# NavList:

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

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Re: My plotting board
From: Gary LaPook
Date: 2015 May 8, 09:35 +0000
One minute of latitude at the equator is 6,048 feet and at the pole is 6,108 feet. Since a nautical mile is 6,076 feet a minute of latitude at the equator is 28 feet short and at the pole it 32 feet long of a nautical mile so each are within 1/2% of a nautical mile. A minute of LONGITUDE at the equator is 6,087 feet, just 11 feet longer than a nautical mile. 1.0018 NM, only 0.18% long. Since minutes of latitude anywhere and minutes on longitude at thee equator are so close to a nautical mile in practical navigation all are considered to be exactly one nautical mile. (and any minute on any great circle is also considered to be exactly one nautical mile.)

But at the pole a minute of LONGITUDE is ZERO feet long since all meridians come together at the pole. The length of a minute of longitude at any latitude can be considered to be one nautical mile times the cosine of the latitude. At the equator the cosine of zero degrees of latitude is 1 times one NM equals 1 NM. At the pole the cosine of 90 degrees is zero so the length on one minute of longitude is also zero. At 60 degrees of latitude the cosine is 0.5 so the length of one minute is 1/2 NM. At 39° the cosine is 0.777 so the minute of longitude is 0.777 NM (4,722 feet) and at 40° the cosine is 0.766 so one minute of longitude is 0.776 NM (4,654 feet) 67 feet shorter.

If you are drawing meridians one degree apart then the difference is 60 times larger 4,028 feet, 0.66 NM. In celestial navigation such small inaccuracies disappear into the noise of the observation. Since your AP should be within 30 minutes of longitude of your position the difference is actually only one-half as big, 0.33 NM. Statistical studies i posted before on Navlist showed that for very experienced navigators the expected errors are about 1.5 NM, almost five times any error introduced by the difference in the spacing of the meridians on your plotting sheet. So don't worry about, use either the 39° or the 40° spacing on your plotting sheet it will make no discernible difference in you fixes.

gl

To: garylapook@pacbell.net
Sent: Wednesday, May 6, 2015 4:26 PM
Subject: [NavList] Re: My plotting board

Gary,
When the Longitude lines are drawn on the UPS the difference between N40d and N39 are somewhat impressively large. Yes, it's small but enough to lead to have asked the question in the first instance. Can you explain the reason...simply?

Sam L.

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