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    Delay of "Noon" by vessel motion
    From: Frank Reed
    Date: 2019 Oct 17, 12:19 -0700

    You're waiting for the Sun to reach its maximum altitude for the Noon Latitude. You might also hope to get a quick estimate of longitude from the time of the peak altitude or by making a little plot of altitudes "around" noon. But if we are in motion north or south, the altitudes we measure around noon are changing due to our motion as well as the normal daily arc of the Sun across the sky near the meridian. If the Sun is to the south of my vessel, and I am sailing south at 15 knots, then the Sun is climbing at a rate of 1 minute of arc for every four minutes of time. This will significantly bias the timing of the maximum latitude. 

    How wrong could it be? There are simple enough equations for calculating the delay of noon, and there are tables for these. In fact, I'm working on a table this afternoon for this purpose. The delay in the peak altitude if we're approaching the Sun is proportional to v·[tan(Lat) - tan(Dec)]. But that's not something you're likely to remember easily. I've found a quick approximation for this (it works because the tangent function is reasonably linear for angles from 0 to about 60°. The delay of "noon" in seconds is approximately given by
       v · ZD / 3
    where v is the north/south component of the speed in knots and ZD is the peak zenith distance at noon in degrees. That's easy to remember. It's not accurate, but it's a good quick estimation for latitudes within 30° of the equator, and it's an adequate estimate for latitudes up to 45°. And that may be useful for thinking through the consequences of ignoring this issue

    An example: I'm travelling south at 10 knots in Latitude 20° N on Oct. 22. The Dec of the Sun is just about 11.5° S so the ZD at noon is 31.5°. The delay estimate is 
       v · ZD / 3 =    10 · 31.5 / 3 = 105 seconds.
    That's within 10% of the correct value with almost no computation. 

    Frank Reed

       
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