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UNITS OF MEASUREMENT AND TERMINOLOGY USED IN NAVIGATION
The basic units of measurement for navigation are degrees and minutes of latitude and longitude.
Latitude
There are 90 degrees of Latitude both North and South of the line dividing the Northern and Southern hemispheres, called the EQUATOR. Each degree consists of 60 minutes and each minute is made up of 60 seconds.
The accepted way of expressing Latitude is:
| e.g. 20º 44’ 30’’N or S. | (20 Degrees 44 minutes 30 seconds North or South). |
You will find a button on your calculator designed for entering this value which we will cover later. For calculations, this Latitude could also be expressed as 20º 44.5’N as 30 seconds is the equivalent of 0.5 minutes.
1.2 Longitude
The basic units for Longitude are also in degrees, minutes and seconds but in the case of Longitude, there are 180 degrees, measured Eastwards or Westwards from the Meridian passing through Greenwich (London) and expressed either as East or West. This is often referred to as the Greenwich Meridian which bisects the Earth into two hemispheres and Longitude is measured from 000º to 180º, referred to as the anti-meridian, 180º East, as well as 180º West.
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The accepted way of expressing Longitude is:
| e.g. 120º 36’ 42’’E or W. | (120 Degrees 36 minutes 42 seconds East or West of Greenwich). |
Once again for calculation purposes this could also be expressed as Longitude 120º 36.7’ East or West as 42 seconds is the equivalent of 0.7 Minutes (42/60 = 0.7).
1.3 Terrestrial positions
As a result, any position on the Earth can be uniquely identified in terms of Latitude and Longitude. Navigation is simply the art of calculation of the angle and the distance between any two positions. If we use the above values then, a position would be expressed in terms of both Latitude and Longitude as follows:
e.g. Lat 20º 44.5’N Long 120º 36.7’E
1.4. Nautical Mile
The unit of distance used in Navigation is the Nautical Mile. This is defined as the distance subtended from the centre of the Earth by one minute of arc D.Long on the surface of the Earth measured along the Equator.
In Parallel sailing, the Distance between two points on the same parallel of Latitude is the Departure between their Meridians.
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1.5 Departure
The Earth is not a perfect sphere – the surface becomes flattened towards the Poles – and is in fact an Oblate Spheroid. Due to the shape of the Earth, the curvature creates a problem when using ‘Flat Earth’ mathematics on a spherical structure. As the Meridians converge towards the poles, the length of one minute of D.Long, our standard Nautical Mile measured at the Equator, becomes distorted and diminishes in length.
From the diagram in Figure 1.2, the distance between the meridians passing through the positions at A and B is 600 minutes of D.Long at the Equator which is equivalent to 600 Nautical Miles distance. Further North the Difference in Longitude betweeen CD is still 600 minutes of D.Long but clearly the distance is much less than that at the Equator.
To overcome this anomaly we introduce Departure. This is defined as the distance made good in an Easterly or Westerly direction betweeen two positions, in this case CD, measured in Nautical Miles. Departure (distance in E/W Direction) = D.Long × Cosine Latitude.
By referring to the diagram in Figure 1.2 we can show how the distance on the Earth’s surface between two points due East or West of each other changes in a direct proportion to the cosine of the Latitude.
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In order to overcome this apparent variation in the length of a mile and allow us to use plane right-angle trigonometry to calculate true course and distances, we have derived that the distance CD (DEPARTURE) which varies and is inversely proportional to the cosine of the Latitude at that position. In order for the calculation to give accurate internal angles of the triangle formed, and hence provide the correct course, all the units of length for the sides must be compatible. We know that there are 60 minutes in a degree of Latitude and hence can calculate the D.Lat (difference of Latitude) in minutes. We also know that distance is measured in Nautical Miles. The definition of one Nautical Mile is taken as the length of one minute of D.Long (Difference of Longitude) at the Equator, so the hypoteneuse of the triangle is also going to be in units of minutes. The remaining side is the Departure and the length will be derived using the formula Dep = D.Long × Cos Lat, to give the equivalent number of minutes f...
