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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Ed Popko
Date: 2015 Jun 6, 03:36 -0700
Gary LaPook's comments on the impact of latitude errors on longitude results in time sights (g31583 Re: The Nautical Mile and the arc minute) reminds me of similar spherical relationship between the impact of timing errors on computed Hc.
It's likely this topic has been covered in the past but I could not find the thread with quick searches so I'll state it here for discussion and clarification if I got it wrong myself ...
It is said that a four-second error on the observer's chronometer will result in a one-minute of arc (one nautical mile) error with respect to the computed altitude (Hc) from a sextant. Statements like this appear in many celestial navigation books.
But what statements like this do not say is that this is only true at the equator and only when the azimuth to body is 90 or 270. The overall effect of timing error on the computing of HC is actually less as you approach the poles and the body's azimuth is other than 90 or 270. If the azimuth of the body is 0 or 180, there is no impact. Maximum impact is when the body's azimuth is 90 or 270. The relationship of time errors to Hc error is:
Error arc minutes of Hc = error seconds of time * ((cos(Latitude)*sin(azimuth of body))/4)
Some examples:
Nautical Mile
Latitude Azimuth to body Watch error Impact on Hc
-----------------------------------------------------------
0 90 1 second 0.25
0 90 4 seconds 1.00
0 180 4 seconds 0.00
42 90 1 second 0.18579
42 180 4 seconds 0.00
42 45 1 seconds 0.1313
90 N/S Pole 90 1 second 0.00 Time error does not matter at pole
90 180 4 seconds 0.00 Time error does not matter at pole
