## Saturday, April 17, 2010

### The Nautical Mile

Another fundamental measure -- the nautical mile has a much simpler and more straightforward origin. It was originally quite simply a minute of arc of latitude. While longitude is the measure of degrees east or west from Greenwich where it is zero and the center of the British Empire. France had its own prime meridian running through Paris but that is another story less well told. Latitude is the angular measurement of the earth in the north and south direction starting with zero at the equator and ending at 90 degrees at the poles. If one knows the distance from sea level (approximately) to the center of the earth or its radius we can calculate the distance of a nautical mile. But it is not that simple a matter. The earth is not entirely spherical but actually an oblate spheriod. Some say it is shaped like an egg and that I must say it is not. It is more like a beach ball flattened at the top and bottom. There are many models that try to estimate the earth but probably the best one is that used for GPS called WGS 84 and its radius from the earth's center is approx 6357 kilometres to sea level at the north and south poles, and approx. 6378 kilometres to sea level at the equator, a difference of about 21 kilometres more at the equator. So the nautical mile will be a little bit larger at the equator compared to the poles.  A convenient conversion constant called rho (ρ) is the number of degrees in a radian calculated as 180 degrees divided by pi (π). So ρ is about 57.3 degrees. The nm can be calculated as the radius (6357 or 6378 km) divided by ρ to get degrees and divided by 60 to get minutes of arc. So at the equator the nm is very close to 6378/57.3/60 = 1.855 km. Similarly at the pole it is nearly 1.849 Km.
This of course was the original nautical mile before we standardized it. As stated in an earlier post, today we use a fixed standard for the nm which is 1.852 km. exactly by definition. This is likely to simplify its application in computerized processes.

Seafaring navigators used this nautical mile for its convenience on a chart. The edges of a chart show the degrees and minutes of latitude on the sides and longitude at the top and bottom.
The distance between longitude coordinates vary as we go north and get closer together. But for latitude it stays pretty constant as shown in the calculations above. On a road map one would use a legend to determine a distance with a ruler or a pair of dividers, well on a nautical chart the navigator could simply use the latitude minute marks on the left and right edges of the chart and not have to go turn the chart over looking for a legend. Also on some chart projections like the Mercator projection, the scale varied with latitude. For example you know how on some maps Greenland is bigger than the US. In these cases the scale would only be accurate at the same latitude where the reading was taken off the left and right edges.

The nautical mile is a pretty ingenious invention.