The Nautical Mile
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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. -
Pacing Is a Simple Means of Measuring Linear
FOR-47 by Dr. Deborah B. HilI Department of Forestry acing is a simple means of measuring linear Pdistance by walking. It can be used outdoors or indoors, in the woods or over land. Pacing's measurement dates back to Roman times. The Roman pace, measured from the heel of the foot to the heel of the same foot in the next stretch, was about 58.1 inches. Today this is known as the geometric pace, which measures about 5 feet. Apace . To make pacing work for you, you need to know how much distance your pace covers. You can determine this by walking a pre-measured course a few times and then checking the pacing chart below. A pace equals two normal steps, beginning and ending on your dominant foot. A common use for pacing in forestry is to pace off 66 feet from a tree in order to get a measurement of tree height. This is why you detem1ine your pace on a 66 foot course. 1. Begin by measuring a 66-foot course with a tape measure. You will use this distance to establish your pace accurately. 2. Pace off the course measured at Step # 1. Repeat two or three times and compare results. 3. Look lip the number of your paces on the chart below to determine how many Unear feet each of your paces covered. EX.: Ifit takes you 24 paces to cover 66feet, each ofyour paces is 2. 75 feet. 4. When you need to go from one point to another and do not know how far it is, pace the distance. -
Soaring Weather
Chapter 16 SOARING WEATHER While horse racing may be the "Sport of Kings," of the craft depends on the weather and the skill soaring may be considered the "King of Sports." of the pilot. Forward thrust comes from gliding Soaring bears the relationship to flying that sailing downward relative to the air the same as thrust bears to power boating. Soaring has made notable is developed in a power-off glide by a conven contributions to meteorology. For example, soar tional aircraft. Therefore, to gain or maintain ing pilots have probed thunderstorms and moun altitude, the soaring pilot must rely on upward tain waves with findings that have made flying motion of the air. safer for all pilots. However, soaring is primarily To a sailplane pilot, "lift" means the rate of recreational. climb he can achieve in an up-current, while "sink" A sailplane must have auxiliary power to be denotes his rate of descent in a downdraft or in come airborne such as a winch, a ground tow, or neutral air. "Zero sink" means that upward cur a tow by a powered aircraft. Once the sailcraft is rents are just strong enough to enable him to hold airborne and the tow cable released, performance altitude but not to climb. Sailplanes are highly 171 r efficient machines; a sink rate of a mere 2 feet per second. There is no point in trying to soar until second provides an airspeed of about 40 knots, and weather conditions favor vertical speeds greater a sink rate of 6 feet per second gives an airspeed than the minimum sink rate of the aircraft. -
Lesson 1: Length English Vs
Lesson 1: Length English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer B. 1 yard or 1 meter C. 1 inch or 1 centimeter English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 yard = 0.9444 meters English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 inch = 2.54 centimeters 1 yard = 0.9444 meters Metric Units The basic unit of length in the metric system in the meter and is represented by a lowercase m. Standard: The distance traveled by light in absolute vacuum in 1∕299,792,458 of a second. Metric Units 1 Kilometer (km) = 1000 meters 1 Meter = 100 Centimeters (cm) 1 Meter = 1000 Millimeters (mm) Which is larger? A. 1 meter or 105 centimeters C. 12 centimeters or 102 millimeters B. 4 kilometers or 4400 meters D. 1200 millimeters or 1 meter Measuring Length How many millimeters are in 1 centimeter? 1 centimeter = 10 millimeters What is the length of the line in centimeters? _______cm What is the length of the line in millimeters? _______mm What is the length of the line to the nearest centimeter? ________cm HINT: Round to the nearest centimeter – no decimals. -
16.00 Introduction to Aerospace and Design Problem Set #3 AIRCRAFT
16.00 Introduction to Aerospace and Design Problem Set #3 AIRCRAFT PERFORMANCE FLIGHT SIMULATION LAB Note: You may work with one partner while actually flying the flight simulator and collecting data. Your write-up must be done individually. You can do this problem set at home or using one of the simulator computers. There are only a few simulator computers in the lab area, so not leave this problem to the last minute. To save time, please read through this handout completely before coming to the lab to fly the simulator. Objectives At the end of this problem set, you should be able to: • Take off and fly basic maneuvers using the flight simulator, and describe the relationships between the control yoke and the control surface movements on the aircraft. • Describe pitch - airspeed - vertical speed relationships in gliding performance. • Explain the difference between indicated and true airspeed. • Record and plot airspeed and vertical speed data from steady-state flight conditions. • Derive lift and drag coefficients based on empirical aircraft performance data. Discussion In this lab exercise, you will use Microsoft Flight Simulator 2000/2002 to become more familiar with aircraft control and performance. Also, you will use the flight simulator to collect aircraft performance data just as it is done for a real aircraft. From your data you will be able to deduce performance parameters such as the parasite drag coefficient and L/D ratio. Aircraft performance depends on the interplay of several variables: airspeed, power setting from the engine, pitch angle, vertical speed, angle of attack, and flight path angle. -
The Discovery of the Sea
The Discovery of the Sea "This On© YSYY-60U-YR3N The Discovery ofthe Sea J. H. PARRY UNIVERSITY OF CALIFORNIA PRESS Berkeley • Los Angeles • London Copyrighted material University of California Press Berkeley and Los Angeles University of California Press, Ltd. London, England Copyright 1974, 1981 by J. H. Parry All rights reserved First California Edition 1981 Published by arrangement with The Dial Press ISBN 0-520-04236-0 cloth 0-520-04237-9 paper Library of Congress Catalog Card Number 81-51174 Printed in the United States of America 123456789 Copytightad material ^gSS3S38SSSSSSSSSS8SSgS8SSSSSS8SSSSSS©SSSSSSSSSSSSS8SSg CONTENTS PREFACE ix INTROn ilCTION : ONE S F A xi PART J: PRE PARATION I A RELIABLE SHIP 3 U FIND TNG THE WAY AT SEA 24 III THE OCEANS OF THE WORI.n TN ROOKS 42 ]Jl THE TIES OF TRADE 63 V THE STREET CORNER OF EUROPE 80 VI WEST AFRICA AND THE ISI ANDS 95 VII THE WAY TO INDIA 1 17 PART JJ: ACHJF.VKMKNT VIII TECHNICAL PROBL EMS AND SOMITTONS 1 39 IX THE INDIAN OCEAN C R O S S T N C. 164 X THE ATLANTIC C R O S S T N C 1 84 XJ A NEW WORT D? 20C) XII THE PACIFIC CROSSING AND THE WORI.n ENCOMPASSED 234 EPILOC.IJE 261 BIBLIOGRAPHIC AI. NOTE 26.^ INDEX 269 LIST OF ILLUSTRATIONS 1 An Arab bagMa from Oman, from a model in the Science Museum. 9 s World map, engraved, from Ptolemy, Geographic, Rome, 1478. 61 3 World map, woodcut, by Henricus Martellus, c. 1490, from Imularium^ in the British Museum. -
Maps and Charts
Name:______________________________________ Maps and Charts Lab He had bought a large map representing the sea, without the least vestige of land And the crew were much pleased when they found it to be, a map they could all understand - Lewis Carroll, The Hunting of the Snark Map Projections: All maps and charts produce some degree of distortion when transferring the Earth's spherical surface to a flat piece of paper or computer screen. The ways that we deal with this distortion give us various types of map projections. Depending on the type of projection used, there may be distortion of distance, direction, shape and/or area. One type of projection may distort distances but correctly maintain directions, whereas another type may distort shape but maintain correct area. The type of information we need from a map determines which type of projection we might use. Below are two common projections among the many that exist. Can you tell what sort of distortion occurs with each projection? 1 Map Locations The latitude-longitude system is the standard system that we use to locate places on the Earth’s surface. The system uses a grid of intersecting east-west (latitude) and north-south (longitude) lines. Any point on Earth can be identified by the intersection of a line of latitude and a line of longitude. Lines of latitude: • also called “parallels” • equator = 0° latitude • increase N and S of the equator • range 0° to 90°N or 90°S Lines of longitude: • also called “meridians” • Prime Meridian = 0° longitude • increase E and W of the P.M. -
Fuel Efficiency: Modes of Transportation Ranked by MPG | True Cost
Fuel Efficiency: Modes of Transportation Ranked By MPG | True Cost -... http://truecostblog.com/2010/05/27/fuel-efficiency-modes-of-transportati... Fuel Efficiency: Modes of Transportation Ranked By MPG May 27, 2010 at 4:57 pm ∙ Filed under Energy, Environment, Ideas ∙Tagged bicycle mpg, fuel efficiency, running mpg, transportation, walking mpg Building on a previous post on the energy efficiency of various foods, I decided to create a list of transportation modes by fuel efficiency. In order to compare vehicles with different passenger capacities and average utilization, I included both average efficiency and maximum efficiency, at average and maximum passenger loads. The calculations and source data are explained in detail in the footnotes. For human‐powered activities, the mpg ratings might appear high, but many calculations omit the fact that a human’s baseline calorie consumption must be subtracted to find the efficiency of human‐powered transportation. I have subtracted out baseline metabolism, showing the true efficiencies for walking, running, and biking. For vehicles like trucks and large ships which primarily carry cargo, I count 4000 pounds of cargo as equivalent to one person. This is roughly the weight of an average American automobile (cars, minivans, SUVs, and trucks). The pmpg ratings of cars, trucks, and motorcycles are also higher than traditional mpg estimates, since pmpg accounts for the average number of occupants in a vehicle, which according to the Bureau of Transportation Statistics is 1.58 for cars, 1.73 for SUVs, minivans, and trucks, and 1.27 for motorcycles. List of Transportation Modes By Person‐Miles Per Gallon (PMPG) Transport Average PMPG Max PMPG Bicycle [3] 984 984 Walking [1] 700 700 Freight Ship [10] 340 570 Running [2] 315 315 Freight Train [7] 190.5 190.5 Plugin Hybrid [5] 110.6 350 Motorcycle [4] 71.8 113 Passenger Train [7] 71.6 189.7 Airplane [9] 42.6 53.6 Bus [8] 38.3 330 Car [4] 35.7 113 18‐Wheeler (Truck) [5] 32.2 64.4 Light Truck, SUV, Minivan [4] 31.4 91 [0] I used these conversion factors for all calculations. -
Yd.) 36 Inches = 1 Yard (Yd.) 5,280 Feet = 1 Mile (Mi.) 1,760 Yards = 1 Mile (Mi.)
Units of length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 36 inches = 1 yard (yd.) 5,280 feet = 1 mile (mi.) 1,760 yards = 1 mile (mi.) ©www.thecurriculumcorner.com Units of length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 36 inches = 1 yard (yd.) 5,280 feet = 1 mile (mi.) 1,760 yards = 1 mile (mi.) ©www.thecurriculumcorner.com Units of length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 36 inches = 1 yard (yd.) 5,280 feet = 1 mile (mi.) 1,760 yards = 1 mile (mi.) ©www.thecurriculumcorner.com 1. Find the greatest length. 2. Find the greatest length. 9 in. or 1 ft. 3 ft. or 39 in. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 3. Find the greatest length. 4. Find the greatest length. 1 ft. 7 in. or 18 in. 4 ft. 4 in. or 55 in. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 5. Find the greatest length. 6. Find the greatest length. 1 ft. 9 in. or 2 ft. 7 ft. or 2 yd. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 7. Find the greatest length. 8. Find the greatest length. 26 in. or 2 ft. 6 yd. or 17 ft. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 9. Find the greatest length. 10. Find the greatest length. 5 ft. or 1 ½ yd. 112 in. or 3 yd. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 11. Find the greatest length. 12. Find the greatest length. 99 in. or 3 yd. 11,000 ft. or 2 mi. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 13. -
Tail Strikes: Prevention Regardless of Airplane Model, Tail Strikes Can Have a Number of Causes, Including Gusty Winds and Strong Crosswinds
Tail Strikes: Prevention Regardless of airplane model, tail strikes can have a number of causes, including gusty winds and strong crosswinds. But environmental factors such as these can often be overcome by a well-trained and knowledgeable flight crew following prescribed procedures. Boeing conducts extensive research into the causes of tail strikes and continually looks for design solutions to prevent them, such as an improved elevator feel system. Enhanced preventive measures, such as the tail strike protection feature in some by Capt. Dave Carbaugh, Chief Pilot, Boeing 777 models, further reduce the probability of incidents. Flight Operations Safety Tail strikes can cause significant damage and cost taiL strikes: an overview a constant feel elevator pressure, which has operators millions of dollars in repairs and lost reduced the potential of varied feel pressure revenue. In the most extreme scenario, a tail strike A tail strike occurs when the tail of an airplane on the yoke contributing to a tail strike. The can cause pressure bulkhead failure, which can strikes the ground during takeoff or landing. 747-400 has a lower rate of tail strikes than ultimately lead to structural failure; however, long Although many tail strikes occur on takeoff, most the 747-100/-200/-300. shallow scratches that are not repaired correctly occur on landing. Tail strikes are often due to In addition, some 777 models incorporate a tail can also result in increased risks. Yet tail strikes can human error. strike protection system that uses a combination be prevented when flight crews understand their Tail strikes can cause significant damage to of software and hardware to protect the airplane. -
Useful Forestry Measurements Acre: a Unit of Area Equaling 43,560
Useful Forestry Measurements Acre: A unit of area equaling 43,560 square feet or 10 square chains. Basal Area: The area, usually in square feet, of the cross-section of a tree stem near its base, generally at breast height and inclusive of bark. The basal area per acre measurement gives you some idea of crowding of trees in a stand. Board Foot: A unit of area for measuring lumber equaling 12 inches by 12 inches by 1 inch. Chain: A unit of length. A surveyor’s chain equals 66 feet or 1/80-mile. Cord: A pile of stacked wood measuring 4 feet by 4 feet by 8 feet when originally conceived. Cubic Foot: A unit of volume measure, wood equivalent to a solid cube that measures 12 inches by 12 inches by 12 inches or 1,728 cubic inches. Cunit: A volume of wood measuring 3 feet and 1-1/2 inches by 4 feet by 8 feet and containing 100 solid cubic feet of wood. D.B.H. (diameter breast height): The measurement of a tree’s diameter at 4-1/2 feet above the ground line. M.B.F. (thousand board feet): A unit of measure containing 1,000 board feet. Section: A unit of area containing 640 acres or one square mile. Square Foot: A unit of area equaling 144 square inches. Township: A unit of land area covering 23,040 acres or 36 sections. Equations Cords per acre (based on 10 Basal Area Factor (BAF) angle gauge) (# of 8 ft sticks + # of trees)/(2 x # plots) Based on 10 Basal Area Factor Angle Gauge Example: (217+30)/(2 x 5) = 24.7 cords/acre BF per acre ((# of 8 ft logs + # of trees)/(2 x # plots)) x 500 Bd ft Example: (((150x2)+30)/(2x5))x500 = 9000 BF/acre or -
The Future of the Knot As a Unit of Speed
FORUM The Future of the Knot as a Unit of Speed Oliver Stewart FEW will deny the merits of the knot as a unit of speed. It does in one syllable what all other units of speed take three or more to do. It is accepted and used by a great many countries, including those like France which show a general pre- ference for the metric system. Aviation has taken to it as well as shipping. It is not therefore surprising that the full acceptance of the Systeme International d'Unitis (or S.I.) is meeting with some opposition when it offers to supplant the knot. At present the situation is that the knot is to continue for a 'limited time' as a speed unit for use in aviation and shipping. Just how limited the time will be has not been revealed, but the member countries of the European Economic Com- munity have set i January 1978 as the date after which 'only a prescribed system of metric units may be used'. Strictly interpreted the S.I. admits one and only one speed unit, the metre per second; if the minute or the hour were to be intro- duced in place of the second, decimalization would break down. This would mean that the familiar kilometre per hour would be inadmissible as a substitute for the knot, although the present trend is in that direction. Both the metre and the second are now denned in terms of atomic radiation with a precision far ahead of anything previously known and give the measurer the highest attainable accuracy.