CHAPTER - 12

POSITION COORDINATES

Learning Outcomes

1. Understand Basic Concepts of Position Coordinates

Define position coordinates and explain how they are used to determine a ship's location.
Understand the concepts of latitude and longitude as the primary coordinate system for navigation.

2. Interpret Latitude and Longitude

Identify latitude as the distance north or south of the equator, and longitude as the distance east or west of the Prime Meridian.
Read and interpret coordinates from nautical charts and navigation systems.
Convert coordinates between degrees, minutes, and seconds.

3. Use Position Coordinates in Navigation

Plot positions using latitude and longitude on nautical charts.
Determine the ship’s current position using GPS and other navigational instruments.
Calculate distances and bearings between two coordinates.

4. Apply Position Coordinates for Course Planning

Use coordinates to plan safe navigation routes.
Identify waypoints and calculate the distance and direction between them.
Apply position coordinates to avoid hazards and ensure safe passage.

5. Solve Practical Positioning Problems

Determine the estimated position (EP), dead reckoning (DR) position, and fix position using coordinates.
Apply coordinate data to determine the closest point of approach (CPA) and time to CPA (TCPA).

6. Interpret and Communicate Position Data

Accurately record and report position data in the ship’s logbook.
Communicate the ship’s position using standard maritime formats.

7. Check Accuracy of Position Coordinates

Cross-check positions using multiple navigational methods, such as visual bearings and electronic systems.
Identify and correct errors in coordinate data to ensure navigational safety.

It was previously stated that when a sphere is rotated it acquires a reference line, its spin axis. In the case of the earth this axis terminates in the north and south geographic poles. Midway between the poles a plane perpendicular to the spin axis intersects the surface of the earth in a line knows as the Equator. All points on the Equator are equidistant from the poles and the plane of the Equator divides the earth into the Northern and Southern Hemispheres.

LATITUDE AND THE NAUTICAL MILE

Other planes can be passed through the earth which are all perpendicular to the spin axis and parallel to the Equator. These planes interest the surface of the earth in lines known as parallels of latitude.

All points on the same parallel will have the same latitude which is named north (N) if the position is located in the Northern Hemisphere and south(S) if it is located in the Southern Hemisphere. However, because the earth is spheroidal in shape there are two types of latitude:

Geocentric latitude (GcLat) is defined as the angle measured from the centre of the earth north or south of the Equator.

Geographic latitude (GgLat) is defined as the angle between the normal to the spheroid and the plane of the Equator, i.e. it is measured from the centre of curvature of that place. It is geographic latitude that is used for surveying and navigational purposes.

Geographic coordinate system

The "geographic coordinates" are expressed in terms of latitude and longitude.

"Latitude" is the north-south angular measure from the equator to the point of interest.

"Longitude" is the east-west angular measure along the equator from the prime meridian to the point of interest's longitude.

An infinite number of planes can be passed through the earth with the spin axis and both poles in the same plane. These planes intersect the surface of the earth in circles known as meridians.

That half of a meridian extending from pole to pole on the same side of the earth as the observer is referred to as the upper branch and the half on the other side of the earth as the lower branch.

All meridians will intersect the equator and the parallels of latitude at 90º. The reference meridian (0º) from which longitude is measured is the meridian of Greenwich, located in London, England and is often referred to as the prime meridian. Longitude is the angular measure east or west between the Greenwich meridian and the meridian passing through a given place.

Latitude parallel is a small circle joining all points having the same angular distance N or S of the equator.

CAHD is a latitude parallel.

It is parallel to the equator

∴CÂB = 90°

Latitude of any place is the ARC of a Meridian from the equator to the parallel passing through the place, named N or S.

Arc AB or AÔB is latitude north of point “A “.

Longitude of a point is the angle at the pole between the planes of Meridians or the angle subtended at the centre of the earth by the arc of the equator measured between the prime Meridian and the Meridian passing through that point. It’s measured east or west from prime Meridian ( Greenwich ) up to 180°.

If NABS is prime Meridian ( Greenwich ), longitude of point “G” is

BÔG = B𝑁 G = BŜG

Longitude of point “H” is A𝑅 H = A𝑁 H = AŜH

Difference of latitude ( d. lat ) is the ARC of a Meridian between the parallels of latitude passing through the two points.

Difference of longitude

( d.long ) between two points is the smaller angle at the pole between the planes of Meridians or the smaller are of the equator between the Meridians of both places ( points ).

ARC XY = D.long between X, Y,

X𝑁 Y = XŜY = D.long between X, Y.

Geocentric latitude and longitude

Assuming that the earth is a sphere, geographic coordinates are determined relative to the center of the sphere - these coordinates are called "geocentric latitude and longitude". The earth is not a perfect sphere – it is elongated along the equator due to centrifugal force - its "equatorial radius" is longer than its "polar radius". (The figure below is drawn using the real difference in length between the two axes which is not noticeable at this scale.)

Therefore, instead of assuming that the earth is a sphere, we can more accurately assume it is an "oblate ellipsoid of revolution" (a sphere that is slighted squashed in at the poles), which we usually just call an "ellipsoid". Rather than use coordinates defined by the spheroidal approximation of the earth, we use geographic coordinates expressed as latitude and longitude that are referenced to a particular ellipsoid of a defined shape and size. These coordinates are called "geodetic latitude and longitude", and they will be slightly different from the geocentric ones.

Nautical mile

The nautical mile was historically defined as a minute of arc along a meridian of the Earth, making a meridian exactly 180×60 = 10,800 historical nautical miles. It can therefore be used for approximate measures on a meridian as change of latitude on a nautical chart. The originally intended definition of the metre as 10−7 of a half-meridian makes the mean historical nautical mile exactly (2 × 107)/10,800 = 1,851.851851…historical metres.

Geographic latitude also gives rise to a further definition, that of the nautical mile (M). This is defined as the length of the arc of a meridian subtending an arc of 1’.0 at the centre of curvature of that place. Since the radius of curvature is minimum at the equator and maximum at the poles, the nautical mile will have minimum length at the equator and maximum length at the poles.

The International Nautical Mile is used especially by navigators in the shipping and aviation industries, and also in polar exploration. It is commonly used in international law and treaties, especially regarding the limits of territorial waters. It developed from the sea mile and the related geographical mile. The nautical mile remains in use by sea and air navigators worldwide because of its convenience when working with charts. Most nautical charts are constructed on the Mercator projection whose scale varies by approximately a factor of six from the equator to 80° north or south latitude. It is, therefore, impossible to show a single linear scale for use on charts on scales smaller than about 1/80,000. Since a nautical mile is, for practical navigation, the same as a minute of latitude, it is easy to measure a distance on a chart with dividers, using the latitude scale on the side of the chart directly to the east or west of the distance being measured.

The International Nautical Mile

The International Nautical Mile was defined by the First International Extraordinary Hydrographic Conference, Monaco (1929) as exactly 1852metres (6076.12 feet) although in many countries a standard nautical mile of 6080 feet (1853.2 metres) is used. The unit of speed used in navigation is the knot which is defined as a nautical mile per hour. In other words, a vessel moving at 15 knots is proceeding at 15 nautical miles per hour.

Nautical mile is the length of a Meridian subtending at its centre of curvature an angle of one minute. The real length of a N.M varies at the pole and at equator. So 6080 feet(1852metres.) can be used for practical purpose. Sea mile

The sea mile (in English use) is often confused with the nautical mile. Strictly, the sea mile is the distance of one minute of arc of latitude at a given (current) latitude and along the current meridian: as such, it varies from approximately 1842.9 m at the Equator to approximately 1861.7 m at the Poles, with a mean value of 1852.3 m. The international nautical mile was chosen as the integer number of metres closest to the mean sea mile.

Geographical mile

The geographical mile is equal to one minute of arc of longitude along the Equator: it is equal to approximately 1855.4 m for the International (1924)Spheroid, or approximately 1855.325 m for the WGS 84 ellipsoid. The term "geographical mile" has also been used to refer to the mean sea mile, which would later become the international nautical mile. Geographical mile is the length of the equator subtending at the earth’s centre an angle of one minute = 6087.2 feet

Unit symbol

The nautical mile (symbol M, NM, Nm or nmi) is a unit of length corresponding approximately to one minute of arc of latitude along any meridian. The International Hydrographic Organization, whose membership includes essentially all seafaring nations, and the International Bureau of Weights and Measures use M as the abbreviation for the nautical mile. The statute mile is arbitrary measure of 5280 feet. Not used in Navigation.

Departure Since all meridians converge to meet at the poles, any two meridians will become closer together in high latitudes, although the angle between their planes (d.Long) remains the same.

The east-west distance between the two meridians measured in nautical miles is called the departure (dep).

In above figure, the departure between A and B which are both in the same latitude is the distance AB measured along the parallel whose latitude is DA or the angle DOA. The d.long between A and B is the arc DE which is equivalent to the angle DOE. O is the centre of the earth and ON the earth’s axis. AC is the radius of the parallel AB.

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