NavList:

Frank,

Hmm... Now I see the time sight epiphany experienced by Sumner. To illustrate a modified Sumner line all that needs to be done (as you describe) then is to draw a line perpendicular to the observed bearing to the body through the assumed latitude on time sight longitude. The result is ... the Sumner Line without a second calculation.

Greg Rudzinski

[NavList] Re: Longitude by Time Sight...good enough at sea?
From: Frank Reed
Date: 13 Dec 2012 09:09
Greg, you wrote:
"I just did a time sight of the morning Sun (my first ever time sight) using my exact latitude and then a latitude that was off by 6'. The 6' change in latitude shifted the longitude by about 6'. This puts it in the realm of good enough even when away from the prime vertical."

Sumner Line! Don't forget that the standard "line of position" is always the fundamental concept. You can analyze the error behavior of a time sight (or any of the "Old Navigation" special sights) by thinking about the corresponding LOP. You can readily estimate how much error will be introduced by a change in latitude just by drawing a line perpendicular to the Sun's azimuth on the your chart (or in your head). For example, if the Sun is exactly southeast, halfway between the meridian and the prime vertical, the LOP runs NE/SW. A change in latitude along that line yields exactly the same change in longitude when expressed in nautical miles. If the lat is off by 5', the longitude will be shifted by 5 nautical miles. The error in minutes of longitude is larger by 1/cos(lat), but it's really position error that concerns us so that latter factor is not really necessary. You can convert this easily enough into equations, which if you like you can work out directly from the time sight equation, too, but the "chart in your head" approach will tell you how much error there will be with reasonable accuracy.

-FER

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