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    Re: Longitude by Sunrise example
    From: Henry Halboth
    Date: 2010 Feb 5, 18:15 -0800


    Hi Jeremy,


    For what it may be worth, I have worked your Longitude at Sunset/Sunrise problem by the old fashioned conventional method, i.e., the Time Sight, utilizing the following data:


    July 1, 2009; Latitude 17 degrees North; ZT (+9) of Sunset (LL) 18-58-26, and come up with the following:


    At ZT 1858

    Longitude 129-26-16 East

    LOP running 205/25 degrees, through posit 17 degrees N x 129-26-16 E

    Potential error in Longitude/1 degree error in Latitude = 0.5’, applied (-) for error to south and (+) for error to north. Thus if the Latitude was actually 16-30 N, as has been suggested, the calculated Longitude would be in the order of 129-11 E, which should then also fall on the fg LOP at 16-30 N.


    Should you be stationary, or making but little way, you might be able to X this with a subsequent Sunrise LOP to obtain a reasonable fix. This is something for you to try at anchor, with a view of both E/W horizons.


    To work this method, you of course must have a logarithmic table of trigonometric functions or an appropriate calculator, in addition to a Nautical Almanac, and who is to say what you will or should have in any emergency situation – perhaps it all boils down to a matter of advance preparation consistent with your individual level of competence.



    --- On Thu, 2/4/10, Anabasis75@aol.com <Anabasis75@aol.com> wrote:

    From: Anabasis75@aol.com <Anabasis75@aol.com>
    Subject: [NavList] Longitude by Sunrise example
    To: NavList@fer3.com
    Date: Thursday, February 4, 2010, 10:11 AM

    I commented on the article online and asked if he had rough error expectations as well as asking him for some sort of real world data if it was available.  I suspect that there is little to be had, which just means that I will have to do some observations this Spring when I am on my ship.  I'll try to take several, and also repeat my LOP experiment.
    I will start a new thread with my example of ultra-low altitude LOP's.  I did indeed take into account T/P, which I do for all sights, especially below 10 degrees Hs.  I am at the point in my quest for precision that I account for any and all factors even if they are 0.1' of arc. I just looked in my NavLog again and I made an error (I left in my index error, despite not using a sextant for this observation.)  I will correct it and will get slightly better result, although still not particularly good.
    Typing this has gotten me thinking. I can probably re-create a Long by sunset with my sunset LOP data from this past summer.
    If anyone else would like to join me, here is the data.
    On 1 July 2009, the 1900 ZT (ZD -9) DR is Lat 17 deg N; Longitude 129 deg E.  The course is 190 deg T and the speed is 13.2 knots.  Temp is 82 deg F and Pressure is 1008 MB. 
    1) Determine time of sunset
    The lower limb of the sun touches the visible horizon at 18:58:16 ZT and the upper limb touches at 19:00:48 ZT. 
    2) Determine Longitude at sunset.
    Since I don't have a paper NA, I can't calculate LMT of the sunset since my program directly gives me ZT.  This will not allow me to follow David's method's directly.  I can do it in a round about way by comparing the time difference in local time.
    1) I have a sunset at zone time of 19:01:39 at the DR position.
    2) Delta-T is 3m 23 seconds between the calculated Sunset and when the LL touches the visible horizon. This is equal to 50.8' of arc .  That would give me a Longitude of 129 deg 50.8' East since the sun set earlier we must be more to the East of our DR.  The GPS Longitude was 129 deg 7.5'E  That is a difference of 43.3' of Longitude which is a significant error.  Now I will admit that the DR Latitude is nearly 30 minutes off of the GPS Latitude which will account for an error in sunset and therefore longitude.
    If we correct the DR to the GPS position and recalculate sunset we get 19:00:18.  This reduces the delta-T to 2 min 2 seconds.  This is 30.5' arc.  This gives us an error of 23' of longitude, which is still significant. 
     I am not too confident that I will get much better results in more observations. 
    I will be interested to see the results using the tabular methods of sunset as opposed to the software I use.

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