuracy of one to three meters Consolan increases coverage by using higher may be achieved. power levels and lower frequencies (190 to 194 Itaydist equipment, including the transmitters, kHz). The pattern generated is the sameas that is generally small, compact, and light in weight. provided by Consol. Special charts and tables are The equipment isfully automatic, providing a provided for use with Consolan, by the U.S. Naval direct reading of phase comparison. Oceanographic Office. U.S. Consolan stations are located in San Francisco and Nantucket. 904. LORAN-D 907. OMEGA This is a low-frequency, pulsed-type, semi- mobile,hyperbolic,navigationsystem. Being A new electronic, hyperbolic, navigational transportable, it can be moved to new areas and system, similar to Loran, is Omega. It is a long usedasneeded. The frequency range, asin range, pulsed, phase-difference, very low fre- Loran-C,is90 to110 kHz and signal charac- quency (VLF) system, operating on a frequency teristics are similar except that Loran-D usesof 10 to 14 kHz. It is a worldwide, all-weather groups of 16 pulses, repeated each 500 micro- system, of use to ships, aircraft, and submarines, seconds. The system is (a) highly accurate over including submarines submerged. Its accuracy is a range of 500 miles using ground waves; (b) about one mile during the day and two miles quite resistant to electronic jamming; (c) rela- during the night. Phase difference measurements tively mobile; and (d) equally useful in surface are made on continuous wave (CW) radio trans- vessels and high speed aircraft. missions. Like Loran, shore transmitting stations are used. Theoretically, six such stations are 905. CONSUL required for worldwide coverage; however, two additional stations are required to provide a de- Consol is a long-range, azimuthal, radio navi- gree of redundancy necessary to accommodate gation aid. It was developed and used by the Ger- station repair. mans (and known as SONNE) during World War II. In the Omega system, the phase-difference It was later improved bythe British. Asa system, measurement of a 10.2 kHz signal transmitted it c.ai be considered as an improved version of from two stations provides a hyperbolic line of the radio direction finder (RDF). An observer, position. At least one additional phase-difference using an o:dinary receiver, interprets a pattern, measurement is required to establish a fix, and and through either RDF or dead reckoning infor- two or more are desirable. Unlike other hyper- mation, determines his sector of the pattern. bolic navigation systems, any two stations from Lines of position, with much greater accuracy which signals can be received may be paired to than obtainable with Ril7, are plotted on special produce a line of position. Special charts are charts. Maximum rangesreach 500to 1400 provided by the U.S. Naval Oceanographic Office nautical miles, generally with an LOP accuracy for Omega plotting. of a fraction of one degree. Minimum range is Since the wavelength of a 10.2 kHz signal is 25 to 50 nautical miles. It operates in a frequency approximately 16 miles, and phase readings re- range of 250 to 350 kHz. peat themselves twice within this distance (see Consul is highly reliable because of the sim- figure 9-1), lanes eight miles in width are estab- plicity of equipment. Consul transmitters, situ- lished. Thus each lane or band is the equivalent ated at consul shore stations, feed three antennas in distance of one half of a wave length. The

79 A NAVIGATION COMPENDIUM

SIgnal A

wave length 16 miles --

360 315

Phase Signal A 0 45 90 135 1h0 225 ;"Ii 31c .4hto Phase Signal B 360 315 270 225 180 135 9u 45 Phase Diflerente 0 90 la/ 27U 38( tit t b. i 2 -:' . i 360 0

lane width 8 iitles tun base line between .taii..11,1

190.14X Figure 9-1.-1.2 kHz phase-difference measurement. actual phase-difference reading establishes thefrom the difference in tneir readings. For ex- line of position within the lane. ample, one may be located at a known position To avoid ambiguityin lane identification, ashore and its reading continuously broadcast, Omega stations transmit also on 13.6 kHz, a for comparison with readings obtained by vessels frequency having a wave length exactly one third nearby. In this manner, long distance propagation shorter than 10.2 kHz. Every fourth contour oferrors can be generally eliminated. this frequency coincides with every third contour Omega was developed in the early 1960's by on 10.2 kHz, and thus one broad lane matchesthe U.S. Navy for use throughout the Defense three narrow lanes obtained on the 10.2 frequency. Establishment and commercially.Itis simple All Omega stations transmit on the same dual for the user to operate, accurate, and provides frequencies,at different times. Eight stations worldwide coverage. At some future time it is share a ten second time interval. The receiver possible that Omega will replace Loran. (see figure 1) identifies each station by its place inthe. equence and by the precise time duration of its signal. 903. SATELLITE NAVIGATION (NAVSAT) Long base lines of approximately 5000 nautical miles and sometimes as much as 6000 miles, As Project Transit, the U.S. Navy developed are used. The systemis serviceable to about a Navy Navigation Satellite System at the Applied 6000 miles. For greater accuracy of position, Physics Laboratory of the John Hopkins Univer- the navigator should consider the geometrical sity. In use since 1964, the system now known as relationshipandselect station pairs yielding "NAVSAT" provides for accurate, all weather, lines of position which will cross at angles ofworld-wide navigation of surface ships, subma- 60 to 90 degrees. rines, and aircraft. The accuracy is exceptional, A technique known as differential Omega has the navigational error normally not exceeding' 00 been established to att2in greater accuracy in a yards. Although NAN:SATwasdeveloped initially particular area. Two or more receivers are com- for naval use, it has been available to commercial pared and the distance between them determined shipping since 1968.

80 Chapter 9ADVANCED ELECTRONIC NAVIGATION SYSTEMS

tb4.-1

120.48 Figure 9-2.AN/SRN-12 Omega Shipboard Navigation Receiver. The operation of NAVSAT involves a phenom- them. The orbital planes are separated by Ap- enon known as Doppler shift, which in radio waves proximately 45° of longitude. Only one satellite is the apparent change in frequency when the need be used to establish a position. Each satellite distance betweentransmitter andreceiver continuously broadcasts data giving the fixed and changes. Dependent upon relative motion, Doppler variable parameters which describe its own orbit, shift is proportional to the velocity of an approach- togetherwith a time reference. Periodically, ing or rec..ding NAVSAT satellite. With the ap- approximately every 12 hours, a ground injection proach, the frequency shifts upward: accordingly, station broadcasts to each satellite, updating the with a satellite in recession, the frequency shifts data stored and enabling the satellite to broad- downward. The Doppler shift actually experienced cast current information. This updating informa- depends upon the position of the receiver with tion passed by an injection station is obtained respect to the path of a transmitting satellite. from a computing center at Point Mugu, Cali- Components of the NAVSAT system include one fornia which receivesorbitalinputs from a or more satellites, ground tracking stations, a ground tracking station, and time from the Naval computing center, an injection station, accurate Observatory. See figure 9-3. Greenwich mean or Universal time from the Naval Because of the effect of the ionosphere upon Observatory, and the shipboard receiver and com- radio waves, NAVSAT satellites use two ultra puter high broadcast frequencies, 150 and 400 mHz. Each NAVSAT satellite travels in a polar orbit, As each frequency is differently affected by the at an altitude of approximately 600 nautical miles, ionosphere,Dopplersignalsreceived can be circling the earth once each 105 minutes. The compared and the effect determined.Allowance is orbital planes of the satellites, while essentiallythen made in position calculations for the iono- fixedin space, intersect the earth's axis and spheric effect. makethe satellites appear to lw traversing the Unlike a planet in space, which travels in an longitudinal meridians as the earth turns beneath elliptical orbit in accordance with Newton's laws

81 TIME Ti TIME T2 SATEUJTE ORBIT ..- --- TIME T3 PARAMETERS CRSITAL . NEW NAVIGAIDR TRACKINGSTATION DOPPLERTIMEORBITAL SIGNAL PARAMETERS COMPUTES FUTURE LATITUDE LONGITUDE TIME ORBITAL PRUNE TIME 7' CENTER' CONTROL DATA PROCESSOR COMPUTER : = : . RECEIVER 1141110 STATIONTRACKING REFRACTION - ` - .. , : ,:. : ...... :It SIGNALSDIGITALIZERECEIVES,".._ RECORDS S DOPPLER "... DOPPLERCORRECTED DATA -* - ..- .. ,..--- -.. t." -. ,- ...v.! . a Figure 9-3.NAVSAT. 162.58 BEST COPY AVAILABLE Chapter 9ADVANCED ELECTRONIC NAVIGATION SYSTEMS

of motion (see Appendix 13), a NAVSAT satellite States continued the development of inertial sys- operating at an approximate altitude of 600 nau- tems, with the first satisfactory system appearing tical miles is affected by the shape of the earthin the early 1950's. U.S. models were first de- and its irregular gravitational field. Since it is veloped for use in aircraft, later were used in not operating in a complete vacuum, the satellite ballistic missiles and spacecraft, then widely experiences some atmospheric drag. It is also used in Polaris submarines, and finally were affected by the gravitational attraction of the accepted for general use in surface ships and sun and moon, charged particles in. pace, and attack submarines. The system used in the U.S. the earth's magnetic field. These disturbances Navyiscalled the Ship's Inertial Navigation to the Keplerian orbit are predictable and can be System (SINS), an early model of which was computer programmed. designed by the Massachusetts Institute of Tech- nology and was installed by the Sperry Gyroscope Four satellite tracking stations monitor theDivision of Sperry Rand Corporation in USS Doppler signal of the satellites as a function of COMPASS ISLAND in 1956. time. The Naval Observatory monitors the sat- The inertial navigator through instrumentation ellite time signal. Comparison information is measuresthetotalacceleration vector of a passed to the computing center. NAVSAT users vehicle in a gyroscope stabilized coordinate sys- receive operational information of the satellites tem. Integrating acceleration with time, and ap- or"birds" through messages from the U.S. plying the computed components to initial veloc- Naval Astronautics Group, Point Mugu, Cali-cities, makes itpossible to determine actual fornia. velocity components and distances traveled. As Shipboard equipment consists of a receiver, a in other forms of dead reckoning, any error, computer, and a tape read-out unit. The ship's small though it may be, will with time contri- estimated position and speed are required as bute to a position error. Accordingly, using the localinputs to the shipboard equipment. The systems approach, the position data iF not only estimated position need not be accurate; however, subjected to internal monitoring, but it is peri- accuracyof the speed inputis essential. An odically corrected, based upon itavigational in- inaccuracy of one knot in ship's speed may cause formation from external sources. For example, an error of 0.25 miles in a NAVSAT fix. Speed SINS can be associated with NAVSAT, sharing in errors with a mainly north-south component some instances a SINS general purpose computer; cause a greater position error than speed errors the inertial position can be updated based upon largely with an east-west component. The ship- satellite information. board equipment is quite sophisticated and requires expert maintenance. The basic sensors used in inertial navigation A NAVSAT fix can 1.)e obtained when a passing are gyroscopes and accelerometers. Three gyro- satellite's observed maximum altitude is between scopes are normally mounted on a platform as 10° and 70°. NAVSAT is most convenient to use follows: inasmuch as the tape readout unit provides the latitude and longitude of the ship's position in (a) Gyro "x" with its spin axis aligned in a typewritten form. In addition to being a conven- North-South direction; ient, all-weather system, NAVSAT has proved to be extremely accurate and reliable. (b) Gyro "y" with its spin axis aligned in an East-West direction; 909. INERTIAL. NAVIGATION (c) Gyro "z" with its spin axis perpendicular Inertial navigation is essentially an improved to the "x" and "y" gyros. form of dead reckoning in which velocity and position are determined through relatively ac- curatesensing of acceleration and direction. The purposes of the "x" and "y" gyros are to Inertial system-;, used for long range navigation, sense roll and pitch 01 the ship, and through the are completely self contained, require no shore use of torqueing motors, to keep the platform support, and are indept.mdent of weather. perpendicular to a line passing from the center of the platform to the center of the earth. The The first known appliation of inertial naviga- purpose of the "z" gyro is to nupply heading. tion was in the guidance :;ystern of German V-2 Thus the gyroscopes provide a stable platform rockets.Following World \Aar II,the United and a direction reference.

83 A NAVIGATION COMPENDIUM

Two accelerometers are usedtoestablish Shift" as in satellite navigation; it differs opera- acceleration in the North-South and the East- tionally from NAVSAT in that the Doppler shift West directions. The accelerations and deceler- measured is in a sea-water medium. Importantly, ations sensed by accelerometers are algebra- the Doppler shift phenomenon occurs throughout icallyadded to the speed stored in the com- the frequency spectrum, and is equally applicable puter,thereby continually updating the ship's tovisiblelight,electromagnetic waves, and speed. Such inputs in N-S and E-W components, acoustic or sound waves. Of prime consideration are resolved by computor into actual or truein Acoustic Doppler is the speed of sound,and speed. True speed and heading are continually signalattenuation and reverberation of sonic used to update the ship's position, giving read- radiation in the sea-water medium, outs in latitude and longitude. Acoustic Doppler is in one respect similar Since the force of gravity can be interpretedto inertial navigation since both systems repre- as an acceleration by the accelerometers, it is sent improvements to ordinary dead reckoning. vital that the accelerometer platform be kept inUnlike inertial navigation, Acoustic Doppler is the proper plane and that unusual gravitational limited in depth. When the ocean bed is used for anomalies, such as unusually laige vertical land a reflecting surface, its use is limited bysignal masses, be noted and compensated. attenuation to depths under the keel of less than Advances in computer technology have made 100 fathoms. However, echoes from thermal gra- it possible to make quite complicated mathemati- dients and marine life can be used in Doppler cal calculations which are essential to inertial navigation, provided such reverberations produce navigation, Sophisticated instrumentation meas- a signal level greater than the noise level atthe uresthe progress of a vessel in a spatial di-receiver. rection. By mechanization of Newtonian Laws A "DopplerNavigator" developedby the of Motion, thiscomplex system can provide Raytheon Company and designated the AN/SQS-12, position coordinates etnd other related informa- uses four beams of sonic energy, spaced90° tion. For example, SINS provides a continuous apart. Transducers, activated by a transmitter, read-out of latitude, longitude, and ship's heading. send out the sound signal and receive the echo. For stabilization purposes, it provides data onServing as hydrophones, the transducers con- roll, pitch, and velocity. It provides information vert the echoes into electrical energy. A re- on ship's motion to NAVSAT; without SINS, in- ceiveramplifies and compares the electrical puts for course and speed must be given to the input from the four transducers and develops NAVSAT computer by the gyrocompass and logthe Dopplerfrequency. The receiver also, by respectively. Currently, various inertial systems comparison of frequency shifts, senses motion are coming into use to meet expanding naviga- and direction. The transducer array is oriented tional and other guidance requirements. geographically by an input from the ship's gyrocompass. Itis also stabilized in the horizontal 910. ACOUSTIC DOPPLER NAVIGATION plane by the gyrocompass. AcousticDoppler, or Doppler sonar,isa Acoustic Doppler Navigation withthe relatively new development. It provides a new ANISQS-12, as in satellite and inertial systems, form of motion sensor, making it possible toprovides a highly accurate direct read-out of measure (a) speed with respect to the bottom: latitude and longitude, and automatic tracking. (b) distance traveled: and (c) drift angle, which A smaller Doppler navigator developed for use in when aaded to true heading provides the true depthsless than 250 feet by small craft, and course made good over the bottom. In principle, designated the Janus Sti-400, displays the results it makes use of the phenomenon of "Dopplerin digital form and requires manual plotting. CHAPTER 10 NAUTICAL ASTRONOMY

1001. ASTRONOMY Johann Kepler. Through his work, which followed that of Tycho Brahe, the true nature of planetary Celestial navigation is dependent upon certain orbits was realized. (See Appendix B for Kepler's principles of astronomy, particularly as the latter laws.) relates to the positions, magnitudes, and motions of celestial bodies. Astronomy is considered to be Withthis brief introduction to astronomy, the oldest of the sciences. The term "astronomy" that portion with nautical significance is further is derived from the compounding of two Greek considered. Predictedpositionsofcelestial words, "astron" meaning a star or constellation, bodies will be compared with observed positions. and "nomos" or law, and is translated literally Such comparisons provide the basis for celestial as the "law of the stars." Ordinarily, it is de- lines of position. fined as the science which treats of the heavenly bodies. It is indeed a science of great antiquity. 1002. UNIVERSE IN MOTION Three greatsystemsofastronomy have evolved. The Ptolemaic system, now considered Motion in the universe is viewed as actual an hypothesis, was originated by the Alexandrian and apparent. We will commence our study by astronomer Ptolemy in the second century A.D. considering the actual motion of (a) the earth, Ptolemy placed the earth at rest in the center of (b)the sun,(c)the planets, (d) the moon, and the universe, with the moon, Mercury, Venus, (e) the stars and galaxies. the sun, Mars, Jupiter and Saturn revolvingabout it. The second system, also an hypothesis, was a. The earth, the platform from which we originated by Tycho Brahe in the sixteenthcen- observe the universe, engages in four principal tury. Brahe had tried to reconcile astronomy with motions as follows: a literal translation of Scripture, and in so doing, developed a new concept of the solar system. 1. Rotation. The earth rotates once each In the Brahean system, the earth is at rest with day about its axis, from west to east. The period the sun and the moon revolving about it; the other of rotation is the basis of the calendar day. We planets are considered to be revolving about the can prove the direction of rotation by observing sun. The third system, which actually antedated the flow of water from an ordinary wash basin that of Tycho Brahe, was conceived earlier inthe filled with water; when the stopper is removed sixteenth century by the mathematician and as-and the water is allowed to run down the drain, tronomer Nicolaus Copernicus. The Copernican the water will spiral clockwise in the southern theory, now universally adopted as the true solar hemisphere and counterclockwise in the northern system, places the sun at the center, with pri- hemisphere. The reason for this action by the mary planets, including the earth, revolving a- wateristhat two forces are acting upon it. bout the sun from west to east. The earth iscon- First, gravity acts to cause the water to flow sidered to be turning on its axis, and themoon down the drain. Secondly the rotation of the earth, isrevolving about the earth. Other secondary a forcethat is considered to be concentrated planets revolve about their primaries. l3eyondat the earth's equator, acts upon the column of the solar system, fixed stars serve as centers water causing spiral motion, the direction of the to other systems. The Copernican concept is the spiral depending upon which side of theconcen- basis of modern astronomy. Further refinements trated force the water column happens to be have been made by noted astronomers suchas located.

85 A NAVIGATION COMPENDIUM

2. Revolution.The earth revolves about above the north pole of the earth. In years to come the sun once each year (365 1/4 days), from west a vertical line through our north polewill point to east. The period of revolution is the basisto other stars, It will point in the direction of of the calendar year. The difference betweenDeneb in the year 10,000 and in the direction of rotation and revolution is that rotation is com- Vega in 14,000. Again in the year 27,900 Polaris monly used to refer to turning on an axis while will be above our north pole. revolution usually refers to travel in an orbit. The actual length of time required for the earth 4. Space Motion, The earth and the other to complete one revolution is a little less than members of our solar system are moving through 365 1/4 days and therefore the establishment of space in the direction of the star Vega at a speed an accurate calendar has been a problem. The of about 12 miles per second. Gregorian calendar, which replaced that of Julius Caesar, practically eliminated the discrepancy by b. The sun, the center of our solar system, the elimination of 3 leap years (3 days) per 400 rotates upon its axis, which is inclined 7 degrees years. This was accomplished by eliminating leap to its path of travel, and travels through space as years on turns of the century not divisible by does the earth. 400. For example, the years 1700, 1800, and 1900 were 365 days in length, while the year 2000 will c. The planets of our solar system rotate upon be 366 days (leap year) in length. Although the their axes from west to east, revolve about the sun calendar of Pope Gregory leaves something to be from west to east in ellipses of small eccentricity, desired, its error is only 3 days in 10,000 years. and engage in space motion. The earth's orbit is elliptical; during the d. The moon, a secondaty planet, rotates upon winter months in the northern hemisphere, the its axes from west to east, revolves about the earth earth travels nearer the sun, thus making the sun from west to east once in 29 1/2 solar days, and appear wider in diameter at that time. Also, due joins other members of our solar system in space to the sun's proximity, the relative speed of the motion. The period of rotation of the moon upon earth as compared to that of the sun is greaterits axis, the rotation of the earth, and the revolu- in winter than during the summer months in the tion of the moon about the earth, is so synchro- northernhemisphere,resultingin northern nized that from the earth we see but one side of winters being 7 days shorter than northern summers, and southern winters being 7 days longer the moon. than southern summers. The average speed of e. The stars engage in space motion and also the earth in its orbit is 18 1/2 miles per second. rotation as does the sun. They are arranged in 3. Precession. The earth precesses about groups called galaxies. Our galaxy, the Milky an ecliptic axis (i.e., a line passing through the Way, contains possibly 100 billion stars. The earth's center perpendicular to the plane of the universe may contain 100 million galaxies, all of earth'sorbit)once each25,80C'yearsin a which have space motion independent of, and more counterclockwise direction. This motion is anal- significant than, the space motion of our solar ogous to the motion sometimes observed in a spin- system. The stars are considered to be an infinite ning top. When a top is spun, two forces act, distance from the earth. (1) the spinning force which tends to keep the top upright and (2) the force of gravity which tends to A notable observation in the case of actual pull the top from an upright position. The result motion is that most bodies of the universe rotate of these two forces is precession, which is the from west to east, travel from west to east in conical motion of an axis around a perpendicular their orbits, and according to some theories, be- to the plane upon which it is spun. The earth has have in general as electrons !n the structure of a spinning motion of rotation about its axis, which the atom. is not perpendicular to the plane of its orbit, and it is acted upon by the gravitational forces of The astronomer studies actual motion; the attraction of the moon and the sun; these gravita- navigator concerns himself with apparent motion. tional torques tend to align the earth's axis with The ilavigator stops the earth, so to speak, and the ecliptic axis. The result of the earth's pre- obserses the celestial bodies rise in the east, cession is a difference in location of the stars travel westward, and set in the west. The astrono- in our heavens with respect to our north Dote. mer tabulates information which the navigator At present, Polaris (north star) is almost directly uses to fix his position.

86 Chapter l0 NAUTICAL ASTRONOMY

1003. CELESTIAL SPHERE CONCEPT the celestial meridians, moves with the celestial body progressively with tints from east to west (since we consider apparent motion), while the Because of the necessity for location of celes- position of the celestial meridian remains fixed. tial bodies in the heavens, we use a system ofWith knowledge of the earth's rotation (one turn coordinates similar to latitude and longitude onupon its axis per 24 hours) we can realize that the surface of the earth= the system etitablishei each celestial body crosses our meridian once is known as the oelestial sphere concept. The each 24 hours. Dividing 360 degrees (number of following terms uonstitute the concepts degrees in a circle) by 24 hours, we find that an hour circle advances about 16 degrees per CELESTIAL SPHERV. A sphere of infinite hour. radius with the earth as center. Whenever convenient we think of the earth as a point, and as a DECLINATION, The angular distance of a point it has no magnitude. We portray all of the body north or south of the equinoctial measured heavenly bodies on the surface of the celestial along the hour circle. Declination resembles sphere. We consider apparent rather than actual latitude and like latitude must be labeled north motion, and thus actual distances are immatertala or south.Declinationisabbreviated "dec." GREENWICH HOUR ANGLE (GHA), The an- CELESTIAL POLES, Points on the surface gle between the celestial meridian of Greenwich, of the celestial sphere which mark the point of England, and the hour circle of a body, measured intersection of the celestial sphere and the earth's westward along the arc of the equinoctial, and axis extended. The north celestial pole is abbre- expressed in degrees from 0 to 360. Also equal viated Pn and the south celestial pole is abbrevi- to the angle at the celestial pole between the ated Ps. Greenwich celestial meridian and the hour circle, measured westward, ELEVATED POLE,The celestial pole which corresponds in name to the observer's latitude. LOCAL HOUR ANGLE (LHA), The angle between the celestial meridian of the observer and EQUINOCTIAL, A great circle on the sur- the hour circle of a body, measured westward face of the celestial sphere everywhere 90 de- along the arc of the equinoctial, and expressed grees from the celestial poles. Sometimes called indegrees from 0 to 360, Also equal to the theCELESTIAL EQUATOR, the equinoctial lies angleat the celestial pole between the local in a plane which is the plane of the equator ex- celestial meridian and the hour circle, measured tended to intersect the celestial sphere and which westward. In west longitude LHA is found by is perpendicular to the axis of the earth (and ofsubtracting the longitude of the observer from the celestial nphere). The equinoctial, like the the GHA, In east longitude LHA is found by adding equator, supplies a reference for north-south the longitude of the observer to the GHA. measurement, ECLIPTIC, The apparent path of the sun among the stars over a period of a year; a great CELESTIAL MERIDIAN.A great circle on circle on the surface of the celestial sphere lying the surface of the celestial sphere which passes in a plane which intersects the plane of the equi- through the celestial poles and over a givenposi- noctial making an angle of approximately 28 1/2 tion on earth. There are an infinite number of degrees. celestial meridians. Each meridian has an upper branch (180 degrees of arc passing over a position ZODIAC, A belt extending 8 degrees to each and terminating at the celestial poles) and a lower side of the ecliptic, The apparent paths of all the branch (remaining 180 degrees of arc). In common planets within our solar system fall within this usage, the term "celestial meridian" refers to belt except for Venus which occasionally appears the upper branch. to travel outside the zodiac, The zodiac was divided into 12 sectors (signs) by the ancients to HOUR CIRCLE. A half of a great circle on correspond to months, each sector being named the surface of the celestial sphere which passes for the constellation which the sun appeared to through a celestial body and terminates at the be passing through or near at that time. Each celestial poles. The hour circle, contrasted to sector or sign extends 30 degrees in arc.

87 A NAVIGATION COMPENDIUM

EQUINOXES. Two great circles one epheri- we may establish an hour circle through itfor Cal surface share two points of intersection. The measurement of sidereal hour angle and right points of intersection of the equinoctial and the ascension. ecliptic are called the vernal equinox (March equinox) and the autumnal equinox. The sun nor- VIDEREAL HOUR ANGLE (SRA). The angle many arrives at the vernal equinox on March 211 between the hour circle of the first point of Aries at that time (the beginning of epring) I the declina- and the hour circle of a body measured westward tion of the sun is 0 and the sun passim from south along the arc of the equinoctial, expressed in to north declination. The sun normally arrives degrees from 0 to 860. The word "sidereal" at the autumnal equinox on September 23; at that normally means "of or pertaining to stars" and time. ( the beginning of autumn), the declination is the SHA for navigational stars is tabulated in the also 0 and the sun passes from north to south Nautical Almanac. SBA, unlike the other hour declination. ang es,oes nor norease with time but remsins relatively constant. The reason for this is that the hour circles between which the measurement SOLSTICES.When the sun reaches its maxi- is made are traveling at practicallythe same mum northern declination;291/2 N) on or about speed, and thus have a relative speed of nearly June 22, we speak of the time as the summer zero. solstice (the beginning of summer). When the sun reaches its maximumsouthern declination RIGHT ASCENSION, Thu angle between the (29 1/2 S) on or about December 22, we speak of hour circle of the first pointof Aries and the hour the time as the winter solstice (the beginning of circle of a body, measured eastward along the aro winter). of the equinoctial, and expressed in either degrees or in hours. Right ascension(in degrees) plus DIURNAL CIRCLESA small circle on the sidereal hour angle equals 360 degrees. surface of the celestial sphere which describes the apparent daily path of a celestial body. The TRANSIT. The passage of a body across a diurnal circle of the sun at the summer solstice meridian. The crossing of the upper branch of projected to the earth is called the Tropic of the celestial meridian is the "upper transit "; the Cancer; located 23 1/2 degrees north of the equa- crossing of the lower branch is the "lower tran- tor, and named for the sign of the zodiac con- sit," taining the sun at that time, it marks the northern limit of the tropics. The diurnal circle of the sun CULMINATION. A synonym of "upper tran- at the winter solstice projected to the earth is sit," called the Tropic of Capricorn; located 291/2 degrees south of the equator, and named for the MERIDIAN ANGLE (t),The angle between sign of the zodiac containing the sun at that time, the celestial meridian of the observer and the hour it marks the southern limit of the tropics. When circle of a body measured eastward or westward the sun is over the Tropic of Cancer (summer along the arc of the equinoctial from the celestial solstice),its rays extend 90 degrees to either meridian, and expressed in degrees from 0 to180. side causing continual daylight (midnight sun) in Meridian angle always carries a suffix "E" or the region north of 66 1/2 degrees North Latitude, "Woo to indicate direction of measurement. When and continual darkness in the region south of LHA is less than 180 degrees, t equals LHA, and 66 1/2 degrees South Latitude. When the sun is is labeled west, When LHA is greater than 180 over the Tropic of Capricorn, theregion north degrees, t equals 860-LHA, and is labeled east. of 66 1/2 degrees North Latitude has continual darkness and the region south of 66 1/2 degrees South Latitude has continual daylight. This is the POLAR DISTANCE. The angular distance of basis for our establishment of the Arctic and a body from the elevated pole measuredalong the Antarctic Circl.s. hour circle. When declination and elevated pole are of the same name (both north orboth south), FIRST POINT OF ARIES.Abbreviated by polar d' stance is the complement of declination (the ram's horns or the Greek letter upsilon), the and may be referred to as co-dec. When elevated first point of Aries is a reference point on the pole and declination are of differentnames (one ecliptic and is another name for the vernal or north and one south), polar distance equals 90 March equinox. Although it is an imaginary point, degrees plus declination.

88 Chapter 10 NAUTICAL ASTRONOMY

1004. TIME DIAGRAM its zenith is called the star's geographic painted. sub..astral, or ground point. The relationship between various reference circles of the celestial sphere which measure angular quantities in an eattwest direction may NADIR. Point on the celestial sphere direct- be beat understood through the construction ofly below the observer. Abbreviated "Na." a time diagram. This is a view of the celestial sphere, in the plane of the equinoctial, as seen CELESTIAL HORIZON, A great circle on from the south celestial pole. Easterly direction the surface of the celestial splier: everywhere Is clockwise and westerly direction is counter- 90 degrees from the zenith, The visual horizon clockwise. A radial line is drawn from Ps in the is the line at which the earth appears to meet center, in any direction, but generally in thethe sky. If a plane is passed through the observer's vertical, to locate the celestial meridian of the position and perpendicular to the zenith-nadir observer. From the celestial meridian, usingaxis we have the sensible horizon. The visual the observer's longitude, the celestial meridian horizon Is corrected to the sensible horizon by of Greenwich is located and plotted. From the application of a correction for height of observer's celestial meridian of Greenwich, using tabulated eye. If a plane Is passed through the center of CHAIN, the hour circles of the sun, the planets, the earth perpendicular to the zenith-nadir axis, the moon, and the first point of Aries may be we have the rational horizon. When projected to plotted. From the hour circle of the first point the celestial sphere, both the sensible and the of Aries, using SHA as tabulated, the hour circle rational horizon meet at the celestial horizon. of the stare may be located and plotted. This This occurs because the planes of the sensible diagram makes possible the derivation of(1) and rational horizons are parallel and parallel LHA, and (2) t, lines meet at infinity (the radius of the celestial Typical time diagrams are illustrated in fig- sphere). ure 10-1. Figure l0-2 illustrates certain additional relationships. From the time diagram we may, derive the VERTICAL CIRCLE. A great circle on the following relationships: surface of the celestial sphere passing through the zenith and nadir and through some celestial LHA GHA W 04 body. Although it is by definition a complete cir- LHA GHA + E cle, in actual usage we speak of the 180 degrees OHM GHAT+SHA. through the body and terminating at the zenith LIIA* LHAT+ SHAG and nadir respectively, as the vertical circle. RA in 960 - SHA In practice we make use of the 90 degree arc SHA = 960 - RA from the zenith to the horizon through the body; t = LHA, if LHA is less than 180 degrees the remaining 90 degrees below the horizon is t 360 - LHA, if LHA is greater than 180 not visible and serves no purpose. degrees, If t = LHA, t is west, PRIME VERTICAL. A vertical circle pass- If t= 360 - LHA, t is east. ing through the east and west points of the horizon. The prime vertical arc above the hori- 1006. HORIZON SYSTEM OF COORDINATES zon terminates at the points of intersection of the equinoctial and the celestial horizon. Location of points on the celestial sphere by declination and hour angle is not always practical ALTI'l TIDE (h),The angular distance of a for an observer, since the equinoctial is an ima- body above the horizon measured along the verti- ginary circle. For the observer, the horizon offers cal circle, a better reference, The horizon system employs the following terms. ZENITH DISTANCE.The angular distance of a body from thezenith measured along the ZENITH. Point on the celestial sphere di- verticalcircle;itis the complement of the rectly above the observer. Abbreviated "Z", A altitude and is abbreviated either "z" or "co- point on the surface of the earth having a star in alt."

89 A NAVIOATION COMPENDIUM

m m A.WEST LONGITUDE B.EAST LONGITUDE LEGEND: M -Upper branch of observer's meridian m -Lower branch of observer's meridian G Upper branch of Greenwich meridian

g -Lower branch of Greenwich meridian o-Hour circle of sun Y-Hour circle of First Point of Aries Hour circle of star

Ps MN South Celestial pole

N Longitude GHA Greenwich hour angle LHA Local hour angle t Meridan angle SHA Sidereal hour angle 190.15 Figure 10-1. Time diagrams. (a.West Longitude, b, East Longitude.) AZIMUTH (Zn).The true direction of aprefixed by N or S to indicate which is the celestial body; the angle between the celestial elevated pole, and suffixed by E or W to indicate meridian and the vertical circle measured right the diret.tion of measurement, If meridian angle or clockwise from north to the vertical circle. is east, the suffix will be "E"; if meridian angle is west, the suffix will be "W." AZIMUTH ANGLE (Z). The angle between We may ereablish certain relationships be- thelocalcelestial meridian and the vertical tween azimuth and azimuth angle (see fig, 10-3) circle; the arc of the horizon measured from as follows: either the north or south points of the horizon (depending upon which pole is elevated) right (a) When azimuth angle is measured north to or left to the vertical circle and expressed in east (north pole elevated, east meridian angle), degrees from 0 to 180. Azimuth angle must be azimuth equals azimuth angle.

90 Chapter 10NAUTICAL ASTRONOMY

distance between the equinoctial and the zenith, measured along the celestial median. POLAR DISTANCE OF THE ZENITH, The angular distance between the senith and the elevated pole measured along thecelestial meridiem the complement of the latitude and usually referred to as "co-lat."

1008. ASTRONOMICAL TRIANGLE Combining the celestial sphere concept and the horizon system of coordinates (fig. 10-4A), we derive a triangle on the surface of the celestial sphere known as the astronomical triangle (fig. 10-413). This triangle projected back to the earth's surface is the navigational triangle; in practice, the term a astronomical and navigational as applied to triangles are synonomous. In the astronomical (or navigational) triangle as illustrated, two sides and the included angle are given (co-lat, t, co-deo) and the opposite side (co -alt) and one angle (Z) are solved for. Actually, latitude of the observer and co-lat are From the time diagram WU may derive tilt:not known exactly, but are assumed, as is longi- following relationships: tude in arriving at "t," The actual altitude is LHA = GHA . W measured, and, by its comparison with the com- LIlAGII;1+Eta puted altitude, the discrepancy in the assumptions GHA* = Gut\ LHA*. 'ur +SIIA* of latitude and longitmde may be determined. Solution of the astronomical triangle may be ItA = 360 - SIIA sHA is 360 . HA accomplished using the cosine-haversine law. However, practical navigators no longer resort t n 1.11A, if LIlA is less than 180 degrees to spherical trigonometry for the solution of t 360 - 1.11A, if 1,11A is greater than 180 the triangle. Instead they make use of such tables degrees as H.O. 214 which actually are tabulations of the If t t. is west results oi solutions of all possible triangles. In If t360 - t is east. preparing these tables, it was customary to break the astronomical triangle into two right spherical 190.16 triangles by dropping a perpendicular from one Figure 10 -2. Time diagram. vertex to the opposite side. For convenience, these tables are so tabulated as to make unnec- (h) When azimuth angle is measured north to essary the computation of complements. west (north pole elevated, west meridian angle), azimuth equals the explement of, or 360 minus, 1007.SPECIAL CELESTIAL RELATIONSHIPS the azimuth angle. The relationships below are worthy of note (c) When azimuth angl.is measured south to east (south pole elevated, east meridian angle), in any studyof the celestial sphere: azimuth equals the supplement of azimuth angle. (a) Abody on the observer's celestial merid- (d) When azimuth angle is measured south to ianhas an azimuthof either 000 or 180 and is west (south pole elevated, west meridian angle),either at itsgreatest or least altitude depending azimuth equals 180 degrees plus azimuth angle. upon whether it istransiting the upper or lower branch of the meridian. LATITUDE OF THE OBSERVER, This value (b) A body on the primevertical has an az- is projected on the celestial sphere as the angular imuthof either090 or 270.

91 A NAVIGATION COMPENDIUM

N N

S S LAT. NORTH LAT. NORTH t EAST t WEST

N N

5 S LAT.. SOUTH LAT.. SOUTH t EAST WEST

190.17 rtgure 10-3.Azinrath angles and azimuth. (a) When a body is on the horizon it is either (f) When the declination is of the same name rising or setting. as the latitude and numerically greater than the (d) When the declination and ixtitude are of co-ht, the body is circumpolar (it never sets). the same name, the lady will. be nbove the horizon more than half the time, anti it will rise and (g) when declinationis 0 degrees, a body set between the prima vertical and the elevatedrises in the east and sets in the west. pole. (h) When the declination is of contrary name (e)If declination and latitude are of the same (as compared to latitude), and gr..-iter than the name and equal, the body will pass through the co-lat, the body never rises. zenith. When in the zenith, it has no azimuth or (i)At the equator, the celestial poles coin- azimuth angle. cide with the celestial horizon. There are no

92 Chapter 10-.' NAUTICAL ASTRONOMY 1111.111=111111111111111111111MINP' N1111111111111111011111

Tho parte Of the 'discoid fitire area A C COMMenter of Went- trial 6 celestial sphere.. Observer's!with,easi, south west plats respectively ea the bottles. NEIMAN Observer's horisos, PsPs North 6 South celestial poles(also poles of the eart).h Z ft Na IfeetthNadir, 0;1614' Points of latersection of equinoctial with upper and lower branches of the observer's meridian, NPoZQIIPstiaQ'Celestial meridian of the observer, EQ?DWQ Equinoctial, Vernal equinox or first point of Arise. ZQ Latitude of the observer, 0 Terrestrial point of the ob- lierVer. PoMDP5 Hour circle of celestial bof,Itial Celesdy body. ZMA Vertical circle of body M. O ()mod point. DM Declination of star M. eD INA of star M. orQEQIWD RA of star M. QD LHA of starM. rte NA Azimuth angle of star M. NE8WA Azimuth of star M. AM Altitude of star M. Meridian angle. a A aimuth angle measured at senith. PnM Co-deo or polar distance. MZ Co-alt or zenith distance. PoZ Co-lat or polar distance of the zenith. PoZM Astronomical t riangie. POO Navigational triangle.

6946 Figure 10-4. The celestial sphere. B, Astronomical triangle. circumpolar stars nor stars that never rise. those with a declination of the same name as Stars rise and set in planes wh4ch are perpen- latitude, and all these are circumpolar. Altitude dicular to the plane of the horizon. then equals declination, and azimuth is insigni- ficant since all directions at the north pole are (j)At the poles, the equinoctial coincides with south and at the south pole all directions are the celestial horizon, the only bodies visible are north.

93 CHAPTER 11 TIME

1101. INTRODUCTION because as we have seen, of its relationship to longitude, With the nautical astronomy background gained Two general types of time measurement are through the study of Chapter 10 as a prerequisite, solar time and sidereal time. Solar time is based the practice of celestial navigation may now beupon the rotation of the earth with respect to the approached, commencing with a brief study ofsun while sidereal time is based upon the rota- time and timepieces. tion ofthe earth with respect to the stars. During the Newtonian era, great adl nces in mathematics and in the physical sciences made 110S. SOLAR TIME available (a) a great deal of information cow:ern- ing the positions of stars and planets; (b) greater We will at first restrict our discussion to solar knowledge of gravitation; and (0) more information time, commencing with a type called apparent time in general concerning the celestial bodies beyondwhich is time measured upon the basis of the ap- our solar system. The Post-Newtonian era was parent motion of the real sun. By apparent time, characterised by the practical application of thewhen the sun transits the upper branch of the new knowledge of astronomy. local celestial meridian, the time is spoken of as local apparent rmon (LAN) or 1200 apparent time. An early problem was that of determiningWhen the sun transits the lower branch of the longitude at sea. As we shall see in Chapter 13, local celestial meridian, the time may be spoken latitude can be readily determined by a meridian of as local apparent midnight or 2400 (also 0000). sight without knowledge of exact time or resort to spherical trigonometry. However, longitude Unfortunately, the length of the apparent day var- can not be so easily obtained. Accordingly, in ies. This results because of two reasons: 1714, British sea captains petitioned the House (a) The ellipticity of the earth's orbit. The of Commons for a solution to the problem ofearth when relatively near the sun rotates once determining longitude. By 1726, John Harrisonwith respect to the sun in less time than when had produced a marine chronometer which ad- relatively far from the sun. This occurs because vanced considerably the practice of navigation, the earth is moving in its orbit while rotating. making it possible to more accurately compute (b) The sun's apparent movement with respect longitude. to the earth is faster at the solstices, when the sun is moving almost parallel to the equinoctial, 1102. TIME MEASUREMENT than at the equinoxes when the direction of the With this brief historical intl,duction, timesun's apparent motion hail a larger north-south riay now be defined as the sum of ull the days in component. the past, today, and all the days of the future. Since apparent days are unequal in length it However, we think of time, as a quantity which is impractical for man-made timepieces to keep can be measured. Time may be expressed as a apparent time, and as an expedient we have av- measured duration, such as throe hours, and alsoaraged the length of the 365 1/4 apparent daysi as "clock time," for example, 0200. The instru- (1solar year) and arrived at a measurement ment for making this measurement is a time- known as mean time. One mean day is 24 hours piece. The earth is our celestial timepiece. Each in length, each hour consisting of 60 minutes turn upon its axis provides a unit of time known and each minute consisting of 60 seconds. We can as the day. Time is important to the navigator say that mean time is based upon the motion of

94 Uhapter 11 --TINV an imaginary sun moving westward in the equi-OMT, For example, longitude 175 West is in ti noctial at a uniform speed. At the instant thetime suns known by the ?One description + 12 imaginary sun transits the upper branch of the(175/15). If the zone time is1109-22(conventional local celestial meridian, we witness local meanmeans of expressing hours, minutes, and se noon (1200 local mean time), and at the instantcondi), then GMT is 1109-22 plus 12 -00-00 or the imaginary sun transits the lower branch of23-04-22. If our longitude is 36 East, our ZD the local celestial meridian, we observe localmust be and if ZT is 08- 16 -32, GMT must mean midnight (2400 or 0000 local mean time).be 084642 minus 02-00-00 or 06-16-32. Since The difference between mean time and apparentwe can find GMT by applying the ZD according time is the "equation of time," a value which isto sign to the ZT, conversely, we can find ZT tabulated in the Nautical Almanac, by applying the ZD with the sign reversed to GMT. Mean time changes with longitude, and since there are an infinite number of local celestial The 110th meridian is the central meridian meridians the keeping o; mean time is a system of time zone 12 which is common to both hemi- lacking in uniformity. To keep a timepiece setspheres. However the half in the eastern hemi to mean time, we would have to reset it withsphere has a ZD of -12, and the MAO in the each change in position. Since this woulei oe just western hemisphere has a ZD of +12, For this as impractical as using apparent time, we have reason, and since the Greenwich time zone is established standard or zone Jrne, (fig. /1-1) known as 0, we have 24 time zones but 25 zone abbreviated ZT, which provides that a tone 15 descriptions, degrees wide in longitude may keep the same time throughout the zone, THE ZONE TIME OF ANY ZONE IS THE MEAN TIME OF THE CEN- Sometimes, in order to make the beet use of TRAL MERIDIAN. The geographic extent of the daylight hours, all clocks are advanced 1 hour; time zone is 7 1/2 degrees to either side of the this system of keeping time is call daylight sav- central meridian. The local mean time for aing time, In time of war, clocks may be advanced meridian nifty be converted to zone time, This 1 hour and the time referred to as war time. When is accomplished by (1) converting the difference either daylight saving or war time is being kept, in longitude (between locs1 and standard merid- in effect, the zone is '.gaping the standard time ians) from arc to time, and (2) adding suchof the adjacent zone to eastward, and instead of correction to the local mean time if the local observing the sun on the meridian between U30 meridian is to the west and subtracting it if to and 1230, upper transit of the central meridian the east, See articies 1303 and 1305 for examples will occur normally between1230 and 1330. of conversion of local mean time to zone time. Conversely, zone time may be converted to local mean time, The origin of time zones is the The time zone system has been generally meridianof Greenwich whichis the centraladopted except in Saudi Arabia, in the polar meridian of time zone "0," Time zone 0 keeps regions,and in a few remote islands,Saudi standardorzonetime which is exactly the Arabiakeeps"Arabictime" by whichall same as the mean time of Greenwich, abbre-timepieces aresetto midnightat sundown. viated GMT, In all time zones, except 0 zone, Through island groups and over land, the time the longitude of the central meridian is divisible zone boundaries may be somewhat irregular, For by 15. E &oh time zone is assigned a zone descrip- example, the eastern time zone in the U.S, (ZD tion (ZD). The zone description consists of a + 5)is separated from the oentral time zone number from 0 to 12 commencing with 0 at Green- (ZD +6)in thenorth by the west shore of wich and counting both to the east and to the west. Lake Michigan and in the extreme south by Time zones in the eastern hemisphere are dis- the Appalachicola River of Florida. Ordinarily at tinguished from the time zones in the westernsea, as a ship proceeds from one time zone to hemisphere by a prefix; eastern time zones are anothel, ship's clocks are reset. When traveling prefixed by a minus sign while western time in company with other vessels, the officer in zones are prefixed by a plus sign. The zone tactical command may be expected to initiate the description indicates the hours difference between signal, When steaming independently, the zone the zone time of a zone and GMT; applying the ZD time is changed at the discretion of the command- in accordance with sign to the LT we arrive at ing officer. When traveling eastward, zone time

95 A NAVIGATION COMPSNDIUM BEST COPY AVAILABLE

AFRICA

TIME ZONE CHART AU,ITRALAA Zone Time (VI') is LMT Por meridian of center of Zone To find GMT Apply Zone Description to ZT

ennui tilmiltura Ce*Iii4fa riui

19.76(69) Figure 11-1. Standard time zones. is changed by advancing the clocks 1 hour. When we retard the calendar 1 day (for example, traveling westward, the clocks are retarded 1 2 Jan. to 1 Jan.). hour upon entering a new time zone. In a time diagram if the hour circle of a celestial body plots between the lower branches When the sun transits the celestial meridianof the local celestial meridian and the Greenwich of Greenwich,thedate throughout the worldcelestial meridian, the local date differs from the is the same. At every other instant, thereareGreenwich date. If the local meridian is in west two dates in the world simultaneously. The newlongitude the Greenwich date is 1 day later than local date at a given location on the earth be-the local date; if the local meridian is in east gins with the sun,s transit of the lower bre.nchlongitude, the local date is one day later than the of the celestial meridian, the new GreenwichGreenwich date. When ZD is applied to ZT to date begins with the sun's transit of the 180thobtain GMT, if the GMT is over 24 hours, then meridian (which with occasional deviations for24 hours must be subtracted; the remainder is the benefit of island groups is the internationalthe GMT and the Greenv.ich date is 1 day later date line). Within the 12th time zone all timethan the local date. If, when ZD is applied to is the same but the date in the ,,extern hemi-ZT to obtain GMT, the result is anticipated to sphere section is always 1 day earlier than inbe a minus value because of the necessity of the eastern hemisphere section. When travelingsubtracting ZD, the navigator adds 24 hours to from thewestern hemisphere to the Pastern the ZT before subtracting the ZD and notes that we advance the calendar 1 day (for examlle,the Greenwich date is a day earlier than the 2 Jan. to3Jan.); when traveling from thelocal 'late. I is necessary to know the Green- eastern hemisphere to the western hemisphere wich mean time and Greenwich date bet:.ause upon

96 MOW 11..411111 111111111MMIMISIIIMIII, it all Ululatedsetronomicaldstausedby thenavibasis for the conversionof aro to time and time gator is based. to aro. The conversion isas follows:

EXAMPLE 1: Convert ZT 080015 Deo. in ZD + 4 nal to GMT. 24 hrs. 360'

1 hr. 16' 0800 15 Deo. SOLUTION: ZT 60 min. 16' +4 ZD 4 min. a 1' 014T 1200 15 Dec. 4 min. 60' 1 min. 15' longi- EXAMPLE 2: Convert ZT 1600 28 Deo. in 15' tude 81% to GMT. 60 see, 4 see. 1' a 60" SOLUTION: ZD 81/15 -5 4 see. 15" ZT 1500 28 Dec. 1 see. ZD -5 EXAMPLE 1: Convert344° 16'33"to time. GMT 1000 28 Dec. 344° 22 hrs. 56 min. 16' 1 min.4 secs EXAMPLE 3; Convert ZT 0500 12 Jan.inlongi- 33" 2.2 see. tudo 167° 30'E to GMT. Answer: 22 hrs. 57 min. 6.2 sec.

SOLUTION: ZD 167 - 30/15 -11 EXAMPLE 2: Convert 18 hrs. 37 min. 20 sec. ZT 0500 12 or2900 11 Jan. to aro. ZD -11 18 hrs. a 2706 GMT 1800 11 Jan. 37 min. - 9°15' 20 sec. 5' EXAMPLE 4: Convert 0600 14 Feb. GMT to ZT in longitude120°W. Answer; 279°20'

SOLUTION: An easier method of conversion is offered by a conversion tablein the back of the Nautical ZD 120/15 +8 Almanac. (See AppendixF-3) GMT 0600 14 Feb. or 3000 13 Feb. ZD +8 (with sign reversed) -8 2T 2200 13 Feb. 1105. SIDEREAL TIME

1104. TIME AND ARC Sidereal time, or star time, is based upon the earth's rotation with respect to the stars. Sidereal and solar time differ in the four following ways: Since the equinoctial is a circle containing (a) Reference, The sun is the reference point 360 degrees, and since there are 24 hours in afor solar time; the first point of Aries is the day, we may use these figures toestablish areference point for sidereal time.

97 A NAVIGATION COMP UM

210L2IMXPIRC HS

Timepieces, as previously introduced in arts 309, consist of chronometers, comparing watches,' ship's clocks, and stop watches.

The chronometer (fig. Ilul) is the navigator's most MUSA timepiece. There are two files. The larger, referred to as sift BC is a regular ship's chronometer, made by the Hamilton Watch Comm. The smaller, ails 35, is a high -grads witch, and is often referred to as a chronometer watch. It is usually stowed so as to be protected against shock, electrical influence, and extreme changes in temperature. Most vessels carry 3 chronometers for comparison purposes thus making it possible for the quartermaster to readily detect the error in any instrument which may develop an erratic rate. The chronometer is set to GMT and never reset until returned to a chronometer pool (source of chronometers used in Navy ships) for cleaning and adjustment which is necessary every 9 to 3 years. The chronometer is wound daily at 1130; this (and the fact that a comparison was made) is reported at 1155 to the commanding officer as part of the 12 o'clock report. Chapter 9240, Section I, Part 69.38 3, of the Naval Ships Technical Manual and the Figure 11-2. chronometer record book contain detailed in- Ships chronometer in its case. struction for chronometer care. (b) Commencs.nent of Day. A solar day commences when the sun transits the lower branch Time signals, for checking the current ac- of the local celestial meridian (midnight); a si-curacy of chronometers, may be received from dereal day commences when the first point of Radio StLions WWV and WWVH, of the National Aries transits the upper branch of the local Bureau of Standards, Department of Commerce, celestial meridian (sidereal noon). transmitting from Colorado and Hawaii respectively, and from Naval Radio Station, NSS, Anna- polis, Maryland. Upon releiving a radio time (0) Date. There is no sidereal date. signal, the quartermaster checks the chronometer and establishes the chronometer error, labeling it fast or slow as appropriate. The average daily (d) Length of Day. A sidereal day is 3 min- difference in error, called the daily rate and utes and 66 seconds shorter than a solar daylabeled "gaining" or "losing," is also computed which provides for 386 1/4 sidereal days in aand recorded. With the chronometer error for solar year (365 1/4 solar days). The reason fora given date to the past, and the daily rate, we a sidereal day being shorter is the fact thatcan predict the oltronometer error for either while the earth rotates with respect to the sun the present or a future date. it also travels in its orbit. When the earth has rotated once with respect to the stars, its travel Quartz oscillator clocks are coming into use in its orbit has necessitated that it turn almost as marine chronometers. Currently, military an additional degree in order to have rotated specifications for such timepieces are beingpre. once with respect to the sun. pared. These clocks, which are electrically

98 Chapter Il 11MB

(usually battery) powered, are known to be ex corded. At a given instant, upon completion of oeptionally accurate. They are also quits ryacelestial observations, a comparison may be Mutant to shook and vibration and do not require made with the chronometer and the chronometer gimbal mounting. time of observation (or observations) computed. By applying the current chronometer error to The comparing watch is a high grade pocketthe chronometer time we arrive at correct GMT. watch carried by the navigator or quartermasterThe only advantago of a stop watch is that the when making celestial observations. It may be set second hand reading is easier to make. Whenever exactly on ObiT since by extenditi the stem the reading time for an observation, the hands should second hand may be stopped; to set the watchbe main the order of their speedsecond hand, on GMT the quartermaster mustmentally con- minute hand, hour hand. sider current chronometer error. Some navi- Marine clocks, designated according to usage gators prefer setting the comparing watch toas boat, deck, or general purposeclocks, are sone time which necessitates theapplication of normally of the eight day mechanical type. Some ZD in order to find GMT. If the quartermastergeneral purpose clocks have 24 hour dials; all is unsuccessful in setting the watch exactly toothers have 12 hour dials. Marine clocks are sone time or GMT, he should ascertainthe watch manufactured by the Chelsea Clock Company, and error (WE on ZT or WE on GMT). Such correc-by Seth Thomas Cloaks, Division of General tion must be applied to the watch time of eachTime Corporation. Clocks are normally wound observation. weekly, and reset as necessary when wound. A stop watch may be started upon makingAfter winding and setting, the beael or case celestial observation; then upon subsequentmust be closed to prevent dust from entering observations the seconds elapsed may be re.the Me.

99 CHAPTER 12 SIGHT REDUCTION

1201. INTRODUCTION established, a line of position is drawn,at right angles to the azimuth line. This celestialline In the advanoement of the practice of celestial of position, althougha straight line, is repre- navigation, perhaps the milestone next following sentative of a short arc, taken froma circle the appearance of Harrison'schronometer was the of equal altitude drawn aboutthe geographical discovery in 1837 by an American ship-position (GP) of the observed body.See figures master, Captain Thomas A. Sumner, ofa solu- 12-1 and 12-2. Mathematically,a Sumner's line tion for a celestial line of poition. From the is actually a chord of sucha circle; the Maroq de observation of an altitude of thesun, he made St. Hilaire line is a tangent. three computations for longitude usinga different latitude in each, because of uncertaintyas to The altitude intercept methodas introduced his latitude. After a plot of three positionsfrom by Commander St. Hilairewas widely adopted. these computations, he noted that the threecould For solution of the astronomicalor navigational be connected by a straight line, whichhe cor-triangle for computed altitude andazimuth, the rectly assumed to be a locusor line of position. use of a cosine-haversine formulawas adopted, Subsequently, a landfall gave further evidence of a haversine of an angle being equal toone half thecorrectnessofhisassumption.Since the quantity of one minus the cosineof such Sumner's discovery, solution for anduse of such angle. Thus, the solution of the triangle, while a lineof position, has been the essence of somewhat easier, still required resort to spheri- celestial navigation. cal trigonometry. However, thesolution was further simplified by Ogura of Japan,among Unfortunately, to obtain a "Sumner's line," others, and in the 1930's severalnew methods multiple computations are required. However,in were introduced, making use of tables of solu- 1875, the computation was simplified bya pro-tions for spherical triangles of variousdimen- cedure introduced by Commander Maroq deSt. sions. Hilaire, French Navy. By the St. Hilaireor "Altitude Intercept" method, thealtitude and azimuth of a celestial body are computed foran approximate or assumed position of the shipat CIRCLES OF ALTITUDE EQUAL a given time of observation. By comparison of the observed altitude and the computed altitude, the difference, knowh as "intercept,"is determined in minutes of arc. A line is drawnthrough RADIUS the assumed position from which the computed GP altitude was obtained, in the direction of the a 0((CO-ALTITUDE) azimuth. U the observed altitude is greater than the computed, the observer isnearer the body, OBSERVED ALTITUDE a COMPUTED and conversely,ifthe computed altitudeis BASED ON APPROXIMATE POSITION greater than the observed, theobserver is farther away; accordingly, the intercept inminutes OBSERVED ALTITUDE 4 COMPUTED of arc is directly converted to nauticalmiles and is measured from the assumed positionalong 190.18 the azimuth line, toward oraway from the celes- Figure 12-1. Relationship of circles of equal tialbody,as appropriate. At the point thus altitude and intercept "a."

100 Chapter 12SIGHT REDUCTION

ALTITUDE INTERCEPT "A" IS ALTITUDE INTERCEPT "A" IS "TOWARD", AS ALTITUDE OBSERVED "AWAY", AS ALTITUDE OBSERVED IS GREATER THAN COMPUTED, IS LESS THAN COMPUTED. 190.19 Figure 12 -2.-- Plot of LOP.

In this chapter, sight reduction by later and The marine sextant consists of the following more modern methods will be described, together parts; with the plotting of celestial lines of position and celestial fixes. Preliminary to actual sight A. FrameSupport for other parts. reduction, the marine sextant and its use, cor- B. LimbAn arc (approximately 1/6 of a rectionstosextant altitudes, the use of the circle) graduated in degrees. Nautical Almanac for finding Greenwich hour C. Index armArm pivoting from center of angle and declination, and the computation ofcurvature; lower end indicates reading on limb meridian angle from Greenwich hour angle, willand mounts the micrometer drum, be considered. D. MicrometerProvides a scale for reading minutes and tenths of minutes. 1202. MARINE SEXTANT E. Index mirror Mirror on upper end of index arm which is perpendicular to the plane Previously introduced in Art. 308, the sextant of the limb. (figure12-3)isused to measure altitudes of F. Horizon glassA glass window, the left celestial bodies above the visual horizon. Meas- half of which is clear glass and the right half urement is effected by bringing into coincidence a mirror, mounted on frame and parallel to the the images, one direct and one reflected, of the index mirror at an instrument setting of 0 de- visual horizon and the celestial body. The sextantgrees. was so named because its arc represents approx- G. TelescopeInserted in collar attached to imatelyone-sixthofacircle. Nevertheless, because of its optical principle of double re- frame to magnify field of vision. flection as briefly described herein, the sextant H. Index and horizon filters (in some instru- can usually measure twice as much arc, or ments, shades). something greater than a third of a circle. Its optical principle was first described by Sir Isaac The optical principle upon which the sextant Newton and later independently rediscovered in is based is that the angle between the first and 1731byHadleyinEngland and Godfrey in last direction of a ray of light that has undergone Philadelphia. two reflections in the same plane is twice the

101 A NAVIGATION COMPENDIUM

-111r1411$/-

d taw

I D

29.268(190) Figure 12-3. Marine sextant. angle that the two reflecting surfaces make with In observing stars, if difficulty is experienced each other. in bringing stars to the horizon, the instrument To make a reading with the sextant, set themay be inverted and the index arm moved to index arm to 0 degre3s, Look through the mirror bring the horizon up to the celestial body without half of the horizon glass at the celestial bodyany tilt of the instrument or movement of the which also appears in the clear glass half. Move field of vision. the index arm fov.. rd slowly, at the same time When the horizon is "fuzzy," or indefinite directly beneath celestial body, the navigator tilting the instrument forward, until the reflectedmay face the reciprocal of its azimuth and use image is in coincidence with the horizon. Finethe sextant to measure the supplement of the adjustment may then be made using the microm- altitude. When this is done in the case of the eter drum on the index arm. Read altitude insun or the moon, if a lower limb observation degrees on the limb, read minutes on the forwardis desired the navigator makes what appears movable part of the drum at the 0 mark, and read to him to be an upper limb observation, other- tenths of a minute on the micrometer scale wise he must add the sun's (or moon's diameter (which makes a 10:9 ratio with the minutes scale). to the sextant reading. In observing a star or a planet, bring the Before or after observing altitudes with the center of the star or planet into coincidence sextant, the navigator determines index correc- with the horizon. In the case of the sun, normallytion, a current error in his instrument. To do the lower limb (lower edge) is brought into coin- this, he sets the instrument on absolute zero and cidence; however, if the upper limb is morelooks through the horizon glass at a distant clearly defined, an upper limb shot may be taken horizon. If the horizon forms an unbroken line if so identified. Moon observations, like sun ob- in both halves of the horizon glass, the index servations, may be of either limb. correction (abbreviated IC) is 0. If the line is

102 Chapter 12SIGHT REDUCTION broken, he should move the micrometer drum INDEX CORRECTION (IC). A correction until it is straight and read the discrepancy be-peculiar to an individual instrument and change tween absolute 0 and the corrected reading, Uable in value. May be a plus or minus correc- the corrected drum setting moves the index armtion, to the right of 0 on the limb, the IC is additive. If the corrected drum setting moves the index DIP (D).The horizon from which measure- arm to the left of 0 on the limb, the IC is sub-ment is referenced depends upon the altitude tractive, (height above sea level .1 the observer); at U a sextant is in complete adjustment thehigher altitudes the horizon is at a greater dis- following will be true; tance and sextant altitude will read in excess of altitude based upon the true celestial horizon. (a) The index mirror will be perpendicular Dip is always a minus correction and increases to the plane of the limb. with the height from which the observation is (b) The horizon glass will be perpendicular made. to the plane of the limb. REFRACTION (R). When the rays of light (c) The horizon glass will be parallel to thepass from a less dense medium (space) to a index mirror at absolute zero. more dense medium (earth's atmosphere), they are bent toward the vertical, resulting in the (d) The line of sight of the telescope (if used) celestial body appearing higher than its actual will be parallel to the plane of the limb. position. Refraction error is maximum at low The index mirror is perpendicular to the plane altitudes, making observations of bodies having of the instrument if the limb and its reflectionaltitudes less than 10 degrees less reliable; the appears in the index glass as an unbroken line.error decreases at higher altitudes, and is zero The horizon glass is perpendicular to the planeat an altitude of 90°. The correction for refrac- of the instrument if when tilted and set to 0, the tion is always a minus correction. horizon appears as an unbroken line in both halves of the glass. The horizon glass and the AIR TEMPERATURE ATMOSPHERIC index mirror are parallelif at a 0 setting PRESSURE (TB). An additional correction for (unlined), the horizon appears as an unbrokenrefraction due to nonstandard atmospheric con- line in both halves. To adjust, two setscrews are ditions. May be a positive or negative correction, associated with each mirror. Always slack off PARALLAX (P). The center of the earth is on one set screw before tightening its mate. In considered to be the center of the celestial sphere. addition to the mirrors, the collar of the tele- For all bodies beyond our solar system, the dis- scope should be adjusted if the extended line of tance is so great as compared to the radius sight (axis of the telescope) diverges from the of the earth that the latter is of no consequence. In extended plane of the instrument. the case of bodies within our solar system, their Sextants are equipped with colored filters or distance is not so great when compared to the shades for sun observations; these lenses pro-earth's radius and we must take into account the tect the navigator's eyes from the bright raysearth's radius to reduce the sight to the altitude of the sun. as measured from thecenter of the earth. Parallax at altitude 0° is called horizontal paral- An excellent marine sextant used today islax (HP). Parallax is always a plus correction, known generally as the endless tangent screw and is maximum at altitude 0°. sextant. S ElVIIDIA M ET E R (SD), Tabulated A stronom- 1203. CORRECTING SEXTANT ALTITUDES ical data is normally based upon the center of celestial bodies. However, it is not practicable The altitude of a celestial body as observedto measure the altitude to the center of either by a navigator does not necessarily correspondthe sun or the moon as their diameters are tothealtitude measured from the celestialwider and their centers do not afford a definite horizon. To differentiate, we abbreviate sextant reference for measurement. Accordingly, all altitudeas Hs and observed altitude as Ho.measurements are made to either the upper Sextant altitude (Hs) is corrected or convertedlimb (upper edge) or lower limb (lower edge), to Ho by applying corrections for the following: abbreviated UL and LL respectively, and the

103 A NAVIGATION COMPENDIUM semidiameter is subtracted or added as appro-centers of the planate Venus and Mars. It may priate. Also, tables may be compiled so thatbe positive cr negative:. semidiameterisalways a plus correction. These corrections may be summarised as Whether the upper limb or the lower limb of the shown in Table 12-1, the Otters "NA" signify sun or moon is used depends upon which limbing "Nautical Almanac," Curroctions (1) and (2) is most clearly defined. for instrument error and height of eye (dip) are applied to the sextant altitude (Hs) to deter- AUGMENTATION (A),An increase in themine the apparent altitude (lia), which in turn semidiameter of the moon which increases withis used as the argument for entry in the ether altitude. Correction has the same sign as the tables by which corrections (3) and (4) are com- semidiameter, puted. However, for simplification of computations, Ha is generally computed mentally and IRRADIATION (J). Correction for the ex-all corrections are totaled and applied to He to pansion of the upper limb of the sun and the con- find Ho. traction of the horizon because of optical illusion. Always a negative correction. Note 1: In tables A-2 and A-3 for the sun, separate PHASE (F).A correction for compensation corrections are given for "Oct, - Mar." and for the difference between the apparent and actual "Apr. - Sept." Table 12-1.=- Corrections to sextant altitudes Correction ApplieP to Found Corrects + or Notes (1) Index All sights Sextant IC Either (2) Height of All sights NA, Table D Minus eye A-2 and inside of back cover

(3) Altitude Stars & NA, Tables R Minus Planets A-2, A-3

Sun NA, Tables R, P +(LL) See Note 1 A-2, A-3 & S.D. -(UL)

Moon NA, Inside R, P Plus See Note 2 back cover A & S.D. (Standard values)

(4) Additional All sights NA, Table TB Either A-4

Venus & NA, Table P, F Plus See Note 3 Mars A-2

Moon NA, Inside P Plus See Note 2 back cover

190.21

104 Chapter 19-111011T REDUCTION

Note 2: EXAMPLE 2: Given: Hs of Venus is 17 -10.5' on 2 Jan, The altitude and additional corrections for the 1970, Twilight observation. Height moon are to be added regardless of which of eye is 37 feet, IC is -Ur. Temp. limb is observed, but 30' must be subtracted 62*F, Bar, pressure 30.00 in, from the apparent altitude in an upper limb Required: Ho. observation. Horizontal parallax (HP) is taken Solution: from the daily page of the NA for use as Corrections Plus Minus argument for entry in the table for the addi- IC tional alt. corr. H E 5.9 Alt. 3.1 Add. 0,2* Note 3: Sum +6,2 -10,0

The correction in table A-2 for Venub applies -9.8 only when the sun is below the horizon, (For Ha 17-10.5 daylight observation of Venus, parallax ami Ho I Mo.= phase are computed directly using the formula *0,1 From Table A-2, p cos H - k cos 0, where H is the altitude, 0,1 From Table A-4. 0 istheangle of the planet between the EXAMPLE 3: o vertical and the sun, and p and k are f Given; Hs of the moon's lower limb is tions for parallax and phase related to da = s 26-19,5' at 1200 GMT on 3 Jan 1970. and recorded in the explanation pages in Height of eye is 49 feet. IC is plus back oftheNautical Almanac.In actu 2,0'. Barometric pressure and temp- practice,theadditional computationor erature normal. daylight observation of Venus can be omitted. Required: Ho, Solution: Corrections Plus Minus EXAMPLE 1: IC 2.0 HE 6,8 Given: Hs of the sun (lower limb) is 69-18,7' Alt. 60,4 on 1 Jan 1970, Height of eye is 64 Add, 5,6* feet. IC is plus 1.5'. Standard at- Sum +68.0 -6,8 mospheric conditions. -6,8 1.2 Required: Ho. He Ho 27 -20.7 Solution: *LP, From Daily Page is 58.2 Note: Had this been an observation of the upper Corrections Plus Minus limb, an additional -30' correction would have been applied. IC 1.5 EXAMPLE 4; HE 7.8 Alt. 15.8 Given; He of Capella is 54-10.5'. Height Sum +17.3 -7.8 of eye is 30 feet, IC is 0.0. -7.8 Required: Ho. +9,5 Solution: Corrections Plus Minus Hs 69-18.7' Ho 69-28.2 HE 5.3 Alt. 0,7 Note: There is no additional correction for the sun from Table A-4 because the altitude He 54-10,5' exceeded 50°. Ho 54-04.5'

105 A NAVIGATION COMPENDIUM

1204, FINDING GREENWICH HOUR ANGLE isfound in the yellow pages of the Nautical AND MERIDIAN ANGLE Almanac, entering with minutes elapse-Mr-6m beginning of hour, and the code. The code cor The Nautical Almanac tabulates: notion is always plus for GHA except in the case of the inferior planet Venus, which has an a. For each hour of GMT, the GHA of the orbit inside the earth's orbit, Its apparent motion first point of Aries, navigational planets, sun,westward, as compared with the sun's motion, and moon, shows that Venus has a numerically lesser, relative speed; when its correction should be b. The SHA's by dates for all navigationalsubtracted, the code letter "v" will be prefixed stars. by a minus sign. The purpose of the code cor- 0. Additional increments of GHA for minutes rection is to simplify interpolation and to keep and seconds elapsed after the hour, tabulated values at a minimum, For the planets, the code correction makes possible the use of The first step in finding meridian angle "t"the GHA value for minutes and seconds as is the computation of GHA which is accomplished tabulated for the sun. as follows: STARS, Determine the SHA from the daily SUN, Using GMT, and Greenwich date of page, entering with the star name and Greenwich observation, enter Nautical Almanac and recorddate. Find the GHA of 7,in the same manner as tabulated hourly valueof GHA, Turn to theused to find the GHA of the sun (except that in yellow pages of the Nautical Almanac, and enter- the yellow pages a separate column is provided ing with the minutes and seconds after the hour,for it )Adding the GHA of T and the SHA of find the increase in the sun's GHA since the the star we find the GHA of the star. last tabulated (hourly) value. Add the tabulated A code correction is never used in connection value and the increase for elapsed minutes andwith the sun's GHA, the GHA of or the SHA seconds, of a star. To convert GHA to LHA, and LHA to meridian angle(t), the following relationships, MOON AND PLANETS. Proceed as with tho as developed in art. 1004, are used: sun, but record a code value identified as "v" together with sign which appears at the foot of LHA = GHA Vat the GHA sub-column for planets, and to the rightLHA = GHA + EX of each tabulated GHA for the moon, Find the GHA* = GHAT + SHA* sum of the hourly value and the minute-secondLHA > 180, t = 360 - LHA, andtis east. increment, as in the case of the sun, but usingLHA < 180, t = LHA, and t is west. column headed "moon" or "sun-planets" as appropriate, then apply a code correction accord- The following examples illustrate the complete ing to the sign of the code. This code correctionproblem of finding GHA and "t": EXAMPLE 1: Given: 1 Jan. 1970, ZT 11-18-45, Long. 71-30 W. Required: GHA and t of sun. Solution: ZT 11-18-451 Jan. ZD +5 (71-30/15) GMT 16-18-451 Jan. GHA (16 hrs,) 59 -06.0 Min-sec (18-45) 4-41.3 GHA of sun fig11-137 or423-47.3 Long. -71-30.0 W. LHA 352-17,3 t = 360 - LHA or 7-42.7 E.

106 Chapter 12--EIGHT REDUCTION

EXAMPLE 2: Given: 2 Jan. 1970, 'ZT 09- 19 -55, Long. 169-15 E. Required: GRA and t of moon. Solution: ZT 09 -19 -552 Jan. ZD -11 (169-15/15) GMT 22-1§.551 Jan. GHA (22 hrs.) 231-39.4 (13.8) Min-sec (19-55) 4-45,1 Code Corr. 4.5 GHA of Moon 2$6-29,0 Long. +169-15.0 E. 405-44.0 -360-00.0 LHA 45-44.0 t = LHA or 45-44.0 W. EXAMPLE 3: Given: 2 Jan, 1970, ZT18-20-00, Long, 110-10 W. Required: GHA and t of Venus. Solution: .ZT 18-20-002 Jan, ZD +7 (104-10/15) GMT 01-20-003 Jan. GHA(01 hr.) 199 -34.6 (1.0) Min-sec (20 min) 5 -00.0 Code Corr. 0.3 GHA of Venus 204-34,3 Long. 110 -10.0 W. LHA 94-24,3 t = LHA or 94-24.3 W.

EXAMPLE4; Given; 3 Jan, 1970, ZT 06-00-00, Long. 92-00 E. Required; GHA and t of Vega. Solution; Using star name, enter SHA table on daily page; SHA is 81 -01.6. Find GHA of Aries.

ZT 06-00-003 Jan. ZD -6 (92-00/15). GMT 00-00-003 Jan. GHAT (00 hrs.) 102-12.1 SHA of Vega 81 -01.6 GHA of Vega 183-13,7 Long. +92-00,0 E. LHA 275-13.7 t = 360 - LHA or 84-46,3 E.

107 A NAVIGATION COMPENDIUM

In the actual practice of sight reduction, an EXAMPLE 2: "assumed longitude"is used in lieu of the "actual longitude." This procedure simplifies Given; GMT 18-19-251 Jan. 1970. subsequentcomputationasitpermits the Required: Declination of the moon. assumption of a longitude which, when combined Solution:Declination (18 hrs.) S 1041,3 (14,3) with the GHA, results in a local hour angle, Code Correction +4.6 and a meridian angle, in even degrees. For Declination 10-45.9 South example, in west longitude, the longitude assumed EXAMPLE 3: should include precisely the same number of minutes (and tenths of minutes) as the GHA; Given: GMT 05-18-263 Jan. 1970. upon subtracting the assumed longitude the re- Required: Declination of Saturn. maining local hour angle will result accordingly Solution:Declination (5 hrs.) N 9 -49.8 (0.0) in even degrees. In east longitude, the longitude Declination 9 -49.8 North assumed should include the number of minutes EXAMPLE 4: (and tenths) which when added to the GHA will also result in a local hour angle, and "t," in Given: 2 Jan. 1970. even degrees. In using this procedure, alongitude Required: Declination of Dubhe. should be assumed within 30' of the navigator's Solution:TabulateddeclinationofDubhe is best estimate of his position. 61 -54.5 North on 2 Jan. 1970. 1205. FINDING DECLINATION In most celestial computations, GHA and declination are determined concurrently rather than The Nautical Almanac tabulates declination separately, thereby saving time in obtaining vital for the sun, moon, and navigational planets for data from the almanac. each hour of GMT. At the foot of each declination sub-column which applies to the sun or planets, 1206. GHA AND DECLINATION a code may be found which is useful for inter- BY AIR ALMANAC polation for any number of minutes. The code follows each tabulated declination of the moon, The Air Almanac, as introduced in Art, 412, since the moon's declination changes rapidly as may also be used for the determination of GHA compared tothedeclination of the sun andand declination. Issued thrice annually, each planets. To find the change in declination for avolume tabulates data for a four month period. part of an hour, enter the yellow pages with the Based upon GMT, the daily pages tabulates the number of minutes and the code. The tabulated GHA and declination of the sun, moon, Venus, declination is prefixed by either an N or S. Mars, Jupiter, and Aries at ten minute intervals, indicating north or south declination, respectively; To determine GHA and declination of the sun, thesignofthe code correction for elapsed the planets, and the moon, enter the Air Almanac minutes must be determined by inspection of with the GMT, nearest and prior to, the actual the declination column, noting if declination is GMT. The declination tabulated requires no in- increasing or decreasing, between the two hours cremental correction. The GHA, however, will in question, Combine the tabulated declinationnormally require an incremental correction, and the code correction and label the result with tabulated for minutes and seconds on the inside "north" or "south" as appropriate. front cover; one column provides the correction To find the tabulated declination of a star,for the sun and the planets, (and for Aries), and enter the daily page with the star name and a separate column provides for the moon. If a Greenwich date. No code correction is necessary precision of 0.1' is desired for the GHA of the since the declination is relatively constant andsun (or for Aries), special tables in the back of can not be expected to change within any 3 day the Air Almanac should be used. The incremental period. corrections are always additive. EXAMPLE 1: To find the GHA of a star, the GHA of Aries must be determined, and added to the SHA of Given: GMT 11-18-45 2 Jan. 1970. that star. The GHA of Aries is found by using the Required: Declination of the sun. same procedure as in the case of the sun. The SHA. of a star, and its declination, is found in Solution:Declination (11 hrs.) S 22-56,1 (0.2) the inside front cover of the Almanac, tabulated Code Correction -0.1 to the nearest minute for a four month period. Declination 22-56.0 South If greater precision is desired, separate tables

108 Chapter 12 SIGHT REDUCTION provide such by month for SHA and declination to and as the radius decreased, the altitude would an accuracy of 0.1' in the back of the Air Almanac. increase,Since two circles may intersect at The Air Almanac, although less precise thantwo points, two positions are possible as the the Nautical Almanac, may be used in the cor- result of two observations. However, the correct rection of sextant altitudes. position could be chosen by considering the azimuth, The plot of circles of equal altitude is im 1207. SOLUTION OF THE ASTRONOMICAL practical since the navigator for greater accuracy TRIANGLE BY H.O. 214 uses a large scale chart depicting an area too small to accommodate a plot containing both There are several methods for solving the the GP's and the points of intersection of circles astronomical triangle,and each method hasof equal altitude. For this reason, in our H.U. certain advantages over the others. However,214 solution, we plot an assumed position (AP), for combined accuracy, completeness, conven-and for that position solve for the altitude and ience, and availability, the method that makesazimuth for a given time. The computed altitude use of Tables of Computed Altitude and Azimuth (Ho) is the altitude which would be observed if (H,0, 214) has been generally preferred. H.O.the navigator had been at the assumed position 214 consists of nine volumes, one for each 10 at the given time, and the complement of the degrees of latitude. Each volume is divided into computed altitude, converted to nautical miles, sections, each section tabulating solutions foris the distance to the GP from the assumed a single degree of latitude. Vertical columnsposition, measured along the azimuth. The ob- within a section are headed by declination values, served altitude thus locates the circle of equal usually at intervals of 30'. On the left hand page, altitude which is the observer's locus of posi- solutions are for cases in which latitude and tion. The difference between the computed altitude declination are of the same name. On the right (Ho) and the observed altitude (Ho) is the distance hand page, solutions are usually for cases inbetween the assumed and the actual circles which latitude and declination are of contrary of equal altitude and is called altitude differ- names; however, when it is possible for meridian ence or intercept, abbreviated "a." angle to exceed 90 degrees with declination and If Ho is greater than Ho, intercept is labeled latitude being of the same name, the left hand"away" because theactual position is at a page tabulations may be continued on the rightgreater distance from the GP than the assumed hand page and so identified, Horizontal linesposition, conversely, if the Ho is less than the are labeled with meridian angle, identified notHo, the intercept is labeled "toward" because as "t" but as H.A., with each line or entrythe actual position is nearer the GP than the being 1 degree apart. Against meridian angle, assumed position. A thumb rule is "Coast Guard declination, and latitude, the tabulated altitudeAcademy" meaning "computed greater away." (Ht) and azimuth angle(*), identified as "Alt" See figure 12-1. and "Az" respectively,are gir9n. H.O. 214 To plot a line of position, using the altitude then affords solutions for all possible astronomi-intercept method as introduced in Art, 1201, cal triangles except those based upon certainlocate and plot the AP; through the AP plot the circumpolar stars having declinations extremely azimuth line, Along the azimuth, measure a high and not tabulated. Solutions by other methods, distance equal to the intercept. This is meas- H.O. 249, H.O. 229, and H.O. 211, are brieflyured from the AP, along the azimuth in the described in Articles 1209 -1211. direction of the GP if "toward," and the recipro- A logical approach to the solution for a linecal of the azimuth (away from GP) if "away." of position would be to locate the GP (geographic At the point on the azimuth line established by position) by GHtt and declination, and using the the intercept, erect a perpendicular to the azimuth GP as center, draw a circle with a radius equal line;this perpendicular is a celestial line of to the co-alt in degrees multiplied by 60 (co-altposition, and the intersection of two or more in minutes or miles), thus arriving at our locussuch lines of position will provide a celestial of position (called a circle of equal altitude). fix. The LOP is labeled with the time expressed Since the distance of an observer from the GPin four digits above the line and the name or isa function of the altitude of the star, the symbol ofthe celestial body below the line, altitude would remain constant for a ship travel- See figure 12-2. ing in a circle having the GP as center; as the The Nautical Almanac is generally used in radius increased, the altitude would decrease,conjunction with the appropriate volume of H.O.

109 A NAVIGATION COMPENDIUM

214 to compute intercept and azimuth. The Summarized, the solution for a line of posi- steps in the solution are: tion is as follows: a. Correct Ho, and determine Ho. a. Enter Nautical Almanac with: b, Apply zone description to zone time of (1) Hs of celestial body, sight and local date to find the Greenwich mean (2) IC of sextant. time and Greenwich date. (3) Height of eye. c. With GMT, enter the Nautical Almanac (4) DR or estimated position. and compute GHA. (5) Zone time, zone description, and date, d. With GMT, enter the Nautical Almanac b, Compute, and enter H.O. 214 with: and compute declination. (1) Meridian angle (t). e, Assume a longitude which, when applied (2) Declination (dee). to the GHA (added if east longitude and sub- (3) Assumed latitude. tractedif west longitude), results in a LHA 0. Compute and use in conjunction with asin even degrees. This will later make it un- sumed position to plot LOP: necessary to interpolate for t. (1) True azimuth (Zn). f. From LHA, compute t. (2) Intercept (a). g. Assume a latitude in even degrees to make d. Steps in plotting: it unnecessary to interpolate for latitude. When (1) Plot AP, assuming latitude and longitude, the assumed (2) Plot Zn through AP. position should be within 30 minutes of the esti- (3) Measure intercept from AP along Zn mated or DR position. in proper direction. h. Enter H.O. 214 with t, dec. (to the nearest (4) Erect a perpendicular to Zn at the tabulated value), and assumed latitude. Record altitude intercept distance from AP. the tabulated altitude (Ht), and the azimuth angle (5) Label perpendicular as a celestial line (15). To interpulate altitude for declination difference, record the interpolation factor known of position, as &I wnich immediately follows the tabulated If it is apparent that an error has been made, altitude. Note the value of Ht in the adjoiningAppendix H, which contains the mechanics of declination column having a declination value error finding, may be consulted. which is second nearest to the actual declination. If the previously recorded Ht is the least EXAMPLES OF SOLUTIONS of the two values, theLid is a plus value; if the previously recorded Ht is the greater of the two EXAMPLE 1: values, the Ad is a minus value. Multiply the Sun (LL). He 24° -46.8, IC -1.0, HE 36 ft., Ad value, which is in hundredths, by the dif- Lat. 35-25 N, Long. 77-42 W. at ZT 14-18-10 ference between the actual and the tabulated1 Jan, 1970. Temp. 35°F, Bar. Press. 30.25". declination with which H.O. 214 was entered (in EXAMPLE 2: minutes and tenths of minutes) to find the cor- Venus. Hs 32°-48.2, IC +1.8, HE 35 ft., Lat. rection to tabulated altitude (Ht). This may be 32-40 N. Long. 51-15 W. at ZT 11-19-28 on expedited by using a self explanatory multiplica- 1 Jan. 1970, Temp, 50°F., Bar. Press. 29.80", tion tableintheinside back cover of eau:Daylight observation. volume of H.O. 214. Apply the correction (according to the sign of Ad) to Ht. This. will provide EXAMPLE 3: the computed altitude(He);numerically, the Moon (Lip. Hs 66 °- 38.3', IC -2.0, HE 60 ft., value of He will lie between the Ht's of the twoLat. 35-10 S. Long. 59-38 E. at 7.T 06-18-30 declinationcolumns whicharenearest and 2 Jan. 1970. Temp. and pressure normal. "bracket" the actual declination. In sight re- EXAMPLE 4: duction, it is not necessary to intkarpolate azimuth Peacock, Hs 42°-39.6,, IC -1.5, HE 20 ft., angle for declination difference. LatT 6.57TrS. Long. 82-03 W. at ZT 18-18-05 i. Compare He and Ho. Compute intercept 3 Jan. 1970. Temp. and pressure normal. by subtracting the lesser from the greater. Label intercept as toward (T) or away (A). For solutions to examples 1 to 3, see the follow- j. Label azimuth angle making the prefixing page, a typical, multiple sight form. Example the sign of the elevated pole (latitude) and the 4' next following is a typical, single sight form. suffixthesign of the meridian angle. From Appendix Icontains an alternate sight form azimuth angle, compute and record azimuth (Zn).example.

110 Chapter 12-810HT REDUCTION

SOLUTIONS FOR EXAMPLES 1, 2, AND 3.

DR POSIT Let. 35-25 N Let. 32-40 N Let. 35-10 S 2 Jan Long. 77-42 W i1illnLong. 51-15 W A 'anLong. 59-38 E M M + M g TIME DIAGRAMS

m 0m 0M BODY SUN (LL) VENUS MOON(LL)

Plus Minus Ply! Minis Ptus1 Minus I.C. 1.0 1J8 2.0 H.E. 5.8 5.7 7.5 Corr. 14.2 1.5 33.2 Add'l 0.1 4.3 Totals 14.2 6.9 1.8 7.2 37.5 9.5 Hs 24-46.8 32-48.2 66-38.3 Corr. +7.3 -5.4 +28.0 Ho 24-54.1 32-42.8 67-06.3 WT This space may be used to convert watch time to zone WE time by the application of watch error ZT 14-18-10 11-19-28 06-18-30 ZD +5 +3 -4 GMT 19-18-10 14-19-28 02-18-30 Date 1 Jan 1970 1 Jan 1970 2 Jan 1970 GHA(hours) 104-05.2 35-08.6 289-50.0 min/sec 4-32.5 4-52.0 4-24.9 Code Corr. (-1.0)-0.3 (+13.4) 4.1 SHA(Stars) 360-00.0 Total GHA 108-37.7 400-00.3 294-19.0 a Long. 77-37.7W 51-00.3W 59-41.0E LHA 31 349 354 t 31W 11E 6E Dec. Tab. (-0.2) 22-59.6S (-0.1) 23-37.6S (+14.0) 12-34.8S Code Corr. -0.1 0.0 +4.3 Dec. 22-59.5S 23-37.6S 12-39.1S Enter Dec. 23-00.0S 23-30.0S 12-30.0S H.O. t 31W 11E 6E 214 a Lat. 35N 33N 35S d diff 0.5 Ad +88 d diff 7.6 A4 -99 d diff 9.1 Ad +98 Ht 24-58.4 32-32.1 66-51.2 Corr. +0.4 -7.5 +8.9 He 24-58.8 32-24.6 67-00.1 Ho 24-54.1 32-42.8 67-06.3 a 4.7 A 18.2 T 6.2 T Z N 148.5 W N 168.0 E S 165 E Zn 211.5(T) 168.0(T) 015 (T) Advance*

* See Art. 1208

111 A NAVIGATION COMPENDIUM

SOLUTION FOR EXAMPLE 4

BODY: Peacock DATE: Alitual... DR POSIT:LAT. 86-185 LONG, 82-09!

44 I tor' -"gi I.C. m H.E. CORR, 1.1 -6.9 Hs 42- 39.6 m Ho 42 - 32,7 ZT 18-18-06 t 66W ZD +5 deo, 56-50.2S__ a. Lat. 36S GMT 23-18-05 3 JAN Ht 42-46.7 (-05) GHA T 88- 08.8 CORR -0.5 M-S CORR 4- 32,0 SHA* 54 -11.1 Ho 42-46.2 GHA* 146 - 61.9 Ho 42-32,7 a. Long. 81- 51.9W a 13,5A LHA 65 Z S042.3W Zn 222.3

1208. PLOTTING THE CELESTIAL FIX At morning and evening twilight, the navigator may succeed in observing the Pliit ,des ,A a In celestial navigation, lines of position are number of celestial bodies inP.fe vY minutes rarely obtained simultaneously; this is especially and thus establish a celestial fix. If 2 or more true during the day when the sun may be the minutes elapse between observations, the navi- only available celestial body. A celestial line gator muial, consider: of position may be advanced for 3 or 4 hours, a. elapsed time; if necessary to obtain a celestial running fix h. speed of ship; and (fig. 12-4) in the same manner as described in c. scale of the chart or plotting sheet; chapter 7. It may also be advanced by advancing the AP in direction and distance an amountto determinewhether or not a more accurate consistent with theship'stravel during thefix can be obtained by advancing AP's to a interval between two successive observations.common time. It is possible during the day to obtain ^. In the latter procedure, the azimuth line is drawn celestial fix rather than a celestial through the advanced AP without any change An running fix if two or more of the three following direction; the advanced LOP is drawn perpend10- bodies are visible: ular to the azimuth, a distance from the AP a. sun; equal to the intercept, and toward or away from b, moon; the GP as appropriate. c. Venus.

112 Chapter 12SIGHT REDUCTION

EXAMPLE 1 Star plotting problem (fig. 12 -3); Given. The 0635 DR position of your ship is Lat. 36 Nes Long. 120W. Between 0600 and 0700 your course is 000 (T), speed 20 knots. At morning twilight, you observe available stars and through computations obtain the following data: Time Body a Lat t Long Advance* 'En a 0610 Vega 36N 12046W 8.3 025 6,0T 0620 Peacock36N 119-55W 5.0 100 24.0A 0635 .ianopus36N 12040W Baal 330 10.3T * Computation of advance is necessary because the stars were not observed simultaneously, and to fix our position, we must use a common time (preferable method is to choose as a common time the time of the last sight). To use a common time we adjust our AP's, except ii the case of the AP of the star observed at the common time (in this problem, Canopus, which is considered the base star). Advance is computed as follows: Body Time Speed Distance of Advance Vega 0635-0610 = 25 min, 20 kts. 8,3 mi. Peacock 0635-0620 in 15 min, 20 kts, 5,0 mi, Required: Plot the 0635 fix. Solution; a. Label plotting sheet with center meridian as 120 W. b. Plot 0635 DR. c. Plot AP's of Vega. Peacock, and Canopus, using assumed latitude and longitude, Label AP's. d. Advance AP Vega in direction 000 a distance of 8.3 mi, Advance AP Peacock in direction 000 a distance of 5.0 mi. Erase old AP's of Vega and Peacock, if desired. e. Plot azimuths, intercepts, and LOP's. Label LOP's and fix. NOTE: If the reason for advancement of earlier AP's is not clear, then the following exercise should be completed: a. Plot AP's of Vega, Peacock, and Canopus using assumed latitude and longitude. Label AP's. b. Plot azimuths, intercepts, and LOP's. Label LOP's. c. Advance LOP Vega and LOP Peacock in direction 000, in accordance with the procedure in plotang running fixes in piloting. d. Check latitude and longitude of fix against coordinates Jbtained in previous method of solution. ANSWER: Lat. 36-10.5 N; Long. 120-23.0 W.

1209. SIGHT REDUCTION BY H.O. 249 VolumeIdiffers from H.O. 214 in that the arguments for entry are the LHAT and the Designed for aerial use, Sight Reduction Tables name of the star, rather than meridian angle, for Air Navigation (H.O. 249) are useful in both declination and assumed latitude; it also differs air and surface navigation, when in the latterin that altitudes and azimuths are recorded to case, somewhat less precision is acceptable.the nearest minute and nearest degree respec- See Appendix I. These tables, similar to H.O. tively.Additionally,and more conveniently, 214, consist of three volumes. The first volume Volume I tabulates the true azimuth (Zn) rather is used for seven stars, selected on the basisthan azimuth angle (2). of azimuth, declination, hour angle, and mag- Volumes II and M have greater similarity nitude, and to provide such distribution or con- to H.O. 214 than to Volume I. Volume II pro- tinuity astobe generally useful worldwide. vides altitude and azimuth solutions for latitudes

113 A NAVIGATION COMPENDIUM

F 30'

30.

190.20 Figure 12-4.Celestial running fix. 69,75 0° to 39'; Volume III provides for latitudes 40° Figure 12-5. Star fix. to 89: These two volumes provide for bodies having declinations as great as 29°, and thus are useful in sight reduction of all bodies within latitude. Each volume is divided into two sec- the solar system and for stars having a declinations, based upon latitude, and contains tabulated tion of 29° or less. Entering arguments are altitudes and azimuths for 16° of latitude. For latitude, declination of same or contrary name,example, the two sectionsof Volume I are and LHA, all to the nearest degree. Longitude applicable to latitudes of 0° to 7° and 8° to 15° is assumed so as to provide an even degree ofrespectively; data pertaining to 15° latitude is LHA. Unlike Volume I, Volumes II and III record also emtained atthebeginning of the first azimuth angle (Z) rather than true azimuth (7.n). section of Volume II. An accuracy of 0.1' for Inasmuch as these tables are designed primarily altitudeand 0.1° for azimuth angle may be for aviation use, LHAs are included for starsattained in calculations through the use of sp. with a negative altitude as might be visible fromplioable corrections to the tabulated data. an aircraft. Entering arguments are latitude, declination, In all volumes of H.O. 249, whenever the and local hour angle, all in whole degrees. Al- declination is noi, an even degree, as is the usual though ILO. 229 provides for entry with the case, the next lower declination column is used;exact DR latitude, the tables are intended to to correct the tabulated altitude for the declina-be entered with an assumed latitude of the tion difference, a factor called "d," recorded nearest whole degree, and an assumed longitude after each tabulated altitude, must be multipliedwhich will result in a local hour angle of an by the declination difference, and applied ac- integral degree. The local hour angle deter- cording to sign to the tabulated altitude. Multi- mines the page of entry, upon which altitude plication tables are conveniently located in the and azimuth data is tabulated in columns headed back of each volume for determining this cor- by latitude entries; vertical columns on the right rection. and left margins of each page provides for the declination entry. For each entry of LHA, the 1210. SIGHT REDUCTION BY H.O. 229 left hand page provides tabulations for latitude Sight Reduction Tables for Marine Naviga- and declination of the same name. The right- tion (H2O, 229) is the marine or surface counter-hand page, upper portion, provides for latitude part of H.O. 249 and will eventually supersedeand declination of contrary name; the lower H.O. 214. See AppendixJ.It is issued in sixportion of the right-hand page is a continuation volumes, with one volume for each 15° band of of the page to the left, and contains tabulations

114 Chapter 12SIGHT REDUCTION for latitude and declination of the same name, The following sight reduotion for the star as applicable to values of LHA in excess of 906Aldebaran illustrates the use of H.O. 229. but less than 2706. As in the use of H.O. 249, the declination entry is the nearest tabulated value which is M equal to or numerically less than the actual Local Date declination, To the right of each tabulated altitude, under a column sub-headed as "d, is the 2 JAN 1970 Course060° i incremental changeinaltitude based upon a W declination increaseof one degree, together Speed 15 kts with sign, An interpolation table is conveniently Body Aldebaran included,andis entered with the declination BODY increase (difference between the actual declina- tionandthedeclination integer used as an Lat 34 15N argument of entry) and the altitude difference DR: (d), The interpolation table is entered in two Long 63 45W steps. Inthefirst, the declination increase, ZT 1740-19 and even tens of minutes of altitude differenoe ZD +4 (d),areused; in the second, the declination GMT 2140-19 increase, and the remaining altitude difference Gr Date 2 JAN (d)in minutes and tenths of minutes, are used to find the correction to altitude. In this step, GHA (hrs) 57 04,7 decimals (tenths) may be found as a vertical GHA (m & El) 10 06.4 argument. Values found in these two steps are v corr or SHA 291 26.7 combined and applied to the tabulated altitude Total GHA 358 37.8 in accordance with the sign of altitude differ- a Long 63 37.8 E _&) ence (d). This is the first of two procedures LHA 295 known as difference corrections. --"M "rib 16 27.2 S S For greater precision, a second difference d. corr ( ) ( correction is sometimes appropriate. When this Total Dec. 16 27,2 ([04- S isthecase,thevalue of "d" is printed in Enter LHA 295 H.O. 229 in italics and is followed by a dot. H.O. Dec 16 el s

The second difference is found by comparing the 229 a Lat 34 0 S i altitude differences above and below the base Dec Inc 1( -X) d 27.2 30.1 value; for example, if the declination argument tens 1 DS diff 30 13.6 for entry is 20°, the altitude difference values units I DS corr .1 +00 for 19° and 21° are compared, and the difference Total corr (+) 13.6 between the two is the double second difference. Hc (tab Alt) 29 1 Interpolation tables contain, on their right-hand HC « 29 37.7 edge, a double column which is identified as a - double second difference and correction column; Sext. Corr. + thisa critical table and correction values are I. C. 0.9 taken therefrom directly. The second difference Dip (36 ft) 5.8 correction is always additive. As appropriate, VanCorr T.-7 first and second difference corrections are thusly Add'l obtained, combined, and applied to the tabulated SUMS 0.8 7;5 altitude to determine computed altitude. Corr -6.7 H.O. 229 tabulates, following altitude differ- Hs 29 52.5 ence (d),the azimuth angle (Z) to the nearest Ho 29 45.8 tenth of a degree. For greater accuracy, mental 11c 29 37.7 interpolation may be used, not only to correct a 8.1.0 the azimuth angle for the declination increase Az (interpolate) 089. or difference, but also for differences in latitude Zn 089.4 and LHA. Rules are given on each page of H.O. Advance 229 for conversion of azimuth angle (I) to true azimuth (Zn).

115 A NAVIGATION COMPENDIUM

1211. SIGHT REDUCTION BY H.O. 211 altitude. A unique feature is that the concept is based upon a DR, rather than an assumed, posi- Based upon a concept developed by the late tion. Rear Admiral Arthur A. Ageton, while serving H.O. 211 advanced the practice of celestial as a Lieutenant at the Postgraduate School, U.S.navigation and was widely used until generally Naval Academy, Annapolis, and published by him replaced by H.O. 214 during World War II. H.O. in 1931, Dead Reckoning Altitude and Azimuth211 is briefly described herein because of the Tables (11.0, 211) have, in usefulness, stood the economy it offers; a single volume for sight test of time. This volume, appropriately andreduction is allthatis required. However, the popularly known as "Ageton," includes formulas advantage of its economy is perhaps more than derived from Napier's rules, and in support ofoffset today by the greater convenience of H.O. such formulas, tables of log secants and log214, H.O. 249, or H.O. 229. For the navigator cosecants for each 0,5' of arc. In a small, who wishes, nevertheless, to use H.O. 211, the compact volume of 49 pages, these tables are Ageton method for sight solution or reduction is useful worldwide, regardless of declination or most adequately described therein.

116 CHAPTER 13 OTHER CELESTIAL COMPUTATIONS

1301. INTRODUCTION When the altitude of a celestial body is measured as it transits the meridian, we speak of As important as sight reduction is to celes- the observation, and the subsequent solution for a tial navigation, knowledge of such alone will notline of position, as a "meridian sight." This sight suffice. Essential supplementary celestial com-includes observations of bodies on the lower putations are described in this chapter, and in- branch of the meridian (lower transit) as well as clude the determination of: on the upper branch (upper transit); circumpolar stars may be observed on either branch of the (a) Latitude by meridian sight; celestial meridian. In practice, how ver, bodies (b) Time of transit, including local apparentare seldom observed on the lower branch, and noon (LAN); the sun is normally the only body observed. In (c) Latitude by Polaris; polar latitudes, when the declination of the sun (d) Time of phenomena such as sunrise, moon- corresponds in name to the latitude of the ob- rise and twilight; server, the sun may be observed when in lower (e) Identification of navigational stars and pla- transit, but generally, meridian sights of the sun nets; are made when it is in upper transit (LAN). (f) Compass error by azimuth of the sun; (g) Compass error by azimuth of Polaris. The meridian sight is important for the following reasons; 1302. LATITUDE BY MERIDIAN SIGHT (a) It provides a celestial LOP without resort Since the latitude of a position may be deter-to trigonometry; mined by finding the distance between the equi- (b) The intersection of the LOP, obtained at noctial and the zenith, one needs to know only LAN, and advanced morning sun lines, establishes the declination and zenith distance (co-altitude) a celestial running fix; of a body to determine latitude. The procedure (c) Itispracticallyindependent of time; involved has been used by mariners for many (d) The knowledge of the approximate position centuries because of its simplicity. Before the is unnecessary; and discovery of the Sumner line, and particularly (e) The LOP is a latitude line, and is useful prior to the Harrison chronometer, longitude wasin latitude or parallel sailing. most difficult to compute. Accordingly, early mariners seized upon the technique of "latitude or To observe a body when on the meridian we parallel sailing," by which they traveled northmust first determine the time of local transit. or south to the known latitude of their destination, This may be accomplished by one of the three then east or west as appropriate, often using the following methods: meridian sight as their only celestial computation. The meridian sight as described herein is applicable to all celestial bodies, although in practice (a) MAXIMUM ALTITUDE. At upper transit it is primarily used with the sun. As described the altitude of a celestial body is maximum for a in Art. 1304, latitude by Polaris, a polar star,particular 24 hour period. At lower transit the is a special case of the meridian sight, and is altitude is at a minimum. procedurally a different computation. With this briefintroduction, the meridian sight is now (b) AZIMUTH METHOD. When a celestial considered. body transits the meridian, unless it is in the

117 A NAVIGATION COMPENDIUM observer's zenith (GP corresponding to the observer's position), the azimuth will be either north (000) or south (180). (o) COMPUTATION METHOD.Should the approximate longitude be known, it is possible to compute the time of transit. This, the most common method, is described in article 1303. When making the observation, stand by with a sextant 5 minutes prior to the expected time of transit. Continuously measure the altitude. When the altitude commences to decrease (on an upper branch observation), cease measurement, and record the highest attained value of altitude. The theory of the meridian sight may be con- 190.27 densed as follows: Figure 13-1. Sun on meridian. (a) It is a special case of the astronomical(Q). If the declination is north, the body will be triangle. Since the local celestial meridian andbetween N and Q; if the declination is south, the hour circle coincide, t equals 0 degrees andthe body will be between S and Q. Aro ZQ then we are dealing with an arc rather thane triangle. equals thelatitude of the observer. We can Geometry, rather than spherical trigonometry, readily see the relationship between declination is necessary for solution. and zenith distance, and derive formulae for the (b) The vertical circle, the hour circle, andthree possible cases, as follows: the local celestial meridian, coincide. (0) The azimuth is either 000 or 180, except (a) Latitude and declination of different in the case of a body in the observer's zenith. names: (d) The declination of a body is the latitude of the GP. L = z - d (e) Thezenith distanceof a body is the angular distance between the GP of the body and (b) Latitude and declination of same name the observer, measured along the meridian. with L < d: (f) To find the latitude, it is only necessary to compute declination andzenithdistance L = d - z (co-alt), which may be combined after the derivation of the correct formula. (c) Latitude and declination of same name To derive the correct formula, draw the halfwith L > d; 0.7 the celestial sphere which extends above the horizon, as viewed, by an observer beyond the L = z + d west point of the horizon (fig. 13-1). The circumference of this half circle represents the ob- The following special cases are worthy of server's celestial meridian which, as we have note: already noted, coincides with the hour circle and tlae vertical circle of the body. The zenith- (a) If Ho + d = 90°, then latitude is 0 nadir line, the equinoctial, and the polar axis, are all represented as radial lines extending (b) When latitude is nearly 0, and name of outward from the observer's position at the cen- latitude unknown: ter of the base line of the diagram. Label the north and south points of the horizon and the (1) If (Ho + d) >90, latitude is of the zenith. Depending upon the azimuth (north or same name as the direction of the body. south),using theobserved altitude, measure from the north or south point of the horizon a- (2) If (Ho + d) < 90, latitude is of contrary long the vertical circle and locate the positionname to the direction of the body. of the celestial body; label the position. Using (c) Ho plus polar distance equals the latitude the declination, locate and label the equinoctialat lower transit.

118 Chapter 13OTHER CELESTIAL COMPUTATIONS

EXAMPLE 1: Given: DR Lat. 47-26 S. Long. 130-26 W. ZT 11-45-41 on 2 Jan. 1970. Hs of sun (LL) 65-18.3. Zn 000. IC + 2.0. Height of eye 44 feet. Required: Latitude of the observer. Solution: ZT 11-45-41 2 Jan. PlusMinus ZD +9 (130-26/15) IC 2.0 GMT 20-45-4l 2 Jan. HE 6.4 Dec. S 22-54.1 Code -.2 Corr,15.8 Code Corr. -0.2* Dec. 22-53.9 S Sum +17.8 -6.4 = +11,4 *Dec. code -2 indicates that Hs 65-18.390 = 89 -60.0 declination changes 0.2' north- Corr. +11.4Ho65-29.7 ward per hour and therefore the 117M-29.7 z 24-30,3 change to the nearest tenth for 45 min. is also 0.2'. (1) Plot sun using Ho and Zn (Draw diagram) (2) Plot Q using declination and position of sun. (3) Plot Ps using Q. (4) Z@ equals latitude. Label angles or arcs in diagram which represent dee, z, and latitude, (5) Formula is L = z + d z 24-30.3 d 22-53.9 Lat. 47-24,2-South

1303. COMPUTING ZONE TIME OF LOCAL between 1130 and 1230, plus or minus the equation APPARENT NOON (LAN) of time (unless the observer is keeping E zone time other than standard time for his longitude). The navigator, using the Nautical Almanac, Enter the Nautical Almanac with GHA on the computes zoria time of the sun's upper transit correct day, and determine GMT (the reverse to an accuracy which permits his being on the of entering with GMT and finding GHA). In con- bridge with sextant in hand just prior to LAN. version of GHA to GMT, first select a value in Of a number of methods available for determin- the GHA column nearest, but less than, the sun's ing time of LAN, the GHA method is generally GHA. Record the GMT hours and subtract the used, and for that reason..is described herein. GHA at the tabulated hour from the sun's prede- In west longitude, when the sun is on the termined GHA at LAN. Enter the yellow pages, meridian the GHA equals the longitude. In east and in the column headed by SunPlanets, lo- longitude, when the sun is on the meridian the cate the remainder (minutes and seconds correc- GHA is the explement of the longitude. These tion to GHA), and record the minutes and seconds. relationships are illustrated in figure 13-2. Timearc conversion tables are also sufficiently For the purpose of establishing a dead reck-accurate for this computation. Combine hours, oning position to use as an initial estimate, we minutes, and seconds to obtain the GMT of LAN. may assume that the sun will transit our merid- Apply the zone description, reversing the sign, ian at zone time 1200; we accordingly use the to obtain zone time of transit. longitude of the 1200 DR position for computing The time of transit as computed above is the the GHA of the sun at LAN, as LAN will occur zone time the sun would transit the meridian of

119 A NAVIGATION COMPENDIUM

EXAMPLE 2: Given; 1200 DR Lat. 31-10S; LOng,16340E. 1 Jan 1970 Required; ZT of LAN. Solution: ZT 1200 Long. 163-10,0 E GM at LAN 196-50,0 (360-163-10') 01 hours 194-10,5 10 min, 38 sec. GMT 01-10-38 ZD -11 (rev) ZT 12-10-38 If the time of LAN is required only to the 190.28 nearest minute, which is often the case, it can Figure 13-2. GHA of sun at LAN. be more quickly determineu, One need only to apply a difference in longitude correction to the the 1200 DR position, If this time differs fromtime of meridian passage of the sun over the 1200, and you are the navigator of a moving ves-Greenwich meridian, as recorded on the daily sel, then obviously the sun will not transit yourpages of the Nautical Almanac, See Appendix F. meridian exactly at the time computes: becauseThe timo of meridian passage, as recorded, is of the difference in longitude between your posi-both the Greenwich mean time (GMT), and the tion at 1200 and your position at your first esti-local mean time (LMT) of local apparent noon, mated time of LAN. Ship's speeds are relativelyAs mean time, it differs from apparent time slow, and a second estimate is generally not(1200) by the equation of time, which is also re- considered necessary, However, if a secondesti-corded, As local mean time, it is also the zone mate is desired, plot the DR corresponding to thetime on the central meridian of each time zone. time of the first estimate, With dividers, deter-Thus, to find the zone time of local apparent mine the difference in longitude (in minutes ofnoonon meridiansotherthanthe central arc) between the 1200 DR and the DR positionmeridian, the local mean time is corrected corresponding to the first estimate of time oftozonetimebyconverting the difference LAN. Convert the difference in longitude (in arc)inlongitude between the central and the ob- to time, and apply as a correction to the zoneserver's meridians from arc to time, and applying time of the first estimate, Keeping in mind thatthe result to the mean time of meridian passage. the sun appears to travel from east to west, addThe correction is subtracted when east of the the correction if the last plotted DR position iscentral meridian, and added when west. west of the 1200 DR, and subtract the correction if the last plotted DR position is to the eastward, 1304. LATITUDE BY POLARIS EXAMPLE 1:

Given: 1200 DR Lat. 36-18 N; Long. 71-19 In diagram used in the derivation of for- W. 2 Jan 1970. mulae for the solution of meridian sights, we found that arc ZQ equals the latitude of the ob- Required: ZT of LAN. server. We can prove geometrically, using the same diagram, that the altitude of the elevated Solution: ZT 1200 Long. 71-19W. pole equals the declination of the zenith (arc GHA at LAN 71-19.0 ZQ), and also the latitude. 16 hr s. 58-59.0 Although Pn and Ps are not well defined po- 49 min. 20 sec. 12-20.0 sitions which make measurement feasible, a GMT equals 16-49-20 second magnitude star called Polaris (north star) ZD +5 (rev)provides a reference for measurement in the ZT 11-49-20 northern hemisphere; Polaris has no counterpart

12) Chapter 13OTHER CELESTIAL COMPUTATIONS 11.14111. in the southern hemisphere. Polaris may be lo-month of the year. In table a0, the correction is cated in the northern sky between the constella- based upon a mean value of SHA and declination tions Ursa Major (big dipper) and Cassiopeia, of Polaris, and a mean value of 50 north latitude The two stars in the bowl of the dipper at theas the position of the obsorver. Table al, entered greatest distance from the handle, point towardwith LHAr and latitude, corrects for the differ- the north star. ence between actual latitude and the mean. Table Polaris travels in a diurnal circle of small , entered with LHATand the monthof the year, radius around Pn as shown in the diagram incorrects for variation in the position of Polaris figure 13-3. The polar distance, or radius of the from its selected mean position. All corrections diurnal circle, is "p," The meridian angle is from these tables contain constants, which make "t." Point 0 is the intersection of the observer's the corrections positive, and which when added celestial meridian and the celestial horizon. Hotogether, equal 1 degree. Thus, the correction is equals the observed altitude. PnH equalsp cos t,added to the Ho, and 1 degree is subtracted to and is the correction which must be added ordetermine latitude. subtracted, depending upon whether Polaris is below or above Pn. In summary, latitude may be ascertained in It can readily be seen that the value of the the northern hemisphere by observing the Hs of correction will depend upon the meridian angle Polaris, at a known time. From the time, and (t), or the position of the observer's meridianthe DR or estimated longitude, compute the LHA with respect to the hour circle of Polaris. Since ofAries. Correct Hs to Ho, and using the LHAT, the SHA is relatively constant, the correction isapproximate latitude, and date, determine correc- also a function of the LHAT For Polaris, the tions from Polaris tables ao, at and a2.Add total Nautical Almanac tabulates corrections based correction to Ho, and subtract 1 degree to obtain upon the LHAr, the observer's latitude, and the latitude.

EXAMPLE 1: Given: Date 2 Jan. 1970. DR Lat. 67-25.0 N; Long. 116-35.0 W. WT 18-18-45, WE on ZT is 10 seconds fast. He 68-21.3. IC +1.5. HE 42 feet. Required: Latitude of the observer. Solution:

Plus Minus WT 18-18-45 2 Jan IC 1.5 WE -10 fast HE 6.3 ZT 18-18-35 Corr. 0.4 ZD +8 Sum + 1.5 -6.7 GMTY02-18-35 3 Jan +1.5 GHA 132-17.0 Corr. -5.2 M-S 4-39.5 Ha 68-21.3 GHA 136-56.5 Ho 68-16.1 Long. 116-35.0 W Table LHAY 20-21.5 ao 7.6 Ho 68-16.1 al 0.6 Corr. -51.1 se 0.7 Lat. 67-25.0 North Sum +8.9 -60.0 Corr. -51.1 The reason the n'olaris sight cannot be worked byHO 214 is that itsdeclinationisabout 89 degrees North, and HO 214 does not contain solutions for astronomical triangles basedupon any celestial body with such an extreme declination,

121 A NAVIGATION COMPENDIUM

OBSERVATIONAL TWILIGHT.The sun is 10 DIURNAL degrees below the horizon. Best for observations. CIRCLE CIVIL TWILIGHT. The sun is 6 degrees below the horizon. Too light for observations. Also recorded in Nautical Almanac.

HOUR In practice, the navigator should be ready to CIRCLE commence his morning observations about40 minutes before sunrise. For evening observations, he should be ready not later than 15minutes after sunset. POLARIS In the Nautical Almanac the times of sunrise, morning nautical and civil twilight, sunset, and evening nautical and civil twilight, are tabulated CELESTIAL against latitude on each daily page for a 3 day MERIDIAN period. The time tabulated is Greenwich mean time on the Greenwich meridian but may be re- HORIZON 0 garded as local mean time (LMT) of the phenomena (also the zone time at the central meridian of each time zone). To find the time of sun- 190.29 rise, for example, we turn to the page of the Figure 13-3.Polaris. Nautical Almanac for the given date; interpolating for latitude, we find the local mean time of sun- 1305. SUNRISE, MOONRISE, AND TWILIGHT rise (zone time on central meridian). If desired, interpolation for latitude can be simplified by the We associate the following phenomena with theuse of a self explanatory table in the back of the apparent motion of the sun and the moon: Nautical Almanac (see appendix F). Next, we con- SUNRISEThe instant the upper limb of thesider the difference in longitude between our sun appears on the visible horizon; meridian and the central meridian. Keeping in MOONRISE The instant the upper limb of themind that 1 degree of arc equals 4 minutes of moon appears on the visible horizon; time, we convert the difference in longitude to SUNSET The instant the upper limb of the suntime, and apply this correction to the LMT, to disappears beyond the visible horizon; find zone time. If the local celestial meridian is MOONSET The instant the upper limb of theto the east of the central meridian of the time moon disappears beyond the visible horizon;zone, subtract the correction; conversely, if the TWILIGHTThe period of semi-darkness oc-local celestial meridian is to the west, add the curring just before sunrise (morning twilight), orcorrection. Round off answers to the nearest just after sunset (evening twilight). minute. The navigator utilizes morning and evening On a moving ship the problem is slightly twilight for star observations because duringmore involved. The latitude and longitude chosen twilight the darkness makes the stars visible,forsolutionshould be found by entering the yet permits sufficient light to define the horizon.Nautical Almanac with an approximate latitude Both conditions are necessary if an accuratefor sunrise (or sunset, or twilight) and noting Hs is to be obtained. There are four stages ofthe LMT. Plot the DR for the LMT, and using twilight, based upon the position of the sun withthe coordinates of the DR, work the problem respect to the horizon. They are: in the usual manner, first interpolating for latitude, and secondly applying the correction for ASTRONOMICAL TWILIGHT. The sun is 18longitude. A second estimate is seldom neces- degrees below the horizon. Too darkfor observa-sary because this required accuracy of 1 minute tions. would not be exceeded unless the vessel tra- versed more than 15 minutes of longitude be- NAUTICAL TWILIGHT. The sun is 12 de-tween the position of the first estimate and the grees below the horizon. Favorable for observa-position reached at the actual time of the phe- tions. Recorded in Nautical Almanac. nomenon.

122 Chapter 13OTHER CELESTIAL COMPUTATIONS

EXAMPLE 1:

Given: Position Lat. 22 N; Long 1.8 W, 3 Jan. 1.970

Required: ZT of sunrise, beginning of morning nautical twilight, sunset, and end of evening civil twilight.

Solution:

Morning Nautical Evening Civil Sunrise Twilight Sunset Twilight

LMT 30 N 0656 0600 1712 1738 LMT 20 N 0635 0544 1732 1.756 Jiff. for 10 21.0 16.0 20.0 18.0 cliff. for 1 2.1 1.6 2.0 1.8 cliff. for 2 4.2 3.2 4.0 3,6 LMT 22 N 0639 0 547 1728 1.752 d Long.* +12.0 +12.0 +12.0 +12.0 ZT 0651 0 559 1740 1804

*(18 - 15) x 4

The Nautical Almanac also tabulatesthe EXAMPLE 1: GMT ofmoonrise and moonset, which close- ly approximates values of LMT. The time of moonrise (or moonset) on two successive dates Given:1 Jan 1970 at Lat. 37-30 N; Long. 63 W. differs a great amount, which makes interpolation for longitude as necessary as interpolation Required: ZT of moonrise. for latitude. To find the precise time of either moonrise or moonset, first find the GMT of Solution: moonrise (or moonset) for your latitude; this may necessitate interpolation between given val- Jan. 1 GMT Lat. 37-30 N 0 016 ues in the Nautical Almanac, or use of table I. Jan. 2 GMT Lat. 37-30 N 0119 Determine the GMT of moonrise or moonset for Difference 63 min. the desired date and the preceding date when in Correction (from table II) +10 east longitude, and for the desired date and the LMT (0016 + 10) 0026 succeeding date, when in west longitude. Com- Corr. for longitude: (63-60) x 4 +12 pute the time difference between the two GMTs ZT of moonrise 0038 and enter table II with this difference and your longitude. Apply the resulting corection to the GMT of moonrise or moonset on the desired day, generally adding in west or subtracting in 1306. STAR IDENTIFICATION east longitude as necessary to arrive at an IMT which in sequence lies between the two previously It is just as necessary for the navigator to computed GMTs. Apply a time correction forcorrectly identify an observed star as it is for longitude to the LMT; the result is zone time of him to identify a navigational landmark in pilot- moonrise (or moonset). ing. There are two general systems available,

123 A NAVIGATION COMPENDIUM

* 1/y, 4 '10 4 .4 4400

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bQi

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, / . c'..., / / 45e. Ot 7(" 'Aoroede/ 44k #0) / 0 'Or 10 Oe co S.

69,67 FignrA 13-4.Star finder with template.

124 Chapter 13OTHER CELESTIAL COMPUTATIONS identification by constellation, and identificationare appropriately labeled, Eye interpolation is by azimuth and altitude, The latter method isnormally used, and azimuths and altitudes are most practical, since it permits identification of noted to the nearest degree, single stars at twilight when the constellations are The planets of our solar system do not ap- not clearly outlined, and of stars visible through pear upon the star base because of their con- breaks in a cloudy sky when constellations are stantlychanging SHA. To locate or identify partially or completely obscured, planets, the navigator computes the right as- The navigator's aid to star identification is cension and declination using the Nautical Alma- the Star Identifier (HO 2102D) (fig, 13-4). It con- n_ ac, The right ascension of a planet equals the sists of a star disc, and a circular transparent GHA of Aries minus the GHA of the planet. HA template for each 10 degrees of latitude (5, 15,may be computed using the GHA's tabulated a- 25, 35, 45, 55, 65, 75, and 85); it also includes gainst a given hour, Once computed and plotted, a meridian angle template. The star disc is sothe navigator will find it unecessary to replot constructed that the stars 'normally seen in north the planet more often than once every two weeks latitudes are shown on the north side located so because the daily change in RA is relatively small. as toindicatetheir proper Right Ascension To plot the planets on the star base, use the (RA) and declination; similarly, those stars nor- red-lined meridian angle template, which can be mally seen in south latitudes are shown on the quickly identified as it contains a rectangular south side of the disc. The center of the northslot. Mount tht. template according to latitude on side of the disc represents the north celestial the appropriate side of the star base. Set the red pole, and the center of the south side represents pointer, which is adjacent to the slot, so that it the south celestial pole. The edge of the starindicates the RA of the planet, as read on the disc is graduated in degrees (0 to 360) for mea-periphery of the star base. The planet may then surement of both SHA and RA. be temporarily plotted through the rectangular To identifystars by their location, using slot, using a declination scale on the template altitude and azimuth, first compute the LHA of adjacent totheslot,to' locateits position. Aries for the desired time of observation. Using the side of the star base which corresponds to The celestial bodies commonly referred to as latitude (north or south), select and mount the morning and evening stars are actually planets, transparent template which most nearly corre- having GHAs which approximate the GHA of the sponds to DR latitude. Since the templates are sun. If the GHA of the planet is less than the printed upon both sides, in order to serve forGHA of the sun, the planet may be called an .both north and south latitudes, it is necessary evening star, If the GHA of the planet is great- to place the template with the side up whicher than the GHA of the sun, it may be called a corresponds in name (north or south) to your ,norning star. latitude. The template is rotated until a north- Consideratior in selecting stars for observa- south line on the template coincides with the tion are: LHA of Aries on the star disc. The printing on the template, which now covers the star base, (a) AltitudeBetween 15 and 70 degrees is consists of a network of concentric ellipses and preferable. Bodies below 15 degrees have refrac- radial lines. The stars which appear within the tion corrections which are predicted with slightly network are visible at the time of observationless accuracy. Altitudes above 70 degrees are (or at least are above the horizon), and have difficult to measure, altitudesgreaterthan 10 degrees. The stars outside the network either are below the horizon (b) AzimuthThe stars selected should huve or will have altitudes less than 10 degrees, and azimuths which will provide a spread essential therefore are poor for observation because ofto establishing an accurate fix. inaccuracies in predicted refraction errors. The center of the network represents the observer's (c) Magnitude Solutions are available for zenith. The radial lines represent azimuth, andapproximately sixty of the brightest stars. Stars are 5 degrees apart; at their extremities, the of the first magnitude (brightest), are generally value of the azimuth of any star on that line may used in preference to second magnitude stars be read directly. The concentric ellipses repre- because the measurement of the Hs of a bright sent circles of equal altitude from 10 to 90 de- star is easier than the measurement of the Hs grees, and are 5 degrees apart; these ellipses of a dim star.

125 A NAVIGATION COMPENDIUM

EXAMPLE 1: Givens Ho 2102D, North latitude, 1 Jan, 1970. Required; Plotting of planets. Solution; RA of a planet equals GHA of Aries minus GHA of planet, yaw mei 4110...er Saturn GHA of Aries 460-13,8 460-13,6 460 -13,8 10043.8 GM of Planets 165-22,2 116-me 249-40,2 8 RA of Planets 274-51.6 3413.55.9 itir:337 751161- Dec. of Planets 23-37,95 7 -43.3S 11-08,9S 9-49.3N The GHAY is actually 100 -13.8, as indicated above under Saturn; however, it is appropriate to add 360 to the GHAT in the above cases for Venus, Mars, and Jupiter, to facilitate subtraction of the GHAs of those bodies. For simplification, the GHAs have all been reoordedfor 0 hours on 1 Jan., the giver date. This is feasible because the hourly change in GHAT is practically the same as the hourly change in the GHA of the planets. The difference, or RA, does not differ appreciably during a given day, In fact, the change is so small that once plotted, planets can be used without re- computation and replotting for a fortnight. Planets arc plotted using the red-lined, meridian angle template in accordance with their computed right ascensions and declinations, The moon may be plotted, if desired, using its right ascension and declination, EXAMPLE 2: Given: ZT 18-20-00 1 Jan, 1970 at Lat. 34-00N, Long, 77-45W, HO 2102D, Required: Listoffirst magnitude stars. and planets visible with altitudes between 15 and70degrees. Solution: ZT 18-20 i Jan. Star finder set -up: ZD +5 Diannorth side up. ZIRT,I-20 1 Jan. Template35North, GRAY 86-10.5 LHAY -13 -26.3 Planets should M/S 25-00 8 already be plotted as required by GHA 91-3 example (1) above. Long.77-45.0 W LHA TgZT:3

Body 'Zn H Capella 056 40 Betelgeux 093 17 Aldebaran 096 38 Rigel 112 15 Fomalhaut 207 20 Deneb 302 41 Vega 30C 18 Mars 220 40 Saturn 126 55

126 Chapter 13OTHER CELESTIAL COMPUTATIONS

1307. AZIMUTH OF THE SUN accuracy ciepends upon thenavigator's knowledge of 1115 position and the correcttime. Computation of compass error at seadepends To compute 2n by HO 214, use the_Nautical upon the observation ofthe azimuth of celestial Almanai *ie solve fort and deo. Usinial-W, bodies; the sun is most commonly usedfor this al-dri.t. (all to the nearest tabulated value) purpose. Upon observation,the observed azimuth, enter h0 214, and record the baseazimuth an- which is abbreviated Zo, is recorded.The time gle (2tab). Next, make an interpolation for (to the nearest second), and theDR position, are difference in t, deco and Lat.; add algebraically also noted, With DR position and time,the navi-the changes in azimuth angle for thedifference gator computes Zn. Thedifference between 'Le between actual and tabulated values. Applythe (compass direction) and Zn (truedirection) is total interpolative correction to Z tab toobtain compass error (C.E.). It should beappropriatelyZ. Convert Z to Zn. Compare Znwith Zo to labeled.Thefactmust be kept in mind thatdetermine compass error.

EXAMPLE 1:

Given; le 054.6 at Lat. 33-48 So Long.161-51 E at WT 11-19-16, 3 Jan. 1970. WE on ZT is 1 min. 6 sec. fast.

Required: Compass error.

Solution;

WT 11-19-16 GHA 178-56.7 WE 1-06 fast M/S 4-32.5 ZT 11-18-10 Long. 161-51.0E ZL) -11 LHA 345 -20.2 GMT 00-18-10 3 Jan. t 14-39,8E dec S22-53.2 Code -2 code corr. - 0.1 dec 22 -53.18

Plus Minus

t 14-39.8E t diff + 2.2t corr. 0.7 d 22-53.2 d diff + 1.2 d corr. 0.3 L 33-48MS L diff - 2.7 L corr. 0.5 Z tab 12, Sum +1.0 -0.5 Corr. +0.5 Corr. +0.5 Z S126.5E Zn 053.5 Zo 054.6 C.E. 1,1 West

127 A NAVIGATION COMPENDIUM

EXAMPLE 2: (By H.O. 229)

DATE 2 JAN 1970 GB 227.5 DR LAT 3S°12'N DR LONG 2122'W ZT 1554 12 ZD (+W) (-E) +1 . GMT 1654 12 OR DATE 2 JAN 1970 GHA (hrs) . 58 59.0 GHA (m&s) 13 33.0 TOTAL GHA 72 2%0 DR LONG (+E) (-W) 21 22.0 LHA 51 10.0 , TAB DEC 22 55.0 d CORR ( .2) .2 TOTAL DEC 22 54.8 (CORR is FACTOR x AZ DIFF) LOWEST AZ AZ EXACT FACTOR AZ CORR TAB TAB INTER'?DIFF +

DEC 22 54.8 22 .N.J1 7 131.3 60 ' 132.0 +.7 .64 DR 33 12.0 33 12 131.3 LAT to- 2 131.5 +.2 .04

10 LHA 51 10.0 51 -6-ryNB .8 131.3 130.5 -.8 .13

AZ TAB 131.3 TOTAL CORR +.55 or .6

CORR +.6

AZ N 181.9 W** CONVERT AZ TO ZN 360.0 NORTH LATLHA GREATER THAN 180°.. ZN = AZ -131.9 LHA LESS THAN 180°...... ZN = 360°- AZ ZN 228.1 SOUTH LATLHA GREATER THAN 180 °... ZN = 180°- AZ LHA LESS THAN 180° ZN = 180° + AZ GB 227.5

GE .6 E

COMPASS BEST ERROR WEST COMPASS LEAST ERROR EAST

128 Chapter 13 OTHER CELESTIAL COMPUTATIONS

1308. AZIMUTH BY POLARIS agg in the Polaris table entitled "Azimuth" with the arguments (1) LHA of Aries and (2) latitude of the observer. Zn is read directly from this To determine compass error at night in north table. Compare Zn and Zo, in the manner de- latitudes, find Zo of Polaris by observation.Com- scribed for the sun in the preceding article, and puts the LHA of Aries. Enter the Nautical Alma-, determine compass error.

129 CHAPTER 14 DUTIES OF THE NAVIGATOR

1401. INTRODUCTION movements and, if the ship is running into danger, as to a safe course to be The duties of the navigator are basically the- steered. To this end he shall: same regardless of the type or the employment of the vessel; differences arise in methods em- (a) Maintain an accurate plot of the ployed because of available equipment. The duties ship's position by astronomical, visual, of the navigator of a Navy vessel stem from, and electronic or other appropriate means. are found in, Navy Regulations as revised in 1948 and since amended. (b) Prior to entering pilot waters, study all available sources of informa- 1402. DETAILED DUTIES tion concerning the navigation of the ship therein. Extracts from Navy Regulations governing navigation are quoted herewith: (0) Givecarefulattentionto the course of the ship and depth of water "0929. General Duties when approaching land or shoals. The head of the navigation department (d) Maintain record books of all ob- of a ship shall be designated the navi- servations and computations made for gator. The navigator normally shall be the purpose of navigating the ship, with senior to all watch and division officers. results and dates involved. Such books The Chief of Naval Personnel will order shall form a part of the ship's official an officeras navigator aboard large records. combatant ships. Aboard other ships the (e) Report in writing to the com- commanding officer shall assign such manding officer, when under way the duties to any qualified officer serving ship's position (fig. 14-1) at 0800, 1200, under his command. In addition to those and 2000 each day, and at such other duties prescribed elsewhere in the regu- times as the commanding officer may lations for the head of department, he require. shall be responsible, under the commanding officer, for the safe navigation (f)Procure and maintain all hydro- and piloting of the ship. He shall receive graphic and navigational charts, sailing all orders relating to navigational duties directions, light lists, and other publi- directly from the commanding officer, cations and devices for navigation as and shall make all reports in connection may be required. Maintain records of therewith directly to the commanding corrections affecting such charts and officer. publications. Correct navigational charts and publications as directed by the com- 0930. Specific Duties manding officer and in any event prior toany use for navigational purposes The dutiesof the navigator shall from such records and in accordance include; with such reliable information as may 1. Advising the commanding officer be supplied to the ship or the naviga- and officer of the deck c.s to the ship's tor is able to obtain.

130 Chapter 14DUTIES OF THE NAVIGATOR

that the ship's clocks are properly set in accordance with the standard zone time of the locality or in accordance with the orders of the senior officer pre- SNIP'S POSITION rovsmp5.1111 (REV 5.621 sent. TO (c) Insure that the electronic navi- COMMANDING OFFICER. US$ //04 POR VAT (40404) gational equipment assigned to him is At (Ti.,ofd.,) Pet /200 I? /.c MAY, 1961 kept in proper adjustment and, if ap- ,A,,,ube ..., , propriate,thatcalibration curves or 35.047/N74°36.54./4"//45- tables are maintained and checked at In find 00000 y 00000it 1s) prescribed intervals. E:1 © D. O.IgLOAM El NADA* viiVAl sit OMIlT OiltACE %int WOO !MCI (tall) I) 240'0.4ifr,0800 R 60 Hi. 3. The care and proper operation 0ISTARCE TO blitI5 of the steering gear in general, except rra/kook' BRewrov ReeF 1/qir 420 Afl ,' MAY the steering engine and steering motors. MA HOG.Itame VAR AT:cm 4. The preparation and care of the 0 026° ..0Of SE at AO °w deck log. He shall daily, and more often COMPASS q)14G (CAM, 0401 ! ciMOW( when necessary, inspect the deck log SID [sl 14. IMD "" 055: S 0IWIATICM 1104 toltt OtotofION DO. (but 00000 IT ,Sal it its) and the quartermaster's notebook and / °w 1:3 *" shall take such corrective action as may 1111411! be necessary, and within his authority, to insure that they are properly kept. 5. The preparation of such reports and records as are required in connection with his navigational duties, including those pertaining to the compasses, hydrography, oceanography, and 4114INT meteorology. 6. The relieving of the officer of the deck as authorized or directed by the 112.97 commanding officer. Figure 14-1. Ships position report. 0931. Duties When Pilot is on Board The duties prescribed for a naviga- 2, The operation, care, and main- tor in these regulations shall be per- tenance of the ship's navigational equip- formed by him whether or not a pilot ment. To tido end he shall: is on board. (a) When the ship is under way and weather permits, determine daily the 1403. LEAVING AND ENTERING PORT orror of the master gyro and standard magnetic compasses, and report the re- The navigator may expect to employ all meth- sult to the commanding off! cer in writ- ods of navigation except celestial, when leaving ing. He shall cause frequent compar- or entering port. Between a ship's berth and the isons of the gyro and magnetic com- open sea, the diversified tasks which the navigator passes to be made and recorded. He must perform may be organized with the use of shall adjust and compensate the mag- a check-off list. netic compasses when necessary, sub- The following check-off lists are, with slight ject to the approval of the command- modification, appropriate for ships of any type: ing officer. He shall prepare tables of deviations, and shall keep correct copies (a) Navigation Check-Off Listf. o r Getting posted at the appropriate compass sta- Under -way tions. (b) Insure that the chronometers are 24 hours before wound daily, that comparisons are made to determine their rates and error, and 1. Make a pre-voyage check of instruments.

131 A NAVIGATION COMPENDIUM

2. Check chronometer; determine error and thumb tacks. Drafting machine should be daily rate. oriented to chart. 3, Check adjustment of electronic equipment, 7. Check readiness of navigation publications 4. Read coast pilot or sailing directions which (inoluding information concerning local nap, apply to harbor. vigational aids). 5. Determine estimated time of departure. 8. Insure that hand lead is on deck. 6. Consult Chief Quartermaster; locate and 9. If anchored, take frequent rounds of bear- study desired charts and insure that appli- ings during weighing of anchor to detect cable corrections have been made. drift. 7. Plot courses and distances on harbor and sailing charts. Include route points and Upon getting underway- times of arrival at route points. 8. Plot danger bearings and danger angles. 1. Keep running plot of ship's position using 9. Determine state of tide upon departure. available landmarks. 10. Determine state of current upon departure. 2. Advise conning officer of desired courses 11. Study light list; plot visibility arcs for and speeds and upon ship control, lights. 3. Man chains. 12. Study harbor chart of destination, particu- 4. Man searchlights at night. larly noting peculiarities which will affect 5. CIC commence radar navigation regardless navigation. of weather. If fog Is encountered, make a decision 13. Check proposed track against dangers to either to proceed by radar navigation or to anchor. navigation such as wrecks and shoals. 6. Note dangers to navigation and deficiencies 14. Determinetntaldistance and required in navigational aids for reporting to Oceanogra- average speed for the ETA if established. phic Office. 15. Note available electronic aids. 7. Check state of tide and current, and com- 16. Instruct the navigation detail as to indi- pare with predictions. vidual piloting tasks while leaving port. 17. Study pilot charts for information relative Upon leaving channel and passing sea buoy- to the voyage (current and weather). 18. Check markings on the lead line. 1. Lower pit sword(if so equipped); commence 19. Determine boundary between inland and operation of log. international waters. 2. Secure. chains. Continue operation of fa- 20. Confer with commanding officer. thometer, 4 hours before - 3. Set latitude and longitude dials, and start DAT. 1. If not in operation, start master gyrocompass. Before losing sight of land- 30 minutes before- 1. Obtain departure fix. 1. Station navigation detail. 2. Secure fathometer, unless desired. 2. Test fathometer, DRT, electronic equip- 3. Secure piloting instruments. ment, and communication system. 3. Check gyro and repeaters against magnetic (b) Navigation Check-Off List for Entering compass to determine gyro error. Port - 4. Check vicinity of magnetic compass binnacle to insure that all gear is in place ,Before sighting lane- and that no stray magnetic material will influence compass. 1. Read coast pilots or sailing directions 5. Record the draft of the ship. and note comments. 6. Check availability of bearing book, binocu- 2. Determine estimated time of arrival. lars, stop watch, drafting machine, parallel 3. Consult Chief Quartermaster; locate and rulers, navigator's case, charts, maneu-study desired charts and insure their correction vering boards, nautical slide rule (for corn - (cheek for late changes in local navigational aids). putations involving time, speed, and dis- 4. Determine state of tide upon arrival. tance), sharp pencils, art gum eraser, and 5. Determine expected currents.

132 Chapter 14-DUTIES OF THE NAVIGATOR

6. Start fathometer; record sounding periodi- 9. Set watch on lookout sound-powered phone cally and check approach. circuit (JL), 7. Determine expected landmarks and their 10. Man searchlight at night. oharacteristios. 8. Locate ranges and study buoyage. Upon entering channel or harbor - 9. Plot courses to be used while enteringport. 10. Plot danger bearings and danger angles. 1. Continue above as practicable. 11. Study anchorage chart and determine as- 2. HOWpit sword and sound dome, if re- signed berth. quired. 12. Ascertain pilot regulations and require- 3. Determine anchorage bearings; note adja- ments. cent ships and other possible dangers, 13. Check local harbor regulations and/or 4. Plot anohorage approach course (against applicable operation order or plan (garbage, current if possible). landings,customs, quarantine, forbidden an- 5. Clear sides if mooring alongside ship or chorage, cable locations, dredges, survey sta- dock. tions, survey boats, speeds, and special orders). 6. Man the chains. 14. Locate electronic aids to navigation (radio 7. Advise conning officer of desired courses direction finder, radio beacon, coast radar sta- and speeds. tions, loran stations, etc.). 8. When approaching berth, advise upon ship 15. Determine whether or not a degaussingcontrol (including theletting go of anchor). range is available and if a degaussing check is necessary or desirable. After anchoring or mooring - 16. Determine boundary between inland and international waters. Log time of crossing; notify 1. If anchored, get actual anchorage bearings, captain and conning officer. plot and enter them in the log. Use sextant and 17. Ifat night, determine characteristics of 3-arm protractor if necessary. expected lights and check chart data w1'.h light 2. Determine draft of ship and enter in the list;record the expected time of sighting of log. major lights. Give a list to the COD. 3. Adviseasto desired scope of anchor 18. Check markings on lead line. chain if anchored. Plot scope of chain (radius 19. Exercise watch on both surface search of swing). azidairsearch radar to determine distance 4. Determine and log the actual depth of and shape of coast. water and type of bottom. 5. Check distancestoadjacent ships and landmarks. Compare with radar ranges. Upon sighting land - 6. Ifin unsurveyed anchorage, determine soundings and character of bottom in circular 1. Locate position of ship by landmarks as soon area having a radius equal to 1 1/2 times the as practicable. Correct latitude and longitude swingiAg circle,with theanchor at center. dials on DRT. 7. Check expected currents and if anchored, 2. Take soundings continuously. put over drift lead. 3. Check compass error on available ranges. 8. Locate landings if anchored. Notify OOD Insure proper speed setting on master gyrocom- of boat compass course to and from landings. pass. 9. Recheck ship's positionif anchored as 4. Note dangers to navigation and deficiencies soon as ship is steadied against current. Advise in navigational aids for reporting to Oceanogra-captain whether anchor is holding. phic Office. 10. If anchored, station the anchor watch. Take 5. Station navigation detail. Prepare bearingbearings to detect dragging. book. 6. Keep running plot of ship's position using 1404. COASTAL PILOTING available landmarkii. 7. CIC commence radar navigation regardless Coastal piloting makes useofthe same of weather. If fog is encountered, make a decision principles as harbor piloting. Although the period either to proceed by radar navigadc ar to anchor. practiced may be so extended as to work a physical 8. Check state of tide and current, and com-hardship on the navigator, safety requires that pare with predictions. the navigator identify all aids and be on deck to

133 A NAVIGATION COMPENDIUM witness all course changes. This requirement is (2) Position: In line three, record latitude necessary because of the proximity of danger. and longitude (for 0800, 1200 or 2000) and time of The navigatorshould constantly be governedobservations upon which position is based. In by the thought "a mariner's first considerationline four, indicate type of fix (celestial, D.R., is the safety of his vessel," loran, radar or visual). Label latitude and longitude. Label time, indicating zone. 1405. NAVIGATION AT SEA (3) Set and drift: Compute and record on line five as follows: The set is the direction of The navigator's sea routine is as follows:the fix from the DR position of the same time. The drift in knots is the distance in nautical Morning twilightObserve stars and compute miles between the fix and the DR position divided star fix. by the number of hours between the times of the last two fixes. Drift is speed. Sunrise (or after)Compute compass error. (4) Distance: Also on line five, record dis 0800Make position report. tance made good since last report, giving the time first and the distance second, After "Distance to," ForenoonObtain morning sun line. Compute on line six, write 'neither the name of the destina- time cf LAY tion, or a designated route point, and record the LANObserve sun on meridian and compute distance' in nautioal miles. Note the time and date latitude. Advance morning sun line and obtain of ETA. running fix. (5) Compass data: Record true heading and gyro error. Two blanks are available for gyro 1200Make position report. error since heavy ships may carry two gyro- AfternoonObtain afternoon sun line. Advance compasses, Record variation. Check "STD," latitude line obtained at LAN and plot afternoon "Steering," or "remote IND" to identify the running fix. Compute time of sunset and prepare magnetic compass. Record the compass heading list of evening stars. which differ t from true course by compass error. Record actual and table deviation. Remember Evening twilightObserve stars and compute that the algebraic sum of variation and deviation star fix. is compass error. Use degrees and tenths of 2000Make position report. degrees and label all values except heading as "east" or "west." Check degaussing as either NightCompute time of sunrise and prepare"on" or "off." alistof morning stars. Plot DR for night, (6) Remarks: Make recommendations as making allowance for expected changes in course, tochanges in course, speed, ana zone time. speed, and zone time. Observe Polaris, if a Inform the captain of navigational aids expected compass error check is desired, and if in northern to be sighted, using back of report if necessary. latitudes. Provide navigational data for captain's This report ordinarilyshould be sufficiently night orders. complete to provide the captain with all information necessary to write the night orders, 1406. PREPARATION OF THE POSITION Example: "Recommend c/c to 050 (T) at 2200 REPORT with Frying Pan Shoals Lt. Ship abeam to port, distance 4 miles. Sight Diamond Shoals Lt. Ship The following condensed instructions should bearing045(T) at06z3, distance 16 miles. enable the navigator to properly fill in and sub-Characteristics GpF1 W ev 26 sec (3 flashes). mit written reports of the ship's position: At 0700 with Diamond Shoals Lt. Ship abeam to port, distance 7 miles, recommend c/c to 000(T); (a) OBJECTIVETo inform the commandingc/s to 17 kts." If you are unable to obtain neces- officer and flag officer (if embarked) of the ship's sary data, leave appropriate spaces blank and position, together with recommendations that may explain under remarks. be appropriate. (7) Signature: Sign name and indicate rank. (b) INSTRUCTIONS FOR PREPARATION (8) Addressees: The report always goes to (1) Heading: Record name of ship, time and the commanding officer. If any flag officers are date on first and second blank lines. Time willembarked, insert their titles under "commanding be 0800, 1200, 2000, or such time as the COofficer" and prepare copies for them. Retain desires. one copy for your file. 134 Chapter 14DUTIES OF THE NAVIGATOR

1407. LIFE BOAT NAVIGATION size, appropriate information should be extracted and retained. (1) PORTABLE RADIO. To obtain time sip Should an emergency arise which restricts the nals, a portable radio is useful. navigator's tools to the equipage of his life boat, (j) SLIDE RULE. A slide rule with a sine then he must modify the procedures described in scale can be used in sight reduction. this' compendium to fit the situation. Success in (k) DRAMAMINE. Since a sea sickness pre- life boat navigation may be a measure of theventative may act in the interest of the naviga- navigator's foresight and resourcefulness. tor's personal efficiency, dramamine tablets have The forehanded navigator accepts the possi- a place in the kit. bility of shipwreck and prepares one or more navigation kits to supplement the equipage regu- When the ship is abandoned the navigator larly carried by his ship's life boats. The navi-should accomplish thefollowingifpossible: gation kit should contain the following: (a) Wind the watch and determine the watch (a) An OILCLOTH CHART of sufficient areaerror. to show the ship's position if abandoned. (b) Record (or at least remember) the date. (b) SEXTANT. 1%; inexpensive instrument may (c) Record the ship's position. A recent fix be substituted for' the commonly used endless or a fairly accurate EP is most essential when tangent screw sextant since accuracy is notabandoning ship and also on the occasion of paramount. "man overboard." (c) COMPASS. A pocket compass is small (d) Record magnetic bearing of nearest land and inexpensive and may be the only direction and the magnetic variation. reference if the beat compass carried by your (e) Insure presence ofthe navigation kit. life boat becomes lost or damaged. (d) ALMANAC. The convenience of using the After the ship is abandoned, make an ostimate Nautical Almanac and especially the star dia- of the situation. Consider every possibility, then grams which it contains makes this publication(1) mentally list and compare the advantages and worth its space. An oilcloth copy of the star disadvantages of each, (2) compare the possible diagrams, such as may be found in the Air Alma- outcomes of each, and (3) formulate an alternate nac, should be carried if available, plan to be followed in the event of failure of (e) TABLES. The appropriate volume of H.O. each major plan. Make a decision as to your 214, or other navigational table. course of action. Generally, the choice will be (f) PLOTTING EQUIPMENT. A Hoey position between remaining in the immediate vicinity and plotter, pencils, and erasers are essential. Theproceeding toward .some land or haven. Record Hoey plotter is especially important since itthe decision in your notebook and start a log. provides both a protractor and a straight-edge;Make a compari.Jon of watches, if more than itis alsoa crude substitute for a sextant.one is present, as insurance of correct time. (g) NOTEBOOK. Thisbook should contain Check speed by the chip log method (art. 303) space for computations and a section devoted toand insure that the compass is free from mag- a compilation of useful formulae; if an Almanac netic influence other than the earth's. Establish is not available within the navigation kit, then your daily routine. extracts may be recorded in the notebook. In Start a dead reckoning track upon your chart, addition to this notebook, position plotting sheets or commence dead reckoning mathematically, or other suitable plotting paper should be included in order to .tarry out your course of action. If in th3 kit. If a chart is not available, then the dead reckoning is to be accomplished by mathe- coordinates of several ports should be recordedmatical rather than graphic means, the navigator in the notebook. It is advisable to include datamay use the traverse tables which provide a on prevailing winds and currents. simplified method of solving any rignt triangle; (h) AMERICAN PRACTICAL NAVIGATOR. if desired, extracts from these tables (which This volume can be most valuable. It containsappear as Table 3 in the American Practical much information on weather and currents, tables Navigator) may berecorded in the notetx-i.,.: for sight reduction, a long-term almanac, traverse urging the preparation of the navigation kit. tables for mathematical dead reckoning, and tab- Check theaccuracy of your compass in the ulated coordinates of world ports. If includingnorthern hemisphere by observing Polaris, as- the entire volume is not desirable because ofsuming that its Zn is 000. Magnetic variation

:.35 A NAVIGATION COMPENDIUM

should constitute the entire compass error in athe end of the drafting arm of the Hoey plotter. life boat, in either north or south latitude, anySight along the straightedge of the protractor body will reach its highest altitude when in(diameter) and allow the weighted drafting arm uppertransit (azimuth 000 or 180) and willto seek alignment with the direction of the force thereby provide a compass check. At night,of gravity. Record the angle on the protractor not only Polaris, but any star near the prime scale between the 0 mark opposite the body and vertical, if 'visible, can be used for a directionthe center of the drafting arm. This angle is the reference. altitude. To correct a measured altitude when the To measure the altitude of celestial bodiesNautical Almanac is not available, the following in the absence of a sextant, attach a weight toinformation should be tabulated in the notebook:

Refraction Correction for Altitude Semidiameter Alt. Corr. Alt. Corr. Sun (upper limb) -16' 5-6° -9' 13-15° -4' Sun (lower limb) +16' 7° -8' 16-21° -31 8° -7' 22-33° -2' 9-10° -6' 34-63° -1' 11-12° -5' 64-90° -0

To find the approximate declination of the sun, To obtain a line of position by a horizon sight, draw a circle with horizontal and vertical dia-no sextant is needed, For a horizon sight in the meters. Label the points of termination of thecase of the sun or the moon, either limb may be diameters as follows, commencing at the topused, The Hs, which is 0°, is correctedfor height and moving clockwise: June 22, Sept. 23, Dec. 22, of eye (dip), refraction and semidiameter. Sight and Mar. 21. Locate a given date on the circlereduction may be accomplished using H.O. 211 with respect to the equinoxes and solstices or H.O. 229; H.O. 214, however, is not applicable using proportional parts of any quadrant. Divide for sights of less than 5° altitude. It should be the upper vertical radius into 23.45 equal partsnoted that when both Ho and He are negative, the to indicate north declination, and dividethe lower intercept is "away" if Ho is the greater, and vertical radius into 23.45 equal parts to indicateconversely, the intercept is "toward" if He is south declination. Draw a line from any giventhe greater. date on the circle perpendicular to the vertical Horizon sights may be reduced through the to determine the declination on the given date.use of a slide rule with a sine scale. The following The LATITUDE may be determined as follows: formula applies:

(a) In the northern hemisphere, by an observa- sin He =.sinl-sin d + cos L cos d cos t tion of Polaris. . (b) By a meridian sight of any body. In the formula above, if t<90°, and latitude and (c) Note bodies at or near the zenith. Thedeclination are of the same name, the sign is latitude of an observer equals the declinationpositive; when latitude and declination are of of a body in his zenith. contrary name and t<90°, the lesser quantity is (d) If the Nautical Almanac is available and subtracted from the greater. If t.90°, and latitude the date is known, note the duration of daylight and declination are of the same name, the lesser which is a function of latitude. quantity is also subtracted from the greater; if latitude and declination are of contrary name and The LONGITUDE may be found by observingt>90°, the sign is positive. If the sine of His and noting time of meridian transit. negative, HC is negative. Azimuth angle may be found using the formula: A LINE OF POSITION may be obtained by noting the time of sunrise or sunset, or the instant an,: cos d sin t celestial body coincides with the visual horizon. sin Z =cos He

136 Chapter 14DUTIES OF THE NAVIGATOR

Since the cosine of He in a low altitude sight then when Diphda is in upper transit, the local approaches one, or unity, division by cos He sidereal time is 0042 because Aries transits our is generally unnecessary. local meridian (LST 0000) earlier than any given In horizon sights, the azimuth should also star by an amount of time equal to the RA. From be checked to determine compass error. Tosidereal time we subtract the difference between compute Zn, one needs to know only the declina- it and solar time (which depends upon date as tion. With north declination, the body will rise explained above) and we arrive at solar mean and set at points on the horizon north of thetime. prime vertical an angular distance equal to the It is generally best to practice latitude or declination. With south declination, the body will parallel sailing, since latitude computations are rise and set at points on the horizon south of the apt to be more accurate than longitude computa- prime vertical an angular distance equal to thetions. In parallel sailing, the navigator sails in declination. a general direction of either north or south until Should the watch or other timepiece stop, he reaches the latitude of his destination. Then it can be reset by an observation of the stars andhe changes course to east or west and makes a reference to a star chart. The navigator re-adjustments as necessary enroute in order that members that sidereal time and solar time arehis track will adhere to the parallel of latitude equalat the autumnal equinox; at the vernalof the destination. The navigator should try to equinox, sidereal time is 12 hours fast on solar compute his daily advance, which among other time. For any date in between the equinoxes, uses, acts as a check against the longitude when we can compute the difference between siderealtraveling east or west, and as a check against time and solar time as we know that siuereal the latitude when traveling north or south. time gains 3 minutes and 56 seconds daily. If When landfall is finally made, identify avail- we see on the star chart that the RA of Diphdaable landmarks and approach with caution until (for example) is 10-30' or 42 minutes of time, able to select a safe landing site.

137 APPENDICES

Appendix A Nautical Chart Symbols and Abbreviations (Chart No. 1) Appendix B Useful Physical Laws and Trigonometric Functions appendix C Extracts from Tide Tables, East Coast, 1970 Appendix D Extracts from Tidal Current Tables, East Coast, 1970

Appendix E LuminousRangeDiagram/Distance of Visibility of Objects at Sea

Appendix F Extracts from The Nautical Almanac,1970 Appendix G Extracts from Tables of Computed Altitude and Azimuth, H.O. 214, Vol. IV

Appendix H Mechanics of "Error Finding" in Sight Reduction by HO 214

Appendix 1 Extracts from Sight Reduction Tables for Air Navigation, IM 249, Volume 1 Appendix J Extracts from Sight Reduction Tables for Air Navigation, HO 229, Volume 3

Appendix K U S. Navy Navigation Workbook, Format and Instructions, including Forms Appendix L Additional Celestial Work Forms

138 Appendix A MA1LASILE 6ES100 GENERAL REMARKS

('blurt Su. I contains the standard symbols and abbreviations which have been approved fur use on nautical churls published by the United Statesof America. Synohols and abbreviations shownOn(*hart No. 1 apply to the regular 'mut iettl Omni.) and may differ from those shown on certain reproductions and special charts. Symbols ?mt.l abbreviations on certain reproductions and on foreign charts may be interpreted by reference to theSymbol Sheet or Chart No. 1 of the originating country. TerMN, NyillboN um, abhreiqut inns are numbered in accordance with astandard form approved by a Resolution of the Sixth International Hydrographic Conference,1952. Vert/eft/y/we:4 indicate. those items where the symbol an.i abbreviation are in accordance with the Resolutions of the International Hydrographie Conferenees. Slanting figures indicate no International Hydrographic Bureau symbol adopted. Slanting figures underscored indicate U.S.A. and I,H,B, symbols do not agree. Slanting figilreN UNterisked indicate no U.S.A. symbol adopted. An up -to -dote euplintio of symbols and abbreviations approved by resolutionsof the Inter- national Hydrographic Conference is not currently available. Use of I.H.B, approved symbolsand abbreviations by member nations is not mandatory. Slanting letters in parenthesesnalicate that the items are in addition to those shown on the approved standard form. (Vors are optional for characterizing various features and areas on the charts. 1ot/yin/1 styles and capitalization as used on ('hart No. I are nut always rigidly adhered to on the charts. Lottgitmies are referred to the Meridian of Greenwich. Sett/es are computed on the middle latitude of each chart, or on the middle latitue of a series of charts. 110/dingsA conspicuous feature on a building may be shown by a landtmo:k1.mbol with descriptive note (See I-n & L-63Prominent buildings that are of assistance to the mariner are crosshatclted( See I -3 a.:1. & 66l. Simefirw is the line of Mean High Water. except in marsh or mangrove areas, where the outer edge of vegetation t berm !Mei is used. A heavy line t A-9 is used to represent a firm shoreline. A light line( A-7) represents a berm line. Heights of land and conspicuous objects are given in feet above Mean High Water, unless otherwise stated in the title of the chart. bepth rimtmies mid Smidings may be shown in meters on charts of foreign waters. l'isitn'ity of a light is in nautical miles for an observer's eye LI feet above water level. ilimys owl lletirons On entering a channel from seaward, buoys on starboard side are red wit h even numbers. on port side black With odd numbers. Lights onbuoys on starboard side of channel are red or white. on port side white or green. Mid-channel buoyshave black-and-white vertical stripes. Junction or obstruction buoys. which may be passed on either side, have red-and-black horizontal bands. This system does not always apply to foreign waters. The dot of the buoy symbol, the small circle of t he light.essel and mooring. buoy symbols,and the center of the beacon symbolindicate their posit ions. bnprord ciottito/N are shown by limiting dashed lines, the depth. month. and the year of latest examination being placed adjac-nt to the channel, except when tabulated. U. S. Coast Pilots, Sailing Diretions, Light Lists, Radio Aids, and relatedpublications furnish information required by the navigator that cannot be shown conveniently on thenautical chart. S. No idiot! Chart Catalogs and Indexeslist nautical charts, auxiliary maps. and related publications, and include general information t marginal notes, etc.) relative to the charts. .1 //Jos:ult.!, of foreign terms and abbreviations is generally given onthe charts on which they ale used. as well as in the SailingDireetions. churl,i,lrrurllton issue will he brought into conformity its soon as opportunity affords. All hangeu since the September 1963 edition of this publication are indicated by thesymbol t in the margin immediately adjacent to the item affected.

Published at Washington, D.C. U.S. DEPARTMENT OF COMMERCE ENVIRONMENTAL SCIENCE SERVICES ADMINISTRATION COAST AND GEODETIC SURVEY

139 The Coastline (Natureof the Coast) lsee General Remarks) awe.Y. WAY. 14.11;) 10

4.1:fZ"t ; ,3

11d Rock, unc-ets al sounding Mangrove .Shoreline tin3u,'1,tredMlaim....3 Mum(See A-119) A-4:7,4.,-73VVVhu:,..;ia-1`41'"zit.2"5

fa.

!le Sand and mud

:,1 esism.voi 12 Preakers along a shoie I5,?1, 0 251

t(Aul APproirunale low water line V_ -, r

Orr

..cdoch's, Dunes laLulu,of unsu,vflyed wpas

5 cf,,nv n Si)11(21y..ht"''''? r MI) Rubble I I hland

/ it",ryies, Sh,nzi Gravel L.= 140 B. Coast Features The Land (Natural Features) C. _ I (i 2 11 Bay ( au) Bayou (\ 5c,_,ev, Leon 3 Ft, fjord i7-0' 15 Lake; Pond 4 L Loch, Lough, r \l4W.

Lake 1 Contour. lines (Contours,5e Pato 5 Cr Cteek 01111141 5a C Cove 1414,*: :ii; V- .; ,, It V + 16 Lagoon (Lag) //1 Intel 116...... it,ii:I') .... 1 t'N% 5f Casuarina 6.1..... 7 Strait it ,11'Al,;,..,::.% ,' 8 Sd Sound !,1,. ; Zg,',xR:.. "s - ' 0 e 9 Pttss Passage, Pass 2Evergreen tree Nvitihei (MN/ .1o:rig/Ara/Tees, ,,,.iiiii 11 urvo% 1 Thar() Thorofare 1 a (Contours) °Yother than coniferous)

10 Chan Channel 610 .""si.. Milli :II- l flt s Nea.-'' Cultivated il..,....,... Swamp ) 10a Narrows I , uno : ks, II r Entrance %. 6Cii!livaed fields 17 A 'ars'', Jwatnp 13 ES1 Estuary 62:;06 4,, ...... 12a Delta ,- -,-iA 111;2"""44N Grass 13 .111h Mouth 2 Hachures. 6a Grassfords 14 Rd Road, Roadstead 18 Slough ISlu ) 15 Anrh Anchorage N.,7_,,...--".... jiiii.. :4:::::vs% .,, r. ice %AI, VIlib 16 Hbr Harbor , . 7 r,At 41,1* )° Paddy (rice) fields 16a lin qa le 6 ' .z. ..1 17 P Part rt '' AlOW.*Th\ % 19 Rapids 111h) P Pond Form lines, no definite 2a 7a Perk, Garden 18 1 Island interval 19 It Islet i , 1 . ' 11111111111110111 Bushes ' ' ;. 20 Arch Archipelago .., 40001 . ,.., 21 Pen Peninsula 8Bushes 20 Waterfalls 22 (. Cape .....:.P 1% . ., 23 Prom Prumontory . Adis''V... %. *. ii ,,..Tree plantahon 24 ild Head, Headland 2b Shading a" in general 25 Pt Point 21 Spring 26 NI Mountain, ::14 ..,-,...... ,,,,' Woode.,i 046!I:10*A; mime

Mount 4.. , .1 , t9 Deciduous wood /and 27 Kilt. Range -...---..-4;4,.44 27a Valley Wooded 1:1".14.44. 28 SUMMIt 1` 3Glacier 10 Coniferous wood /and 29 Pk Peak 30 Vol Volcano der. ...-. Wooded 44Ve 4 31 Hill tili4411.4 32 lild 80.,Ider t 1 Oa Wnods in gene, a/ 33 IAA Landing 4 Si cS 2560 34 Table-land Tree tor elevation (Plateau) QTREE 11(above height datum! fa? 35 Rk Rork r 4 36 mdock 5 Isolated trees 4' ." ifir :,,, (11(.) Stream _4',--,,, 4 tlid1 ,..... , ---..1,..--e- 1.. we) .S/u 5l::,/9 h 12 Lava flow '811 Lay Lagoon Decidi.ous or of :inknow (110Apprs 5a c, -nsceified type (llh) Rk y Rocky 13 P.,en; Stream 5b Coniferous

5c Palm tree 14in er-, ile,), stream.

141 jectives, verbs D. Control Points and other abbreviations

A Tr iangulation point (station) 1 Kt Great lit Little tia Astronomic Station 2 3 IN Large 2 0 Fixed point (landmark) (See L-63) 4 sibl two 0 Fixed nom, (landmark, posion approx 5 (Lie, Ei 3 256 ,Sumn.t 01 heiyht Wed.() (when not a landmark) 7 Middle 8 Old (1)b) 6256 Peak, accentuated by contours et 9 anc .incient (1k).04256 Peak, accentuated by hachures 10 New (Mb Peak, elevation not determined 11 St Saint 12 conspic Conspicuous 0 256 Peak, when a landmark 13 ReindrAable 4 Ohs Spot Observation spot 14 0Pest,Destroyed 5 BM Bench mark 15 Projected 16 dist Distant t6 ViewX View point 17 abt About 7 Datum point for grid of a plan 18 See chart 8 Graphical triangulation point 180 See plan 19 Lighted; Luminous 9 Astro Astronomical 20 sub Submarine l0 Tr, Triangulation 21 Eventual 22 AER 0 Aeronautical ( Of) C114E Corns of Engineers 23 Higher Great trigonometrical survey station 12 t 23a Lower 13 Traverse station 24 exper Experimental 25 discontdDiscontinued 14 BO Mon Boundary monument 26 prohlb Prohibited (I)o)0 Inteinational boundary monument 27 explos Explosive 28 estab Established 29 elec Electric 30 prtv Private, Privately 31 prom Prominent Units 32 !,td Standard E. 33 subm Submerged hr Hour tl4a Greenwich 34 aprox Approximate t35 Maritime 2 n rtlit! Minute fof time) 15 pub Publication 36 maintd Mdintained 3 t.: E1 Second (of time) 16 Edition t 3 7 aband Abandoned 4 111 Meter 17 ( Correction t38 temp Temporary 4a Decimeter 18 q Altitude t 39 occas Occasional t 40 extr Extreme 4b Centimeter 19 ht Height,. Elevation t41 Navigable 4c ,T1 r1 MIIIIMeter 20 Degree t42 N M Notice to Mariners 4(1 '71; Square -etw- 21 Minute (of arc) t(ha)L N M Local Notice to Mariner 4ert C<,trc meter 22 Second (of arc) t 43 Sailing Directions t 44 List of Lights 5 Kilometer 23 Nu Number (Ph)onvetd U17Velif,P(J 6 Inch WO St M Statute mile , (Pc) AUTH A,. 'horsed 41 7 Foot (Eh) msec Microsecond (Pd) CL Cleardnce (Pe)(or Corner 8 . 1 Yard if Er) Hz Hertz (cps) ron(r Concrete 9 Fan9m tlEd) kHz Kilohertz (kc) (Pp)f! Flood MHz Megahertz (Mc) /0 h. Cable length tr/5 (Ph) mod Mod,?rate 11 M Mle MY) cps Cycles/second(Hz) (Pi)bt Hetwee,, 12 Knot tlet k( Kilocycle (kHz) (F)) 1st First (Fic)2nd Second 12a t t(Eh)Mt Megacycle (MHz) (PI)3rd Third 12b (Pm) 4th Fourth 13 Latitude 14 Longitude

142 Ports and Harbors 1 I AnchAnchorage (large vessels) 20 Berth 12 AnchAnchorage (small vessels) 3 Hbr Harbor 20a Anchoring berth 4 Hn Haven Part 206 3 Berth number 6 11 B k vv Breakwater 21 Dol Dolphin 22 Bollard WI/WY WiM11111111MBIA 6a AMPIPM Dike 23 Mooring ring Mole 24 o- Crane 25 Landing stage 25a Landing stairs 8 Jetty(partly below MHW) 26 Q Quarantine

27 Lazaret 8011111.1 Submerged jetty 26 Harbor MasterHarbor master's office 29 Co. HoCustomhouse Wa11111111' Jetty (small scale) 30 Fishing harbor 31 Winter harbor 32 Refuge harbor P,.,1 Pier 9 33 Hbr Boat harbor 34 Stranding harbor (uncovers at LW) 10 Spit 35 Dock

11 Groin /partly below MHW) Dry dock (actual shape 36 on large-scale charts) Anchorage prohibited 12 Floating o'ock(actua/shape ISee P-25) 37 on large-scale charts) t 12a Anchorage reserved 38 Gridiron, Careening grid Patent slip, Slipway, 39 Marine railway 1126 Quarantine anchorage lir Ill"- 39a OIL Ramp Ramp Lock (point upstream) 13 Spoil vcund t40 (See H -13) 41 Wet dock Oc mpi grouriy (Gb)111.1.11 42 Shipyard 43 Lumber yard r-8707sposar4rea 851 (GE l Depths hot, surney Lli;05d1 area 44 LQJ Health Office Health officer's office of JUNE /968 90 Hulk (actual shape on irg L 45 111111b-, Hk --IQj scale charts)ISee 0-11) 14 NIVAINII ishties, Fsh,ng5takes 46 Prohibited area Fish tr,w, F.sh 14a c hd, fP(11 Calling-in point for vessel t46a 14h Dock bhnd traffic control

15 Tinny nets :See G-14d/ 47 Anchorage for seaplanes ION 48 Seaplane landing area

15a Oys Oyster bed Under Work in progress 50 construction Under construction 1 Larchng place 491 Work projected 17 Weer ,'g place T51 Whdri ((;il) Submerged ruins M 11111116M1111 19 Quay

143 H. Topography(Artificial Features) Canal lock ASCII ,Sluice (Tidegate, Floodgate) Small Kok chon t13Canal, Ditch, Lock, Sluice (point upstream)

1 Road (Rd) or Highway (Hy )

to o11.tallt chair --4.---4.--4.-4 . t Ha 1Highway markers 11=Er t14 Bridge BR Iin genera/ 2 Track, Footpath, or Tral: MEL $ RR 14a Stone, concrete bridge (Same as H-14) 44 iii I 1 1

41. Wooden bridge (Same as 1-1-14) -11. Tr- Same geode h abon h 14C Iron bridge /Same as H14) 3 Railway( (single or double track), Railroad ( R R ) 14d Suspension bridge (Same as H-I4) 4 4 a , 1 1 1 1 I I 30 Tramway

3b Railwdy stahon 15 Drawbridge lin general,

16 Swing bridge (Same as H-15) 3c Tunnel (railroad or road)

...waymp imail...141.1&111.14.1A Wayuhmuu. .4.,nrownrwrnn...nwnwfwm...149.... 3d Embankment, Levee 16a Lift bridge ., iiiiiiiiiii ..,..al.bas4LIM1Y dada V1.1.1.1.11111.1.14.11.11.1.1. 3e Cohn

t31 Causewa OVERHEAD POWER CAE LE 40E501412ED CL 140 FT 16b Weighbridge or Bascule bridge

TOWER TOWER

Overhead power cable ,ovHD P*17 CAB 1

17 Pontoon bridge

Power transmission line 17a

5u Power transmission mast Transport'', tr dge 1..)ame as H-I4) - - - - . __ 18 Tel VERT CL 6 cf 6 1-3rnm,nent telegraph or telephone line 18a Bridge clearance, vertical

7 A .lueduct, Water pipe HOP CL 26 FT Viaduct 18b Bridge clearance, horizontal Ferry 814adv:

Ferry PI,ehne t8a 0- pipeline 19 Ferry (F y) 0n wall gait chg.

Atig ;ffiitMON ea Mil Cableforty t9PilePiling, Post (above MI1W, ISee L (; 30/ t(tlb)Cable terry 20 Ford 9a Mast ()MAST °Mast

21 Dam 10 -I,ghway /see H-I) r--22 Ferke 11 Sewer 23 Training wall

12Culvert 24 Log boom 144 I. Buildings and Structures(see General Remarks)

Locust Ave 1 -tr-nr City or Town (large scale) 26a Ave . Avenue 110 tfJ # 0 nCity or Town (small scale) t26b Blvd Blvti Boulevard

2 Suburb 27 Tel Telegraph

3 V.1 Village 28 Tel Off Telegraph office 3a L_ J Buildings in general 29 P 0 Post office

4 CdN Castle 30 Govt Ho Government house

5 Um 0 House 31 Town hall 6 Villa 32 Hasp Hospital 7 Farm 33 Slaughterhouse 8 + i C Church 34 M agz Magazine 8a + Cath Cathedral 34a Warehouse, Storehouse Ilh OSPIRE0 Sote. Spire, Steeple

9 Roman Catholic Church 35 °MON 0Mon Monument t10 Temple 36 OCUP Cup Cupola

11 + 37 OELEV 0Eiev Elevator, Lift t12 CMhods:e (lel Eie, Elevation, Elevated Minaret t120 <.) 38 Moslem Shrine 39 6-, o t13 O Marabout 40 _..:Runs Ru Ruins 0 t14 Pd4, Pagoda 41 OTR I i Tower t15 , Buddhist Temple, Joss-House'KM °ARANO LT HO Abandoned 1.9nthouse t15a 1:4 Shinto Shrine 42 .6 *-OwINoMiLL Windmill

16 Monaste-y, Convent t43 zs Water/nil/ 17 Calvary, Crass 43a oWiNOMOTORWindmotor 17a i Cemetery, Non-Christian Cem 44 OCR / Chy Chimney, Stack 18 Cemetery, Christian

o 18u Tomb 45 OSPIPE 5 punt Water tower, Standpipe

19 Fort loCrad .;nd.Oe f.na,tedi 46 ID Oil tank t20 \.r Battery 47 D F.tc ty Factory 21 Barracks 48 Saw mill

22 Powder magazine 49 Brick kiln

23 Airplane landing field 50 X Mine, Quarry Airport; 24 Airport, large scale (See P-13)51 °weii Well

Airport. military (small scale)52 Cistern

Eft. 'NM) .1 krpor, t,Civil (small scale) 53 °TANK oTk Tank

25 Itifoorg mast 54 Noria King St 26 St Street 55 Fountain

145 I. Buildings and Structures(continued)

61 in 50,',cite 72 0 DAS 006b Gable

62 73 Wdlr

63 !Jo, ,n,t,et!t t 74 Pyramid

64 Ct Hi,Courthouse 175 Pillar

65 Slit School 1'76 darich

(4))r t IS High school Ltd Limited

(M1 ; Why (IP A Apaitineni

66 EScl Bldg Bu,c1,/t9 (1k) Capitol

67 Pav Ravi/ion 1111 Cu Company

68 Hut Curt, :of ow --own

69 Sladum (In)0 Landmark (conspicuous object)

70 T Telephone (M) Landmark (position approx.)

/1 Cid, lank, Gasz-,^otef J. Miscellaneous Stations

I Sta Any kind of Vahan 13 Tide signal station

2 Sta Station 14 Stream signal station

3 xC G Coast Guard station 15 /ce signal station (Similar to Lifesaving Sta.) 16 Time signal station

OWALLISC Coast Guard station t 16a Manned oceanographic station SANDS (when landmark) t16h Unmanned oceanographic station

t4 0 LOOK TR Lockout StV:0/,, 'Cr) tower 17 ball

5 L,febcat station 18 5,(ra

6 Lifesav ng station r°FS Opp ar LS S (See -3) 19 FIdOSldif i;dypol, 0 FS 0FP

t 19a ofIt ' /dg tower Rkt Sta Rccket station OF TR 20 Signal 8 ct O IL STA P1,), sdhor 21 Observat:,v 9 S 'It., staton 22 Ott 10 a (.1c) BELL Bel' tor, lard) JI S S St.'SOf r 3 4rd' Std',) rldJ ° HECP Harbor entrancecontrol post 12 5

(.1b1 Ow8 SIG STA t/eahe But-ea, ;tindi stat, ;

146 K. (I new optionol symbol) Lights

* Position ol 1,9h, 29 F Fixed and flashing light

Light 30 F iiF. f,xeo' dno' group (lashing light tKo' t30a M o Morse coo'e light

3 t PI 31 Hot Revo/..,,,y or Rotating light

4 tik AEPO Aeronautical light (See F-121 e,.0 e ,.d. ,.ght 41 Per ,ocl

5 Bn Bn Light beacon 42

6 43 Wi ii'

9 S'ieet lamp (Kb) M Aid .7 fee - 10 REF Reflector (Kc) m min (See 1-2; 11 Lcie Lt Leading light ,(Kcl) sec (See 1-31 12 Sector light 45

13 Directional light 46 0., 0

46a t.:01 se 14 1-1d, bo, bythi 47 15 F 37ftit

16 'Ord/ qh 48 0 b hgh. 9h ;PIA is: 17 'S, te 49 `-t4

21 -tev 50 :.),

22 9.r,t 51

23 52 t23a E Int Iso,ohase light (equal interval) 61

24 :v.. I f.- 62

25 lilt QkFl 63 I Qk F1 64

25a "tie s 65

26 t.. .1 , 66

27 67

28 ; 07,p,h,n; b9h 67a A..

28a sq,15h,r9 68 OBSC Ob... ..ed 19ht

281' ,9frit t68a fog De. L, Fog de'ector light 'See N-Nb) L_

147 Lights(continued)

69 itat.It.k/ ;. 79 Pi ow

70 OCCAS .Q 80 Vert Vet ',Lai /'ones

71 Iffeg ;",e4, -d. 1,9h 81 Hor Ho, zo-a,yhts

72 Pro, (Kf) VB Ve-''Cd%Dews,

73 Temp re,'!Ou'd'y (Kg) ROE Range

(KO D Destr 3e,o, (Kh) Expo: E...oe,inenrai

74 E xtmg f she° (KO T R LB Temporarily replaced by lighted buoy showing the 75 ird,r het same characteristics (KJ) T RUB Temporarily replaced by 76 yh unhghed buoy 77 t..14,e;in (Kk) T LB Temporary lighted buoy 78 Rea Or (K1) TUB Temporary unlighted buoy Buoys and Beacons (see General Remarks) Fos !,or of b,Cy 17 U Bifurcation buoy IRBHB) Loh' b,Oy 18 Junction buoy IRBHB)

3 Be 19 Isolated danger buoy !AWNS)

3u ti.Cy 20 Wreck buoy IRBHB or G)

W"r5 e OuOy 20a Obstruction buoy IRBHB or G)

Ca" C, 9) Telegraph-cable buoy

itifoor ri , (colors of moor - Nun Jr Co,ca bw.). 22 ing buoys never carried) Saner' a c,or 22a Mooring Mooring buoy ev,th fe/egedPh/C 22b commun..:afions

22c Moor,6g buoy w. h telephonic Pillar or Spindle buoy commurdca,ions Buoy with topmark (ball) 23 Warping buoy (see L-70) U 24 Qua, aht-ne buoy Ba. t24a Practice area buoy

25 anchorage tug, :.0, 25g1111111 Aeronaurica' anchorage buoy

26 Compass adiastment buoy 27IIII Fish trap (area) buoy (BWHB) 'way O or 'BPVVS) 27u Spoil ground buoy tr'.7.nae 18.4/./S1 1.28 Anchorage buoy (marks (,mits) S.i. ."- ior sea wa Private aid to navigation (buoy) t29 (maintained by private interests, f-1-a 7 ' /' use with caution) wa-d)

148 L. Buoys and Beacons (continued)

30 Tei-oor 55 Cardinal marking system (See Ki,j,k.1

30a W^ter buoy 56 Compass adjustment beacon

31 HO Horiontai st,pes or bands 57 Topmarks (See L- 9, 70)

32 VS Vertical str,pes Telegraphcable (landing) II 58 beacon

Checkered Piles (See0-30, H.9) 33 111 Chec t ag Diag Diagonal bands Stakes II t59 Stumps (See 0.30) 41 1:1 W itio, e

42 S B Black Perches

43 0 R Red

0, 44 Y yellow 6) ()CAIRN ;Am Cairn

4h .. G Green 62 Painted patches

46 Br i_?....w" 63 0 Landmark /conspicuous object) (See 0 -2) .- 47 dray (1.4) o Landmark (position "De approximate)

48 BL, 6;ue 64 PET Reflector

t48c1 A.- A ...t.e 65 ()MARKER Range ta-gets, markers

t48h 0, ::-.1-;. (Le) Special-purpose buoys

t66 Oil installation buoy

Drilling platform 51 r%)arng beacon t67 (See 0-0b, 0-0c)

Fred beaC9r hed of 70 Note: TOPMARKS on buoys and beacons may 14,bear, be shown on charts of foreign waters. Black beaf.or The abbreviation for black isnot shown adjacent to buoys or beacons. Cc,b, :,."kncrel

Radar reflector (See M-13) Private aid to nav,gation

53 n Beacon. ,n 9enedi (See L-52)

54 Towe,

149 M. Radio and Radar Stations

oR Sta 1 Rdcho te/espaph station 12 0Racon Radar responder beacon

2 °R T Radio telephone station 13 Ra Ref Radar reflectoi 'See 1.40 3 (6)R On Aphobed- on 14 Ra (console) Radar conspicuous object

4 C01R Bn C ri ti tar radmbeacon 14a Rainarli

Distance finding station 15 D S echonal radiobeacon, (synchronized signals) 5 R0 Rao range AFRO R Bn 6 Rotating loop ,dthobecicon t16 302 Aeronautical rachobeacon

t17 Dacca Ste Dacca station 7 R D F -each° diteolon finding5tdhon Loran Ste t18 Venice Lo an station (name) (Ma) TELEM ANT Telemetry antenna CONSOL Bn t19 190 Kc Consol (Consolan) station t(.v/h) 0 n RELAY MASTRadio relay mast MMF

t (Mc)°MICRO TR Microwave tower AER 0 R Rae 342 LI: Aeronautical radio range R MAST Radio mast Re Ref 9[0 pi TR Radio tower We) Calibration BnRadar calibration beacon

t 9a 0 Ty TR Television mast; Television tower (-) LORAN TR (IVI1 SPRING ISLAND Loran tower frame) Radio broadcasting Station 10 0 &TALI R TR 1090 Kc IcOmme,c,air F R Lt Obstruction light

oR 10a Sta Q T G Radio Ita.on

11 Ra Rada, station

N. Fog Signals

rf.s.g'S(7'.,1, 13 .4, )RN Fog horn

2 i I,11,., t 13a HORN Electric fog horn

.1 f. r,, I 14

(3..1)"'d-f ; I" 15 3.. isksve

17 09 aig

5,9,7o, not s"o'e /See N- 5. 6 . 7/

/See N. 5. 6. 7)

( f,, F09 je?ector lap)! (See K 68a)

150 O. Dangers 1 ii ail INN HO, k A,.. 3. t- ..t I Wreck showing any WNW) of hull or 27 Obs 4.I..,14., supers', ac fur e (above sounding datum) ton /See General Remarks) r ti 28 Wreck /See 0.11 to 16)

MIS 12 Wreck with only seble (above sounding datum) 29 WI ec. kage 13 Old symbols !or wreck.. 251a Nref:k ,emains (dangerous 2 only for anchoring) 1111 13a 14,,e_k d,nch.S L'd duy ..beerged

30 Submerged piling (Sets H-9, L-59) 3 t14 Sunken wreck dangerous to surfac navigation (less than II fathoms over wreck)(See 0-6a) III . . . _ vVre"-;,-R of 0-2 or 0.3 is con- 30,1 SnagsStit 'P'ged stumps sidered a danger to navigation (See L-59)

15Wreck over whiCh depth known 31 ,site lio. Or --(See A-I0, 0-2, /0) t4 Sunken rock dangerous to 11111 33 Coy 1See 0.2, 10) surface navigation tl5aWreck with depth cleared by wire drag 34Uncor (See A-10; 0-2, 10)

16 Sunken wreck, not dangerous to 5 Shoal sounding on isolated rock surface navigation (replaces symbol) Reported (with date)

I7Foul ground t6 Sunken rock not dangerous to 35 Reported (with name and date) surface navigation (more than II fathoms over rock) DiscolDiscolored (See 0-9) 18 Overfalls pr .,en 37 Isolated danger Tide rips .unott woos INE 11.11 1 6a Sunken danger with depth cleared by were drag (in feet or fathoms) Jsei o 19 Eddies atas t38Limiting danger line

7 Reef of unknown extent 4 39 Limit of rocky area 20 Kelp, Seaweed Sr^bo, .sea famil seat 41 PA Posit,on approximate 42 P D Position doubtful 8 Submai,r,e volcano 21 8k adnk 43 E D Existence doubtful 22 Shl Shoal 44 P PosPosition 23 RI Reef (See A-11d,11g,0-10) 45 D Doubtful 23a Rdge MEN t46 Unexamined 9 C',,co:oeed water 24 le Ledge

Crib 10 reef, detached (;,'?Covers 25 Bedkers

1111 11101 ((II)) Offshore platform (unnamed) 26 Sunken

Whe .1 C ,dy le,.tee A-/id. ;, ((h) Olisho e DiaPfOrm(named

151. FRVarious Limits, etc,

111111111111111111MIS Leading line, Range hne t 13a Limit of military practice areas Transit Limit of sovereignty MMINNVIVEN (Territorial waters) In line with 15 WaNdettrail Customs boundary 4 Limit of sector International boundary ale . 16 (a /so State boundary) Channel, Co' c,se, Track 17 Stream limit tecommended (marked by buoys Or beacons) (See P21)18 attabLAV,Zirta. Ice limit Age, Pate course 19 Limit of tide

20 Limit Of navigation Radar guided track Course recommended (not Submar.ne cable (power, t21itirOLEVEVA marked by buoys or beacons) telegraph, telephone, etc ) MASA (See P-51

Submarine cable area 22 District or province limit

Abandoned submarine cable 23 Reservation line (includes disused cable)

Submarine pipeline 24 Measured distance MARKERS MARKERS Submarine pipeline area 25 Prohibited area (See G-12,46) Maritime lima in general

Limit of restricted area t(Pd) Shipping safety fairway Limit of fishing tone (fish trap areas) U S Harbor Line Limit of dumping grow t(Pe) Directed traffic lanes spoil ground /See R-S

Anchorage limit t(Pf) Fish haven (fishing reef) Limit of airport (See 1-23. 241 Q. Soundings Doubtful sounding tlo Ha,, -bile depth figures 2 41!: Dottom foz:na iside; 0.14 Figures for ordinary soundings 3 Out of position Soundngs taken from foreign 11 Least depth in narrow channels. gle charis Dredged charnel r with 5 1C %.fri 4PQ -tpt, Soundings taken from older ..PMAMMATIMIT controlling depth indicated) 12 WI so veys (or smaller scale chts)

13 ESi itF4 Echo soundings 6 Nov 4t Dredged area 14 Ma Slop.qg f,gurer, /See 7 Swept charnel ne,ghts, 15 ukEtu Upright figures (See 0-10a) 8 tvt- Jr ''t1' t16 Bracketed figures /See al, 21 Swept area. gn adequately Underlined sounding figures 9 so,.^ded Or" ti 17 iCee0-81 Soundings expressed in 18 to ?tom: fathoms and feet Swec' E, t22 9a e Unsounded area . ((Juliffules811"4"j"" -ill earn

152 FR. Depth Contours and Tints (see General Remarks) Feet Fathoms Feet Fathoms 0 0 300 50 6 600 /00 /2 2 , 11_;-- 4200 200 r ; -e /8 3 1,800 300 24 4 2,400 400 30 5 3,000 500 36 6 6,000 1,000 60 /0 ----- /2,000 2,000 120 20 18,000 3,000 - - /80 30 ------Or continuous (blue or 240 40 with values black)----Job Quality of the Bottom

t1 Grd Ground 24 Oys Oysters 50 spk Specked

2 S Sand 25 Ms 44ssels 51 gty Gritty

3 M Mud, Muddy 26 Spg Sponge t52 dec Decayed

4 Oz Ooze t27 K Ke ip 53 fly Flinty

5 MI Mart Wci Sea-weeo 54 g/ac Glacial 28 6 C./ C id, Gi s Grass t55 ten Tenacious

7 G Grave, t29 Stg Sea -tangie 56 wh W/?..e

8 Sn Sh,ngle t31 Sp, Spicules 57 bk Black

9 P Peoo es 32 Fr Fordimnifera 58 vi Violet

10 St .Stones 33 G/ Globigerind 59 bu Blue

11 Rk rky Roc*, Rocky 34 Di Diatoms 60 gn Green

Ila Bids Boulders 35 Rd Ratholar,a 61 yl Yellow

12 Ck Chak 36 Pt Per °Pods 62 or Orange

37 Po Polyzoa 63 rd Red 12a Ca Caicareous i

13 Qz Quartz t38 Cm Cirr Ipeda 64 br Brown

t 13a Sch Sch,st t 38a Pc, Fucu5 65 ch Chocolate

14 Co Cora, t38h Ma Mattes 66 so Gray

(Su) Co Hd Cora, t:ecia 39 The Fine 67 It Light

Coarse 68 dk Dark 15 Mds Maur epores ; 40 crs

16 Vol Volcanic 41 s ft Soft

(Sh ) Vol Ash Volcanic ash 42 km' Hard t70 yard Varied

17 La Ld vd 43 st, Stiff t71 unev Uneven

18 Pm Pumice 44 so,/ Smai/ t(Sc) S/M Surface layer and Under laye. 19 T Tula 45 /rg Large

20 Sc Scoriae I 46 stk Sticky

Cn Cinders 47 brk firoken 21 Fresh wafer springs in t21a Ash 47a I'd Ground (She:Is) 76 sea -bed 22 Mn Manganese t48 rt Rotten

Sh Shel:s It49 str Streaky I 23

153 T. Tides and Currents U. Compass

1 HW HHW i:"t' otitet 2 LW LOW*lit.' ( iVe) Ictt- thOwn JoI I 3' .1. 1 .1.11 3 41 .1'4 't

4 .%4 t 1,4 t t'I' on t,

JAL>. e. . I tios.1,c1mql ddlum . 1.41s.,11,5 ' ".;edv, h(7p) 6 S; t h

7 'Vt 1. .1t t 7E1 it .1, ' 8 V444.' t'.;.1 r

tifritt 41 t I .41 Pe -s /411 t 41" fri 1. t""" ;1 .4 Pe tibit P,' tl t .1 Compass Rose 9 t 1.. 1 The outer c,PCIe '5 al degrees with eel.° al true t . ..4 I'''"PSi I north. The Innei orcles dre in porn'sdna degrees with $#h 1'.. $«, 'A.1.1 'e .:edi I OW indicatingIndy11e11c north

It, , Si'}') 11 0, Pro.fte I .fPheth)11 1 N North 12 2 F. EdS, 1.1 t1 -I t 'it 3 S South 1,1a .11 14 4 W Wes 15 5 NE No, theas1

Iti fi SE Sou Theas1

17 Sr. 7 S W .So.. 'hives? 18 8 N W NOI 19 SINN 9 N Alor fhp, 20 NNW 'e' Tide p. ye, 7 depo-e, ito MIN ,cie 11 S So,,thern

2,1 12 W iVes,ern

" I.

;.13 P. 21 1'W. Hew ,ny li 122 T 23 41dg"t: 24 Va. ..t 0., 25 ',dive.

2.5(1 Ah.1Pqr ,' 26 Abnf,vdi ,dhOn, ii/rdne dttrdef,,,.

; . 7 I.74 27 .1t.4 1)051..ps (See

28 .1.. .di." , //

4t ne'e

154 AIDS TO NAVIGATION ON NAVIGABLE WATERWAYS except Western Rivers and !ntracoastal Waterway

LATERAL SYSTEM AS SEEN ENTERING FROM SEAWARD

PORT SIDE MID CHANNEL STARBOARD SIDE ODD NUMBERED BUOYS OR STRUCTURES NO NUMBERS MAY BE LETTERED EVEN NUMBERED BUOYS OR STRUCTURES WITH WHITE OR GREEN LIGHTS WHITE LIGHT ONLY WITH WHITE OR RED LIGHTS

MORSE CODE IMInems= FILED FLASHING=====1 FLASHING=====:1 OCCULTING OCCULTING =11=1 QUICK FLASHINGKE1=10 QUICK FLASHING'S:I= fig8W

BELL OR *LIGHTED BELL oR WHISTLE WHISTLE 0 ekv ekv CAN NUN At-8-

/.\, LIGHTED BUOYle"8" LIGHTED BUOY19 BW

MID CHANNEL DAYMARK

JUNCTION MARKS JUNCTION AND OBSTRUCTIONS. NO NUMBERS PASS ON EITHER SIDE. MAY BE LETTERED INTERRUPTED QUICK FLASHING 1113213===== WHITE OR GREEN WHITE OR it RED 0 NUN CAN C 7" N"6" IRS

LIGHTED 1 3 PREFERRED IPREFERRED CHANNEL CHANNEL DAYMARKS "3" STARBOARD PORT DAYMARK "4" TOPMOST BAND TOPMOST BAND BLACK REO

% N"L" CAN C"N" NUN ILA POINTER "3" POINTER "6"

R B R B

BUOYS HAVING NO LATERAL SIGNIFICANCEALL WATERS

NO SPECIAL S. PES, NO NUMBERS I MA BE LETTERED) WHITE LIGHTS ONLY WO Y W 8W!OGW r. C C"N" C C SPECIAL QUARANTINE FixED ANCHORAGE FISH NET DREDGING PURPOSE ANCHORAGE FLASHING OCCULTINGT=ISB

DANGER DAYMARKS RANGE DAYMARKS NON LATERAL SIGNIFICANCE I I I I

155 Artpendix B USEFUL PHYSICAL LAWS AND TRIGONOMETRIC FUNCTIONS.

A. Kepler's Laws 1. The orbits of the planets are ellipses with the sun at a common focus. 2. The straight line joining the sun and a planet sweeps over equal areas in equal intervals of time. 3. The squares of the orbital (sidereal) periods of any two planets are proportional to the cubes of their mean distances from the sun. B. Newton's Laws of Motion 1. A body at rest or in uniform motion will remain at rest orin uniform motion unless some external force is applied to it. 2. When a bodyis acted upon by a constant force, its resulting accelerationis proportional to the force, and inversely proportional to the mass. 3. To every force there is an equal and opposite reaction force. C. Newton's Law of Gravitation (Universal Law of Gravitation) Every particle of matter attracts every other particle with aforce that varies directly as the product of their massesand inversely as the square of the distance between them. D. Foucault's Law A spinning body tends to swing around so as to place its axisparallel to the axis of an impressed force, such that its direction of rotation is the same as that of the impressed force. E. Trigonometric functions

b 1. side opposite Sine A = a/c =hypotenuse

156 Appendix 13 USEFUL PHYSICAL LAWS AND TRIGONOMETRIC FUNCTIONS

Consine A = b/c side adjacent

side opsosite Tangent A = a/b side aulacent

si de adi went Cotangent A = b/a =side opposite hypotenuse Secant A = c/b sine adjacent hypotenuse Cosecant A = c/a = opposite 2. Versed sine A = 1- cosine A Co-versed sine A = 1 - sine A Haversine A = 1/2 (1 - cosine A) 3. The cosecant is the reciprocal of the sine. The secant is the reciprocal of the cosine. The cotangent is the reciprocal of the tangent. The tangent equals the sine divided by the cosine. 4. The complement of an angle equals 90°- that angle. The supplement of an angle equals 180°- that angle. The explement of an angle equals 360°- that angle. 5. The sine of an angle is the cosine of its complement. The tangentof anangleis the cOrgent of its complement. The secant of an angle is ththe cosecant o its complement.

157 Appendix C-1

MAIPORTI FLA., 1470

TIMES AND MONTS OP N1011 AND LOW WATERS

JULY AUGUST UPHAM

TIME NT. TIME 141. TIME 1111. TIME NT. TIME NT. TIME NT. OAV OAV DAV DAV OAV DAV N.M. PT. M.M. PT. N.M. PT. M.M. FT. N.M. PT. N.M. Fl.

0.0 16 0336 301 1 0136 0.2 16 0100 -0.1 1 0212 0.3 16

11 :::: 30 TN 1116 .0.4 SA 0140 3. SU 0712 4.0 TU 0836 4.7 11 12021131112 0113.03 12111 -0.3 1810 3.0 1321 0.0 1418 0.3 1436 .001 1400 . 2006 4. 1:!: 1:: 2048 4. 2100 4.2

2 0112 0.0 ST0030 -0.1 2 0212 0.1 17 0148 .0.4 2 0242 0.3 17 0300 -0.1 TM 0118 167 i 0666 3. SU0824 4.0 M 0806 %I 14 0406 4.11 TA 0424 6.0 1300 0.2 1230 .0.6 11100 0.1 1406 .0.8 0.4 1530 -0.2 1442 4. 1412 4.3 2042 4.8 2036 4.1 ITO 2148 9.3

1 0144 0.0 18 0124 -0.4 1 0242 0.1 III 0236 .0.2 1 0312 0.3 18 0342 .0.3 P 0806 3.7 SA 0210 4.2 M0400 4.1 TU 01100 1.3 TM 0942 4.1 7 10111 1. 1342 001 1316 4.0.11 1442 0.1 1444 .00 1530 0.4 1618 0.1 2024 4.8 2006 1.4 2111 4.7 2124 1.6 2144 4.6 2236 4.2

4 0236 0.0 1 0212 .0.6 4 0318 0.1 1 0324 -00 4 0142 0.3 1 0430 0.0 SA 08118 3.7 SU 0824 4.4 TU0456 4.2 M 0448 3.3 F 1018 4.1 SA 1106 Sol 1424 -0.1 14111 .0. 1418 0.2 1341 -0.6 1601 0.6 1212 0.5 2101 4.7 20% 3.3 MO 4.6 2212 SA 2224 4.5 2324 4.1

1 0312 0.0 200300 .0a .5 0341 0.1 20 0612 .0.6 1 0418 0.4 20 0524 Oa Su 0924 3.7 M0418 40 A 1012 4.2 TN 1042 4.4 SA 1044 4.8 SU 1200 4.11 1406 0.0 1412 441.11 1494 0.3 1642 -0.3 1648 0.8 1112 0.1 2142 4.6 2148 4.4 2224 4.4 2306 5.1 2300 4.1

6 0341 0.0 21 0344 .0.8 6 0424 0.1 21 0406 -0.4 6 0444 0.4 la 00111 4.4 M 1006 3.7 TU1012 4.0 TN 10411 4.2 P 1136 4.11 SU 1136 408 0 0618 00 1561 0.1 1606 -0.7 1616 0.4 1241 0.0 1236 0. 1300 Sol 2218 4.4 2216 4.3 2244 4.2 2344 4.7 2342 4.1 1411 1.1

7 0424 0.1 220442 -0.1 7 0464 0.2 22 0594 -0.1 7 0436 Oa 22 0118 4.1 TU 1042 30 A 1106 4.41 P 1114 44 SA 1230 4.2 M 1218 11.8 TU0711 1.0 1614 0.3 1701 .0.4 1218 0.6 1842 0.4 1130 1.1 1400 4. 2254 4.3 2310 4.0 2310 4.1 2024 1.3

8 0500 0.1 230416 .0.6 8 0950 0.2 23 0040 4.4 S 0060 4.0 230224 4.0 14 1124 11.6 TN 1200 4011 SA 1206 4.3 1112 0644 0.2 TU 0610 0.6 M 0024 1.1 1106 0.4 1101 -0.3 1606 0.7 1330 4.0 ISIS 4.11 2330 4.1 111411 0.7 1430 1.2 IX: ::: 0116 0.1 240024 4.7 0012 3 24 0148 4.0 0130 3. 24 0330 4.0 TM 1206 1.11 P 0610 -0.4 SU0612 Oa M0794 0.4 w 0736 0.7 TN0930 1.2 1754 Oa 1300 4.8 1144 4.3 1430 4.8 14111 4.8 1600 4.8 1000 0.0 1400 0.11 2034 0.0 2042 1.1 2124 1.2

10 0012 3. 250118 4.3 10 0100 3.7 24 02411 3.8 10 0242 4.0 29 0430 4.1 P 0611 0.2 SA 0724 .0.3 M0706 0.3 TU 0644 0.6 TN 0848 0.6 F 1030 1.1 1248 3.11 1134 4.7 1145 4.4 1436 4.7 1610 9.0 1700 4.8 1842 0.6 2012 0.2 2000 0.9 2200 0. 2149 0f, 2312 1.0

11 0094 3.1 260218 4.0 11 0154 3.6 26 0400 3.8 11 0148 4.2 26 0524 4.4 SA 0700 0.2 SU0024 -0.1 TU0806 0.) M 0944 0.6 P 1000 0.4 SA 1118 0. 1316 3. 1500 4.7 14118 4.4 1636 4.7 1636 9.2 17118 4.9 1436 0./ 2118 0.4 2106 0.8 2300 0.1 224$ 0.6 2394 0.1

12 0142 3.6 270311 3.8 12 0244 3.6 27 0400 3.8 12 09100 4.6 27 0612 4.6 SU 0744 0.1 N0424 0.0 M 01106 0.2 TN 1046 0.6 16 1100 0.1 SU 1200 0.0 1624 4.1 1600 4.7 1448 4.7 1730 4.8 1736 4.4 1830 5.0 2036 0.7 2224 0.4 2212 0.6 2348 0.7 2148 0.2

13 0230 3.4 280414 3.6 13 0406 1.7 28 0334 4.0 13 0600 91.0 20 0030 0.7 M 0042 0.1 TU 1018 0.0 TA 1012 0.0 F 1142 0.3 SU 1200 -0.2 M 0648 4. 1924 4.3 17C0 4.7 1634 4. 111111 4. 1810 5.7 1242 0.7 2142 0.6 2318 0.4 2312 0.4 11106 9.1

14 0730 3.1 2 090111 3.6 14 0512 4.0 2 0010 0.6 14 0016 -0.1 29 0100 0.6 Tv 01142 -0.1 If 1112 0.1 F 1118 -0.2 SA 0642 4.2 A 0634 1.4 TV 0724 5.1 1618 11.4 1754 4.4 1734 5.2 1224 0.4 1254 -0.4 1311 0.6 2242 0.4 1000 1.0 1924 Sol 1142 S.1

11 0436 3.91 30 0012 0.3 15 0006 0.0 30 0106 0.4 11 0124 *0.1 30 0116 0.3 A 1036 -0.2 TN 0612 3.7 SA 0610 4.4 SU 0711 4.4 TU 0741 5.0 M 0000 S.2 1711 4.7 1200 0.1 1212 .0.4 1306 0.4 1148 .0.5 1354 0.1 2336 0.1 1142 4.4 18511 5.5 1436 5.0 2012 5. 2010 5.0

31 0054 0.2 0142 F 0700 1.8 3! 0.34.6 1242 0.0 1142 0.3 1924 4.9 2012 9.0

TIME MERIDIAN 7S'14. 0000 IS N1ONIONT. 1200 IS NOON. NC1ONTS ARE RECOLONE0 FROM THE OATOO OF SOONOINOS ON CHARTS OTHE LOCALITY WHICH IS MEAN lOw WATER.

158 Appendix C-2

TIDAL DIPPIPINCIS AND 011111 CONSTANTS

POIMON 00111INCel !Mae PLACE 1160 MIMI Tide High Lew 11,0 Lew lawSO!Level we* water wiser wooer A. et. GEORGIA and FLORIDA Cumberland Sound onSAVANNAHRIVERENT.,PODS Flu meridian,75'N. 2821 St. Marys Entrance, north Jetty 30 43 81 26+0 15+0 15 -1.1 0.0 5.8 6.8 2.9 2823Crooked River entrance 30 51 81 29+1 23+1 12 -0.1 0.06.8 8.0 3.4 2825Harrietts Bluff, Crooked River 30 52 81 35+2 09+2 12 -0.5 0.06.4 7.5 3.2 2627St. Marys, St. Marys River 30 43 81 33 +1 21 +1 13 -0.9 0.06.0 7.0 3.0 2629 Crandall, St. Marys River 30 4381 37+2 10+1 59 -1.6 0.05.26.0 2.5 on HAYPORT, Pe1 4 2831Fernandina Beach (outer coast) 30 3881 26 -0 18 -0 01 +1.2 0.0 5.7 6.7 2.e 2833FernandinaBeach,Amelia 30 40 81 26+0 32 +0 16 +1.5 0.0 6.0 7.0 3.0 2835 Chester, Bells River 30 41 81 32 +0 49 +0 41 +1.9 0.0 6.4 7.5 3.2 2837S. A. L. RR. bridge, Kingsley Creek- 30 38 81 29*0 59+0 43+1.5 0.0 6.0 7.0 3.0

FLORIDA Nassau Sound and Fort George River

2839Nassau ------30 31 81 27 -0 03+0 06+0.9 0.05.4 6.3 2.7 2841 Amelia City, South Amelia River 30 35 81 28 +0 54+1 03 +1.1 0.0 5.6 6.6 2.8 2843 Nassauville, Nassau River 30 34 81 31 +1 04+1 37+0.3 0.0 4.8 5.6 2.4 2845Mink Creek entrance, Nassau River 30 3281 34 +1 58+2 32 -0.6 0.0 3.9 4.6 1.9 2847 Halfmoon Island, highway bridge 30 34 81 36+3 00+3 21 -1.0 0.0 3.5 4.1 1.7 2849 Sawpit Creek entrance 30 31 81 27.0 02+0 30+0.5 0.0 5.0 5.8 2.5 2851 Fort George Island, Fort George R - -- 30 26 81 26 +0 29 +0 39 +0.3 0.0 4.8 5.6 2.4 St. Johns River 2853South Jetty- 30 24 81 23-0 23 -0 17 +0.4 0.04.9 5.7 2.4 2855 MAYPORT 30 24 81 26 Daily predictions 4.5 5.3 2.3 2857Pablo Creek bascule bridge 30 19 81 26+1 39+1 15'0.6460.64 2.9 3.4 1.4 2859 Fulton 30 23 81 30+0 29+0 42 -1.1 0.03.4 4.0 1.7 2861 Dame Point 30 23 81 33 +0 46+0 55'0.670.673.0 3.5 1.5 2863 Phoenix Park (Cummers Mill) 30 23 81 38 +0 58 +1 25'0.4460.44 2.02.3 1.0

2865 Jacksonville (Dredge Oepot) 30 21 81 37 +1 24 +1 50'0.44'0.44 2.0 2.3 1.0 2867 Jacksonville (RR. bridge) 30 19 81 40+2 06+2 13'0.27'0.27 1.2 1.4 0.6 2869Ortega River entrance ------30 17 81 42+2 27+2 5060.2060.200.9 1.1 0.5 28 71 Orange Park 30 10 81 42 +3 49+4 14'0.160.160.7 0.8 0.3 2873Green Cove Springs ------30 0081 40 +5 26+6 13'0.18'0.18 0.80.9 0.4 2875East Tocol- 29 51 81 34+6 47+7 18'0.2260.22 1.0 1.2 0.5 2877Bridgeport 29 45 81 34+6 58+7 32'0.24'0.24 1.1 1.3 0.5 2879 Palatka 29 39 81 38 +7 26+8 21'0.27'0.27 1.2 1.4 0.6 2881Weiaka 29 29 81 40+7 46+8 25'0.11'0.11 0.5 0.6 0.2

FLORIDA, East Coast

2883Atlantic Beach 30 20 81 24.0 25 -0 18 +0.7 0.0 5.2 6.0 2.6 2885 St. Augustine Inlet------29 53 81 17 .0 21 .0 01 0.0 0.0 4.5 5.3 2.2 2887St. Augustine 29 54 81 18+0 14+0 43 -0.3 0.04.2 5.0 2.1 2889Daytona Beach (ocean) 29 14 81 00 -0 33 -0 32 -0.4 0.04.1 4.9 2.0 On MIAMI HBR. ENT., p.118 2891 Ponce de Leon Inlet 29 04 80 55 +0 06 +0 20 -0.2 0.02.3 2.7 1.2 2893Cape Canaveral 28 26 80 34 -0 41 -0 41 +1.0 0.03.5 4.1 1.8 2894 Sebastian Inlet 27 52 80 27 -0 23 -0 31 -0.3 0.0 2.2 2.6 1.1 2895Fort Pierce Inlet (breakwater) 27 28 80 17 -0 14 -0 18 +0.1 0.02.6 3.0 1.3 2897Fort Pierce (City Dock) 27 27 80 19 +1 51 +2 11'0.28'0.28 0.7 0.8 0.3 2899St. Lucie Inlet (Jetty) 27 1080 09-0 20 -0 21 +0.1 0.02.6 3.0 1.3

2901 Sewall Point, St. Lucie River 27 11 80 12 +1 34+2 33'0.40"0.40 1.2 0.5 2903 Jupiter Inlet (near lighthouse) 26 57 80 05 +1 04+1 380.520.52 1.3 1.5 0.6 2905 Port of Palm Beach, Lake Worth 26 4680 03 0 00 +0 12 +0.1 0.0 2.6 3.1 1.3 2907 Palm Beach (ocean) - 26 43 80 02 -0 21 -0 18 +0.3 0.0 2.8 3.3 1.4 2909 Hillsboro inlet 26 15 80 05 0 13 +0 36 -0.2 0.02.7 2.7 1.2 Fort Lauderdale 2911 Bahia Mar Yacht Club 26 07 80 06+0 28+0 32 -0.2 0.02.3 2.8 1.1 2913 Andrews Ave. bridge, New River- 26 07 80 09+1 06 +1 28 -0.7 0.01.8 2.2 0.9

'Ratio.

159 Appendix C -3

TAMA: ,;.--micia OF ME AT ANY TIM

Time from the waresr high water or 10o- water h. inh. 9., I. :,5. in. h. m.th. in h. inA. InI h. m.h. m.h. m.h. in.h. in.h. in.h. ,nh m. 4 000 0.10 160 240 3210 400 lx0 46 1 01 1 12 1 201 28 1 311 1 44 1 52 2 00 0 20 t1o..10 17 0 2t10 350 430 521 01 1 09 1 IS 1 27 1 34 1 41 1 63 2 01 2 10 4 400 U9u III0 280 37U 470 361 05 1 ... 15 1 241 33 1 43 1 52 2 01 2 11 220 5 000 100 200 300 400 601 (8) I10 1 201 0 1 40 160 2 110 2 102 202 30 3 200110'210:1'2043063 1 01 1 15 1 25 1 3o 1 47 1 67 208 2 1(1 2 292 40 6 400 110 230 340 460 571081 19 1 31 1 421 63 2 062 16 2 272 39 250 I6000 120 210 380 481001 121 24 1 36 1 48 2002 12 2 24 2 362 4n3 00 6 200 130 250 '.040 511 031 16 1 29 1 41 1 54 2 072 192 322 452 67 3 10 -4, 0 400 130 270 400 531 071 201 33 1 47 2 002 13 2 27 2 40 2 53 3 073 20 41 7000 140 280 420 561 101 21I 38 1 522062202 342 48 3 023 163 30 5 7 90 150290 440 401 131 28 1 43 1 57 2 122 272 41 2 Afi :i11 3 25 3 40 t7 400 150 310 461 01 1 171 321 47 2 032 IN2332 493043 193 35350 1- 6000 160 320 481 011 201311 1.52 2Us 2 24 2 40 256 3 12 3 2x3 44 4 00 .38 200 170 330501 071 21 40I 672 132 30 2 473 03320 3 37 3534 10 a8 400 170 350 52 1 271 44 el 109 2 01 2 19 2 362533 11 3 283 48403420 v-1 0 000 180 36 0 541121 301 482 062 242 423 01)3 183 34 3 544 124 30 0 200 190 370561 151 331 522 11 2 292 483 073 25 3 44 4 03 4 21A 40 A 0 400 190 390681171 371 562 15 2 35 2 543 133 333 52 4 11 4 31 4 60 10 000 2 00 401 00I 201 402 002202 403003203 404004204 40600 10 20021041102123143201226245306327347408429449510 10 400 210 431 041 261 472 082292 51 3 123 333 554 16 4 374 396 20 _ n VOITertIon to height

Ft. Ft.Ft Ft.Ft.Ft.Ft. FL Ft. Ft. FL Ft. Ft. l't. Ft. Ft 0.50. 00. 00. 0 0.00.00.0 0.1 0. 1 0. 1 0.1 0.1 U. 2 0.2 0.2 0. 2 1.0U.00.0000.00.10.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.5 1.5000.00.00.10.10.1 0.2 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.S 2.0a 60.00.0 0. 1 0. 1 0.2 0.3 0.3 0.4 0.5 0.6 G. 7 0.8 0.9 1.0 2.50.00.0'1.1 0.10.20.2 0.3 0.4 0.5 0.8 0.7 0.9 1.0 1.1 1.2 3.00 00.0 0. 1 0. 1 0 20.3 0.4 0.5 0.6 0.8 0. 9 I.0 1.2 1.3 1.5 3.60 00 0 (1.1 0. 20.20.3 0.4 0.6 0.7 0.9 1.0 1.2 1.4 1.6 1.8 4.00.00.00.1 020.30.4 0.5 0.7 0.8 1.0 1.2 1.4 I.6 1.8 2.0 4.60.00.00.1 0.20,30.4 0.6 0.7 0.0 1.1 1.3 1.6 1.8 2.0 2.2 5.00.0 0. 1 0. 1 0.20.30.6 0.8 0.8 1.0 1.2 1.5 1, 7 2.0 2.2 2.5 5.50 00 1 0. 1 0.20. 4 0. 5 0.7 0.9 1. 1 1.4 I.6 1.9 2.2 2.5 2.8 0.0000.10.I030.40.6 0.8 1.0 1.2 1.5 1.8 2.I 2.4 2.7 3.0 6,60.00. 1 0 20.30.40.6 0.8 1.1 1.3 1.6 1.9 2.2 2.6 2.9 3.2 w 7.00 00. I 0. 2 0. 3 0 50.7 0.9 1.2 1.4 1.8 2. 1 2.4 2.8 3.1 3.5 :: 7.60.00. 1 0. 20.3 0. 50.7 1.0 1.2 1.5 1.9 2.2 2.8 3.0 3.4 :i. 8 ..4 8.0000I02030.50.S 1.0 1.3 1.6 2.0 2.4 2.8 32 3.6 4.0 1 8.5 U.0 0I 0.20.40.60.8 1.1 1.4 I.8 2.1 2.5 2.9 3.4 3.8 4.2 - 0.00.00.10.20.40.60.0 1.2 1.5 1.9 2.2 2.7 3.1 3.6 4.0 4.5 '.. II 5 U. 0 U. 1 U. 2 U. 4 0.60.9 1.2 1.6 2.0 2.4 2.8 3 3 3.8 4.3 4.8 c 10.00.00.10.20.40.71.0 1.3 1.7 2.1 2.5 3.0 3.5 4.0 4.5 5.0 ...1 10.5000.1030.50.71.0 1.3 1.7 2.2 2.6 3.1 3.6 4.2 4.7 5.2 b.."' 11.00 00. 1 0.3 0. 50. 7 1 I I. 4 1.8 2. 3 2.8 3. 3 3.8 4.4 4.9 5.5 °11.6 0 00 10.30.5 0 8 1. 1 1.5 1.9 2.4 2.9 3.4 4.0 4.6 5.1 5.N go' 12.0000.103U.508 1. 1 1.5 2.0 2.5 30 3.6 4.1 4.8 5.4 6.0 012.50. 0 0. 1 0. 3 U. 5 0. 8 1. 2 1.8 2. 1 2.6 3. 1 3.7 4.3 5.0 5.6 6. 2 al13.000010.30.40.9 1.2 1.7 2.2 2.7 3.2 3.9 4.5 5.1 5.8 8.5 13.500010.3 U.60.9 1.3 1.7 2.2 2.8 34 4.0 47 5.3 8.0 6.n 14.06 00 2 0. 3 0 60.9 1. 3 1.8 2. 3 '2.9 3. 5 4. 2 4 14 5.5 6. 3 7.0 14.50. 00. 20. 40 61 0 1. 4 1.9 2.4 3.0 3. 6 4, 3 5.0 5.7 6.5 7. 2 15,00.00.204061.01.4 1.9 2.5 3.1 3.8 4.4 52 5.9 6.7 7.5 15.5000204u71 0 1. 5 2.0 26 3.2 3.9 4. ti 34 6. 1 6.9 78 14,0 1 0 00 20.40 7 1 1.5 2. 1 2.6 3.3 4.0 4. 7 6.5 6.3 7.2 8 0 16.50 00 20 4 U. 7 1 11 1. 1 2. I 2. 7 3. 4 4. 1 4.9 5. 7 6. 5 7. 4 8.2 17.00 00 2 0. 4 0. 7 I 1 1.6 2, 2 2. 8 3.5 4.2 6.0 5.9 6.7 7.6 in 5 17.501)0'2040.81.21.7 2.2 2.9 3.8 4.4 5.2 6.0 8.9 7.8 8.8 6 0 1 +.0 0 20. 40.8 1.2 1. 7 2.3 3.0 3. 7 4.5 5. 3 6.2 7. 1 8. 1 0.0 0. 2 1 is. 50 1 U. 5 U S 2 1.8 2. 4 3. 1 3.8 4.6 4. 5 64 7.3 8.3 0. 2 19.00 1 0 20 50.9 1.i 1 8 2.4 3. I 3.0 4.8 6.6 S.6 7.5 8.5 95 19.5 0 1 0 2 n .5 1) 5 1 1.9 i 2.5 3 2 4. 0 4.9 5 S 6. 7 7.7 8 7 9.8 20.0U I 11.2 0 50.9 1 1 1. 9 2.6 3 3 11 5.0 5.9 a. 4 7.0 9 010.0

tltt on from the predictions the high water and low water. one o which is he ore and the other aft, r the Lune ,-,r. which the heightisrequired. The (Iflatlt:et. hit a ern the tunes of occurrent'', of these tales is the durate.ii of riqe or fill, 811 I Owcilttrinr. bvtt4"1'n their heights IS therange of tide for he above t.:e.Find theditterenee between thenearest high or low water and the time fot a hich It., to11.911 ii required. Enterthe 1.thle with toe duition of rise or fall. printed in heavYfaced type, whichmost nearly agrees with the actual % due,an.lonttit horizontalline find the time from the nearest highor low u.:Iter which agrees t110-,l nearly witht he correspondineactual difTereneeThe correction sought is in the column directlybelow. on the IMPWith the ran 1 of tole %5 hen the nearem I -le is :iigh water, subtract thecorrection. 11hen the ne.irest tele i: low %met..;;t1.1the correction.

160 Appendix D-1

ST. JOHNS RIVER ENTRANCE, FLA.. 1910

4-FL000, OIR. 2736 TRUE 1880 OIR. 1004 TRUE

MARCH APRIL

SLACK MAXIMUM SLACK 444111UR SLACK MAXIMUM SLACK MAXIMUM WATER CURRENT WATER CURRENT WATER CURRENT WATER CURRENT TIME TIME WEL. TIME TIME VFL. TIME TIME WEL. TIME TIME VET. 044 044 044 067 H.M. H.M. KNOTS H.M. H.M. KNOTS H.M. H.M. KNOTS H.M. N.M. KNOTS

I 0116 1.94 16 0012 0230 1.54 1 0048 0318 2.04 16 01)6 0348 1.44 SU 04)0 0106 1.111 M 03)0 0900 1.4E W 0612 0912 2.1E TH 0636 0961 1.71 1212 1406 1.14 1312 1500 0.94 1136 1348 1.74 1412 1618 1.44 1612 1918 2.2E 1730 2030 1.31 1424 2130 2.2f 1834 2206 1.7E 2142 2 0216 1.114 17 0112 0330 1.54 2 0144 0418 0210 0416 1.54 M 0316 0818 1.9E TU 0630 1036 leSE TM0112 1018 ;::: 1: 0724 10)0 1.8f 1112 1106 1.24 1406 1600 1.04 1424 1648 2.04 1448 1700 1.61 1724 2024 2.21 1430 2148 1.31 1930 2242 2.44 1944 2300 1.111

1 0054 0346 2.14 18 0206 0430 1.64 3 0248 0512 2.24 18 0312 0324 1.64 TU 0636 0910 2,0E V 0711 1111 1.61 F 0806 1112 2.34 SA 0006 1106 1.9f 1406 1606 1.4F 1454 1654 1.24 1512 1742 2.3F 1524 1748 1.84 1836 2136 2.11 1924 22411 1.71 20)0 2)42 2.61 2016 2336 2.1E

4 0200 0436 2.3f 19 0234 0118 1.7F 4 0342 0606 2.34 19 0400 0606 1.7f W 0716 1016 2.2E TH 01106 1142 1.8E SA 0434 1206 2,6E SU 0848 1162 2.14 1434 1706 1.14 1330 1742 1.4F 1600 1810 2,64 1600 1810 2.11 1942 2248 2.31 2018 2336 1.81 2124 2118

4 0300 0336 2.31 20 0342 0600 1.44 S 0016 2.81 20 0018 2.2E TH 0830 1142 2.51 4 01148 1206 1.91 SU0410 0654 2011 14 0442 1542 1800 2.11 1606 1818 1.7F 0942 1148 2.7E 0924 TI: 12::: 2042 2394 2.21 2106 1642 14118 2,74 1610 1412 2.2F 2218 2200 6 0334 0624 2.64 21 0012 2.01 6 0124 2.81 21 0054 2.61 4 0924 1230 2.7E SA 0424 0642 1.84 M0526 0742 2.1F TU 0524 0710 1.74 1624 1854 2.141 0910 12)0 2.11 1024 1330 2.8E 1006 1254 2.61 2142 1642 1900 1.9F 1724 2006 2.11 1700 1948 2.44 2148 2306 2242 7 0048 2.9E 22 0044 2.2E 7 0212 2.7E 22 0116 2.5E SA 0448 0718 2.7F SU 0506 0718 1.9F TU0612 0830 2.14 Id 0606 0818 1.64 1012 1318 2.81 1006 1100 2.21 1106 1412 2.7E 1042 1316 2.51 1712 1942 2.64 1712 1942 2.0F 1812 2068 2.74 1710 2036 2.44 2230 2224 2346 2324 e 01)6 2.9E 23 0118 2.1E 4 0234 2.6E 2) 0218 2.SE SU 0536 0806 2.6F M 0542 0800 1.81 K 0700 0912 1.91 TN 0648 0900 1.61 1054 1400 2.9E 1042 1130 2.1E 1148 1448 2.6E 1118 1418 2.51 P754 2030 2.84 1742 2014 2.1F 1900 2136 2.51 1806 2118 2.41 2124 2306 9 0224 2.9E 24 0200 2.61 9 0016 0336 2.41 24 0012 0)00 2.5E 0756 1.7F 4 07)6 0948 1.51 61 0624 0854 2.5F TU 0626 0842 1.8F TN 1000 1500 1136 1662 2.9E 1112 1606 2.41 1210 15)0 2.4f 1200 2.51 2.31 154: 7118 2.7F 1812 2100 2.2F 1948 2224 24.34 1854 2206 2348 0348 2.0 10 0012 0312 2.91 25 0236 2.5E 10 0124 015111 2.2E 23 0100 4 0849 1048 1.41 SA 0824 1016 1.47 TU 0716 0916 2.24 Id 0706 0926 1.64 1554 2.4E 1224 1514 2.4E 1144 1442 2.0 1111 1612 2.2E 124$ 2.27 1924 2206 2.6F 14)6 2164 2.21 2016 2312 2.01 1942 2300 1.9E 26 0148 0436 2.0 11 0100 0400 2.51 26 0030 0314 2.51 11 0212 0500 0918 1110 1.47 W 0812 1024 1.9F TM 0746 1006 1.0 SA 0962 1136 1.21 SU 1106 1600 2.61 1224 1524 2.51 1406 1654 1.9E 1148 1648 2.0 2354 2.14 2014 2254 2.4F 1912 2230 2.2F 2136 204$ 27 0248 0530 2.21 12 0144 0442 2.21 27 0118 0400 2.4E 12 0006 1..1g 1018 1226 1.0 Im 0906 1112 1.64 1 0836 10541 1.14 SU 0300 0544 1448 1742 2.2E 1148 1642 2.0 1106 1612 2.6E 1042 1230 1.14 2206 2112 2142 2.11 2000 2324 2.14 1500 1745 1.0 22)6 1.64 28 0054 2.01 11 0242 0510 1.9E 28 0206 0454 2.1E 13 0100 1.61 11.1 0142 0616 1 1012 1206 1.31 SA 0936 1148 1.24 M 0354 0642 1.01 1118 1324 N: 14)6 1730 2.04 1154 1700 2.0 1142 13)0 1.5E 1600 1856 2.11 2206 2054 1434 1842 2162 2324 14 0154 1.44 29 015. 1.91 16 0016 1.91 29 0016 2.01 0744 1.SE W 0662 0742 2.11 SA 0136 0624 1.71 SU 0306 0448 2.0 TU 044$ 1430 1.01 1212 1624 1.0 1112 1100 1.14 1042 1242 1.24 1216 1.51 1706 2006 2.0 1124 1416 1.4E 1454 1400 2.24 1700 1944 2112 2212 15 0042 0254 1.41 30 0010 0254 1.91 IS 0170 1.71 30 0112 1.91 IF 0854 1.64 TN 0542 0868 2.21 SU 0410 0710 1.0 N 0404 0648 2.01 0562 1424 1.2f 1106 1424 1.94 1218 1600 0.9F 1162 1342 1.21 1124 1800 1.SE tote 2124 2.2E 1424 191$ 1.114 1600 1900 2.0 2100 2316 11 0216 I.91 TU 0512 0744 2.0f 1262 1446 1.41 1716 2012 2.11

T1Mt 4E41014N 75.M. 0000 IS MIDNIGHT. 1200 IS NOON.

161 Appendix D-2

CURRENT DIFFERENCES AND OTHER CONSTANTS

AINIIMUM CUN6M47$ TIME DIP. VELOCITY fOSITION MOOS RATIOS Flood Ebb

PLACE NWmp Mom. PeociDittcAve.. Aver. Slack Lat. mum mum mum hen 091 hoe age wafer curved flood ebb Pr*VOW(Mw)Woo ify ity

A. me. Si . M. dep. keels dimp. koW4

ST. JOHNS NIVE16.ContIntiod R. W. onST. JOHNSRIVERENTRANCE,i1.W1 Pima meridian,7e4; 245 1.6 602.2 5380 St. Johns Bluff - 30 2381 30+0 054060 0.8 1.0 230 1.6 5366 Drummond Point, channel south of 30 2581 36+2 00+18 30 0.7 0.7 1.3 60 1.0 5390 Phoenix - - 30 2381 38 +2 40+3 10 0.6 0.4 1901.1 350 1.6 5395 Chaseville, channel near 30 23 81 37 +2 35+3 20 0.6 0.7 1501.1335 0.6 186 1.1 01.4 5400Quarantine Station,Long Branch- - 30 2181 37 +2 30+3 05 0.6 81 38+2 35+3 10 0.5 0.42101.0 601.0 5405Cbamodore Point, terminal channel - - 30 19 1.9 5410 Jackeonville, off Washington St------30 19 81 39+2 20+2 50 0.9 0.6280 1.6220 1.7 5415 Jadcsonville, F. E. C. RR. bridge 30 1981 40 +2 20+3 00 0.6 0.72401.6 60 0.6200 1.1 15 1.1 5420 Winter FbInt------30 1881 40+2 55+3 10 0.6 0.3 1800.6 150.7 5425 Mandarin Point --- -- 30 0981 41 +3 CO+3 20 0.3 0.5 0.31150.93000.6 5430 Red Bay Point, bridge draw P9 5981 38 (I) (I) to be 5435 Tocol to Lake George Cormttee peeksodwettable erodlotod.

FLORIDA COAST on MIAMI HARBOR ENTRANCE. p.100

25 1.4 1.5 2502.6 703.1 5440 Ft. Pierce Inlet ------2728 8016+0 5040 1.3 1.72752.4 3.6 544f Lake Worth Inlet, (between Jetties) - 26468002-0 10-0 15 95 0.2 5 0.61300.5 5450 Fort Lauderdale, New 26078007-0 40-0 40 0.4

PONT EVERSLADES

NI NI NI 0.2 0.4 5455 Pier 2, 1.3 miles east of 26068006 (2) (I) 275 0.7 5460 Entrance, betweenjetties - - - -26068006 -0 40-0 55 0.3 0.3 0.6 95 1.7 5465 Entrance from southward (canal)------2605 8007+0 20-0 15 0.7 0.8 1651.3 0 5470 Turning ----- 2606 8007 -1 15 -1 20 3.1 0.2 3200.2155 0.5 1601.8 5475 Turning Basin, 300 yards north of - ----26068007 -0 40-0 55 0.5 0.9350 0.9 0.93501.9 1701.9 6480 17th Street Bridge --- 26068007 -0 50-1 05 1.0

MIAMI MANSON

1.2 2702.9 90 5485 Bakers Haulover Cut---- - 2554 8007-0 10-0 15 1.5 2.5 105 5490 North Jetty (east end) 2546 8007 -0 40-0 35 0.4 0.6 2500.8 1.3 5495 Miami Outer Bay Cut entrance 2546 8006 See table 5. 125 5500MIAMI HARBOR ENT. (between jettles)---2546 8008 Daily predictions 2901.9 2.1 Current too week sod vorlObloto SorodtotOd. 5503 Fowey Rock, Light, 1.0 miles SW. of---2535 8007

FLORIDA REEFS to MIDNIGHT PASS on KEY WEST, p.I06

125 5505 Caesar Creek, Biscayne Bay 2523 8014 -0 05 -0 05 1.2 1.0 315 1.2 1.8 1.1 1.2 5510 Long Key, drawbridge east of 24508046+1 40+1 30 1.1 0.7 0 200 5515 Long Key Viaduct 2448 8052 +1 50+1 40 0.9 0.7 350 0.9 170 1.2 5520 Moser Channel, drawbridge 2442 8110+1 30+1 40 1.4 1.0 340 1.4 165 1.8 5525 Bahia Honda Harbor, bridge 2439 8117 +1 25 +0 50 1.4 1.2 5 1.4180 2.1 5530 No .me Key, NE. of 24428119 +1 10+1 10 0.7 0.5 310 0.71400.9 Ley Meat 0,2 5535 Main Ship Channel entrance 2428 8148 -0 15 0 00 0.2 0.3 40 1800.4 0.2 1350.4 5540 Main Ship Channel 2430 8148 (3) 3+0 30 (3) 65 (3) 1.0 195 1.7 5545 KEY WEST, 0.3 mi. W. of Ft. Taylor -2433 8149 Da ly predictions 20 1.2 5550 0.6 mile N. of Ft. Taylor 2434 8149 +0 05 +0 15 0.6 0.7 40 0.6200 5555 Turning Basin 2434 8148+0 35 +0 55 0.8 0.6 50 0.8 215 1.1 1.4 5560 Northwest Channel 2435 8151 -0 10 -0 05 1.2 0.8 355 1.2 160 5565 Northwest Channel 2437 8153 -0 25 -0 20 0.6 0.4 345 0.6 1700.6 5570 Boca Grande Channel 2434 8204 -0 20 -0 25 1.1 0.7 355 1.1 195 1.2 5575 New Groundt 2439 8225 +1 30 +1 35 0.7 0.4 70 0.7245 0.7

Flood begins, +2A 35w; maximum flood, +34 25; etb beg ins, +54 006; maximum ebb, +44 00. 3F ood usually occurs in a southerly direction and the ebb in a northeastwardly direction. 3 Times of slack are indefinite. Flood is weak and variable. Time difference is for maximum ebb. t Current tends to rotate clockwise. At times for slackflood begins there may be a weak current flowing northward while at times for slack ebb begins there may be a weak current flowing southeastward

162 Appendix D3

TABLE 3.-- VELOCITY OF CURRENT AT ANY TIME

TABLE A

Interval between slack and maximum current

A. m.h. m. A. m. A. m. A. m. A. m.h. m. A. ni. h. m. h.ni. h. m.h.ni. A. m. A. m. 1 20 1 40 200 220 240 300 320 340 400 420 440 500 520 540

1. h. . f I. I. I. I. I. I. I . I. I. I. I f 20 4 3 3 2 2 2 2 1 1 01.'1 1 '1 '1 0. 1 h 040 0.7 0.6 0.5 0.4 0,4 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2

.0 1 00 0.9 0.8 0.7 0.6 0, 6 0.5 0.5 0.4 0. 4 0. 4 0.3 0.3 0.3 0.3 0.4 7 1 20 1.0 I.0 0.9 C. 8 0, 7 0.6 0 6 0.5 0.5 0.5 0.4 0.4 0.4 0.5 0.5 0.4 .g 1 40 ... 1. 0 1.0 0.9 0.8 0.8 0. 7 0.7 0.6 0.6 0.5 8 0.6 0.5 ....ci 200 . . I.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 a 220 ... .. I.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 1 240 1.0 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.7 at ... 1. 0 1.0 1.0 0.9 0.9 0.8 0.8 0.8 0.7 v, 320 1.0 1.0 1.0 0.9 0.9 0.9 0.8 0.8 i340 ...... I.0 1.0 I.0 0.9 0.9 0.9 0.9 ...le 400 ...... _ ...... 1.0 I.0 I.0 1.0 0.9 0.9 ...... _ .. ... 1.0 1.0 1.0 1.0 0.9 I4 40 ...... 1.0 1.0 1.0 1.0 ` ...... - ...... 1.0 1.0 1.0 a 5 20 ...... 1-. 540

TABLE B

Interval between slack and maximum current

H I h. m. Jh. m. A. m. h. m.A. m. h. m.A. m. A. m. A. m. A. m. h, m.h. m.h. m. A. m. 540 1 2 0 1 40 2 00 I 220 240 300 320 3 40 400 420 440 500 520 .... h.m. I. I. I. I. I. 1. I. I. I. I. f. 1 1 I. 020 0. 5 0. 4 0. 4 11.3 0.3 0. 3 0. 3 0.3 0. 2 0.2 0.2 0.2 0.2 0. 2 a040 0.8 0.7 0.6 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 8 - 0.4 0. 4 1 00 0.9 0. 8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.5 0.4 0.4 0.5 1 20 1.0 1.0 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.6 0.6 1 40 ... I 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.7 0.6 'y200 ... : 1.0 1.0 0.9 0.9 0.9 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 9:I=220 1.0 1.0 1.0 0.9 0.9 0.8 0.8 0.8 a 2 40 ...... 1.0 1.0 1.0 0.9 0.9 0.9 0.8 0.8 0.8 0.7 0.8 0.8 1 3 CO ...... 1.0 1.0 1.0 0.9 0.9 0.9 0.9 7 320 1 .. 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.8 . 1.0 1.0 1.0 1.0 0.9 0.9 0.9 4t340 . . .. . 1.0 1.0 1.0 0.9 0.9 ! 4 (X) . _ . . .. 1.0 .. 1.0 I.0 1.0 1.0 0.9 1.0 7., 440 ...... 1.0 1.0 I.0

`' 500 ... .. _ ...... 1.0 1.0 1.0 1 1.0 m 520 ...... 1.0 i 1.0 -.540 I ......

Use Table A for all places except thoselisted below for Table B. Use Table B for Cape Cod Canal, HellGate, Chesapeake and Delaware Canal and all stations in Table 2 which are referred to them.

1. From predictions find the time of slackwater and the time and velocity of maximum current (flood or ebb), one of which is immediately before and theother after the time for which the velocity is desired. 2. Find the Interval of time betweenthe above slack and maximum current, and enter the top of Table A or B with the interval which most nearly agreeswith this value. 3. Find the interval of time betweenthe above slack and the tune desired, and enter the side of Table A or B with the Interval which most nearly agreeswith this value. 4. Find, in the table, the factor correspondingto the above two intervals, and multiply the maximum velocity by this factor.The result will be the approximatevelocity at the time desired.

163 IMO = d . /MEM8/ AB IM MI= M . ,..-- 11=1 MAI MG ;;;:==.7:::::; AN =El a SO MI . = = = ; 70' ; : : ...Om almw IMMIMI=IM611 4=111MS11==11111 DOB Mb ma s 111INIMDIMM 11 MO MIMI1=1M 1101-1=11... a MO 1=ma asa:: IMIa Ma a Oa. =1MMIIMi S ===.1M1a0 ...... / MS ...r 5 C IM .....a =Mas1MEM =MMIMM 11111 =1,MINSOS lIMIM WOO MO ""..11111111 MINIM= EMU'S Waling IMMIMMIUMINI 111INIME11ka I MMENNIMINOMII IMINHMININGIONII =Wit IMIM I= IM IN il IIIMINI111111111111 MOM IMMOMIIMIIII INIMMIP III IMIINIWIlii MINIBOONONIIMINSMEMINIMINNIISIO.M: MOM MNIIMIWIIIIII IMIIIIMMI 551 MMINIMMIISIS IMIII=IMPS.111 MNIIINSIIIIIIIIIIINIMIMIM7-.iMNI SHIM IMMINI111111011111 I=1 II111111 IMIONIMIII11.11 rr:4111111 IMMIIMIIIIIIIIIIIIMMIPIN":-.01111191111 MIMI IMMINOMMI M ...'011i MINIMUM .)-1.eomel wossoloPrimmoseliam IIINIMIIilleriemisi 3rimiiIIININ % _..imm1111111111111M'.:.1211M111111111111 eemmlimmi y;s111111111111M1111111F1111111111111111111111111PMa11111111111111111M11111111 IIIIIMINIIIMM-11111111111111Ezn)ANIIIIIIMIIMI11111-1M1111111PM1111111111111MIIIMIIIIIIIIM ani=101111 MIIMIMM MOM, I MEM NMI UM MI II 11111 =-M-M4-1111 1111 =1MIN61 ANIIM111M111111111 -.1111111111111011111=11s1111111111111=14. iittIIM=11111111111 .=111111MISI11:011MM6111 ..011MOuallIMIIMMIN6811-NO11 Sallee am e-s-sii... _111011111-H-1111-1BIIMMIN11111--11=1=11111111511M1 N OM IM MEM-111111111PIMMINISIIIIIIIIIP"%1111MIIIIIIIIMIIIII MINOMIIIN-1IW-MMINIIII10=11111-!'111111MM111111M111MINOPwi111111M111MIMMI1II 611111MM 111Ill'AMMINI1.1111111=1=Mr.4111111111IN 111!!7110111IIIIMIIIIIIMO1001111 e ntrmmosolimimir.,Anuliwridommelims _ialiME11111111111111111111IIII 1111111=1111111IPAMMIMIIIIIIIIPPIIM11111111Mill11111111111111111M1111111111111111111M111111111M1

11111 411111111M111111111111111111111111 1 P!!:;iiiill1111111111111M 4/111111MIllt:ii11111111111111111111!, Haill111111111111111111111 illingiNith.211111111111M11111111.1"11111MINIME Iriip5011111 1111111.

111.'11111...11.. ,..111111 1111111 111111..116

111 111111 ihi0!l.111"111 11111111111111___...

_ Appendix E-2

Distance of visibility of objects at sea:

Ht. in ft. Naut. Mi. Ht. in ft. Naut. Mi. 1 1.1 55 8.5 2 1.7 60 8.9 3 2.0 65 9,2 4 2.3 70 9.6 5 2.5 75 9.9 6 2.8 80 10.3 r 7 2.9 10.8 8 3.1 90 10.9 9 3.5 95 11.2 10 3.6 100 11.5 11 3.8 105 11.7 12 4.0 110 12.0 13 4.2 115 12.3 14 4.3 120 12.6 15 4.4 125 12.9 16 4.6 130 13.1 17 4.7 135 13.3 18 4.9 140 13.8 19 5.0 145 13.8 20 5.1 150 14.1 21 5.3 160 14.5 22 5.4 170 14.9 23 5.5 180 15.4 24 5.6 190 15.8 25 5.7 200 16.2 26 5.8 210 16.6 27 6.0 220 17.0 28 6.1 230 17.4 29 6.2 240 17.7 30 6.3 250 18.2 31 6.4 260 18.5 32 6.5 270 18.9 33 6.6 280 19.2 34 6.7 290 19.6 35 6.8 300 19.9 36 6.9 310 20.1 37 6.9 320 20.5 38 7.0 330 20.8 39 7.1 340 21.1 40 7.2 350 21,5 41 7.3 360 21.7 42 7.4 370 22.1 43 7.5 380 22.3 44 7.6 390 ...... 22.7 45 7.7 400 22.9 50 8.1

165 Appendix F-1

10 1970 JANUARY I, 2, 3 (THURS., FRI., SAT.)

ARIES VENUS -3.5 MARS 44.0 JUPITER-1.5 SATURN +0.5 STARS G.M.T. G.H.A. G.H.A. Dec. G.H.A. Dec. G.H.A. Dec, G.HA. Dec. Name S.HA. Dee. ilk I. 4,,e.e . . 0010013.818522.2523 37.91161145 7 43.324940.251108.9 6927.8 N9494Apmar 31542.85 40 25.5 01 11516.320021.2 37113118.6 42.626442.3 09.0 8430.2 49.3Acherna 33550.6S 57 234 02 13018.821520.2 37.814619.3 41.827944.5 09.1 9932.7 49.3Acme 17346.35 62 55.7 0314521423019.3 . 37.816120.1 41.029446.6 .. 09.2114354 .. 494Adhere 2553745 28 55.7 0416023.724518.3 37.817620.8 40.330948.7 09.312937.7 494Aldebaran29126.7N 16 27.2 05 17526.226017.3 37.819121.6 39.5324504 09.414440.2 494 06 19028.627516.4523 37.820622.35 7 38133953.051109.515942.6 N9494Alkseh 166491N 56 07.0 0720531129015.4 37.822123.1 38.0354551 09.717445.1 494 15324.6N 49 274 T Alksld 0822033.530514.4 37.823623.8 37.3 957.3 09.818947.6 494Al WV 2824.8S 47 06.7 H0923536.0320134 .. 37.725124.6 36.5 24594 09.920450.1 . 494Alnllani 27619.351 131 U1025038.533512.5 37.726625.3 35.8 4001.5 10.021952.6 494Alphard 21828.0S 8 31.6 R11 26540.935011.5 37.728126.0 35.0 5503.7 10.123455.0 494 S 12 280434 510.5523 37.729626.85 7 34.2 7005.8511104249574 N9494Alpha= 126384N 26 48.6 D13 29545.9 2009.6 37431127.5 33.5 85074 10.326500.0 494Alphas's35817.6N 28 55.7 A14 31048.3 350.6 37.632628.3 32.710010.1 10420021 494Altair 62401N 8 474 y15 32550.8 50078.6 . 37.634129.0 32.011512.2 101 298505.0 494Aka 35347.85 42 28.3 16340: 1 6506.6 37.635629.8 31.2130144 10.6310074 494Antares 11306.8S 26 221 17355554 8005.7 37.5 1130.5 30.514516.5 10.732509.9 49.5 18 1058.2 9504.7523 37.5 2631.35 7 29.716018.651110.9340124 N949.5Arcturus 14625.7N 19 20.0 19 2600.711003.7 37.5 41324 28.917520.8 11.035514.9 49.5Atria 10838.75 68 58.5 20 4103.112502.8 37.5 5632.7 28.219022.9 11.1 1017.3 49.5Avior 23431.05 59 24.5 21 5605.61400143 . 374 7133.5.. 27420525.0..11.2 2519.8. 49.5BellaIrix 27906.8N 6 19.6 22 7108.015500.8 374 8634.2 26.722027.2 11.3 4022.3 49.5Betelgeuse271364N 7 24.3 23 8610.5169591 37.310135.0 25.923529.3 114 55248 491 200 10113.018458.8523 37.311635.75 7 25.225031.551111.5 7027.3 N949.5Canopus 2641015 52 404 01 11615419957.9 37.313136.5 24426533.6 116 8529.7 49.5Capella 281224N 45 584 02 13117.921456.9 37.214637.2 23.6280354 114100324 49.5Dtneb 49544N 45 104 0314620422955.9 . 37.216138.0 22129537.9 .11111534.7 . 49.5Denebola 18306.9N 14 44.3 04 16122124455.0 37117638.7 22.131040.0 11.913037.2 49.5Diphda 34928.65 18 09.1 0517625.325954.0 37.119139.4 21432542.2 12.014539-6 49.6 0619127.827453.0523 37.120640.2S 7 204234044.3S1112.216042.1 N949.6Dubhe 19431.0N 61 541 0720630.228952.0 31.022140.9 19.8355464 12.317544.6 49.6Elnath 27853.7N 28 35.2 08 22132.730451.1 37.023641.7 19.1 1048.6 12419047.1 4%Eltanin 9101.9N 51 29.3 F 0923635.131950.1 . 36.9251424- 18.3 25504 12120549.5 4%End 3419.5N 9 44.2 R1025137.633449.1 36.926643.2 17.6 40524 12.622052.0 49.6Fomalhaut 1600.15 29 47.1 40.134948.2 1 11 266 36.828143.9 16.8 5555.0 12.723554.5 494 D12 28142.5 4474523 36.829644.75 7 16.1 70571S1112.825057.0 N949.6Gacrux 17237.75 56 56.5 A13 29645.0 1946.2 36.7311454 15.3 8559.3 12.9265594 49.6Gienah 17626.05 17 221 y14 31147.5 3445.2 36.732646.2 14.5101014 13.028101.9 49.6Hadar 14935.05 60 136 15 32649.9 4944.3 .36.634146.9 . 131116036 131296044 496Hamal 32837.7N 23 19.5 16 341524 64434 36.535647.7 13.013105.7 13.231106.9 49.7Kaus Aust. 8427.65 34 24.2 1735654.9 7942.3 36.5 1148.4 12.314607.9 13.332609.3 49.7 18 1157.3 9441.4523 364 2649.25 7 11116110.051113434111.8 N949.7Kochab 13718.7N 74 16.3 19 2659.8109404 364 4149.9 10.7176121 13435614.3 49.7Markab 1411.2N 15 02.7 20 4202.3124394 364 5650.7 10.019114.3 13.7 11161 494Menkar 31449.1 N 3 584 21 5704.713938.5 . 36.2 71514 . 09.2206164 13.8 2619.2 49.7Menkent 14846.55 36 134 22 7207.215437.5 36.2 8652.1 08122118.6 134 4121.7 494Miaplacidus 22146.35 69 354 23 8709.616936.5 36.110152.9 07.723620.7 14.0 5624.2 49.7 300 10212.118435.5523 36.011653.65 7 06.925122.9511141 712642 N949.7Mirfak 30927.1N 49 45.7 01 11714.619934.6 36.013154.4 06.226625.0 14.2 86291 49.7Munki 7639.25 26 20.3 02 13217.021433.6 '354146551 05428127.2 14410131.6 49.8Peacock 5411.15 56 50.2 03 14719.522932.6..351161554 04.729629.3 . 14411634.1 . 4%8Poilux 244074N 28 06.0 04 16222.024431.7 35417656.6 034311314 14.513136.5 49.8Procyon 24533.6N 5 18.3 05 17724425930.7 35.7191574 03.23263342 14.614639.0 49.8 06 19226.927429.7523 35.620658.15 7 02434135.751114.716141.5 N949.8RasaMague 9637.2N 12 344 , 0720729.4289281 35.5221584 01.635637S' 14.817643.9 49.8Regulus 20818.0N 12 068 3 0822231.830427.8 35423659.6 00.9 1140.0 14.9191464 491Rigel 2814 %.2 58 14.0 ok 0923734431926.8 35.425200.4 1 00.1 2642.2 15.020648.9 49.8Rigel Kent.14037.15 60 42.6 T 10 25236.833425.9 35.326701.1 6 594 4144.3 15.122151.4 49.8Sabfit 1025045 15 41.5 U 11 26739434924.9 35.228201.9 58.6 5646.5 15.323653.8 49.9 R 1228241.7 423.9523 35.129702.65 6 57.8 7148.651115425156.3 N9494Schedar 35018.2N 56 22.7 D13 29744.1 19224 35.031203.4 57.1 8650.8 15126658.8 49.9Shaula 9706.85 37 05.1 A14 31246.6 3422.0 34.932704.1 56.3101524 15.628201.2 49.9Sirius 25902.25 16 40.3 y15 32749.1 4921.0 34.934204.9 55.511655.1 15.729703.7 49.9Spica 1590545 11 004 16 34251.5 6420.0 34.835705.6 54.813157.2 15131206.2 49.9Suhail 22316.35 43 18.5 17 35754.0 7919.1 34.7 12064 54.014659.3 15.932708.6 49.9 18 12561 9418.1$23 34.6 2707.15 6 53.316201.551116.034211.1 N949.9Vega 81016N 38 451 19 2758 10917.1 341 4207.9 52.517703.6 1613571342 49.9Zubtn'ubi1374115 15 55.1 20 4301412416.2 344 5708.6 514192051 16.2 1216.1 50.0 S.N.A Her.Pus. 21 5803.913915.2 34.3 72094 51.020707.9 164 2718.5 50.0 22 7306.315414.2 34.2 8710.1 50.222210.1 164 4221.0 50.0Venus 8345.9 11 41 23 8808.816913.3 34.110210.9 49.523712.2 16.5 5723.5 50.0Mars 1522.7 16 13 a. ., Jupiter 14918.5 7 17 Mer. Pass. 17 12.3 v-..0 d o.1 v0.7 doa e2.1 d NI o2 d NoSaturn 329 14.3 19 15

166 BEST COPYAVAILABLE Appendix F-2 BEST COPYAVAILABLE

1970 JANUARY I, 2, 3 (THURS.,FRI., SAT.) ii Twilight Sun. Moonrise Lat. SUN MOON Neut. Civil 2 3 4 GM.T. 6 a o I Dec. G.M.A. v Dec. h G.44.A. N7208 2310 40 0121 03 47 a h 08 04 0948 0113 03 21 06 21 S 10.8523 034 27118.0 9.4$ 620414.655.9 N70 100 179 07 49 0916 0104 03 01 05 24 10.5 034 285524 no 635.034.6 68 194 07 37 0852 10 26 0058 02 46 04 51 08 02 20910.2 03.0 3002643 1s3 649.614.656.0 66 06 43 82 34456,0 07 26 083309 49 0052 02 33 04 27 03 22409.9 . 024 31501.1 1s2 704.2 04 08 06 07 16.656.1 (61 07 17 01310 09 22 0047 02 23 04 23909.6 02.6 32935.3 15.2 71843 02 14 03 52 05 41 14.3564 6007 09 080509 02 0043 05 254094 024 34409.5 16 7334 07 02 0754 0 45 0039 02 06 03 39 05 20 09.0S23 ON 35843.6 18.1S 7479144564N 58 06 269 07440831 0035 01 59 03 28 05 04 08.7 02.0 1317.7 14.9 802,5143561 5606 55 284 06 49 0735 0819 0032 01 53 03 1804 50 T 8; 299084 014 2751.6 14.9 817.014.5561 54 06 44 0728 0808 0030 01 47 03 10 04 37 H 09 31408.1 01.6 4225.5 14.9 831.514.5561 52 04 26 14456.3 5006 39 0720 0758 0027 01 42 03 02 U 1 32907.8 01.4 5659.4 14.8 846,0 02 46 04 04 14.556.3 4506 28 0705 0738 0022 01 32 R11 344075 01.2 713.3.2 16.6 900.5 03 46 N 40 06 18 0652 0122 0018 01 23 02 32 S 12 3590;S 23 01.0 860643 14.7S 915.0 la456.3 02 21 03 31 56.4 3506 09il640 0708 0014 01 15 O 13 1406.9 004 10040.5 16.5 929414.4 03 18 06 00 3(330 0656 0010 01 09 02 11 A 14 2906 00.6 11514.0 14.5 943,814.456.4 30 02 56 56.4 0 05 440611 0635 0005 00 58 01 54 15 4406,3 00.4 12947.5 14.4 958,214.4 01 4002 37 120 05 28 0554 0617 0000 00 48 Y 16 5906.0 004 144209 140 1012.614.456.5 N 0 02 19 56.5 05 12 0538 0600 2439 00 39 N. 26 17 1405.7 23 00.0 15854.2 14.2 10274144 0520 05 43 2430 00 30 01 1302 01 8905.5S22 594 173274 14.151041.3 Ia.,56.55 1004 53 18 04 31 050005 24 2420 00 20 00 5901 43 10405.2 59.6 18800.5 14.1 1055414056.6 20 19 043505 03 2409 00 09 00 4201 22 59.4 20233.6 179 1 09914.256.6 3004 02 20 119049 0421 04 50 2403 0003 00 3301 09 59.2 21706.5 13.9 1124.114456.6 3503 44 21 13404.6 2356 24 22 00 2200 55 231394 11.8 1138.314.256.7 4003 22 040304 35 22 14904.3 58.9 48 24 10 00 1000 38 14.1564 4502 52 0341 04 18 23 23 16404.0 584 24612.2 13.7 1152.5 0312 03 56 2338 23 55 24 18 00 18 17903.7S 22 58.5 26044.9 U.6 512064140564 5002 08 57 03 45 2334 23 48 24 0800 08 2 00 58.3 27517.5 134 1220.714.15643 5201 42 02 01 19403.4 40 2329 23 40 23 57 24 23 28950.0 13.4 1234.814456.8 5401 02 02 03 33 02 20903.1 58.1 2324 23 32 23 4524 06 304224 170 1248.814.0569 56 HU 0219 03 20 03 224024 579 2318 23 22 23 3023 46 1302414.0569 nu 0151 03 04 04 23902.5 57.7 31854.7 13.3 23 11 23 1423 21 1111 0108 02 44 2311 05 25402.2 57.4 33327.0 13.1 131643 no569560 30.713457.0 Moves* 06 26901.9S22 57.2 34759.1 13.0 Si) Sun- Twi Ight 28401.6 57.0 231.1 22.9 1344.6134574 Las. 3 4 07 1411 Civil Nut. I 2 08 29901.3 56.8 1703.0 12 1358413457.1 F 14124134574 S h 6 m 6 6 31401.0 56.6 31 34e 12.7 lb It 329004 56.3 4606.5 u.s. 1426.013.6574 R 10 N 72 13 2715 45 1016 09 25 a 11 34400.5 56.1 6038.1 12.3 1439.6/7057.2 1419 16 03 1030 09 54 08 35 um 00.2S 22'559 7509.6u.4$1453.317.657.2 N 70 D 12 359 1452 16 18 1040 10 15 09 33 S 599 55.7 8941.0 u 1506913457.3 68 A 13 13 13 41 1515 16 31 1049 10 32 10 0808 49 2859.6 55.4 10412.3 12.2 1520413.357.3 66 Y 14 1534 16 41 1057 10 46 10 3310 09 4359.3 55.2 11843.5 22.0 1533113.557.3 64 14 19 15 14 45 1549 16 51 1103 10 58 10 5310 46 5859.0 55.0 13314.5 U" 1547411057.4 62 16 15 06 1602 16 59 1109 11 08 11 09 11 12 17 7358.7 544 147454 11.9 1600.713357.4 60 15 23 1614 17 06 1114 11 17 11 2311 33 88584 22 54.5 16216.3 11.251614.0 is.s57.5 N 58 18 1624 17 12 1119 11 25 11 3511 51 103584 54.3 17647.0 11.6 lb27.313.257.5 5615 37 19 1633 17 18 1123 11 32 11 4612 05 54.1 19117.6 no 1640.517.157.5 54 15 49 11857.8 16 00 1641 17 24 1126 11 39 11 5512 18 2 13357.5 539 205484 11.4 1653.6 u157.6 52 16 09 1648 17 29 1130 11 44 12 0312 30 14857.3 53.6 22018.4 9.2 1706.713.057.6 50 22 16 30 1703 17 40 1137 11 57 12 2112 53 23 16357.0 53.4 23448.6 11.1 1719.713.057.6 45 46 1717 17 50 1143 12 07 12 3613 13 178564S 22 53.2 24918.7 9.6S1732.712.857.7N 40 16 3 00 00 1728 17 59 1149 12 1612 4913 29 19356.4 524 26348.7 36.0 1745.512.857.7 35 17 13 43 01 12 1738 18 08 1153 12 24 13 00 02 20856,1 52.7 27818.5 20.7 1758.312.8574 30 17 32 1756 18 24 1201 12 38 13 1914 06 03 22355-8 52.5 29248.2 10.6 1811.112.65743 20 17 51 1813 18 40 1209 12 50 13 3514 27 23855.5 52.2 307174310.5 1823.712.657.9 N 10 17 04 08 1830 18 56 1216 13 01 13 5114 46 05 25355.2 52.0 32147.3 10.7 1836.3120571 0 18 14 0615 06 48.8 1825 1848 19 15 1222 13 12 06 26854.95 22 51.8 33616.610.2518 12.4 57.9 S 10 15 27 201843 1908 19 37 1230 13 24 14 23 07 28354.6 51.5 35045410.3 1901212.758.0 14 4215 51 58.0 30 19OS 1932 20 05 1238 13 38 S08 29854.3 51.3 514910.0 1913.5U.S 17 1947 20 23 1243 13 46 14 5416 05 A og 31354.1 51,0 194399.8 19"e5.812.1584 35 19 2005 20 46 1248 13 55 15 0716 22 328534 50.8 3412.79.7 1937412.158.1 40 1932 16 42 T 10 1950 2027 21 16 1255 14 0615 22 U 11 34353.5 50.6 48414 9.5 1950.012.058.1 45 03 14 20 15 4217 07 630919.6S2002.011.958.2 5 50 2012 20 55 21 59 13 R 12 35853.25 22 50.3 06 14 26 15 51 17 19 13911.858.2 52 2022 21 1022 24 13 D 13 13529 50.1 7738.39.7 20 14 33 16 01 17 33 9.1 2025.711.756.3 54 2034 21 2723 03 1310 YA 14 2852.6 49.8 9206.6 14 40 16 13 17 49 11.758.3 56 2048 21 48 1315 15 4352.3 49.6 10634.79.0 20374 18 08 2104 22 16 1320 la 49 16 26 16 58524 49.3 12102.78.8 2049.111.558.3 58 16 4218 33 23 22 58 1112 1325 14 59 17 7351.7 49.1 13530.5 2100.611.1584S 60 21 18 8851.55 22 489 14958.28.6S2112-011.758.4 SUN MOON 8.4 23.311.258.5 Me r. Pass. A. 19 10351.2 48.6 1642543 21 Day Eqn. of Time Mer. Phu 17853.2 8.7 2134.511.158.5 Pass. Upper lower "Ge 20 118509 484 OCP 12" 50.6 484 19320-56.2 2145.611.058.5 21 133 h m S h m 4 22 14850.3 47.9 20747.78.0 2156.610.958.6 m s ' 0 03 1603 30 12 04 06 05 18 2723 23 16350.0 47.6 22214.77.8 2207.510.85813 1 2 03 4503 59 12 04 06 50 19 1324 04 27 12 04 07 38 20 05 25 ci S.D. 16.3 d 0.2 S.D. 15.3 15-6 15.9 304 13

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'L R9 Appendix F-4 BEST COPYAVAILABLE ALTITUDE CORRECTION TABLES 10'-90'----SUNI STARS, PLANETS OCT.-MAR.------SUN APR.-SEPT. STARS AND PLANETS DIP App.Lower upper App. App. AdditionalHt. of Ht. of App. Lower upper Corrn CorrnEye Corrn Alt. Limb Limb Alt. Limb Limb Alt. Alt. Corrn Eye 1970 ft. ft. 9 56_6.2 1'1 9 34-4 10.8 -a: 5 939 +.10-6 -at s VENUS --11 44 6-5 10 08.- 9 45+10.9-31 4 951 +10'7 5.2 I'4-1'2 45 6.6 10 20 Jan. 1-July 22 1.6 9 564-11'0 -at 3 IO03 +10.8 -ai 0 -5'1 47 6.7 10 08 1015 +10.9 301 10 33.5.0 0 .9 48 6.8 +11.1 -31 3 10 46 -t0.1 2'2-1.4 I0 21+11.2 -21-I 1027 + ti.0 -30 8 42 1.5 49 6.9 II 00 _4.8 2.5 10 34+11.3 -210 1040 +11.1 -30-7 July 23-Sept. 5 -1.6 51 7.0 I I14 2.8 52 to 47tI1.4-20 9 I054 +11.2 -30 6 4.7 O 1'7 7.1 II i I 294.6 t- 0.2 II 01 o8 +11.3205 -1.8 54 7.2 + WS sea 47 3.6 II 15+11.6 -207II2311.4 -204 1 145-41 - 1.9 55 7.3 II 30 II 12 01 Sept. 6-Oct. 4'0 57 +11.7so 6 38+11.5 -20 j 4'4 2-0 7'4 II 46 II 12 18 4'4 58 +11.8ao-s 54 -4- II*6 -261 --4-3 -t-0 .3 7.5 12 02 12I0 +1.a 12 iS 46 4.9 6o .t- 11.S -30.4 'J -20.110'1 -- -4'2 2.2 7.6 12 19 12 54 62 -4-12.0 -3o 3 1228 +11.8--so-0 -4'1 Oct. 2-Oct. :6 5'3-2.3 7.7 12 37 12 13 13 63 + [VI -201 46 +11.9- -4.0 5'82.4 7.8 12 55 13 6.3 65 -I-12 2 -aoI 05 +12.0:9 8 13 33 -3.9 1: + 0'4 7'9 13 14 13 13 5454 -3.88 -t 6.9 67 - 12.3 -20.0 24 +12'1 -19 7 , 41 -2-6 8-o 13 10 68 13 35t 12-4 -19 9 45 +12'219 6 -31 7.42.7 8.1 13 56 Oct. 17-Oct. 24 80 70 -4 12.5 -191 1407 +12.3 -19 5 14 40-3'6 82 O 8.6 72 14 18 14 15 04 2-9 8.3 +12.6- t97 3° -1-12.4 -194 15 ;,0-3'5 0.5 9'2 14 42 121 -19 1454 +125 -19.3 6 o 6 -3'0 74 8-4 15 06 15 57__3.3 20 9.8 +12.8 -19.5 19 ÷ 12.6- *9 a 0.7 3'1 75 8.5 16 26-3'3 10.5 15 32+12'9-194Is46 +12.7-19 I 31 3.2 77 8.6 15 ,6 56_3.1 11'2 79 59+13'0 -191 i614 -12.8e9.0 -3.1 Oct. 25-Nov. 28 3.3 8.7 1628 16 17 28 11'9 8i I3.L -19 a 44 +12.9 18 9 -3.o O 3'4 8.8 16 17 18 02 o6 12'6 83 +13.2-191 15 -13.0le a -2.9 4 3.5 89 17 32 17 18 38 0.7 13'3 85 + 13.3-190 48+13.1- t11-7 12 -36 -g.o 18 o6 i8 19 I7 o8 14'1 87 +-13.4 -189 24 +13.2 -i9 6 -2.7 22 3.7 18 42 19 14'9 88 -111 8 18.5 19 5° -2 6 3'8 97 19 21 01 -13.3 20 42 Nov 29-Dee. 6 -4-13.6 -18 7 1942X13.4 _184 -2.5 15'7 90 9 3 20 03 20 21 28 :6.5 92 13-7 -18 6 25 r 13.5 -*II 3 -24 O 5 4'0 9.4 20 48 22 19 6 94 + 13-8 21II 4-13.6 -18 2 -2 3 0.6 17'44'1 95 21 35 22 23 i3 20 18.3 96 13'9 -18'4 °43c, 413.7 -1a1 --2.2 0.7 4.2 96 22 26 22 24 II 19.1 98 183 J .9 I3.8 18 o _2/ 31 4.3 9.7 23 22 14.0 2514- 20'1 lox 14.1 18.1 2351r 13-9 -17'9 2'0 Dec. 7-Dec. 21 4.4 98 24 21 z622 0 21.0 103 14 2 -18.: 2453 t I4'017 3 45 99 25 26 26 36 1.8 0.4 22.0 105 14'3:Jo t 14.1 -17 I 4.6 to o i6 36 27 z8 56 t0.5 22'9 107 14'417 9 13 14-2 17 6 47 to 1 2752 28 30 41 23.9 109 14'5 '17 8 33 14'317 5 24 t 6 4.8 10 2 29IS 30 00 32oo Dec. 22-Dec. 31 24.9 II 14'617 7 14'4. 174 --I 49 1o3 3046 33 45 / 0 26o 1'3 147 17 6 31 35 14.517 3 5-o 1o4 3226 33 20 35 40 0.3 271 116 + 14.8.175 14.6 -17 2 46 5.1 10 5 17 281 118 34 -t-14.9 -17 4 35 17 14 7 -17 1.2 52 10.6 3620 37 26 29.2 120 4 15'0 17 3 t14 170 II 53 10 7 36 344702 ii 304 122 38 +.15 I v2 39 50 14 9:6 9 - I 0 MARS 5.4 It) 8 41o8 45 31'5 125 15'2 17 42 31. 15 0 16 8 0.9 Jan.1-Dec. 31 5 5 10 g 4359 47 32'7 127 +153170 45 31 /5 1 167 o-8 56 110 O 129 47I0 48 55 5 52 18 33.9 15 4X69 2 -166 0.7 1 5.7 11 1 5046 52 44 56 II 6o 35-I 132 1155:6 8 . 153 i6 5 0.6 58 112 5449 /5 6o 28 36'3 134 -4 15 6 16 7 57 02 4164 o 5 59 11 3 5923 61 51 65 o8 37.6 136 157:66 5 16 3 0 4 6o 114 64 67 17 7o I I 38 9 139 30 15 8165 -6 16 O 3 6.1 11 5 7012 73 16 75 34 40-I 141 11 6 + 159 164 157 16 O 2 62 7626 79 43 811.3 41'5 144 16 0 1I5 3 ./58 16 0 O 1 63 II 7 86 32 87 03 428 146 83 05 16 1 16 915 9 00 64 118 90 00 go oo go 00 44 2 149 App. Alt. Apparent alutude = Sextant altitude corrected for indot error and dip. For daylight observations of Venus, see page 26o. N:. `4 :a I 169 Appendix F-5 BEST COPYAVAILABLE ALTITUDE CORRECTION TABLES 0r-10'--SUN, STARS, PLANETS A3

OCT.-MAR. SUN APR.-SEPT. oct-mmt. SUN APR.-SEPT. ! App. STARS App. ?STARS Alt. Lower UpperLower Upper PLANETS Alt.I LowerUpperLower Upper 'PLANETS Limb 1-00b Limb Limb Limb Lamb Limb Limb . - - - I I I I O 00 -18'2 -50 5-18'4 so 2-341 3 3o 4-3.3-29-0 I 3.1 -Ail 130

17.8 ! 03 17'5 49.8 49 6 33.8 35 I 3.6 28-7 3.3 211 12'7 06 16.9 494 17'I 48'9 :13.2 40 3.8 283 3'5 28.3 121 09 16.3 48 6 16.5 41.3 32.6 45 I 40 111.3 i 3.7 281 121 12 15'7 41.0 15'9 47 7 32.0 50 4'2 21.1 3.9 27.9 121 15 15'1 474 15'3 47 1 31'4 3 55 I 4.4 27 9 4'1 27'7 11'9 O :8 14-5-46.8 14'8-46 6- 30.8 4 00 + 4.5-241 t4.3-17.5 11.8 21 05 14*0 461 14'2se o 30.3 i 47 27 6 4.5 27-3 11.6 24 135 45 13.7 45 3 29.8 49 27-4 4 6 27.2 27 12.9 45.2 13'2 45.0 29.2 15 5.1 272 48 27.0 11.2

30 12'4 44'7 121 44'5 281 20 i 5.2 27-1 50 268 33 11.9 44 2 12.2 44.0 28.2 25 i 5'4 26.9 5*I 26.7 10.9

O 36 -11.5 43 1 - 11'7 -43 S-27'8 4 30 I .4-5.6-26.7 + 5.3-26 3-10.7 39 11.0 43.3 11.2 43 0 27'3 35 5.7 26 6 : 5'5 s6 3 10.6

42 10.5 42.8 10.8426 26.8 40 I 5'9 26 4 5.6 26 2 10.4 45 l01 42.4 10.3 42.1 26.4 45 6o 26 3 5.8 26.0 10'3 48 9.6 41.9 9*9 41.7 25'9 50 6.2 26.1 5.9 25 9 10.1 51 9.2 41'5 9.5 41.3 25.5 4 55 6.3 260 6o 25 8 10.0

O 54 - 8.8 -41 1 9.1 40'9 25.1 5 00 I + 6.4-25 9+ 6.2-25 6- 9.9

O 57 8.4 407 87 40 5i 241 05 6.6 25.7 . 6.3 23.5 9'7 00 8J 4o3 8.3 so 1 24'3 zo i 6.7 23.6 6.4 25.4 9.6 03 7.7 4o0 7 9 39 7 24.0 :5 6.8 25.3. 6.6 25.2 9'5 06 73 39.6 7'5 39.3 23.6 20 I 6.9 251 6.7 231I 9*4 09 6.9 392 7.2 39.0 23.2 25 7.1 ss s 6.8 25.0 9'2 I 12 - 6 6 -311- 6.8 38 6 - 22'9 5 30 + 7.2-25 t t6.9-24.9 9-1 15 6.2 31.5 6.5 38 3 22.5 35 7.3 25 0 7.0 241 90 18 5*9 38 2 6.2 38 0 22.2 40 7 4 241 7'2 24 6 8-9 21 5.6 37 9 5.8 37 6 21.9 45 7.5 241 7 3 24 s 8.8 24 5.3 37 6 5.5 37 3 21.6 50 7.6 24 7 7.4 244 37 4.9 372 5.2 37 o 21.2 5 55 7.7 24.6 7'5 24 3 8.6 1 30 - 41'6 36 9 4'9 36 - 20.9 6 oo - 8.5 35 4.2 36 5 4.4 3627 20.5 TO 80 24335 ± 77.86-;24402 83 23 8 40 1 3.7 36 o 4 0 35 s 20.0 20 .8.2 24.1 8'0 Si . 45 32 355 3.5 35 3 19.5 30 8. 4 23 9 8.1 23.7 7'9 50 28 351 3.1 14 9 ! 19.1 40 8.6 23'7 8 3 23.5 7.7 1 55 24 34 7 2 634 4; 18/ 6 50 8 7 23.6 8.5 23 3 7'6

3 00 20 343 2.23i0-18.3 7 00 t8.9 23 4 1- 8 6- 23 2 7'4 05 1.6 33 9 1 8 33 6 17.9 zo 9.1 23 2 8.8 13 0 7.2 To 1 2 3) 5 1 5 333 17 5 20 9 2 23 1 9 0 22 8 7'1 15 09 332 I 1 32 9 17.2 3o 9.3 23 0 9 1 22 7 7 "0 20 05 328 0.8 32 6 16.8 40 9.5 228 92 a26 68 25 0.2 32 5 04 32 2 {6'5 7 so 9.6227 9.4 22 4 i 6.7

2 30 02 32 I O I It9 16 1 8 00 I- 9.7-226 r95-2231 66 3t8 O 2 3t6 zo 35 05 158 r 224 96 112 64 40 o b 31 5 O 5 313 15.5 30 ; 10%9 112 9'7 22 1 6 3 45 1 1 31 2 O 8 31O 15 2 3o 101 22 2 98 as 0 62 50 1 4 30 307 14.9 40 102 2111 IO 0 2181 6i 2 55 1 6 30 7 1'4 to4 147 8 50 , 103 22.0 10 I 21.7' 6.0 3 00 1 9 104 1 7 30 1 14 4 9 00 1-104-219 10 2- 21 6 59 05 2 2 30 1 1 9 29 9 14 1 10 to 5 21 8 to 3 21 5 5'8 Io 2 4 29 9 2I a, 13 9 20 to 6 217 104 214 5 15 2 6 19 - 2 4 29 4 13.7 30 107 2t 6 105 213 5u 20 29 294 2 6x92 134 40 t08 at 5 10 6 at a 55 25 31 3,, 2 29 2s 9 132 9 50 109214 10 6 21 a 54

330 3 29 0 Io 00 II 0-at 10 7 - atI 53

Additional t-orrections for tomp,:rature and pressure are given on the following page. For bubble sextant observations ignore dip and usethe starLorrc,:tions for Sun, planets, and %tars.

170 Appendix F-6 BEST COPY AVAILABLE

ALTITUDE CORRECTION TABLES-ADDITIONAL CORRECTIONS ADDITIONAL REFRACTION CORRECTIONS FOR NON-STANDARD CONDITIONS Temperature

-20F.-to. o' to' 20' 30' t1'50' 60' 7o'So'90°too'F. -r 1 I 1 I I I I I 3o C. 30 -W 0' -10" 10- 30' 40'C. v 3111'0 I 10507----7- 1 7 I / 7 / /

, ,/ __IL , ..;.. ... , T,030- 3 71.1 /A:13/C D E/F/GiH

O0 wl I0I0,- /+J + U / t//-1-I 2 / / E ! i' 4: / / / / 990 r- - ,/ + ' /1-1- ;, / /N-29.0 970.

AppAlt. A B.CD E F!G 1-1 J K L MIN AAPIPt:

o oo 69 57 4.6 34 23 It 00 . It 2 3 3.4 46 5 -7 6 9 0 00 0 3o 5.2 44 3.5 2-6 I7 0900 09 I 7 26 35 44. 5.2 0 30 1 00 : 4-3 3 c 2 8 21 1 4 0.7 o0 0.7 2I 2.8 3.5.4.3 I00 1 3o'35 29 24 18 I2 o 6 :00 06 t2 1.8 24: 2 9 35 t30 2 00 3C 2c 2 -0 1.5 : 10 0 5 io -0 0 -5 I 0 15 2 o I 2-5 3o2 00 2 30 2 5 2I 1 6 1 2 O8 0400 o 4 o 8 .1 2.1 6 I.2 I 2 5 2 30 3 00 2 2 I 8 1.5 11 , 0/ o 4 .00 04 tI t5 18 2 2 3 oo 3 30 20 1 0 13 I o 07 03; 00 0.3 O ' O I 3! 1 6 2.0 33o 4 00 t 8 ic 12 09 o6 o 3 :00 03 06 0 -9 I2 c 1 -8 4 00 4 30 t 6 t 4:II.o8 O 5 0300 03 O 5 o 8 14 16.4 30

5 00 I C 1 31 1 0 , 08 O 5 -0.200 02 5 o 8 1 0 1 3 1.5 5 00 6 13 09:o6 04 0 2 0-0 0-2 O 4 06 09) 13.6 7 II 0 -9 0 -7 06 04 02 0-0 0-2 04 o6 o7 o 9 II 7 8 I 0 )S 071 0.5 O 3 02 0.0 0.2 O3 0.5 0.7 o 8 , 1 0 9 0 9 0.7 0 6 04 03 O 1 0.0 0.3 0 4 06 o 7 0.9 9 to oo c8 o-0 04 03 O 1 00 0 1 o 3 0 -4 -0 5-0 8 e51 to 00 12 C 06 0-5 03 O 2 O 1 0.0 0-1 02 O 3 o 5 O 6 o 712 14 06 O 5 o 41 03 02 0.1 00 0-1 0.2 O 3 04 .3 5 o6 I14 16 e 5 04 0 3 j03 02 0 00 0-1 02 O 3 03. O 4 o5 '16 t8 0 4 04 0 -31 o 2 02 0 00 0 O 2 O 2 0 3 ; 04.o 4 j18 20 00 04 o 3 03.02 0 0 00 0 1 0 1 C 2 0 3 O3o.440 00 25 C 3 03 02'02 O t1 O 1 0 0 0 1 0 1 O 2 0 21 O 3 ' 0 3 ;25 30 03 02 02 0.I. 0 0-0 00 001 O I 0 2 O 2 O 3: 30 35 02 02,J 1 0 I 0 0c00 e I o t O I O 2 02' 35 40 02 01 0 II 0 0 0000 o o I 0 t OTI O1- 0 240

SO0.r. 0 I 0 I 0 I 0 t 00 0000 0010 0OI 0 , 0 I 0 T. SO 00 The graph is entered with arguments temperature and pressure to rind a zone letter; using as arguments this zone letter and apparent altitude (sextant Atitude corrected tor dip), a correction is taken from the table. This correction is be applied to the sextant altitude in addition to the corrections for standard conditions .tor the Sun. planets and stars from the inside front :over and for the Ninon trom the inside hack cover'.

171 Appendix F-7

AVAILABLE BESTCOPY ALTITUDE CORRECTION TABLES 0°-350-MOON

0 -4 5 -9 to -14...15 -1924) -2425 -2930 -34App. DIP Alt. t ,,rr Com t orr, ttr l...rto Corr" ('o44 144,;,1 0 5 n 10 20 30 00 33S 5n-2 62 115 02 8 02 2 5 60'44 38 9ou 10 349 58c 622 625 621 6o8 588 10 ft. ft. ft. 20 3'8 62 2 62 8 62 1 607 58-8 20 40 44 63 3o 39 6 58 9 62 3 62 8 62 1 58 7 2 0 ,4 9 7.8 6o" 30 44 2o 65 40 412 59 1 62 3 62 IZ 62 60.6 58-6 21 .5'o 79 40 4 9 27 67 50 42 59 3 62 4 62 62 j 6o6 58 5so 2 2 ;5-1 8 0 5 3 28 68 00 6 11_. 16 , 21 26 , 31. -2 3 5 2 1 8 i 144 59 4 02 o2 %) 00 5 5 00 5.8 29 70 10 452 54" 62 4 24 53 82 6: - 614 604 584 10 30 72 20 46; Syo 62 5 62 - 61 1) 60 4 58 320 25 5 4 6 9 34 74 83 30 4'3 60 0 6: i 62 ^ 61 4 6,-; 3 55-2 2 5 5 8 4 30 74.2732 75 40 48 3 hc 2 6:5 62" 618 603 58240 80 7 ....5 50 .19 2 6o; 626 627 618 6o2 58 2 8 77 8.6 50 8 6 5.7 2 7 , 7 22, 7 35 00 0 60 5 62 61. 62 01 60. 32 29 8.7 cn 000 92 36 , 84 TO 5 60 6 626 6: 6 61 601 57 910 -3o 9 8 8 9 5 387 8 20 41 4 60 62 6 6: 6 61 6 6c., o 57 820 34 6 89 to 5 ° i 81 5 60 -4 340 30 5: 62 ^ 62 6 61 6 5o 9 57 830 -3 2 6 t. 9.0 40 610 6:7 626 6:c 11 2 87 52 " 599 5-.740 II 93.3 62 9t 50 1 3 61 1 41 -6.3 88 62 - 62 6 61 c c9 )4 47-640 3 4 9.2 13 111 23 28 12 6 42 oo 3c;S 012 62 c 61 59'7335 "-5 no 3.5 6 41 90 9.3 446.i 92 10 44 3 61 3 62- 6: s 61 4 59 7 5- 4 10 3 6 9.4 44-1 45 _6 6. 94 20 5.4 61 4 62 62 5 61 4 54 6 5" 420 37 91 14 93 8 476.,9! ;0 cc 2 61 5 62 S 62-5 61 3 59 6 57 330 61 1 157 486 8 90 40 5s 6 62 8 62 4 6r 3 59 5 5' 240 3 9 56 61 6 62 8 16 -5 49 ., lot 50 6: 4 6t 2 59 4 57.1 50 4 0 o 9 9 8 29 17 4 51 103 no 4 56 4964"1462 19 62 4 34 4 4 24 61 2 00 103. 52 99 to 50 618 62 8 62; 61 1 543 c6yto 4'2 49I 20 5- t 61 0 6: 24 62 1 01 1 4 ?547.2107 tott 20 t; S5 30 4 ,1 62 6.:3 61 55919 2 55(6)8 1: 4 7 3"9 -to 2 21 0 57 III 40 62 62 1 6.. 0 59t c6 "40 45 to 3 co 22 0 48-.4113- 5" ,, 62 1 6: 62 2 4 59 o 56 650 4 6 22 9 607 5116 .1°.4 11 P. L U 1.12 I.1: 1,1:11.1) 4 ' - 6 rots It: 23 9 L, 62 448 ._- 4a 24 9 63 120 540 4J9 3 4 1 o< 1 612 0714 3915 440 543 1 I "1: 1 '41 4 1 4 1 1 1 5 I2 1 "54 3 MO( tN CORRECTIC)IN

1 .4 44 6 I 11:4 111; 12, 1316 1 41^ icis 54 6 A111.F. 44 9 1416 1411.1 :16 161 1015 1819 192044 y .1 he ..crreetIon Is in tw0 parts; 552 1815 1518 1010 Ili 2 2 2I2 1 2 2 2 2ci 2 iIafir.: ...trre,:tion it Liken front 55 5 2 2 1_ I 2.1 :I: Z 454 5 1112 1;; :r the Le-le with 55 2 6:2 262: 26:4 12- 24 282 4 20=5 55 N -.59:ocitt app.irentthitude, and 56 1 1 2 4 4. 3 4 41:0 4126 42.:"561 the Ne.ois1 mon the 1,,wer pdrt. c64 44 2' 4 4 1: 4 2 1425 3 2 8 3 2 564 with :a...um:in to the same 56"1 - 9 1 - .; t 510 sz2 '1t 4 S 3 .4 t,3 t-,6 7 1.4.90 sOneh the to.1 ..-,.rrekSlott 5%.1%Takon.Sep- 4"0 4141 4141 1141 1111 4 3I 1232 s 42 4 5 ^0 amit ,ort....11,11,.1142 4.,!Ve11111 the 5-I .1541 .1443.1. 4 4 4,11 45 14 1.441 634 573 i.`44et LIanti 5 64 0 ; I 9 A c4 9 A 4 9 154 0 1<4 9 1 4, 1 3 6 57 6 upper ,t 111 b'. All ,orrections 4,9 .44A 4445 S <.44 .23- ..11- 514" 479 Arc : he added to apt-area: alli- ih 2 : h 4 ; 6 4 . 4 sn; sh1956 3 9 582 to.1e. 3,.) 11r., Fr :rbtr,i,ted 4 58 s 6 1:6 4 :6 h 4 14 1S 9 4 158 5 !he ,'Tr hinb 5S1 8 O 4I 6141 6441 111 1 6 4 1 4 6 4 4 36 2. 4 Si 8 s;rt Us I ions 4rrICSNUte ct,)r 6h A r. r, t, " 66 '4 (1045" 6 4 591 .01.11.1111`ir.ttoteCS'paw! A4. 49 4 '14S " S 4 4 h ') 4 h 494 I. r!,ithhlt! 49 1 ' : s 4 4'I 414 "117597 non. 140.9e !.1kt! the mean no o , I < '64 600 tp.,er 1014,1' lunh COrrei- 61115344 51 8.'4 8254'1-1 ' 2 016413 i41% .111.1 +111.'11%1.1 15'from 00 6s 7 5 S..: s 4.4 S 5 4 ho 6 the I An 90 5 9 LL S s A h + 1. ) 64 4 Apt.\h Atti..ocnt 101 2 I -t 1 ' .4 4 1 c 8 4. 64 2 .0rre.ted tor I.61 5.. 3 st. 1 "h; 6: 4: A 01 :1101 .1141 .11:.

1 7 2 Appendix F-8 BEST COPY AVAILABLE

ALTITUDE CORRECTION TABLES 35° 90°-MOON

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I I 1. U I.U 1. U 1. G 1. 17 1. U 1. ti 1. 1' 1 111).

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56 t S I 3 ;4 2 0 1 6 4 1 I 3 2 3 33 4 344 h4 Z 3 4 4 1 4440 56 564 1 ti 1 1 0 2 1 9 .4 144 I<43 3 64 4 3 4 5 38 4 0 1 9 56 .4

Ch - 1 I 5 4 ; 1 4 41 2I 4 2 3 3 433443 44 16 4 5 37 4 6 38 4 ' 3 8 567

4" 11 4 1 1 4 ; 4 4144 4 ;44535 c15 4 6 1 64 ' 1 6 4 1 ' 4838 570

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1 73 Appendix F-9 BLST COPYAVAILABLE

18m INCREMENTS AND CORRECTIONS 19m

1 1 t 4. t' I t. SUN ARIES 'MOONoi; Corr"oCorr^1 Corr" SUN ARIESMOONor Corror Corr'or COT/. 18gPLANETS 19PLANETS Id d 1 1 i.

8 I

00 4 304 430.7 1417.7 ao0.0 wo 1.9 , 12.4 3.7 00 445.0 4 45.8 4 32.01a)PO I0 2.3 1...i3.9

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03 4 30.8 431.5 418.4 ao01 6.319 1 ..2.33.8 03 4458 4 46.5 4 32.7JOP1 Ib;2.0 1 1234.0

04 4 31.0 431.7 418.1 0.4 01 6.42.0i 12.4 343 04 446.0 4 46.8 4 334 0.4 0.1, 0.42.1 ' 12.4 4.0

05 4 31.1 432.0 418.9 0.502 6.;2.0:!Z.% 3.9 05 44643 4 41.0 4 33.22 02'e2.1 1 ...4.1

06 4 31.5 432.2 419.1 0.602 0.62.0 12.63.9 06 446.5 4 47.3 4 3.342012i 6.42.1 ; 1:64: 07 4 31.8 432.5 419.4 0.0.2 6:2.1 1203.9 07 4468 4 47.5 4 33.7 : 0.2, o2.2 1:4.1 08 432.0 432.7 419.6,0.1 0.2 642.1 11.1 3.9 08 447.0 4 47.8 4 33.90633'4,82.2 ;:i4.2 09 4 32.3 433.0 419.8 4.90.3 6.42.1 1:44.0 09 44; 4 48.0 4 34.2: ...-t 0.3: 6.42.2 ; 1:44.2

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15 4 33.8 434.5 421.3 1 1.' 0.c. '52.3I 13,4.2 15 4468 4 49.5 4 356: 0'; I 1.4 4.4

16 4 34.0 434.8 421.5 11.60.5 7.62.3 : 13.44.2 16 44%0 4 49.8 ' 4 35.8 P5 202.5 !1..04.4 17 4 34.3 4350 i 421.8 II.'3.5 '.'2.4 13'4.2 17 449? 4 50.04 36.1 1-(4 i: 2.5 II:4.5 18 4 34.5 435-3 422.0:1.8P6 '.82.4 11)44.3 18 449.5 4 50.3 4 46.3 83.6 2.5 1' 4.5

19 4 34.8 43 55 1 421.2 1 1.4 0.e. '.42.4 i 13.94.3 19 449.8 4 5054 36.6 Poi .42.6 ! 194.5

20 4 35.0 435.8i 422.5I :.:06sc2.5 i 14.0 4.3 20 4 5P0 4 50.8 4 36.8 37 8.263 14;4o

21 4 353 4364 i 422.71:.: 0.6 8.12.5 . 11.1 4.3 21 4 5P3 4 51.0 4 37.0 O.: 812 b 144 4.6

22 4 35.5 436.3 , 422.9 i:ZP7 8:2.5 I 14.2 4.4 22 450.5 4 51.3 4 3 7..1 . . 0.7 27 14.:4.6

23 4 358 4355 I 423.21' 2.3 07 8%26 ,34.% 4.4 23 450.8 4 51.5 4 37.5 37 !bt2.1 '110

24 4 360 436.8 4234 2.4 P7 8.12.6i:4.44.4 24 451.0 4 51.8 . 4 3 7.;..4 3,818.42.7 1 11.4 4.7

25 4 363 437.0 423.7 2.., 0.8 8`.. 2.6 14.;4.5 25 4513 , 4 52.0 4 38.0 . 08 8. 2.8 14' 4.7 26 4 3645 437.3 423.9 2.60.8 0 to24 I1464.5 26 451.5'452.3'438.1,5 ,18 a4,2.8 14.0 4.;

27 4 3648 437.5 424.1 .3.0.8 0,2.7 1 14.7 4.5 27 451.8 4 52.5438.5 2. 0.9 0 :4.:4.8 39 at;7.4 4.8 28 4 37.0 437.8 424.4 2.60.9 8.82.7 1 14.84.6 28 452.0 ! 4 52.84 38.;;0

29 4 37.3 438.0 424.6:4 0.9 8,12.7 1 11.9 4.6 29 452.3 4 53.1 4 38.9 i 4.424 :14.4 4.8

30 4 37.5 438.3 424.9 3.4 0.9' 4.0 2.8 15.14.6 30 i 452.5 4 53.3 4 34.2 IC 2.4 4.9

31 4 37.8 438.5 4251 3.1 1.0 442.8 :s. 4.7 31 t 452.8 4 53.6 , 4 3%4 3.: 1.0i 9:3 0 ; :14.9

32 4 38.0 438.8 4253 3: 1.0 31.2 2.8 I l',24.7 .32 453.0 4 53.8 4 3%; 1.3 3.3 ..! 4.9

33 4 363 439.0 425-6 1.3 1.0 e.'2.9 . 1,.14.7 33 453.3 4 54.1 4 39.9 j.i 3.3 :35-0

34 4 38.5 439.3 4258 3.4 1.0 4.42.9 . 1'3.1 4.7 34 4515 , 4 54.3 4 43.1 .4 1.4 3.1 :4

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. 1- 3.2 1- 37 4 39.3 , 4400 426.5 0 1.1 4.:3.0 1,.4.8 37 4 4.3 4 55.1 4 43.8 .a SI

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39 i 4 39.8 1 4405 427.0 3.4 1.2 4.e3.1 15-4 4.9 39 454.8 4 556 4 41.3 ). .

4.4 1.1.. 3.3 52 40 I 4 4PC I 440.8 1 427.2i 40 1.2 10: 3.1 6 40 4550 4 5'3.8 4 41.04:

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59 4 44.8 4 4 :rt 431.8' 1-8 '1.41.: 1 :., so. 59 4'4'8 )56

60 1 4 45.01 4 458I,432.01601.9112c 3.7118.4 5.6 60 5000 5 208 4 4 hp A4 .6. 5.1 1 1

174 Appendix F-10 BEST COPY AVAILABLE

20' INCREMENTS AND CORRECTIONS 21"

V V t. t. SUN SUN or Corr" . ARIES!MOONodr Corr"or Corr'or Corr" 21 ARIESMOON or Corr.or Corr. A P LANETS i PLANETS J J J

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15 5 03.8 5 04.6 4 49.9 :.s0.5 '.s2.6 13.64.6 15 5 18.8 519.6; 504.2 05 7.k2.7 4.8 1,6 16 5 04.0 5 04.8 4 50.2 0.5 1.6 2.6 13.4.6 16 5 19.0 5 19.9 5 04.5 1906 2.7 D.e4.9 17 5 04.3 5 051 4 504 ...:0.6 7.7 2613:4.7 17 5 19.3 5 20.1 504.7 1 0.6 ;'2.8 1, 4.9 18 5 04.5 5 053 14 5061106:72.7 11.84.7 18 5 19.5 5 20.4 5 04.9 :.5 1.113 .8 2.8 4.9 II..? 19 5 04.8 5 056 i4 509 1.406 7.92.7 044.7 19 5 193 5 20.8 5 05-2 1.90.7 '.42.8 50

20 5 05.0 5 05.8 4 51.1 :.a0.7 sct2.7 14.04.8 20 5 20.0 5209; 5 054 2.007 e .2.9 :4.:SO 21 5 053 506.1 4 510 2.1 0.7 8.1 2.8 14 4.8 21 5 20.3 521.1' 5 057 2.1 0.8 e12.9 14.1 51 22 5 055 15 06.3 4 51.6 2.2 0.8 6.2 2.8 14.24.9 22 5 20.5 521.41 5 0,9 1.20.8 5.:2.9 14251 23 5 058 15 066 14 51.8 2.1dB 5.32.8 14.14.9 23 5 20.8 5 21.6 5 06.1 730-8 4.43-0 14.351 7.40.9 4.4 3.0 14.4 52 24 j 5 060 15 06.8 4 524 7.4 0.8 8.4 2.9 14.44.9 24 5 21.0 5 21.9 5 06.4

8.5 2.9 14.5 5 21.3 5 224 5 06.6 0.9 4.53.0 52 1 2.1 25 25 5 06.3 1 5 074 4 52.3 09 50 26 5 06.5 5 07.3 4 52.5 7.6d9 5.9 2.9 14.650 26 5 21.5 5 224 5 06.9 2.e 8e.3.1 14.9 52 1 27 5 068 5 07.6 4 52.8 7.:0.9 so3.0 14.7SO 27 5 21.8 5 22.6 5 07.1 1.0 e. 3.1 14.r53 28 5 07.0 5 07.8 4 53.0 281.0 143.0 14.151 28 5 22.0 5 22.9 5 07.3 zs1.0 8 3.2 14.853 29 5 07.3 5 08.1 14 53.3 2.9 1.0 4.9 3.0 t4.951 29 5 22.3 5 234 5 07.6 7.41.0 3.2 14.0 53 14.0 30 5 37.5: 5 08.3 4 53.5 3.0 1.0 933.1 15.05.1 30 5 22.5 5 23-4 5 07.8 '.41.1 4.0 3-2 5.4 1.1 413.3 icI 31 . 5 07.8 5 08.6 14 53.7 %1 1.1 4.1 3.1 15.152 31 5 22.8 5 23.6 5 08-0 16.1 54 32 5 08.0 5 08.8 14 54.0 3.2 1.1 9.2 3.1 ls252 32 5 23.0 5 23.9 5 08.3 '.2 1.1 9.: 5 24.1 5 08.5 %.4 1.2 3.3 Is 33 5 08.3 5 09.1 1 4 54.2 3.114 9.3 3.2 15.352 33 5 23-3 4. 1.2 4.4 3.4 15.4 55 34 5 08-5 5 09.3 j 4 54.4 3.4 1.2 943.2 16453 34 5 23.5 5 24.4 5 08.8 14

4 -s 1 1.3 3.4 Is', 5-6 35 ' 5 08.8 ' 5 09.6 4 54.7 1.5 1.2 9.5 3.2 ls.s53 35 5 23.8 5 24.6 5 09.0 36 5 09.0 5 09.8 4 54.9 1.1.2 9.93.3 15.953 36 5 24.0 15 24.9 5 0+2 %e 1.3 3.4 Ise 56 37 5 043 5 101 4 5523 1.3 9.7 3.3 1s!54 37 524.3; 5 25.1 5 09.5 1.. 1.31 3.5 57 38 5 04.5 5 10.3 4 554 3.11 1.3 4'83.3 154354 38 5 24.5 5254 5 094 Hs 1.4 ..a 4.4 15.4 39 5 09.8 5 10.6 4 556 3 1.3 443-4 16.954 39 5 24.8j 5 25.6 1d0 1.4 3.5 10.0 40 5 100 5 103 4 559 4.0 1.4too 3.4 19.055 40 5250' 5 259 5 10.2I .1 1.4 i;.;3.6 51 41 5 153 5 11.1 4 56.1 4 1.4 14.1 3.5 19.1 5.5 41 5253 5 251 5 10.4 I 4.: 105' :3.13.614158 5 10.;. 5.8 42 : S 13-5 5 11.4 4 564 4.2 1.4 112 3.5 1b.7 55 42 5 25.5 5 264 le% 43 5 108 5 11.6 4 56.6 4.1 1.519.1 3.5 19.356 43 525.8' 5256 5 13.9j1.1.)! 58 1: 4.459 44 5 11.0 5 11.9 4 508 4.41.714.4 3.6 16456 44 526.0 5 259 t: 'VI I 4.4 1.6 '.3 45 5 11.3 5 12.1 4 57.1 4.'15').1 343 1e.556 45 526.3 5 27.1 511.4 I 4 1.1:5; le ->9 3.8 46 5 11.5 5 12.4 4 57.3 1.e1.613.e3.6 16657 46 5 255 5 27.4 7 11-1 4.e ..e3 :e. 47 5 11.8 5 126 4 57.5 4.7 1.61..1. 3.1 lb5-7 47 5258! 527.6 5 11.9 I 1.; 2...4I :e.e 48 5 12.0 5 12.g 4 57.8 4.8 1.6 0.133.7 19557 48 27.0 527.9 5 12.1 4e it .4 14.4 49 5 12.3 5 13.1 4 58-0 4.91.7 10.43.7 13.4 5.8 49 5 17.3 5 28.1 5 12.3 1.81 }2I t71

1.8 1..05.8 . I 3.4 51 50 5 12.5 5 13-4 4 58-3 .,... 1.7.,1.0 50 5 27.5 528.4 5 12.6 181:..: I i 6.1 . ! 1.8; : 4.:. 1:. 51 5 12.8 5 13.6 4 58.5 s..i7111 .8 1 .1 58 51 c 27.8 528.6 5 12.8 .: 1.7 1,2 52 5 13.3 5 13.9 4 58.7 --: 1.8 11.2 3.8 1!25.9 52 528.01 528.9 5 13.1 . 44:33 6.2 55 5 : 3- 3 514.1 4 59.0 s.1.8tis3.9 Ito59 53 5 28.3 15 29.1 5 13.3I -, 1.4' 4.1 1:.4tyl 54 c13.5 5 14.4 4 542 .,41.8 11.4 3.9 17.459 54 5 28-5 5 244 ) 13.5--I 4.1 1.4 55 5 13.8 5 14.6 4 59.5 s- 1.911.. 3.9 t'"50 55 528d 529.1 5 11.8 2- 01. v.-. I3 ,I:(3 4.; 6.3 56 5 14.0 ! 5 14.9 4 594 5.1, 1.91164.0 1:-e50 56 529.01 5 29.9 5 14.0 5 14.3 2.01 11.-4., 53 57 5 14.3 5 15.1 4 59.9 c1.9..14.0 1146.0 57 5 243 5 30-2 5 304 5 14.5 22:11 tl 4.2 b.4 58 I 5 14.5 ' 154 5 002 s.82.0::.5 4.0 17.56.1 58 5 29.5

59 I 5 14.8 5 156 5 004 ..92.011.9 4.1 17.401 59 5 29.8 5 30.7 5 14.7 4.31 II -. 6-5 60 5 15.0 5 15.9 5 007 b02.1 12.4 4.1 15-06.2 60 5 30.0 5 309I 5 15.0 a..

175 Appendix F-11 BEST COPY AVAILABLE. 274 POLARIS (POLE STAR) TABLES, 1970 FOR DETERMINING LATITUDE FROM SEXTANT ALTITUDE AND FOR AZIMUTH

L.H.A.! 0°- Se-120'- 1 30°- 140 So - 6o -170 j So -i go-! loo- 1110 - ARIES , 9' 19" 29 I 39 49 59' 69' ! 79' ! 89 ! 99 i 109° : 119'

a, a, a, a, a, a, a, ! a, I a, I a, I a, ! a,

1 . . 0 . 0 0 0 i . 0 0 I 4 , 0 ' . 0 I i 0 , o '014'20 10'2 0 07'60 06'7 0 07'4 0 09.60 13.4'0 18.60250 . 0 32.4 ! o 40.7 ! 0 49'5 1 I 13.7 09.8 07'5 06.7 07'5 09.9 13.9 i 19.2 ! 25.7 : 334 415 50.4 a 13.3 051.5 07.3 : 061 :07/ 10.3 24.3 19.8 i 26.4 ' 3412 ; 424151.3 3 12.8 09.2 07'2 061 07.9 10.6 14.8 i 20.4 27.2 i 34'8 433 ,52.2 4 12'4.o9.0 07.: . 06.8 08.1 11.0 25.3 I 21'0i 27'91 35'7 :4411531

5 0 12.00 08.7 0 07'00 06.8 0 08.3 0 21.30 15.8 1 0 21.7 o 28.6 ; 0 36.50 45.0 : o 54.0 ! 1 6 i z .6 08.5 06.9 06.9 408.5 11.7 r 6 .4 1 22.3 29'4 ! 37'3 45141 54'9 7 j 11.2 08'2 06'8 07'0 . 08.8 12'1 16.9 23'0 3011 38.1 I46.8 I 55.8 $ 10.9 ; 08.0 06.8 071 091 12.5 17.5 23.61 30.9 39.0 ! 471 56.7 9 10.5. 07.11 06.7 07.2 09'3 13'0 18.0 24'3 311 ; 39.8 48.6 57.6

so 0 10.2: 0 07'6 0 06.70 07.40 09.6 0 134 0 18.6I0 250 , 0 32'4 ; 0 40'7 0 451'50 58.5

Lat. a, a, a, I a, a, a, a, a, a, , as

0 ! 0'5 0.6 0.6 0.6 0.6 0'5 0.5 0'4 0.3 0.2 0.2 ' 110 '6 '6 ; '6 6 '5 '5 '5 '4 '3 1 2 2 30 '5 6 .6 .6 6 '5 '5 '4 '4 .3 '3 '3 30 '6 '6 6 '6 6 6 '5 .5 '4 .4 I 40 0.6 0.6 0.6 0.6 o6 0.6 0.6 0.5 0.5 ; 0.5 0.5 0'5 ' , '6 6 6 6 6 6 .6 .6 I .5 i 45 '5 I '5

6 '6 I '6 1 So 6 6 6 6 6 6 6 '6 I 6 I 55 '6 '6 .6 6 .6 ! 6 6 6 .7 1 '7 I '7 60 6 6 '6 6 6 6 '7 .7 .8 8 8 63 0.7 0-6 0.6 , o6 0.6 0.6 0'7 0.7 o.8 0.8 0.9 0.9 64 .7 '6 6 6 6 '7 .7 -8 .8 -9 0.9 0'9 I 66 6 6 6 '6 '7 8 .9 1 0.9 I 10 1 '0 68 o.7 0.6 0.6 0.6 o6 0.7 0.8 0.8 0.9 j 10 i 1.1 1'1 Month a, a, a, a, a, a, i a, j a, a, a, ' . Jan. 0.7 0'7 0.7 1 0.7 0.7 01 , 0.7 O.7 : 0.7 0.7 0.7 I 0.7

; Feb. 6 '6 7 I '7 8 8 8 , 8 8 i 8 .8 Mar. .6 .6 '5 *5 '7 8 '8 '9 *9 '9 09 Apr. 0.3 0.4 0.4 0'5 0.6 o 6 0.7 0.8 0.8 0.9 0.9 to .2 ! May *3 *3 '4 *4 .5 i .6 6 -7 8 8 0-9 June '2 2 .2 '3 *3 4 4 8

July 0.2 0.2 0.2 0'2 ! 0.2 0.3 0.3 0.4 0.4 0.5 0.3 o6 Aug. -4 *3 '3 '3 , '3 '3 '3 '3 '3 .3 .4 '4 Sept. '5 '5 '4 '4 '3 '3 '3 '3 '3 '3 '3 *3 Oct. 0.7 0.7 0.6 o-6 0'5 0.4 04 0.3 0.3 0.3 0.3 02 Nov. 0.9 0.9 o8 o.7 7 6 '5 '5 .4 *3 '3 3 Dec. 1.0 , 1.0 In 0.9 0.8 0'8 0.7 0.6 0.6 , 0 5 0.4 0 3 Lat. 1 AZIMUTH

a I 4 ' a 4 0 V

1 o 2 0 0 4 0.1 : 359'9 359'8 359.6 , 359'5 ! 359'4359'3 359.2 359.2 359 t so , 0.4 I 0.3 0'1 359'9 359.8 359.6 ' 359-5 359'4 359'2 359.2 359.1 3591 I 0'1 40 ; 0-5 0'3 359'9 ; 359'7 359'5 359'4 359'2 3591 359.0 3589 3589

i so 0.6 ! 0.4 0.1 359'9 359'7 359 4 359'2 359.0 3589 358 8 3587 358 7 55 ! 0.7 0.4 0.2 359'9 359'6 359'4 358 5 358 5 i 359 1 358 9 3588 3586 6o 0.8 0'5 0'2 i I 359'9 359.6:359'3 3590 358 8 358'6 3584 358.3 358.3 ' 65 0.9 0.6 0.2 : 359-8 359.5 359 1 , 358 8 358 5 358.3 3581 358 0 3579

Latitude = Apparentaltitude (corrected for refraction) I a ac. atta, The table is entered with L.H.A. Aries to determine the columntohe used; each column refers toa range ofto'. a,is taken, with mental interpolation, from the upper table with theunits of L.H.A. Aries in degrees as argtunent; a,, a, are taken, without interpolation, from the second and third tableswith arguments latitude and month respectively. (4, a,, a, are always rositive. The final tablegives the azimuth of Poiarii.

176 Appendix F-12 BEST COPYAVAILABLE

TABLES FOR INTERPOLATINGSUNRISE, MOONRISE, ETC. TABLE IFOR LATITUDE .. _ latitudes Tabular Interval Difference between the times for consecutive lb Ortb 10m lb 15",th so" 15"'20m 25m 30m35' 40m ! 551" 60m to' 5° 31. . . cp 111 m b pa m m a, RI III RI / 0 I 0 0 02 0 02 0 02 0 0 I I I I I 2 2 2 2 2 0 02 o 300 ISo 06 05 05 05 05 1 000 3oo 12 I I 2 2 3 3 4 4 5 6 7 7 07 07 07 07 130 o 28 1 I 2 3 3 4 4 53/5 0 45 8 9to 10 10 I0 10 1 2 3 4 5 5 6 74 7 2 00 000 24 13 :3 13 5 6 7 8 9 10 II12 12 3 30 I ISO 30 1 2 4 9 0 26 9I0 II 12 14 0 15 0 15 o 26 036 3 4 6 7 8 13 30013o 1617 :8 18 19 19 0 422 3 5 7 8 to 1213 14 3 301 45 19 20 21 22 22 2 000 48 2 4 6 8 9II 131415 16 18 400 2122 23 24 25 26 4 302 150 S42 4 7 9II13 15 16 18 19 18zo 222325 26 27 28 29 S002 30I 00 2 5 7 10 1214 16 242628 o 29 030 o 31 0 32 I o6 3 5 8 II1316 182022 5302 45 32 34 36 3 oo1 12 3 6 9 12 1417 202224 262931 33 6 oo 36 38 40 6 3o3 151 18 3 6to 13 x619 222426293134 37 41 42 44 7 003 301 243 7 to 14 1720232629 31 3437 39 252831 40 43 44 46 48 7 303 451304 7 11 15 1822 3437 0 48 0 51 0 53 4 8 12 162023 273034 3741440 47 8 004 oo136 0 51 o 53 056 058 4 151424 8 13 172125 293336404448 8 30 055 o 58 1 of 1 04 9 oo4 30 484 9 13 182227 47 5156 I oo z 04 x o8 1 12 5 9 14 192428 33 3842 47 9 304 451 54 455o556o 1 05 to 1 15 1 20 zo 005 002 00 5 to 15 20253o 3540 - sunrise, twilight, moonrise, etc., for latitude.It is to be Table Iis for interpolating the L.M.T. of latitude and the nearest entered, in the appropriate column onthe left, with the difference between true latitude; and with the argument at the topwhich is the nearest tabular latitude which is less than the true higher one; the correction so value of the difference between the timesfor the tabular latitude and the next latitude; the sign of the correction canbe seen by inspection. obtained is applied to the time for the tabular table it is essential to take out the It is to be noted that the interpolationis not linear, so that when using this tabular phenomenon for the latitude lessthan the true latitude. TABLE IIFOR LONGITUDE -- date (for eastlongitude) Differencebetweenthe timesfor given dateand preceding Long. orfor given dateand followingdate (forwest longitude) East . or h 4 h f c)m West 4om 5csn' 6o "'2h WM12h20m21130"2°40m2h 50° 10m 20M 30m40m 5om 60in zon, 30m h h m b h e m m /1) m m m m 0 00 0 00000 0 0 0 0 0 0 O 0 o 000 0 00 000 0 0 0 0 04 04 05 05 2 2 2 3 3 04 04 10 o 1 1 1 1 2 3 IO 6 6 7 07 o8 08 09 09 1 I 2 2 3 3 4 4 5 20 12 12 13 14 15 6 7 7 8 9to I I 30 I 2 2 3 4 5 IS 19 20 8 9to 11 1213 14 16 17 40 1 2 3 4 6 7 021 0 22 o 24025 6 7 8 1011 12 14 15 17 018 o 19 50 3 4 23 25 27 28 30 7 8to 12 13 15 171820 22 6o 2 3 5 29 35 12 141617 192123 25 27 31 33 70 2 4 6 810 36 38 40 1820 222427 29 31 33 So 2 4 911 13 16 22 252730 32 .35 37 40 42 45 90 2 5 7 1012 15 1720 050 2225 28 36 o 39 042 o 44 0 47 zoo 3 6 8 II1417 it) 3133 55 40 43 46 49 0 52 0 110 3 6 9 1215 18 21 .4427 31 3437 50 53 0 57 I00 131720 2327.70 333740 43 47 120 3 7to o 58 I 01 105 22 252932 364043 47 51 54 130 4 7 11 1418 1 02 x o6 I10 394347 51 54 058 140 4 812 161923 273135 5o 54 0 58 I03 1 07 I II 115 13 172125 293338 4246 0 I5o 4 8 I x 16 I20 313640444953 058 I 02 I07 II I6o 4 913 182227 I25 1 01 r o6 I II 1 16 120 192428 333842475257 170 5 914 I 25 30 1 05 I10. .15 1 20 stio 5 10ti 20 2 30 364')45 505560 L.M.T. of moonrise, moonset and theMoon s merufan passage for Table II is for interpolating the given date and for It is entered with longitude and wi hthe difference between the times ful the longitude. following date tin west longitudes).The correction is normally the preceding dateIn east longitudes) or happens, the times become added for west longitudes and subtractedfur east longitudes, but if, as occasionally earlier each day instead of later, the signsof the corrections must be reversed.

177 Appendix G-1

DECLINATION SAME NAME AS LATITUDE '22° 30' 23° 00' 23° 30' la I RA. Alt. As. Alt. ------, BO NII Lt. 1141° 00' 24° so' Lat. As=Alt. As. Alt. Aa. '50 at . ad Al ° 4.- Alt. As. '' ad al 36. 'Ad At 34° 78 30.0 1.0 co 180.079 00.0 1.0 04 180.07930.0 1.004 180.000 'adal 71 21.0 1 0 10 175.47857.9 1.0 10 175.2 001 7900.0 15 03 180.07910.0 Loa 180.0 79 27.8 1.0 11 175.0 1 171 57.9 15 10 175.2 7822.0 90 16 170.87851.7 99 17 170.479 21.3 99 to 170.0 79 27.9 IA 11 175.0 2 27151.5 *17 170.579 21.5 le 15 170.1 7112.1 es 22 166.37841.4 98 24 165.87910.6 97 24 165.2 3 77 56.5 96 26162.078 27.3 96 3o 161.3 873 41.8 es 23 185.97911.0 97 S. 185.3 7856.0 96 31 160.5 4 47127.9 es 60 161.478 56.6 ea s 1601 77 41.4 94 34 157.87109.6 9135 157.078 37.69336 156.105 05 77 21.0 92 39 153.877 48.5 91 40 152.9 71103 *36 157.171138.6 *36 156.3 7815.8 w 42 151.9 6 877 49.8 91 40 153.1 76 57.6 49 44 150.177 24.3 99 45 149.0 7117.1 91 41 152.1 77 50.8 ss 46147.9 7 77121.1 1944 149.277 52.1 s 4,' 148.1 76 31.5 97 46 146.576 57.4 88 49 145.477 23.0 65 so 144.2 7602.8 84 52143.2 8 876 59.6 62 a 145.677 25.3 so ao 144.4 7528.0 63 63 142.07652.8 82 M 140.8 9 976 30.6 614 62142.2 TS 31.9 82 55 1 40.0 76 55.5 82 ea 141.0 7556.3 et 66138.97620.3 79 57 137.610 10 74 59,0 79 58 1 37.17522.6 78 59135.9 7559.5 si 66139.176 23.5 it 67137.8 75 45.8 77 60 134.6 1 1 7526.3 7055 136.175 49.6 7769 134.8 7424.3 77 et 134.47447.1 76 62 133.27509.5 74 63 131.9 2 73 43.0 74 E3 1 31.8 27451.4 7661 133.47513.9 7462 132.1 7410.1 73 64 130.674 31.8 71 65 129.3 3 8 7310.3 72 65 1 29.573 31.7 7161 128.2 7414.9 73 63 130.874 34.7 7264 129.5 7352.7 6067 127.0 4 473 37.0 7165 128.4 72 312 70 67 127.2 73 58.2 7966 127.1 7252.0 89 68126.07312.4 67 60124.815 1572 57.9 0267 126.2' 7151.1 es 69125.27211.3 65 70124.072 31.0 6570 122.7 7318.4 et ss 124.9 6 67217.7 67 e0124.172 37.6 6570 122.9 7110.0 88 70 1 23.27129.5 65 71 122.07148.7 63 72120.8 7 70 27.9 64 71 121.470 47.0 63 72120.2 77136.6 ea 7o 122.27155.9 64 n 120.9 7105.6 61 73 119.0 8 870 54.5 63 71 120.3 69 4 5 . 0 1 3 7 3 1 1 9.77 0 0 3. 6 6 1 7 3 1 1 8 . 5 7113.3 ears 119.1 7 0 2 1 . 7 6 0 7 4 1 1 7. 3 9 97011.$6n2118.670 30.0 eo n 117.4 -F-o6928.3 e073 117.06946.1 3074 115.8 1 68442 *74 115.56901.6 5775 114.3 267 59.6 57 75 114.06816.6 0076 112.9 36714.4 66 Te 112.767 31.1 55 78 1 11.6 4U28., 6677 111.464 45.2 64 n 110.3 25 _6542.9m n 110.26551.9 5378 109.1 M.A. 12° 00' 12° 80' 18°00' Alt. AZ._Alt. .Az. Alt. As. 35° ---- o---"'ia .ii--6--- °' -7;fai 4---- °.--77:iii- g-1- 0067 03.0 1.002 180.06730.01002l80.06800.01.0 :180.0 I 66 58.9 i.o as 177.567 28.91 o 05 177.467 58.9 IA u6 177.4 266 55.7 1 0 09 175.067 2541.0 cpa 174 967 55.51.0 o9174.8 22° 80' 36650.4 99 12 172.567 20.2 w 13172.467 50.0 cc 13 172.2 Lit. 28° 00' 28° 80' 4 330 Alt. As. Alt. Az. Alt. If A. ____ 66 42.9 99 le 170.167 12.6 99 le 169.967 42.3wle 169.7 As. 'Ad al 'ad al e'ad at 068603.4 9s 19 167.6i7 02.9 99 20167.467 32.4 96 20 167.2 79 30.01.004 6 180,08903.0 1804180.08036.0l.004180.000 66 21.9 96 23 165.254 51.2 99 23165.067 20.4 97 52 164.7 7927.81.011174.97957.71.017 76608.4 97 21162.9 174.78027.6 1.0 12 174.5 1 66 37.4 97 28 162.6. .4.4 97 27 162.2 79 21192 18170.07950.8 9:1 19169.5 865 52.9 46 19 160.566 21.7 96 29160.2 80 20.3 vs 20169.0 2 66 58.5 9630 159.8 7910.397 76165.179 39.4 97 25164.48063.4 97 27 163.7 965 35.6 95 32158.3_604.1_9532 157.9 3 64 32.6 9633 157.5___ 76 55.395 31160.47923.8 95 32159.679521 94 34 158.7 4 40-616.iiiss 151Ibii44.ri4 3,5 155.6 . . _ . 6612.844 38 155.2 7836.693 37155.979 04.4 92u ~797932.0 92 4411.13.9- 1 64 55.7 93 37 153.9 -05 65 23.6 93 38 153 1 65 51.4 9239 153.0 7814.490 47151.778 41.4 89 44150.67908.1149 45 149.4 264 33.3 92 40 151.765 00.8 9'2 41 1:,1 365 28.2 u1 41 1:,0 k 6 77 49.087 47147.878 15.169148146.117840.9 Ns '.,145.3 7 36409.2 91 4.1 149 76436.4 911 4.1 1-19 26503.4 90 44 1 1$.7 77 20.8 us si 144.177 46.0 Kv..3 142.' 4 63 43.7 )04 4s 117 7 4., i 7810.9 142 !4 1 4 1.5 8 64 10.5 .. 7 .264 37.1 Kg 0 146 6 76 50.1 h2M140.11 NI SI: .... _ 7714.4 13'1.37738.3 7.,'.137.9 9 . _ ...._ 76 17.079 N.I 137.476 40.5 ;1.70136.17703.5 71.1il 134.7 10 7542.07061134.57604.7 7% Id1 33.17626.8 73rd 131.7 1 75 05.374 64131.775 27.1 72 Iv.130.47548.5 To 1.. 129.0 2 ;, 74 27.071 66129.274 48.1 69 67 127.87508.6 0...1-... 120.4. 3 1, 73 47.3 nu us 120 m74 07.7tir liy 125.574 27.5 66 711 124.1-4 73 06.5 li 701'24.073 26.2 re. :112 3.37345.4 1,1 72 122.015 72 24.664 71122.0 2 43,6 63 72121.37302.2 61 ...I 120.0 6 id 7141.762 73120.772 00.2 61 741 1 14 47218.2 Sti 75 1 1 S 1 7 58° 80' 87° 00' 70 58.061 741 1g 1)71 16.0 69 7!.1 1 7.77133.5s-,- 76 1 1 0 4 8 IA. 7013.6 sum 1 1 7 770 31.1 sr 7.1 I 1.4.07048.1 4: 77 114 71 Alt. Am. 1) 360 Alt. AA* , -55 4243.3oe 6542.97246.706 6442.31 6 42122 07 la42.94214.000 6442.2 7 41 39.205 5642.941 41.407 5442.2 8 41 06203 m42.941 06.9 cc 5442.2 9 40 33.3116642.840 36.410 6442.1 70 40 00.412 M42.740 63.812 6442.0 1 39 27.5 la 5542.639 31.513 5442.0 2 38 54.716 5442.638 59.111 6441.9 3 38 22.0166442.33826.7166441.7 4 37 0.417 6442.237 54.517 6441.6

178 Appendix G-2 BEST COPY AVAILABLE DECLINATION CONTRARY NAME TOLATITUDE

21° 30' 22° 00' I 22°30' 23°00' 23°30' TH.A.Lat. Alt. Az. Alt. Az. Alt. Az. Alt. AZ. Alt. AZ. ° 'Ad At 'Ad At ° ° 33° ° 7.idFAt °w ' .14i At 'Ad At ° 3530.0 1.0 o 180.03500.01.o of 180.03430.01.0 01180,03400.01.0 01180.03330.01.0 of 180.000 59.51.002178.93329.51.002178.9 1 3529.51.00.4178.93459.51.002178.93429.51.002178.933 3328.1 1.004 177.8 2 3528.01.004177.73458.0 1.004177.73428.0 1.004177.83358.1 1.004177.8 06 3325.71.006176.7 8 3525.51,006176.63455.51.006176.63425.61.006176.63355.61.0176.7 22.31.007 175.6 3522.01.0 us 175.43452.1 1.007175.53422.11.007175.53352.21.007175.633 4 33 09 3317.9 1.009174.505 3517.5c.0-09174.33447.6 1.009174.43417.7 1.009174.4 47.81.0 174.5 10 3312.7 9910 173.4 6. 3512.09911173.23442.2 9911173.23412.3 9911173.33342.5 99 173.4 12 3306.4 9912 172.3 7 3505.59912172.03435.7 9912172.13406.0 9912172.23336.2 99 172.3 14 171.2 8 3458.09914170.93428.3 99141 7 1.03358.6 9914171.13328.9 99141 7 1.23259.2 99 15 170.2 9 9916169.83420.0 9916169.93350.4 9915170.03320.7 99151 70.13251.1 99 ,3449.6

22° 307 23° 00' Alt. AZ. Alt. Az. 'Ad At I Ad At 3230.0 1.0 01 180.03200.0 1.0 01 180.0 00 3229.6 Low 178.93159.61.0 02178.9 1 31 58.2 1.00i 177.8 2 3228.1 Loot 177.8 24° 00' 24° 80' 3225.81.0os 176.731 55.8 1.006 176.8 8 Lat. H.A. 3222.51.007 175.631 52.61.007 175.7 4 Alt. Aa,. Alt. AZ. 33° ° ° 'ad at ° °'Ad At ° 32 18.3 Loos 174.531 48.4 1.0 as 174.6 OS 0013 00.01.0 01180.03230.01.001180.0 32132 Ix 10 173.43143.3 23 10 173.5 8 1 3259.5 1.0 el178.93229.51.0 ca178.9 3207.1 09 12 172.331373 90 12 172.4 7 132 58.1 1.0 04177.832 DU1.004177.8 32 00.1 9915 171.331303 03 a 171.4 8 532 55.71.0 06176.732 25.71.006176.8 31 52.2 99 15 170.23122,5 99 14 170.3 9 432 52.4 1.0 07175.63222.4 Eon 175.7 31 43.4 99 is 169.131 13.8 99 16 169.2 10 0532 48.1 1.009174.632 1821.0 00 174.6 3213.000 io 173.5 3133.7 98 18 168.13104.1 99 17168.2 1 632 42.8 99 10173.5 172.43206.999 12172.5 3123.0 cos 19 167.030 53.6 9s 19 167.1 2 73236.6 va 12 8 8 3 2 29.5 9 0 13 1 7 1.331 59.899 13171.4 31 11.5 9s 21 166.030 42.2 cis 20166.1 932 21.5 toils 170.33151.89915170.4 3059.1 0723 164.930 29.9 07 22 165.0 4 103212.5 99 16169723142.99918169.3 30 45.9 97 23 163.83016.8 07 23 164.0 -115 1 3202.6 98 18168.13133.198 1s168.2 30 31.8 97 25 162.930 02.8 07 26 163.0 6 231 51.8 98 20167.131 22.498 19167.2 3016.8 96 if 161.829 48.0 96 26 161.9 7 831 40.1944 21166.031 10.898 21166.2 30 01.0 96 28 160.829 32.3 06 27 160.9 8 431 27.5 97 22165.03058.497 22165.1 29 44.4 96 29 159.72915.8 90 20 159.9 9 15_31 14.0 97 04163.93045.097 24164.1 29 27.0 06 an 158.728 58.5 96 30 158.9 IT 2908.8 0432 157.72840.5 ai al 157.9 1 2849.7 0433 156.728 21.6 34 03 156.9 8 28 21.9 nu 155.72802.0 on 156.0 i8 2809.4 93 30154.82741.5 92 35 155.0 4 27 48.1 92 37 153.827 20.4 92 36 154.0 5 27 26.0 91 as 152.826 58.5 91 as 153.1 6 27032 90 39 151.926 35.9 9019152.1 7 26 39.7 89 40 150.92612.6 89 40151.2 8 2615.5 89 41 150.025 48.5 89 41 150.3 9 ZS 50.6 s9 0 149.1-25 23.9 89 42 149.4 30 ZS 25.0 88 44 148.324 58.4 as 43 148.5 I 1 24 58.8 88 45 147.324 32.5 as 44 147.8 1 24 31.9 87 46 146.424 05.8 67 45 146.7 5 24 04.4 M47 145.523 38.5 86 0 145.8 , 4

179 Appendix H MECHANICS OF "ERRORFINDING" IN SIGHT REDUCTIONBY HO 214

It is not unusual for a student of celestial navigationto make frequent errors in solving for a line of position; hence the following tableillus- trates the mechanics of "error finding." A. If t exceeds values given in HO 214- 1. Check date, ZD, and GMT 2, Check longitude. East Xis added and west A subtracted in the step between GHA and LHA. 3, Check conversion of LHA to t. 4. Check GHA in Nautical Almanac. 5. If working a star sight, check SHA andinsure that the GHA as taken from the Almanac is the GHA of'V. 6. Search for arithmeticalerror. B. If Ht differs from Ho (or Hs) by severaldegrees 1. Check declination. Ncte whether latitude anddeclination are of same name or of contrary name. 2. Check assumed latitude. 3, Assume possible error in t. 4. Search for arithmetical error. C. If He differs from Ho by 1 or 2 degrees ("a"exceeds 60 mi.)-- 1. Check assumed longitude. 2. Check Greenwich date. 3. Check GMT. 4, If correction to Hs islarge (as in a moon sight) check sign of correction. 5. Check sign of correction to Ht. 6. Check values copied from HO 214. 7, Search for arithmetical error. I).If results fail to plot favorably 1. Check labels and fry to isolate LOP (or LOP's) inerror. Keep in mind your DR position, and possible set and drift.Then carry out steps 2 to 9 for sights isolated. 2. Check conversion of WT to ZT. 3. Cheek AP's and their advance. 4. Cheek conversion of azimuth angle to azimuth. 5. Check label of intercept. 6. Cheek correction to lit and the sign of thatcorrection. 7. Check the sign of correction applied to Hs toobtain lio. 8. Check sextant altitude corrections. 9. Cheek the accuracy of your plot. 10. Search for arithmetical error.

180 Appendix 1-1 REST COPY AVAiLiA8LE LAT 40.1S AT 40'N He Zni Mc Zni-Hc Zn He Zn in Ft, intic Zee He 17.142.4c...30 LHAHe Zn in] He Zn1H5 I oenn 1 9114 540115.571 Nom A. 1A41 1:11 t4thit coot Pluto Poe 1 CAMILA 4.1A 14114.4 32 27 16111 49 53 223 3114 210 0 34 10 056 :6 5) 04131 CO 169 2622 259, 21)9 2991 27 19 348 904112 037 29 29 0991 49 01 141 9141 39 0)7 30 14 1001 19 21 143 3? )6 Ite91 slao 226 17 /111 210 I3518 056117 19 091 )108 170.25 37 260' 29 58 298, 27 10 318 12 07 037 )059 1011 49 56 144 82 45 1701 58 41 225 )642 211 35 57 05? '29 25 091 11 lb 171?I S1 260, 28 111 219; /7 31 349 42 36 15 WI 29 11 091. 31 23 112 24 06 261' 27 31 299,27 22 319 4342)) 037 3144 101; SO 23 145 12 52 111' 51 12 229 IS 56 212 ) 4441 03 031 )2 29 1021 50 49 1471 12 39172( 37 37 2)1 33 10 212 4 37 11 (15729 57 093' 31 29 173, 2)21 262 16 57 2991 27 13 319 22 35 262' 3617 301 2704 314 9543 31 039 13 14 103 411) 144 43 05 171, 47151 237 )424 215 1'82 05130 43 094' 31 34 174 41 59 038 53 59 1041 51 )7 ISO 1/10 1111 8624 2)) )3 311 274 38 )1 05811 29 095 31 34 175 21 so 263. 25 37 300 26 56 150 96 39 10 0513! 32 11 095; 31 42 176 21 01 264' 2158 )011 26 47 350 974427 03834 41 10151 59 1511 33 11 176) 55 47 2I5 )252 214 7 9844 56 038 3528 105 5221 153. 33 17 1171 33 09 236 )201 213 839 49 33 00 096. 31 45 1771 20 18 264' 21 18 301; 26 39 3SC 9 40 29 059 11 46 097: 31 47 178' 19)2 265: 2)39 302, 249 )2 350 9945 24 034 )612 106 52 42 1 551 3319 1111' 54 31 217 31 21 27S 45 52 038 36 58 101 5301 156! 3)20 179 5)52 2311 50)5 216 IC41 08 089,3431 097. 31 48130!18 1/ 266,2300302'2624 351 100 18 01 266. 22 11 303 20 17 351 10146 20 03837 10 1075)19 18733 20 110 3)13 240 29 49 277 1141 18 059' 3117 098' 31 11 181 523) 241 29 04 211 4221 060 3602 099 3116 18:17 15 267! 2111 1031 26 09 351 10246 48 038 38 24 108 159i 2 1) 4)01 06006 48 102 31 45 181, 16 29 268 21 04 304 2602 351 103471 703839 08 10953 52 1611 33 11 let 51 52 242 25 11 278 4745 038. 39 51 110 54 071621 )3 16 1141 51 12 24) 21)) 278 144)47 3/ 1) 10C )14: 184; 15 13 :be; 20 20 304'2556 332 104 404 Ifiocrom owl ,41.17.42,15u 0,11.34 WILLA )n0416443 (11,"41 1 uppity ! 04411 I 114,0a 18 1 3 038 40 34 111, 54 20 1641)312 10 51 50 )1 244 69 41 290 15 44 77 06139 18 101' 51 38 185' 71 20 221' 4) 10 199' 25 19 )52 13 16 45 07 261 3501 102 31 34 186 1)15 231 12 30 199 2513 352 100643 41 43811 11 112. 54 )2 166, 33 08 1561 49 49 248 69 05 2% 31 28 187' 73 09 2)). 41 50 299 25 37 353 1J;14 09 0)811 59 11)1 544) 167 3)03 11171 49 07 246 68 24 295 1'4541 001 39 48 103 42 42 114; 54 52 109 32 57 181! 4125 241 01 42 295 13 4511 061 43 33 10)31 :1 1E6' 7131 216 41 10 .113225 31 )53 10849 )7 038 19 4104 06: 41 18 104' 31 15 190171 8) 237; 40 30 300i 252535) 1095005 0381)21 1151 S500 171. 32 50 1891 471) 248 67 01 295 47 48 062! 42 03 105' 31 07 1917 71 11 239 39 50 300 25 20 353 11050)3 03744 05 115, 5507 172 32 42 1404700 249 6619 295 e.:1 44 47 116, SS 12 11432 )3 1921 46 11 250 65 31 295 2143 29 06: 42 16 106' 30 58 192.10 34 241' 3910 301,2115 354 111 51 01 0)7 11251 29 0374 528 11755 16 176. 32 14 193! 433) 251 6456 295 22 4909 00: 13 31 10'30 18 193 69 53 243 )831 301 25 10 354 46 08 118 5519 170, 32 13 194 44 80 252 64 14 298 3 49'0 083 44 11 10930 17194; 69 12 24437 5: 301 2505 354 11351 57 0)7 83 31 063;44 58 108' )026 1951 68 )1 246 37 12 302. 25 00 355 11452 2 5 037 46 48 119' 5520 1741 32 02 1951 44 06 253 63 )2 79S 52 52 037 47 28 12115519 1511 )1501961 43 22 253 62 51 295 3451 12 Ool ! 48 43 109: 30 13 1961 67 11S 247. 36 33 302 21 56 355 115 11853 20 03748 08 122'5518 183' 31)6 197 12)1 254 62 09 29S 76 '1 '.3 0+.1 ;1625 110 30 00 19:61 06 2481 35 54 30: 1452 355 293 47 04 111 2448 198. 66 23 250 35 16 30 24 48 355 117530 016 18 47 1231 55 15 185, 31 22 191. 51 55 255 61 27 '4 54 1 1 030 19 25 1 2 4 ' 55 10 lea' )108 1991 41 09 256 60 46 295 51 15 :15447 SI112 21 )1 199 85 40 2511 34 37 303 24 45 35e 118 18 33 111 29 It, :DO 64 56 252 33 54 303 1 24 41 356 11954 41 0161 500) 1251 55 04 188 30 32 2001 50 23 257 6001 295 /5110 064 041(71.4 1 fet4..i.k.s move i 6414400.1151 MAYAN 1 14111 oak :ore A It 't:4/51 'hit; ' 005 a ; 11414141; 12055 08 0361 50 40 176. 545' 190 46 47 2)01 39 40 251 59 22 295 1'54 364 51 uo 3430 1.58' 29 03 201 6412 25333 70 301 98 41 2% 44 ,1 C.4 :935 14 7503 12/ I842 201 6)78 254 324; 304 12155 35 03651 17 127' 5443 43 191 4612 12 231, 3855 55 251 SE 56 07 035 51 53 129 51 19 193 45 38 2)2.. 38 10 25957 59 295 " ;/..%0 054 30 11 13'25 34 129 28:4 203 62 44 255 31 04 304 122 12356 28 015; 52 29 1301 54 21 195 44 59 233; 37 25 26057 18 295 15 '64; o4%I CI V.3 26 16 124 2306 20481 57 258 3; 26 105 33 19 305 12458 51 035 53 01 1311 51 15 197 44 22 234!36)9 261 56)6 2% 548'15 )6851 4?1,1926 51 129 27 46 205 61 11 257 125 5120 0141 51 18 13). 54 01 198 13 15 235' 35 51 261 55 55 2% 3''9,35 :05 3210 110 2' 133 2121, 204 0324 258 30 11 308 59 44 259 24 34 306 126 57 46 014, 5417 134! 53 46 200 4307 236 35 08 26255 13 2% .3 4e, 368, '111 110 2951 13177 05 207 127 581: OSe 54 41 135i 53 30 70; 42 28 231.34/1 26154 32 296 e; `823 )3 46 II: 2410 1': 26 44 709 54,9 101. 2857 336 1213 54)7 013; 55144 1)71 53 12 203 41 50 218, 33 37 263 5)51 796 33 03 10 065%4 44 :1: 79 13 17522 209 58 14 281 28 70 1,r 53 10 2% 39 6)51 2,5 35 21 113 2941 134 25 59 :10 5128 26227 43 30: 129 5902 0 ) 3 ! 55471 3 8 1 52 53 205 11 10 2391 32 52 264 56 18 1401 52 31 206 10)1 2401)206 265 5228 291 .61 33 Co',16(14 11410 16 118 25 35 2115b41 26) 2701 108 13059 27 30 48 ;18 2511 21255 57 281 26 31304 59 51 032. 564/ 141' 52 13 21.3 39 50 211; 31 20 265 51.7 297 0e46 36 46 11'. 82 :5 03157 15 14351 51 22, 3910 242 30 )4 26651 06 297 11- +1 20 244" 55:1 ,o4 '554 333 " "' 1334.1 '41 0111 574; 141 5124 311 38/9 343 44 111 eoi - 50 26 291 e.5 s.-58 Ci 11531 51151 2471 11484 205 7518 309 rl 134b10: 010; 58 04 1461 51 04 21237 48 244. 29 02 /8e 49 45 291 41t.4 49 11:123; 114 1384 215 53 2bo 24 43 308 40 <411 oo,1,414 1 410au1 , by 1 iloyvil : e.,, 1 ,e/ .1 .144 *441432 118 i molly* 38 51 0201 70 51 002 58 11 118 50 19 214 31 OD 245! 49 04 298 '; 41:6'' ;45 ;743,4,1 11312 51 110 52 54 266 24 0' 310 135 58 58 149 80 14 215: )6 2 5 246 48 21 248 %^ V.+ 1131 141 5234 26' I; 313 1361106 023; 21 44 04.' 1^: :3745a 020 22 1.1 00 54 21 151 4946 216, 3541 24; 4743 256 C 40 1:: 1149 14;31." :OA 21S7 1;! 111 "3 14 268 :1:2 111 31 39 023 ;115 084, 5442 15) 49 18 215 350.2 0/ 47 02 291 4.); 443 ,4 ;": 413: 421 141 084. 63 02 155 48 19 719' 34 18 248 46 72 299 3.4.4") 114'. 39:,4.2. 122. 1445 144 11'; :64.2141 311 139 5. o:.1 4311 02) 24 47 08 5'60 21 157 49:0 220 3)35 24945 42 299 5'413%1 .81 4244 12,58 11 1t5 41:14 :73 :113 31: 140 2,1' 08", 5034 159 4150 722 32 52 250 1501 299 4' 1.3 454; .4h I2 ;14 31.' 1.11 021 1' 1 3 44. o4 :4. 434..1:1! 26 14 08o 60 55 160 47 19 221 32 C8 :5144:1 299 3' 3: 41;1 160 14' 411' 271 23 35 31) 142 31 25 157 43 41 300 4 4:1,/104 Cg 61 0g 107. 416 4/ 214 , elis'' 4 1'111 444. .t 10.:'144 4)4' 11 111 43 14441 1 0,1 2150 08/ 61 22 184' 46 14 225 3841 25: 43 02 300 f);;,,,k)C t)4 It';i4) 1010 160 18 58 314 41 5.0:1; 36 )8 0881 61 34 166 15 41 231 1957 231 42 22 )00 ;25,5 14194 4584 '1 3113 1514'. 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IS%41 20 :la 111: 01:21 19 120 1e; 10 119 4; iv 73338 28 102 1 158 4'41 Po 151 4 01 02: .! , % " 432, O. 21 56 I?'62 13 341 41 31 73437 47 332 ;4' 14 11.148 t: 4 22 4: 1',1,1 %,'1 2" let 1704 '7, 1'!)4 I 4; 0.'11 )444 091' e2 32 128 6108 18 40 55 .2'537 08 301 ,32" 2'1 1/15 1-11 044:1301 129 82 05 385 40 11 236lb 30 103 44, %. 41.. ; I2140 14: 4, l6:3723 2'8 1544' 19 38 217i 35 5130) .11 1, 11 ; 14 4.11 36%17 '4 271 151 44 I' C23. 31,15 0f/4 21 44 110 62 00 1111 t 94 ;1 320413. 0415 241`1 11:61 53 194 18 59 238351, 3114 . 4' 4 ;84 .4 '1' It:1 .443 21 61 1,2 61 45 14138 20 2311 34 lo 304 14 4 -1: '0 . 1.44 45 ..23. 1'4' i21 25 28 11281 45 193 3740 :40.3)57 101 1 4" 1 21; 1"3 4501 3:0'91' 091 4..4; ;68,4 !...4'41: c, 1.14 C31! :b 01 111 61:4 VIC 1700 2411 3) 14 105 ! / t 1.; :5,1 . 160 4,11 0:1' 401 1 098 :2615 114' 61 11 19716 20 24113:47 105 . 5 4;441' 4 4 : :1 ;811% 5; :3: 45.44 2:0 - 401C.7.1 :101 138 6067 199 35 19 :131 3294 106 t 4 1 I.. '' 1144 .:4 1:1 41 03, 41 t'')10C 1740 110 604: 70114 58 244/1 21306 .2 .4, 14 ; . ..1;4. 4). 4.'. 1103' 28 11 11: 63:1 203 34 16 245 1050 306 :33 .1; :Ct :1'4; %,:4' 11.3 45:0 32,.- I ,' :93 I54 46 2;04!;1, 101; 28 42 1144'005 205. 33 )5 24610 13 307 : 4 .c;4, %L. .4 C/03(1.11 .4.84 luta SPICA I 446J11I1 10(141 165 4.,'1 44 10: 1413 1%1, 59 15 107, 48 31 267 1916 301 '. 41' 1 I;4,, tc4. 146 414" 54 ',A,41 41 1%) 10% 744) 1411.591) 209 VI? 170 28 59 .107 144. 4.: . 4 6 - 144 43'1 2, '1 1: 141.5'.01 210 46 11 :7128 ?I 308 .)' 4- ". 1../4 ;.1 13' s 14 4' 4. 1"440 41 14:sa 41?I', 45 45 271 2747 308 2 1 4 I 1 t Ihs4 :'60;4' 4 thl 4151 314 4844 1v,; 71 09 1411 58 1.' 114 44 59 113 21 309 . 4%:. '4) 01: ..%14.'8 62 5 :.. 1,181 31 18 144, 6144 215 44 11 ;13 2t,35 304 '1. 1-. 4' ,'\ ;:c 4-1, 01.1' 47 44 1 it 5; 19 21: 4721 :II 5.1109 ' . :4 . 4,1; 4.1:. 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1 61

li Appendix 1-2

s1Ci°11"°14eLjr...4 Z0 H4 inHt in He in Pic Zn He In =MtA Mc Zn He Zn He ZA Ht ZA Pic A/nH.-(11/..,

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7.3 14.6113 MS!! .7030.4 3.3314341311 .4 0.306 10314 1.71.1 1411 34 35 S 10.0It,11144 .1 11,03.7 7.311014.611.3 A 0.307I 0 1.41.12.1 1.51.1 3.13.534.3 0400 33364.34.1 79,95.010.015.010.011.0 040.9 3.43.94.4 4.9 17.036 73 11.0146 113 0004 071.1 1.519 111.6 3.034 20.0 10015.0 20.0 110 AI 22.131 7.3110147is 0.501 0.00.5 3.03.64.14633401.418P?i 000.4 061.1 1419 131.7 3.03.4 S14O1.015.0 200 15.1 .1 22.23.7 PA III14118.5 2 010.6 3.13.6441 4447 0104 0.51.1 1.61.9 1.331 3.134 t 1815.010015.120.1 151 .1 11.337 74II 114914.6 410 010.6 3137 0101 0.91.2 163.0 1.41.7 3.13.5 30.15.0 15.1 20.1 .1 12.43.7 S id 9147 .40101 0.913 1.61.0 1411 3.135so" 010.7 313.74431 44 IP 5.6 26°' 30.451 10.1 15.120.315.3 .40.10.2 3.33.4 12.531 75 11.315.0186 01 .5020.6 001.3 1.72.1 111.5 3.13603" 30.55 10415.320.311.4 .1 SG 75 113isi141 .6 0.30.41.3162.31.13.3364.3 4.1 0206 101.3 1.71.1 2.52.6 3.136110" 30.65.1 102 15.3 201 155 .6 1.31.42.31.1 1040 H31'7 76 114132119 .7 0.301 3.4394.4 4 9 0306 1014 1.13.1 112.9 3.336137" 30.71.I10.3154 205 15.6 ,7 120°2 31.136 76 11415119.0 0.40.91.4 1.9 1.41.93.4394.4 4 -9 0.307 1.014 1512 311.9 3.337144" 30,53.210.315.410.625.7 .5 13601 39 P 11415.319 .9 040.01.41.0 2.41.0354.04 3.0 0.301 111.5 143.1 163.0 3.33711.1 " 30.05.1 10.315 10.6 III ,90.51.01.510 133.0 455.015210 1/5" 3.54.0 16110 310 3476 11.5 15.3191 .60.004 0.1121.6 2.0 1 1 I . 7 195: 114,1 3135 31.0 10.3%SS20.63$ 0.0051.01.6 1.13.6 2 4 33113477 us 1$4 192 .1 0004 011.115 20 1.4 1 6323621211 3.1 3.7 10.0 131.3677 116 154 193 81.15110.311.1107 .10.10.61.116 141732 3 4 3 4 6 .10.105 09131.6 2.0 3.4213.116 114 ' 23319 12.1 3 81.2 10.411.620.4160 .10.10.41.21.7 141.73.335 4 3 4.6 70 Ile 155 194 1721 1 5 2.0 23 1 1' 0.1050913 3.33634.5: : 31.31.110.415.610.926.1 .5040.711 I.? 1.31.4 134 39PI 117 151 195 .402050 131 7 I 11.5 2.9 3.3 3.4 4.4 4.9 3317161 31.6 10.1 13.9261 .40.10.71.31.5 2.32113.4 3.0 4.4 4.9al ' 115 3971 I14 131 196 .1 279 20 4: 0206 101.41421 7519 3337 31.55.3 136 19ro I16isP 197 6 296 105 15.111.026.3 .40.30.5 1.31.42.4293 4 39 4 $ 5 0100:2 0204 10141611 1.630 3434 31,65.310.115.111.1 /IP le 7 33013 .40.30.1 1.41.92.42.03.54.0 4510296- 19 1'9 Ise 146 0307 1 1 1 41521 1630 3434 1 31.7 111 90 '19 159 1i9 5310615911.2164 .7040.9 1.41.91.5303.540 465131.2 1 9 0 3 0 1 1 1933 2731 34343;,; 31.1153106119 Ito I 10 .170.1 s4or 1113 347 11115.5 .40409 1.5101.5303641 465132.1 t 191311313539 31.9S 10716.0113266 9 to io 05101.51016313641 47523401 le " 6 1 3 i 6 p 6 o 10' NI II'41 10' 5'I' 1 a' 1' f' ' I p141 ^e ,e. 4 tw,ti.m IC." I1 olwaysIs be eddied N the lebelo ed aimed*

184 Appendix K1

U.S. NAVY NAVIGATION WORKBOOK

U.S.S.

PERIOD

OPNAV POI/A 313011 and IA thno U Pew. 7.711 (1)

185 Appiond lx K.2

NAVIGATION WORKII0Olt

VA. Navy Regulations require the navigator to "Maintain record book* of all observationsand tom natation' made for We purpose of navigating the ship, with results and dates involved.Such bank* shall form a part of the ship's oMeial records." This publication has been printedto meet a receitniKed need for a standard computation book. In addition to providinga standard record, the format is in tended W provide optimum utility, economy and flexibility, by providingstrip Instal to anise the nav igator in the below computations: (Strip inserts, marked to for cut out, are printed on the buck pages of this book. An envelope, suitable for stowing inserts when not inuse, is attached to the Inside back cover,) ClUIRWIONT$ *pi LORAN Place proper Computation Strip beside a blank column, and alignso that entries will correspond with information on strip. Insure name of celestial bodyor '11.0IIAN" is entered at top, and that the Fist is entered for appropriate celestial sights or LORAN LOPs, A2IMUTILLAILIUNRITI/SUNitt DOM CUIRINTS, Place proper Computation Strip beside a blank column. Insuretop of column is labeled to identify the typo of computation.

MODIFICATION Of COMPUTATION STRIPS This workbook is to servo navigators, and strip formsmay be used to suit individual preference. Note: Any modified strip form is to become an official part of thisrecord. NAVIOATON'S NUMMI Space is provided at the bottom of each page for requiredsignature of the navigator.

186 Appendix IC.3 WS 010

. . , RV 'MiesOW .....410704 0001 L415041415- 0.155000050

Mama tie** a 14 4 4 VA .0 4.5 .....k.i.b,.1...... s,..igagmbp.i...... k VI 000 1500004100 10, 0. 5441.:A Gm.. 505 655 40.r=1.1410410- II 00154 40001100011400110050140404505. 11006/0004.154150 Iallim6141 iiulliodiAlMilall* J 110li41.1-3111i1MIIMIIMIii IMMISIN*141014 1* Mai 41041 4 ill- .. Y. lit 414144.a 04 1104 11111410 5.40 0 01015014141,4404..4511.a I WI,a i050450 4MA * 11 411010 5...... i.i111,4 1114001001000 Isa 0 41 410 g 4 a 0004001.055 .,...... r...... n_...... A. 4141.0 Ms. ssadi=a*O**0 1St0 .41 =811100004.v 44.0.. -"WS* / -01040510100...totum 1 5 5. 50

111Nme I WM, M NIle .-5555 V 1**I *4 b., da III&Amami*, I I. IS MAIO 1 101011=114 55 am am . mow - I 4. la AP 415 .045 5 , I 0 4 .14. VI I I IM a il l a41.1.

11.. 61 4141014 to e " wmw1041 1.11141 111 1441 11 1 14 17 , V*4 - 141110*111.11*0061141 00 0415 5414 :4...... Ye .% I a11141 Met.....MO t %411.4 114 1 .%II N V .. **Maar a *111****Nema IOtaw* a.** awl.*

.11. Y Mks. 04 11111. an .. - WIMP 1

...MIN bambla we*. 111.0 Oa MN*a* :MC, a Ilsramai .. . 6.arr-a I* 1044.a..

b- 1,1 t S.Idi I. of 12., Mn1., MO fi 0.. II 4111 .%. a 41 Ili

au -a . a INIM1' om=LIa Meta = a.*aa ....4101 atamp.as a=am . mammaMat. s 5 145 . . . ..,. ., , . . . Atm. 1...5 +0M111 .1{MY10.411 ...... 5.13 111W . a. 410$ .. 4 .MA 4111. 111 e 4pw.4.1 .0.4!...... ffilmr..S.".4.0wt....MM./MN . 0=0 =05v...... 5 x.14=4 0 55 55 .. a 'ray ...... ra .4rmarr.-. Aroas.sr. ma or fit M M M ...... arm 111 . ..; reirmr.1.1 1 I .m...... 14.A..../1 I....

.kt 14A \ 00/ 7MMi / / 1111.1=41eMino VIM. MAViCAIL)ii 1 0//011

187 NNW WWI 01111,1416l9 11 11M11S41 al AI Mit1 SIM St4104 $1t tiftVt 1

MS Its Me 110 looldooll11 110 11/10,41i *I 111olight Slo Val 61111mil4 oh1111 ell 1111 1110 VII

MM II* WI i.e.olloo11641 W:101.111 bola Ilmit ...... 0.,010 ...... p...... ,..to ...: .2"."64, 641 010 GUI Gel eh OH SW ...... 4,.41. I a ...... 1.41. ..a. 6 1.111s ta...... 1 el ItPi Ittit Ilt4,4 III II to NAM ...... 1. ...an .M.11, 10.1111.11.10111111. as 1.1 SW 11 SiVI Si I.1 OH III WS 111411 6110 MN.... .1.41.4./.. a . MOW Ms 40.41.111,114 ale44la .4 Is Is I se SW la/w11 1.1 *mow II) ,.-5-:4(29.. al.1.1111111 IA Uhl ka Ws leVel feud tom C.NI .Ma ,Jipaa ...... , "a. 49 --,a -.4.11..4444 4 b. 9.111,1419 11 9 ... U aerie . Oa . Ma . . m. N.*. 1 ll IMI 14 Si. la ha fl .1.silSits WI 1. 1. MI NI 1, 1.. Om ,...... , " ..... I. a mt....4 - d ...N.., I, c,114 .a4.1...1104141..1. ..i I...... 144I.. , 11 a...1 II I I NIIN 1.41 5511 INA MA ...... p...... 114 aama...... : . -...t .9. rm., ar ...... mg.. td . . r VA: Can 001 Cu.% Coe. 1111 1 II Mai IA 11., a 1.4.011. I ft 4.1111Airat , a .4 04 mpa- ...... am, c 11 'VW .airoammairo 4 NI M. NO Ws i Sul II WI NI 141 a .Will a , 4, / N1,. Imo* ,gi I let -I tie : % 91... '1116:s, . to 44,9 109 0.4 41- 9. 0 114 ...... a 0.11V CAM 6 fott11. 001 laws o') Ilya Si 1 - . .. L,. 4 4 a ..I4 ft o - , .4004 4 - .00. 444 41 r...wia £QIt ..g. MVO- 4110 .,11 lift.1111111Its 144.1111III 011A16 le tlit) III* Ott IMA boo 1111 ., .. ..,.....m...... - - aa 3 .5 .....seta...a ...... a..nos 1414.1611.11a ...... 1114e 411 11 101 M 1 1 0 4 5.. tat I.& 01111 11451- itod 1 1 1 II 44 fill OH weAi 51 .... _ ... s e e r 4. MO.Ole .. ..44.0 4. MI ...... IVO C011 sII. 1 ' 1011 t$1111 leitA ION C.145. I Melt wit" sill ,1: ...... 49 .., Si. 'I.' Ita 10411 *II .1. - WI oft 1s1. vii tomes IN tom le. to ,..- ...... - sm.., ..... 11.11114111 Ma" r ....II 1 INS INA 11451 st 114 Iv tau. lil f a. awe ma _'moo 411111. oe ,.5Mglift.ap .m94101.1 10411. ...M 4 4 1 tt *.VI we fesCom Om 14 les 5, Ismi 1 et - Poona% Il At "IN 40,4014. . 4a 10.11194414014 44414..1144 0 loadolixa .. lat Olt K. olitootio me los Imo law Is a. ...II .owe . s 416.Ara ca ... ea...... allierlull .....=1 to met. 144. MOM .,. .iv. aII 410 by, 004 II I le WI Is 41614 - a N. Nava ets-119as c s. . - r No moban. .16.61....m. 9 a11 w Ai 14 114 OH 01 elVal Si Opole. 04 11 m Mt - ..1..1 StOPII.A 0 .11,01*.a, ..t- ANA445...... ma mgr. III bit la tfa II. I el1.1 Ill 01 11 ei MI es 44 11 10 A Wt.10 . t o-444 0 0..41111101.4. .114,10.1.44011 a 10. lit WI . ,. Lob MS MISS a....901,10111Sas .. . ot3 40% 0 Mit .141 t Se1 co i MI blbi .1% l.1111 ...... 0.u I la ...JP it . .. Me 515 4.=r M.1.44. .144.Ilia taw... 4 01 liolAs I el NIsat .a I 151.1.6 11 toff% tit I ...... :11.11.1 -a .....t...... s a.. I. ta . a Ob. a.= t 141,141,14 .4. 0.411144*4 Coe 010 14* Om ...... a...... a .. I cam ...... c.. o .s Yana 61 i I.MAIM 1M 111 t al." -.MY 1154 Mt aet- act,.. 1,10a am 4... I. 11 la 1,111. MDR altLIM ASS NO I. - 10 1411 ...... M. .. El....at ,- 019444.at .4 a ...ti... il I I II . 4 1 1, 4 a 1 lin IN 1 . . a. a//a a a .211 ,al, t, 2 t. n :=L a 7, au.c.i.r._,,,,V. cilPlaMC a.. ,11. lig. 4 1.1101111. 4. du. la. 0 r I Ai i i a kW .-41940.0.404a s. . Is . 4 4 4 4 .4.4 1.0 41111+4 47.,Mi %.7 ...MN. MO a. l ... a, a Au so czA s...gm ...1.9 as I . 04. 4. t.- 0.4...... m.. 0 a MP 11 ." % all - .a, MI MI II l 5 5.55 . N ma ...... a .. 0.. I I h.. 11111410 0. .. 441.4 es 114..4.0, 06.94-

44.4.14 4 17 ...WNW 011001

.4 1111 ma.. . 4. -4

188 Appondix K4 FiMatid WI

Wig eall 41101111111MANNOWNWIlliii-- OWNS 11:11viz"=11 ca=

1 woo ++r.II &fool »=r....11 um ow

VI 111 410.1.1 .O.. 0.. WI A41.10 10. t-a..11 la all41. t.p..0. Mal .:. 10 1.11,0 ...01.. 68M11 1=0M, 1.1. O. O 111104 oi 11. .0e. 0. 11. Ma ...AI..

00.-. 1. we :-

189 Appendix L4 asttoilMOW

LOCAL DATE; Wje, .st1 Wote .._ .. \W/ COURSE eT SPEED...... LAT, D11; LONO. BODY z,T, zail, ...... _. tINIT Or. Date (111A (firs) 4.111A (m 6: 8) corr. or 8111* V URA a Wags EiW E/W E/W E/W 6--...... 1...mo....mormi..1111 LI1A t 111.A.) ....-- ..... Dee. 'at13,

cl. curl% (I, ) l ) ) boo, N/ S N, S N/6 N II ...... ENTER Dec, N/S N/8 N/S N/S 11,0. t (11IA.) 1.../ AV E/W gm E/W 214 a Lat. Ni'S---- N/S N/S N/S d. cliff. MI. or -) ---- lit corr. Ile Az Nr S 1.:/11'N/S E/WN/S E/WN/S E/W + + - LC. Dip Main Cum Add') SUMS Bs Curr, Ho Ile r.____ a '1',. A TA 'I' /A TA zn aT °'1' .T °'I' Advanv 0

An alternate form for multiple sight computations

190 Appendix L-2

PINDIOTINO ?DMoyi spv

0111111111111111

DR LDNOVTUDS I' Die BIN STANDARD NIDIANa DALUNOITUDS DLO MN BTANDAND NSILDSAN

1200 DS LAT Agg13163......

DR LONO I DR LAO

LOCAL DATS I LOCAL BATS

j 1111 or su PASS AL251 PAM ..... lif (IN ?tom) DI&(IN TI/N)

jaiiialia=1161.0 , PISDICTS0 ZT OP MBA INSS

SOLUTION POR **TITUS SOLUTION PUB LTITUDS

ACT ST OP NSA PAIN ACT ST OP NISI PASS

ZDi441) (.1) SD (00) ( 8)

0111 ONT

OR DATS .220102

TAB DSO TAB DSC ...... d CORR t 4 ons ( TOTAL DSO TOTALDIG . L A D ALMSL I. C. (L D+ ZD) I C'

DIP L de D SAMSD 4. DIP MAIM WAS MAIN CONS L A D CONTRARY SUMS (+) (L ZU D) MS (4)

Z SUMS (.) SUMS () 0...... TOTAL 00B1 TOTAL CORA

HS SS

HO HO UNITE 89. 0. 0° ZENITH 6 0. 00

[ZEN DIST GAN DIST

TUTAL DEC TOTAL DEC

LATITUDE LATITUDE ......

191 Appendix 1.4 IMMO SY POLIO 11110111 COINNTIO 11TITVIN « al fie

BATS LOCAL OATS 10CAL

41,1.. DI Mt.' IIIIIIIII 1_0 u.

't A ZD Of) (.D) ZD (.I) (4)

-1.14 AS OD DAT* ...... OD DOI ORA ARM LT ORA ARM los

ORA ARIES (2.11.8 ORA ABM We

TOTAL Oil LRI TOTAL ORA ARM naLONG (+0 (.v) DR IMO (.2) (.11)

IBA ARM LOA ARM

IC MS. IC V A DIP V i MAIM CORR MIN CORR

so (LRA) .0tom) s (LAT) k si(La) 112 (mom) i lk.2 (mu) N. \ ADM VI/ A60. 01 ADD 1 L V / 60. 01 SUMS (+) 8UM8 (+) SUM () SUMS (-)

TOTAL CORR TOTAL CORR

Rs Es

LATITUDE a LATITUDE 1

192 Appendix IA

MMUS, MOUT A LRA ARIAS PLAMST IMPORMETIO1 M.M. PUT RIONT ASC6OMIuM (RA) Asa DicianiutiOFPLANET L.> RAa360° DMA PLAMST

RDA MERIDIAN At DR ANOITUDS

DATE SUN BODY VOUS MARS DR LATITUDE 3 6 0 5 6 0 DR LONGITUDE URA (.)/ STANDARD MERIDIAN RA 4.11w 11 DDT IN LOGITUDS ..,DSC

SUN LAT () BODY JUPITER SATURN p. SCE LAT () 3 6 0 3 6 0 .... o 1 LAT SEA (.)

Din` IN LAT X, RA

DUI IN LONG . X 4m DIM systammalsommsamismilmmomml TOTAL CORR BODY ALIMUTa ,...... ALTITUDE BASET=

ZT OF SUN

EYE. 0eKdi...iiljeluir"Prienr.1771mmurilmmilimilliummi...... -----7----6----- LT OF TWILIGHT ZD () (E)

GMT OF TWILIGHT

GHA ARIES (hre)

GHA ARIL; (aim) TOTAL GHA ARIES

DR LAG (E) (.4)

LHA ARIES

1. SELECT TRIPLATE TU CORRESPOND TO DR LATITUDE. 2, PLACE TEMPLATE UN STARNAJE TU CURRESPUND TU LATITUDE (NuNTN or SuUTH). 3.SEIT ARROW UN TEMPLATE rN CUIU(ESPOND TU LHA ARIES

193 INDEX

A Acoustic Doppler, 24 Celestial, Altitude, IV fix, 112, 113 Alidads, horizon, SO self synchronous, 15 lines of position, 109, 112, 113 telescopic? 15 meridian, 87 Anemometer, 28 poles, 87 Angles, 3 sphere, 87 Aries, first Point of, 88 Celestial navigation, 100-129 Astronomy, nautical, 85-99 azimuths, 127-129 astronomical triangle, 91, 93, 109-116 general, 100, 101, 117 astronomy, 85, 86 local apparent noon, 94, 119, 120 azimuth angle and azimuth, 90, 91 meridian sight, 117-119 celestial relationships, special 9143 moonrise and moonset, 122, 123 celestial sphere concept, 87, 88 planet identification, 125, 126 horizon system of coordinates, 89-91 Polaris, latitude by, 120, 121 motion, 85, 86 sight reduction, 100-116 navigational triangle, 91, 93 star identification, 123-126 time diagram, 89, 90 sunrise and sunset, 122, 123 Automatic dead reckoning, 19, 20 twilight, 122, 123 Axis, Charts and projections, 29-39 definition of, 2 accuracy of, 99 Azimuth, conic, 34, 35 angle, 90, 91 early, 29 circle, 15 gnomonic, 39 definition of, 3, 90 identification of, 30 of Polaris, 129 Mercator, 29-31 of sun, 127, 128 plotting sheets, 31-33 polar, 33, 34 reading of, 39 scale of, 36 sources of, 36, 36 Barometer, 27 Chronometer, 24, 99 Bearing Circles, book, 64, 65 bearing, 15 circle, 15 great, 2 difinition of, 3 small, 2 radio, 66 Clocks, 24, 99 taking devices, 15, 16 Coastal piloting, 133, 134 types of, 3 Comparing watch, 24, 99 Binoculars, 28 Compass, 4-14 Bow and beam bearings, 55 adjustment, 10, 11 Buoyage, 62, 63 comparison, 10, 12

194 INDBX

Compass -Continued Echo sounder, 22 error, 0, 10, 59 Ecliptic, 87 gyro, 4, 11-14 glectronie navigation, 1, 22, 23, 64044 magnetic, 4, 6-11 acoustic Doppler, 84 rose. 9, 31, 92 advanced, 78-84 Course, basic, 86-77 definition of, 3 commie 79 made good, 3 consolan, 79 Culmination, 88 deoca, 23, 76, 77 Currents, 42, 44-47 general, 66, 78 consideration of, 47 inertial, 83, 84 gravitation, 42 loran, 23, 69 -76, 79 introductior. to, 42 marine radio beacons, 66 ocean, 44, 45 omega, 79, 80 tidal, 46-47 radar, 22, 67, 68 radio direction finder, 22, 66, 67 0 radio receiver, 22 Danger angles and bearings, 57, 59 ratan, 78 Dead reckoning, 1, 48-50 raydist, 78, 79 analyzer-indicator, 19, 20 satellite system (NAVSAT), 80-83 current effect on, 49, 50 shoran, 69 definition of, 1 sonar, 22, 23, 69 plotting, 48, 49 tam, 69 tracer, 19, 20 Elevated pole, 07 Dacca, 76, 77 Engine (shaft) RPM table, 19 Declination, 87, 108, 109 Entering port, 131-133 Degaussing, 9-11 Equator, Depth, 3 definition of, 2 Depth measuring devices, 21, 22 Equinoctial, 87 Deviation, 9-11 Equinoxes, ed Deviation table, 9 Direction, 3 F compass, 6, 9, 10 gyro, 12, 14 Fathometer, 22 magnetic, 10 Fixes, 48, 51, 52, 112, 113 measuring devices, 15, 16 Flashlight, 28 true, 10, 12, 14 Distance, definition of, 3 0 Diurnal circle, 88 Drift, 49, 50 Gravitation, 11, 42 Dumb compass, 15, 16 Greenwich hour angle, 87, 106-108 Duties of navigator, 130-137 Gyrocompass, 4, 11-14 coastal piloting, 133, 134 comparison with magnetic compass, 12 detailed, 130, 131 error, 12, 14 introduction, 130 general, 11 leaving and entering port, 131-133 principles of operation, 11, 12 lifeboat navigation, 135-137 repeaters, 14 navigation check-off lists, 131-133 systems, 14 sea routine, 134 Gyroscopic inertia, 4, 11 ship's position report, 131, 134 H E Earth, Hand lead, 21, 22 definition of, 1, 2 Hoey position plotter, 26 gravitational field of, 11 Horizon system of coordinates, 89-91 magnetic field of, 4-6 Hour circle, 87

195 A NAVIGATION COMPENDIUM

Magnetic compass-Continued card, 7 bertha navigation, $3, 64 comparison with gyrocompass, 12 correction, 10 designation, Landmarks, 5153, 61 deviation, 8, 8-11 Latitude, expansion bellows, 8 assumed, 110-119 float, 8 by meridian sight, 117-119 general, 4 by Polaris, 120-122 gimbals, 8 difinition of, 2 lubber.' line, 8 of the observer, 91 magnets, 6, 7 Lead, 21, 22 nomenclature, 6-8 deep sea, 22 practical adjustment, 10, 11 hand, 21, 22 variation, 5, 6, 9, 10 Leaving port, 131-133 Magnetism, 4-6 Lifeboat navigation, 135-137 earth's, 4-6 Lights, 62, 63, 65 ferrous metals, 4, 6 predicting sighting of, 65 fields of, 4-6 sectors of, 65 induced, 4, 8, 11 visibility of, 63, 65 meridians of, 6 Lines of position, 51-55, 58, 73, 74, 78, 109, permanent. 4 110, 112, 113, 117, 136 Maps, 29 Local apparent noon, 117, 119, 120 Marine radiobeacons, 66 Local hour angle, 87, 89, 90, 106-108 Meridian, Logs, 16-19 angle, 88, 90, 91, 106-108 chip, 16, 17 definition of, 2 Doppler sonar, 19 prime meridian, 2 electromagnetic, 18 sight, 117-119 impeller type, 18 Meridional parts, 33 patent, 18, 19 Moon, rising and setting of, 122-123 pitostatic, 17, 18 Motion, 85, 86 rodmeter, 18 taffrail, 18, 19 Longitude, N assumed, 110-113 Nadir, 89 definition of, 2, 3 Nautical slide rule, 26, 27 how to determine, 136 Navigation, Loran, 23, 69-76, 79 basic definitions, 1-3 advantages and limitations, 73 duties uetailed, 130, 131 charts, 73, 74 introduction to, 1-3 general, 69, 70 Navigational instruments, 15-28 interference, 72, 73 automatic dead reckoning, 19-21 loran-A, 69-76 bearing taking devices, 15, 16 loran-C, 76 binnoculars, 28 loran-D, 79 celestial, 23, 24 operation, 70-72, 74-76 depth measuring, 21, 22 plotting procedures, 74, 76 electronic, 22, 23 receivers, 70-76 flashlight, 28 Lubbers line, 8 plotting, 25-27 short range measuring, 20, 21 M speed measuring, 16-19 Magnetic compass, 4, 6-11 timepieces, 24, 25 binnacle, 8 weather, 27, 28 bowl, 7 Navigators case, 25

196 INDEX

Ocean currents, 44, 45, 47 Racon, 69 Omega, 7941 Radar, 67-69 Accuracy, 68 advantages and limitations, 67, 68 beacons, 69 Dims, 68 principal parts of, 67 Parallel rulers, 25 virtual PPI relleotoscope, 68, 69 Parallel, defined, 2 Radio direction finder, 66, 67 Pencil, 25 Remark, 69 Pelorus, 15, 16 Range, 10, 51-53, 60 Piloting, 1, 51-65, 130-134 Ratan, 78 bearing book, 64, 65 Raydist, 78, 79 buoyage, 62, 63 Rhumb line, 3, 30, 33, 35 bow and beam bearings, 55 Right ascension, 88 compass error, 53 Roller ruler, 25 danger bearings and angles, 57, 59 Running fixes, 53-55 doubling the angle on the bow, 55 estimated position, 55, 56 fixes, 51, 52 introduction to, 51 S landmarks, 52, 53, 61 lights, 63, 65 Satellite navigation system, 80-83 light sectors, 65 Sea routine, 134 lines of position, 51-55, 58 Set, 49, 50 precision anchoring, 60, 61 Sextant, running fixes, 53-55 altitude correction, 103-105 soundings, in 56 -58 marine, 23, 24, 101-103 special cases, 55 nomenclature, 101 tactical characteristic,' in, 59, 60 Shoran, 59 visibility of lights, 63, 65 Short range measuring instruments, 20, 21 Plotting instruments, 25-27 Sidereal hour angle, 88, 89, 106, 107 Plotting sheets, 31-33 Sight reduction, 100-116, 138, 137 Polar distance, 88 altitude intercept, 100, 109-113 Polar distance of the zenith, 91 astronomical triangle solutions, 109-116 Polaris, celestial line of position, 110, 112, 113, 117, 136 azimuth of, 129 celestial fix, 112, 113 latitude by, 120-122 declination, 108, 109 Pole, definition of, 2 greenwich hour angle, 106-108 Port, leaving and entering, 131-133 introduction to, 100, 101 Position plotter, Hoey, 26 meridian angle, 106-108 Position report, ship's, 131-134 sextant altitude correction, 103-105 Precision anchoring, 60, 61 Solstices, 88 Prime meridian, 2 Sonar, 22, 23, 69 Prime vertical, 89 Special cases, 55 Protractors, 25-27 Speed, parallel motion, 25, 26 definition of, 3 three-arm, 26, 27 measuring devices, 16-19 Psychrometer, 28 Sperry gyrocompasses, 11-13 Publications, 29, 39-41 Stadimeters, 20, 21 almanacs, 40, 41 Star identification, 123-126 chart supplementary, 41 Stop watch, 24, 25, 99 manuals, 39, 40 Sun, rising and setting of, 122, 123 navigation tables, 40 Swinging ship, 10

197 A NAVIGATION COMPENDIUM -,1111INIMMININIMININ11111411111Ir

T U Tatum, 69 Universal drafting machine, 26 Tactical characteristics, 59,60 Universe in motion, 85, 86 Telescopic alidade, 15 Thermometer, 27, 28 Tides, 42-44, 47 V consideration of, 47 gravitation, 42 Variation, 5, 6,10 tides and tables, 49, 44 Vertical circle, 89 Time, 94-99 apparent, 94 as related to arc, 97 introduction to, 94 mean, 94, 95 measurement of, 94 Watches, 24, 25, 99 solar, 94-97 Weather instruments, 27, 28 sidereal, 97-98 standard, 95 time-pieces, 24, 25, 98, 99 zones, 95, 96 Track, 3 Zenith, 89 Transit, 88 Zenith distance, 89 Twilight, 122, 123 Zodiac, 87

tr. .5. ,:a.1VER\MENT OFFILE. 197iS15BC711.-4

198