Terrestrial Navigation

Earth/Terrestrial &

Orientation Coordinates

Fundamentals of Navigation

◦Capt. P. Jaime Bourgeois

◦Chapter one Bowditch Online: 2002 Edition

◦ http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0002

◦ Chapter One: http://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/Chapt-01.pdf

Bowditch II: Appendix I

Reference Material

Upon completion of this lesson you will be able to: ◦ Understand the coordinates used to label a

position on the earth’s surface

◦ Become familiar with DIRECTIONS on the earth as they relate to circular measurement

Lesson Goals

Upon completion of this lesson, you should be able to explain:

◦ Coordinates on the Earth’s surface◦ Great circle◦ Small circle◦ Latitude (Parallels)◦ Longitude (Meridians)◦ International Date Line◦ Difference of Latitude◦ Difference of Longitude

Learning Objectives

“Terra” = Latin for Earth; therefore terrestrial navigation is land navigation

Earth is an oblate spheroid in shape

◦ Diameter at equator 6,888 nm

◦ Diameter at poles 6,865 nm

◦ Difference of 23 nm

◦ Circumference of a circle = π x diameter (Pi x Dia.)

3.1416 x 6,888 nm = 21,639 nm at the equator

3.1416 x 6,865 nm = 21,567 nm through the poles

72 nm difference

Earth

360 Degrees of a Circle

Circular or angular measurement:

◦ Divisions of a circle; degrees, minutes and seconds

◦ Measured clockwise from 000⁰ through 360⁰

On a nautical chart:

◦ north is up

◦ south is down

◦ east is to the right

◦ west is to the left

Directions

Measured in degrees, minutes and seconds:

◦ Symbols: ( ⁰ ’ ”)

1 degree = 60 minutes of arc

1 minute = 60 seconds of arc = 1 nautical mile

A complete circle contains 360 degrees

Example: 15 degrees, 19 minutes, 47 seconds is written as:

◦15⁰ 19’ 47”

Latitude and Longitude

360⁰ x 60’ = 21,600 minutes of arc or Latitude

Circumference of the Earth ÷ 21,600’ = length of a NM.

Nautical Mile = one minute of Lat. or 6,076.1 feet◦ (Generally accepted average)

International standard: 1 NM = 1,852 meters. 1 yard = 0.9144 meter

1 NM = 1’ Lat. = 6,076.1 feet

Great Circle Small Circle Latitude

◦ Parallel◦ Equator◦ Tropics of Cancer◦ Tropics of Capricorn

Longitude

◦ Meridian ◦ Prime Meridian/ Greenwich◦ International Date Line

Circles of the Earth

Great Circle –

◦ “is the line of intersection of a sphere and a plane through the center of the sphere. This is the largest circle that can be drawn on a sphere” (Bow II)

Circles of the Earth

Great Circles – All Meridians and the Equator. Other circles parallel to the equator are small circles.

Small Circle –

◦ “ is the line intersection of a sphere and a plane which does not pass through the center of the sphere” (Bow II)

Circles of the Earth – Small Circle

To find location on the Earth’s surface we use Latitude and Longitude as the coordinate system.

In the maritime world we measure distance by nautical mile , speed by knots, & time in 24 hours.

◦ 1 Nautical Mile = 1.151 Statute Mile or 6,076.11 feet

◦ 1 Statute Mile = 5,280 Feet (Used on the Great Lakes)

◦ 1 Knot = 1.151 Statute Mile per Hour

Coordinates

Latitude

Parallel or Parallel of Latitude

◦ “is a circle on the surface of the earth, parallel to the plane of the equator.” (Bow II)

Circles of the Earth

LatitudeOR Parallels

Latitude (USCG Boat Crew Seamanship Manual (2003), p. 496)

Equator –

◦ “is the terrestrial great circle whose plane is perpendicular to the polar axis. It is midway between the poles.” (Bow II)

Circles of the Earth

Circles of the Earth Tropic of Cancer – Is the parallel of

Latitude located at 23° 26.0’ N.◦ Approximately 23.5⁰ North

Tropic of Capricorn - Is the parallel of Latitude located at 23° 26.0’ S.◦ Approximately 23.5⁰ South

Arctic Circle – Is the parallel located at 66° 34.0’ N◦ Approximately 66.5⁰North

Antarctic Circle – Is the parallel located at 66° 34.0’ S◦ Approximately 66.5⁰ South

◦ Bowditch (2002) p. 230

Measured from 00° to 90° starting at the equator:

◦ northward toward the geographic North Pole◦ and southward toward the geographic South Pole

Labeling

◦ North Latitudes = N◦ South Latitudes = S

When writing Latitude you write degrees, minutes, and seconds:

◦ Example L 29° 34’ 30” N

L=Latitude 29° = 29 degrees 34’ = 34 minutes 30” = 30 seconds N = North for Northern Hemisphere S = South for Southern Hemisphere

Latitude

Longitude or Meridians

Meridian – “is a great circle through the geographical poles of the earth.” Bow II

(AKA Longitudes)

Circles of the Earth - Longitude

Longitude (Meridians)

Measured from 000° to 180° westward and eastward of the Prime Meridian (000°)

◦ The prime meridian is located through Greenwich England and is therefore also referred to as “Greenwich”.

When writing Longitude you write:

◦ λ 029°34’30” W

λ =Longitude 029° = 29 degrees 34’ = 34 minutes 30” = 30 seconds W = West for Western Hemisphere E = East for Eastern Hemisphere

Longitude

Prime Meridian

The origin of longitude is 000°.

Longitude is measured 180° West and East

Originates at Greenwich England (000⁰)

Prime Meridian

International Date Line

◦ Longitude line (Meridian)

◦ Set 180° from Greenwich

◦ Not labeled West or East

International Date Line

Longitude

Longitude (USCG Boat Crew Seamanship Manual (2003), p. 498)

Global Picture

Latitude and Longitude

Earth Coordinates

Earth Coordinates

Every parallel crosses every meridian at an angle of 90° (perpendicular to one another)

Prime Meridian runs through Greenwich, England and is the starting mark for Longitude = 000⁰

180° Longitude does not have a W or E label, it is the International Date Line

Poles do not have a Longitude since this is where all meridians merge to one final point.

Coordinates

Mercator Chart of the Earth

A Rhumb line crosses all meridians at the same angle on a Mercator chart.

◦ We draw Rhumb lines on a Mercator chart when we navigate.

Great circles do not cross all meridians at the same angle so a Rhumb line can be used to connect waypoints which follow a great circle.

Rhumb Lines

Rhumb Lines Bourgeois (1997) p. 10

Full circle has 360 degrees

½ of a circle is 180 degrees

¼ of a circle is 090 degrees

“Points of a circle”

◦ 11 ¼ degrees (11.25⁰) each

◦ 90 degrees = 8 points

◦ 180 degrees = 16 points

◦ 360 degrees = 32 points

(11.25⁰ x 32 = 360⁰)

Measurement of a Circle

Reciprocal of any direction is the direction 180⁰ away from it.

Examples: The reciprocal of ____ is _____ (either add 180⁰ or subtract, if you add it the answer must be less

than 360⁰)

◦ Reciprocal of 090⁰ is 270⁰◦ Reciprocal of 150⁰ is 330⁰◦ Reciprocal of 223⁰ is 043⁰◦ Reciprocal of 195⁰ is 015⁰

Reciprocal of any direction

The angular distance between the latitude of one place and the latitude of another place.

If both places are on the same side of the equator, the difference is found by subtracting

If they are on opposite sides of the equator, the difference is found by adding

Difference of Latitude

1) Latitude of point A: 55⁰ 23’ 16” North Latitude of point B: 33⁰ 20’ 17” North Difference of latitude: 22⁰ 02’ 59”

2) Latitude of point A: 14⁰ 42’ 10” North Latitude of point B: 39⁰ 54’ 50” South Difference of latitude: 54⁰ 37’ 00”

Examples of difference of latitude

The angular distance between the longitude of one place and longitude of another place.

If both places are in east longitude or both are in west longitude, the difference of longitude is found by subtracting the lesser longitude from the greater longitude.

If one place is in east longitude and the other is in west longitude, the difference of longitude is found by adding the two longitudes together.

Difference of Longitude

1) Longitude of point A: 145⁰ 23’ 16” East Longitude of point B: 053⁰ 42’ 17” East Difference of longitude: 91⁰ 40’ 59”

2) Longitude of point A: 124⁰ 35’ 19” East Longitude of point B: 047⁰ 33’ 20” West Difference of longitude: 172⁰ 08’ 39”

Examples of difference of longitude

Middle-latitude is the mean of two latitudes.

Same side of equator

◦ Add both and divide by two

◦ L 43⁰ 14’ 29” S◦ + L 59⁰ 38’ 41” S◦ 102⁰ 53’ 10”◦ _÷2_______________◦ = 51⁰ 26’ 35” S

Finding Mid-Latitude

Opposite side of equator

◦ Add both, divide by two, subtract from larger.

◦ L 26⁰ 23’ 54” N◦ + L 39⁰ 32’ 24” S◦ 65⁰ 56’ 18”◦ _÷ 2__________◦= 32⁰ 58’ 09” S - 39⁰ 32’ 24” S 06⁰ 34’ 15’ S

Finding Mid-Latitude

You are now: ◦ Able to understand the coordinates used to label

a position on the earth’s surface

◦ Familiar with DIRECTIONS on the earth as they relate to circular measurement

Summary