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So, What Is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations
the International Journal Volume 7 on Marine Navigation Number 2 http://www.transnav.eu and Safety of Sea Transportation June 2013 DOI: 10.12716/1001.07.02.14 So, What is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations A. Weintrit Gdynia Maritime University, Gdynia, Poland ABSTRACT: In the paper the author presents overview of the meridian distance approximations. He would like to find the answer for the question what is actually the distance from the equator to the pole ‐ the polar distance. In spite of appearances this is not such a simple question. The problem of determining the polar distance is a great opportunity to demonstrate the multitude of possible solutions in common use. At the beginning of the paper the author discusses some approximations and a few exact expressions (infinite sums) to calculate perimeter and quadrant of an ellipse, he presents convenient measurement units of the distance on the surface of the Earth, existing methods for the solution of the great circle and great elliptic sailing, and in the end he analyses and compares geodetic formulas for the meridian arc length. 1 INTRODUCTION navigational receivers and navigational systems (ECDIS and ECS [Weintrit, 2009]) suggest the Unfortunately, from the early days of the necessity of a thorough examination, modification, development of the basic navigational software built verification and unification of the issue of sailing into satellite navigational receivers and later into calculations for navigational systems and receivers. electronic chart systems, it has been noted that for the The problem of determining the distance from the sake of simplicity and a number of other, often equator to the pole is a great opportunity to incomprehensible reasons, this navigational software demonstrate the multitude of possible solutions in is often based on the simple methods of limited common use. -
Chapter 13.2: Topographic Maps 1
Chapter 13.2: Topographic Maps 1 A map is a model or representation of objects and terrain in the actual environment. There are numerous types of maps. Some of the types of maps include mental, planimetric, topographic, and even treasure maps. The concept of mapping was introduced in the section using natural features. Maps are created for numerous purposes. A treasure map is used to find the buried treasure. Topographic maps were originally used for military purposes. Today, they have been used for planning and recreational purposes. Although other types of maps are mentioned, the primary focus of this section is on topographic maps. Types of Maps Mental Maps – The mind makes mental maps all the time. You drive to the grocery store. You turn right onto the boulevard. You identify a street sign, building or other landmark and know where this is where you turn. You have made a mental map. This was discussed under using natural features. Planimetric Maps – A planimetric map is a two dimensional representation of objects in the environment. Generally, planimetric maps do not include topographic representation. Road maps, Rand McNally ® and GoogleMaps ® (not GoogleEarth) are examples of planimetric maps. Topographic Maps – Topographic maps show elevation or three-dimensional topography two dimensionally. Topographic maps use contour lines to show elevation. A chart refers to a nautical chart. Nautical charts are topographic maps in reverse. Rather than giving elevation, they provide equal levels of water depth. Topographic Maps Topographic maps show elevation or three-dimensional topography two dimensionally. Topographic maps use contour lines to show elevation. -
General Rules for Contour Lines
6/30/2015 EASC111LabEFor Printing LAB E: Topographic Maps (for printing) MAP READING PRELAB: Any type of map is a twodimensional (flat) representation of Earth’s surface. Road maps, surveying maps, topographic maps, geologic maps can all cover the same territory but highlight different features of the area. Consider the following images from the same area in Illinois. Make a list of the types of features that are shown on each type of map. Topographic Maps The light brown lines on the topographic map are called contour lines. A contour line connects points of equal height above sea level, called elevation. For example, a 600’ (six hundred foot) contour line on a map means that every point on that contour line is 600’ above sea level. In order to understand contour lines better, imagine a box with a “mountain” in it with a clear plastic lid on top of the box. Assume the base of the mountain is at sea level. The box is slowly being filled with water. Since water automatically levels itself off, it will touch the “mountain” at the same height all the way around. If we were to peer down into the box from above, we could draw a line on the lid that marks where the water touches the “mountain”. This would be a contour line for that elevation. As the box continues to fill with water, we would draw contour lines at specific intervals, such as 1”. Each time the water level rises one inch, we will draw a line marking where the water touches the land. -
Bibliographical Index
Bibliographical Index BIBLIOGRAPHICAL ACCESS TO THIS VOLUME Bacon, Roger. Opus Majus. 305, 322, 345 Basil, Saint. Homilies. 328 Three modes of access to bibliographical information are used Bede, the Venerable. De natura rerum. 137 in this volume: the footnotes; the bibliographies; and the Bib ---. De temporum ratione. 321 liographical Index. The footnotes provide the full form of a reference the first Cassiodorus. Institutiones divinarum et saecularium time it is cited in each chapter with short-title versions in litterarum. 172, 255, 259, 261 subsequent citations. In each of the short-title references, the Cato the Elder. Origines. 205 note number of the fully cited work is given in parentheses. Censorinus. De die natalie 255 The bibliographies following each chapter provide a selec Chaucer, Geoffrey. Prologue to the Canterbury Tales. 387 tive list of major books and articles relevant to its subject Cicero. Arataea (translation of Aratus's versification of matter. Eudoxus's Phaenomena). 143 The Bibliographical Index comprises a complete list, ar ---. Letters to Atticus. 255 ranged alphabetically by author's name, of all works cited in ---. De natura deorum. 160,168 the footnotes. Numbers in bold type indicate the pages on --. The Republic. 159, 160, 255 which references to these works can be found. This index is ---. Tusculan Disputations. 160 divided into two parts. The first part identifies the texts of Cleomedes. De motu circulari. 152, 154, 169 classical and medieval authors. The second part lists the mod Cosmas Indicopleustes. Christian Topography. 143, 144, ern literature. 261 Ctesias of Cnidus. Indica. 149 TEXTS OF CLASSICAL AND MEDIEVAL ---. Persica. 149 AUTHORS Dicuil. -
Distances Between United States Ports 2019 (13Th) Edition
Distances Between United States Ports 2019 (13th) Edition T OF EN CO M M T M R E A R P C E E D U N A I C T I E R D E S M T A ATES OF U.S. Department of Commerce Wilbur L. Ross, Jr., Secretary of Commerce National Oceanic and Atmospheric Administration (NOAA) RDML Timothy Gallaudet., Ph.D., USN Ret., Assistant Secretary of Commerce for Oceans and Atmosphere and Acting Under Secretary of Commerce for Oceans and Atmosphere National Ocean Service Nicole R. LeBoeuf, Deputy Assistant Administrator for Ocean Services and Coastal Zone Management Cover image courtesy of Megan Greenaway—Great Salt Pond, Block Island, RI III Preface Distances Between United States Ports is published by the Office of Coast Survey, National Ocean Service (NOS), National Oceanic and Atmospheric Administration (NOAA), pursuant to the Act of 6 August 1947 (33 U.S.C. 883a and b), and the Act of 22 October 1968 (44 U.S.C. 1310). Distances Between United States Ports contains distances from a port of the United States to other ports in the United States, and from a port in the Great Lakes in the United States to Canadian ports in the Great Lakes and St. Lawrence River. Distances Between Ports, Publication 151, is published by National Geospatial-Intelligence Agency (NGA) and distributed by NOS. NGA Pub. 151 is international in scope and lists distances from foreign port to foreign port and from foreign port to major U.S. ports. The two publications, Distances Between United States Ports and Distances Between Ports, complement each other. -
Imperial Units
Imperial units From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the post-1824 measures used in the British Empire and countries in the British sphere of influence. For the units used in England before 1824, see English units. For the system of weight, see Avoirdupois. For United States customary units, see Customary units . Imperial units or the imperial system is a system of units, first defined in the British Weights and Measures Act of 1824, later refined (until 1959) and reduced. The system came into official use across the British Empire. By the late 20th century most nations of the former empire had officially adopted the metric system as their main system of measurement. The former Weights and Measures office in Seven Sisters, London. Contents [hide] • 1 Relation to other systems • 2 Units ○ 2.1 Length ○ 2.2 Area ○ 2.3 Volume 2.3.1 British apothecaries ' volume measures ○ 2.4 Mass • 3 Current use of imperial units ○ 3.1 United Kingdom ○ 3.2 Canada ○ 3.3 Australia ○ 3.4 Republic of Ireland ○ 3.5 Other countries • 4 See also • 5 References • 6 External links [edit] Relation to other systems The imperial system is one of many systems of English or foot-pound-second units, so named because of the base units of length, mass and time. Although most of the units are defined in more than one system, some subsidiary units were used to a much greater extent, or for different purposes, in one area rather than the other. The distinctions between these systems are often not drawn precisely. -
Topographic Maps Fields
Topographic Maps Fields • Field - any region of space that has some measurable value at every point. • Ex: temperature, air pressure, elevation, wind speed Isolines • Isolines- lines on a map that connect points of equal field value • Isotherms- lines of equal temperature • Isobars- lines of equal air pressure • Contour lines- lines of equal elevation Draw the isolines! (connect points of equal values) Isolines Drawn in Red Isotherm Map Isobar Map Topographic Maps • Topographic map (contour map)- shows the elevation field using contour lines • Elevation - the vertical height above & below sea level Why use sea level as a reference point? Topographic Maps Reading Contour lines Contour interval- the difference in elevation between consecutive contour lines Subtract the difference in value of two nearby contour lines and divide by the number of spaces between the contour lines Elevation – Elevation # spaces between 800- 700 =?? 5 Contour Interval = ??? Rules of Contour Lines • Never intersect, branch or cross • Always close on themselves (making circle) or go off the edge of the map • When crossing a stream, form V’s that point uphill (opposite to water flow) • Concentric circles mean the elevation is increasing toward the top of a hill, unless there are hachures showing a depression • Index contour- thicker, bolder contour lines on contour maps, usually every 5 th line • Benchmark - BMX or X shows where a metal marker is in the ground and labeled with an exact elevation ‘Hills’ & ‘Holes’ A depression on a contour map is shown by contour lines with small marks pointing toward the lowest point of the depression. The first contour line with the depression marks (hachures) and the contour line outside it have the same elevation. -
U.S. Coast Guard Auxiliary Nautical Chart Updating Training Guide
` U.S. Coast Guard Auxiliary Nautical Chart Updating Training Guide National Ocean Service Office of Coast Survey Chart Updating Training Guide Ver. 2.4 2016 1 Table of Contents What is New - 3 Plotting (Chart Sections) - 30 Introduction to Chartplotter and GPS Navigation Software -31 Nautical Charts and Coast Pilot - 4 Using the Raster Navigational Charts Google Objective - 4 Earth Tool – 31 Background - 4 Introduction to NOAA Nautical Discrepancy Projections – 5 Report System – 32 Latitude and Longitude Scales - 6 Nautical Chart Feature Corrections – 32 Scales - 6 Coast Pilot Items – 33 Horizontal Datum – 7 Nautical Features Report – 34 Vertical Datum - 8 Instructions – 35 Depths Used on Nautical Charts- 8 Coast Pilot Report – 38 Traditional Paper Nautical Charts – 8 Instructions – 39 Chart Title and Information Block – 9 Reporting of Particular Feature Types - 41 Color Used on Nautical Charts – 9 NOAA’s Nautical Discrepancy Report System Lettering Styles – 10 – 42 Chart Depths – 10 Create a New Report – 43 Chart Edition – 10 Charting Action – 48 Updated Charts – 11 USACE Chart Discrepancy Reporting System - Nautical Chart Catalogs – 11 49 US Coast Pilot – 12 Chart Update AUXDATA Submittals - 52 US Coast Pilot Updates – 12 Individual’s duty for the patrol - 52 Bearings in the Coast Pilot – 12 Currents in the Coast Pilot – 13 Appendices Introduction to Nautical Chart Updating- 13 1. Responsible/Knowledgeable Sources, Objectives – 13 Reportable Chart Features -53 Background – 13 2. Difference Between RNCs and ENCs, Tools and Equipment useful in Print-on-Demand Paper Charts, PDF Chart Updating -14 Nautical Charts, Chart Updates (LNM Obtaining Information from Knowledgeable and NM Corrections) and Sources - 18 BookletCharts - 67 How to determine if an object is chartable – 18 3. -
How to Compute a Distance and Bearing from Two Positions
HowHowHow tototo ComputeComputeCompute thethethe DistanceDistanceDistance andandand BearingBearingBearing fromfromfrom TwoTwoTwo PositionsPositionsPositions ononon thethethe EarthEarthEarth PositionPosition InformationInformation isis neededneeded inin LatitudeLatitude andand LongitudeLongitude formatformat John McHale Sept 2008 Oct 2008 1 What are We Going to Talk About • How did I find your school? • How does the GPS work – is it magic or is it math? • Why study math? 2 Why Do You Need Math? • Why do you need to add & subtract? • Why do you need to multiply & divide? • Why else do you need math? 3 This Seminar is an Example of How Math Can Be Used. • The Law of Squares - Also called the Pythagorean Theorem • Works for any Right Triangle •A2 = B2 + C2 4 C Any Shape of Right Triangle A2 = B2 + C2 A B A B C A B C 5 How is Math Used to Navigate? The Earth is approximately a Sphere. Actually, Earth is an Oblate Spheroid. Earth is squashed at the poles. A Grid of Latitude and Longitude is used to Divide up the Earth’s Surface. 6 7 Position is Definitionsa combination of Latitude, Longitude, and Altitude above Sea Level. Position is Expressed in Degrees (O), Minutes (‘) and Seconds (“) This format is better to use for a more accurate determination of Distance and Bearing. Bearing is sometimes called Course. 8 Earth’s Shape Latitude is the measurement from the Equator at 0 Degrees to 90 Degrees at the North (N) or South (S) Pole. A Minute of Latitude Equals a Nautical Mile. 9 LatitudeLatitute -lines-lines that go around thethe Eagloberth 10 Longitude is the Measurement from Zero MeridianEarth’s (Greenwich, Shape England) East or West to 180 Degrees at the International Date Line, or Antimeridian (in the Pacific Ocean). -
Gradual Generalization of Nautical Chart Contours with a B-Spline Snake Method
GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD BY DANDAN MIAO BS in Geographic Information Systems, Wuhan University, 2009 THESIS Submitted to the University of New Hampshire in Partial Fulfillment of the Requirements for the Degree of Master of Science in Ocean Engineering September, 2014 ALL RIGHTS RESERVED © 2014 Dandan Miao This thesis has been examined and approved. Dr. Brian Calder, Associate Research Professor of Ocean Engineering Dr. Kurt Schwehr Affiliate Associate Professor of Ocean Engineering Dr. Steve Wineberg Lecturer, Mathematics and Statistics Date v ACKNOWLEDGMENTS This study was sponsored by NOAA grant NA10NOS400007, and supported by the Center for Coastal and Ocean Mapping. Professor Larry Mayer introduced me to the world of Ocean Mapping, and taught me new information about geological oceanography; Professor Brian Calder initiated this study and has always been able to selflessly help me with any questions; Professor Steven Wineberg gave me many insights of how to transfer math concepts to graphic behavior; Professor Kurt Schwehr helped me with many intelligent thoughts and suggestion about computer programming implementation. I am grateful for all their selfless help and patience, and I would like to thank all of them for their guidance, encouragement and proof-reading of this thesis: without them and CCOM’s support, this work would not have happened. Finally, I would like to thank my parents and friends, for encouragement and trust. Your love and faith gave me the strength to keep holding on and finally make it work! Love you all! With greatest thankfulness, Dandan Miao vi TABLE OF CONTENTS ACKNOWLEDGMENTS ............................................................................................................. -
Scale NOAA Nautical Chart for Small Boaters When Possible, Use the Full-Size NOAA Chart for Navigation
BookletChart™ Cumberland Head to Four Brothers Islands NOAA Chart 14782 A reduced-scale NOAA nautical chart for small boaters When possible, use the full-size NOAA chart for navigation. Included Area Published by the A special anchorage is on the west side of the lake in Deep Bay. (See 33 CFR 110.1 and 110.8(i), chapter 2, for limits and regulations.) National Oceanic and Atmospheric Administration Channels.–The south 37 miles of Lake Champlain, from Whitehall north National Ocean Service to Crown Point (44°01.8'N., 73°25.8'W.), is a narrow arm. The south 13 Office of Coast Survey miles of this arm, from Whitehall north to Benson Landing, is filled with a marshy flat traversed by a narrow channel of open water. A Federal www.NauticalCharts.NOAA.gov project provides for a 12-foot channel through this reach. In September 888-990-NOAA 2008, the controlling depths in the channel were 2 feet (7½ feet at midchannel) to Benson Landing. Above Benson Landing, natural deep What are Nautical Charts? water is available to Crown Point. The entire narrows, from Whitehall to Crown Point is well marked by lights and buoys. Nautical charts are a fundamental tool of marine navigation. They show North from Crown Point for about 75 miles to Rouses Point, Lake water depths, obstructions, buoys, other aids to navigation, and much Champlain is deep and wide. Prominent points and shoals throughout more. The information is shown in a way that promotes safe and the lake are marked by lights and buoys. efficient navigation. -
Creating a Contour Map of Your School Playground
How to Make a Contour Map of Your School Playground Source: Mountain Environments Novice On-Line Lessons http://www.math.montana.edu/~nmp/materials/ess/mountain_environments/ These instructions are for making a 4 x 4 contour map of a 6' x 6' plot of land. The number of contour intervals or size of the plot may be changed if desired. Step 1: To make a contour map, first stake out with string a plot of uneven land. Step 2: Determine the total change in elevation within your plot, from its highest point to its lowest point, in inches. (To measure this change in elevation you must place one end of a bubble stick level at the high point with the other end pointing towards the low point. Raise or lower the free end of the bubble stick until the bubble shows the stick is level.) With the yardstick, measure the vertical distance from the free end of the bubble stick to the ground. Continue measuring in this manner until you reach the low point and add up all of the vertical measurements that you took at the various points. This is your total change in elevation. Step 3: Divide this elevation change by 4 to determine the contour interval when you build 3 contour lines. (Suppose the change in elevation was 24 inches from high point to low point. If 3 contour lines are needed between the high and low point, you'd divide the 24" by 4—not 3. The contour interval would be 6 inches. ) Step 4: Now that you have a contour interval, you must locate one point for each contour line that will be the starting point for that line.