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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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The Nautical Mile?
From: Mike Freeman
Date: 2020 Oct 30, 00:59 -0700

I am having difficulty correlating all the information I read about the nautical mile and hope you can help. Either confirm my understanding or correct me.

I have a book - The Oxford Companion to Ships and the Sea. Peter Kemp and copy a sentence from it............

A nautical mile is the distance on the earths surface subtended by one minute of latitude at the earths centre.

If the earth was a perfect sphere we could make divisions 5,400 of 1 minute at the earth centre. equator to pole and extend/subtend each minute to the earth surface and we would have 5,400 perfect nautical miles of +/- 1852m.

However with the earth being an oblate spheroid and having a greater radius at the equator if we subtend 1 minute of latitude at/near the equator the radius lines (radians?) travel further and are therefore diverging for longer which when calculated yields a nautical mile a few metres greater than 1852m. Conversely if the same calculation is performed for the pole a nautical mile of less than 1852m is determined.

As we know a nautical mile at the pole is greater (1862m?) and at the equator less (1843?) therefore the above calculation is obviously incorrect.

I have realised the secret to understanding the nautical mile is to understand 1 minute of arc which I guess is "exactly what it says on the tin". The distance along an arc where between 2 points there is a 1 minute change. That is to say where 2 tangents created at each point create an angle of 1 minute where they meet. Therefore on a slight curve the distance between these points is greater than on a more acute curve.

This relates to the oblate spheroid as the reason for the longer nautical mile at the pole is as a result of a lesser curve of the earth surface than at the equator.

Additionally the flatter/lesser curve at the pole suggests it is from a circle with a larger radius than its host - the earth, I have done some dodgy calculations and come up with a figure of 6,395,072m which is 39,773m greater than the earth centre to pole radius.

Similarily with the curve being more acute at the equator this suggests it is from a circle of smaller radius than earth. Calculations reveal a figure of 6,333,218m which is 44,612m less than the radius of earth at the equator.

This now bring me to another dilemma. If we subtend our nautical mile at the pole to the earth centre surely the angle created at the earth centre will be greater than 1 minute.

Equally if we subtend our nautical mile at the equator to the earth centre the angle created will be a little less than 1 minute.

I attempted to calculate the above angles assuming triangles of SSS 6,377,830/6,377,830/1,843 and 6,355,299/6,355,299/1,862 but could not find a calculator accurate enough for the task. I assumed using figures for the nautical miles as straight lines rather than curves would not introduce significant errors but in the end I was unable to achieve the task.

Look forward to replies

Thanks

Mike

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