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Originally Posted by seafarer
Note that the modern, albeit arbitrary, international standard definition is 1852 metres, exactly. The one minute mean meridian arc definition has not been applied in navigation in quite some time (since 1954 in the USA, since 1929 in most of the rest of the world).
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What distorts everyone's beliefs even more today is the use of GPS and other electronic navigation tools. The arc minute (Nautical Mile) is now depeicted on many charts in 10ths of an arc minute as opposed to arc seconds, forcing the pureist navigator to have to convert scales.
For those interested, from 1978 until 1990 I was a navigator in the U.S. Air Force. Most charts used in mid-latitude ranges were Lambert Conformal projection which accounted for some distortion of the curvature of the earth. They also depicted clearly the convergence of longitude toward the poles. But that was using the JNC or Jet Navigation series of charts.
With the exception of the Great Lakes, and perhaps other areas of the planet I am not aware of, nautical navigation charts are projected as a transverse mercator, (or similar projection type) that gives the appearance of lines of Latitude and Longitude running at constant 90 degree angles (like Grid or like they were all lines having the properties of a Great Circle). As such with regard to arc minutes equalling nautical miles, regardless of the earth's natural distortion, and accounting for the relative low speed of a ship vs. an aircraft, the distance between latitudes remain unchanged. Chart error is compensated for at the time of the DR and Fix or Most Probable Position plot. That is of course if your GPS breaks. However, at least as of 2004, aboard U.S.S. Mobile Bay, even though the ships' director system was coupled to the the GPS, the Quartermaster still carried a plot as would have been done in the 1940's and earlier. And on the Quartermaster's chart, one arc minute equaled 1 nautical mile.
The only rule of navigation that I am aware of that relates degrees to miles and is somewhat in error is the 1 degree of course error equals 1 nautical mile of cross track displacement after travelling 60 nautical miles. The actual distance if I recall is something like 57.8 NM, but at 500 knots, it never made much difference to me.