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    Re: Longitude by Sunrise
    From: Jeremy C
    Date: 2010 Feb 5, 09:57 EST
    When using the NA tables for sunrise/sunset, the table specifically says that you can't interpolate since it is not linear.
     
    Jeremy
     
    In a message dated 2/5/2010 1:33:49 A.M. Eastern Standard Time, glapook@pacbell.net writes:

    I had written:

    "The computation requires you to know your latitude to use to enter the table. The table is, in essence, a tabulation of the traditional "time sight." If you are not at one of the tabulated latitudes straight line interpolation between the tabulated values will also introduce an additional error since the time of sunrise and sunset doesn't vary this way but I haven't attempted to quantify the error introduced this way, but it is larger than zero."

    -------------------------------------------------------------------------------------------------------------------

    I decided to do a trial computation to look at this factor. Using today's data, the time of sunset at 30 ° latitude is 14 minutes, 10 seconds earlier than at 20°. Using straight line interpolation for 25° latitude, as stated in the article, sunset should be 7 minutes and 5 seconds earlier but, in fact, it is 7 minutes and 24 seconds earlier, a difference of 19 seconds. So using straight line interpolation would cause an error of almost 5' in longitude. It is certain that there must be even larger differences for other dates and   latitudes and, therefor, larger longitude errors if using this method.

    gl




    Gary LaPook wrote:
    I always start with the proposition that you always know where your are, e.g. on the planet earth, in the middle of the ocean, etc. The real question is "do you know where you are to the precision needed at the time?" If you are in the middle of the ocean it may be sufficient to know only that you are "in the middle of the ocean." As you approach dangers then the needed level of precision increases to the point that you need to know where you are to within a few meters when entering a pass through a reef  at night. The position finding system basically utilizes additional information, as it becomes available, to increase the level of precision and thereby refine the position. Based on this, this method does add information and so improves the precision of the position. In some places it may provide the level of precision necessary but in others it can't. In the middle of the ocean it is adequate but nearing a hostile shore it isn't.

    Looking at specifics. First, it states to use the lower limb when timing sunset when the table itself says to use the upper limb for this measurement. This may be just a typo. This error would make at least a 32' error in longitude.

    The sunrise- sunset table only tabulates the times to the nearest whole minute meaning that the actual event could occur thirty seconds earlier or later. This would cause an error band 15' wide on the calculated longitude.

    The times are tabulated for a three day period based on the middle day so have a built in inaccuracy for the other days. Just glancing at a random page in the table and comparing times on consecutive pages I found, at high latitudes, a change of 15 minutes in the three day period and even at 60° latitude a change of 8 minutes. There are probably larger changes than these on other pages. So using the tabulated times for the two days other than the middle day of the period it is quite likely to introduce a two minute of time error adding an additional 30' error in the calculated longitude. At 72° latitude this error could be, or exceed, 5 minutes causing a 75' error in the derived longitude.

    The computation requires you to know your latitude to use to enter the table. The table is, in essence, a tabulation of the traditional "time sight." If you are not at one of the tabulated latitudes straight line interpolation between the tabulated values will also introduce an additional error since the time of sunrise and sunset doesn't vary this way but I haven't attempted to quantify the error introduced this way, but it is larger than zero.


    In addition to these errors inherent in this method there are also the errors in the observation of the upper limb on the horizon, dip and non standard refraction. Looking at the refraction correction table in the N.A. shows up to a plus and minus error of 6.9' for non standard conditions which introduces a possible additional error band in the LOP of 13.8'. And in some instances the error could be much worse but far from land you will not see the resulting mirages that could tip you off if land were nearby. The error introduced in the derived longitude due to errors in the refraction correction (and dip, if not allowed for) can be much larger than the actual error itself. Except on two days of the year the actual LOP doesn't run directly north and south but is at right angles to the azimuth of the sun which varies with latitude and declination as is clear from an examination of Table 27 in Bowditch, Amplitudes. Because the errors in observation act at right angles to the LOP (along the azimuth to the sun) the error in the derived longitude will exceed the magnitude of these errors, increasing as the azimuth of the sun varies from straight east or west ( the amplitude) which at 60° latitude, for example, is 52.9°. For this case the error in longitude will be 66% larger than the error in the observation itself so the error band in the longitude from non-standard refraction (not counting extreme, mirage, conditions) increases from 13.8 minutes to 22.9'.

    But, since to do this computation you must have the Nautical Almanac, why not just work the sight as a normal LOP with a sextant altitude of zero degrees? This eliminates the timing problems and the multiplication effect on the errors in the observation?

    gl






    Anabasis75@aol.com wrote:
    I just received an email from Ocean Navigator that contains an article by David Berson with a "navigational problem" that uses the sunrise tables in the NA in reverse to determine Longitude.  Basically given a decent DR Latitude you compute the time of sunrise at that latitude and take the time difference between the computed sunrise and the actual sunrise and convert that into a longitude factor (using time to arc) with which you can then derive Longitude.
     
    While in theory this is a great method, it doesn't seem very accurate in practice.  My calculations for sunrise and sunset can be off by several minutes.  The variable and considerable refraction of the sun at the visible horizon would lead me to believe that there would need to be considerable corrections applied which don't appear in David's example
     
    Does anyone know of any real-world data with this method to provide an expected range of error?  This seems an emergency method only, but I'd be interested to know if anyone has tried it, or heard of anyone who has.
     
    Here is the long URL for the article:
     
    As an aside, this fellow lives but 15 minutes from me, and I've never met him.  I really should try to meet up with the guy since we have a shared interest.
     
    Jeremy


       
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