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    Re: Berson's Noon Sun problem
    From: Stan K
    Date: 2013 Feb 11, 21:04 -0500

    Agreed - Berson's solutions are rife with errors.  I used to go on the web site and state my case, but they never responded, so I stopped.

    This is probably my favorite.  It is the response I sent to that 97 year old gentleman back in August of 2011:


    The great circle solution is Ocean Navigator is simply incorrect.  Berson gets LHA from the difference between departure and destination latitudes, but it should be longitudes.  (And even with his numbers, the values he extracted are a bit off anyway.)

    Doing it with longitudes I get an initial course of 104º and a distance of 3269 nm.  This compares well with the values in my earlier e-mails. (Celestial Tools gave 103.44º. 3277.0 nm.)

    You can have the honor of telling Ocean Navigator.

    And from February 2012:


    I finished what I had planned to do, so I went on the the ON problem, and, as usual, had some problems with Berson's solution.

    First, H.O. 249 is like NASR - only good to whole minutes/nautical miles (where H.O. 229, in its six volumes, is good to tenths), but Berson's answer is 16.2nmT.  My answer is 17nmT.  Attached is a (not very good) scan of my solution.  I could have made a mistake, but I don't think so.  BTW, I got the tables from the Maritime Safety Information web site, where I have gotten H.O. 229 in the past.  (Nice of them to still make the tables and other things available.)

    I also think that his EP L does not make sense.  It is the same as his DR L.  I plotted it and got exactly what the CT Sight Reduction tool gave: 25º13.1'N, 58º12.6'W.  Also the distance from the DR to the LOP was 3.6nm, just what the
    CT Sight Reduction tool gave.  Also attached is the (not very well planned ) plot.

    And from May 2012:


    Can't this guy do anything else besides a noon sight problem? 

    As usual, I am not in full agreement with his solution, at least the GMT of LAN part.  Attached is the Celestial Tools solution.

    He takes the time of meridian passage from the daily page as 1200, which is rounded to the nearest minute, introducing an error.  The rest of what he does is OK.  Allowing for the Equation of Time of +5 seconds gives a time of LAN of 115955, but this is at Greenwich.  By the time the sun gets to 115º25'W the Equation of Time is +9 seconds.

    The best way to avoid this confusion and get an accurate time of LAN is by using the GHA method, as is done in Celestial Tools.  The only discrepancy between Celestial Tools and a manual calculation is Celestial Tools gives a Sun GHA for 19 hours of 105º02.2' where the Almanac gives
    105º02.3'.  Either one gives a value of 41m31s, or a GMT of LAN of 194131, 9 seconds different from Berson's solution (as expected), but in agreement with the USNO on-line calculator

    The only other discrepancies are the usual ones:  The Main correction is +15.6' according to the Almanac, but +15.7' according to Celestial Tools, which uses the exact date and time of the sight, instead of a six-month average.  Dip and Sun declination are in agreement, so the calculated latitude differs by 0.1'.

    BTW, we discussed taking a drive up north in the near future.  Even if I take a day off during the week, we still have grandson duty, so it would have to be on a weekend.  Any weekends good for you?

    And from September 2012 (This is the October 2012 problem.  I had similar issues as Robin):


    I received the problem today and was so happy that it wasn't a noon sight that I looked at it right away.  Unfortunately, as usual, I do not agree with Berson's solution.  I did it manually and also with Celestial Tools just to make sure I got the Almanac data close.  Both are attached.

    First, comparing the Celestial Tools Almanac data with the manual reduction, Celestial Tools matches up pretty well.  The 20 hr value of the GHA of Mars is only off by 0.1' (I "guarantee" 0.5'), with everything else in the LHA box matching perfectly, as it should.  The Dec is right on (I "guarantee" 0.3').  The most confusing thing might be the Altitude box, which disagrees by 0.1'.  This is because Celestial Tools displays intermediate rounded values but does not use the rounded values to arrive at a final answer, the only place rounding is used.  In this case the -0.9' is -0.948' (to three decimal places) and the 0.1' is 0.066', for a final result of 0.882', which rounds to 0.9'.  (You can see these values yourself by using "Show Ho corrections as Parameters" rather than "Show Ho corrections as SR Form"

    The big problem is not the almanac data, though.  It is the H.O. 249 reduction.  The manual reduction gives an intercept of 7 nm Toward and an azimuth of 187º. 
    (Oops - I just realized I forgot to circle the T (toward) on the manual reduction.)  Berson gets 12.7 nm Toward.   (BTW, another gripe with Berson's solution is that H.O. 249 should only use whole minutes, so his 12.7 nm should be 13 nm.) My manual reduction agrees with Joe McGuire's spreadsheet (available on the ONCom web site), so it appears that Berson did something wrong, but I don't know what.  Berson does not show the azimuth because he asks for the EP.  I did not bother plotting since my intercept doesn't agree with his anyway.

    It is interesting to note that Celestial Tools Sight Reduction, which uses the calculated values in the Law of Cosines, gives an intercept of 6.5 nm Away (remember that it uses the DR position where H.O. 249 uses an AP), but Celestial Tools LoC/NASR (not attached), which uses the manually determined values of LHA, Dec, and Ho, using LoC, gives an intercept of 6.4 nm Away, with both giving an azimuth of 188º.  I guess this is to be expected since the Celestial Tools values disagreed with the manual values by no more than 0.1'.  The EP determined by Celestial Tools Sight Reduction was 40º50.4'N, 53º35.8'W, which is close to Berson's 40º51'N, 53º33'W.  Even though you would not expect to get exactly the same EP with a method that plots from an AP and is accurate to whole minutes compared to one that plots from a DR position and is accurate to 0.1', the difference is most likely due to the intercept problem.

    Next time I visit I'll have a scanner for you so you won't have to use a stamp.


    Bottom line, Robin, is that we seem to be in the same boat regarding Berson's solutions.

    BTW, in the above messages, CT refers to Celestial Tools, the latest version of which has just become available at http://www.usps.org/eddept/n/tools.htm.  Be sure to at least read the Help>General before complaining
    ;-).  I couldn't find my e-mail regarding the solution to the September problem, but the Celestial Tools output is attached.  It agrees well with Robin's numbers.


    -----Original Message-----
    From: Robin Stuart <robinstuart@earthlink.net>
    To: slk1000 <slk1000@aol.com>
    Sent: Mon, Feb 11, 2013 7:29 pm
    Subject: [NavList 22335] Re: Berson's Noon Sun problem

    Here are the answers as they appear in Ocean Navigator with my answers, where they differ from ON, given in parentheses
    A. GMT of LAN 15h35m20s (15h34m58s)
    B. Hs 73d44.9’
    C. Latitude 25d11’N (25d14.3’N)
    The ON result for latitude is quite a bit different from both what I get with the Nautical Almanac and from Frank’s 25d14.6’N using 19th century methods.
    Let me also say that I agree with Stan K’s pet peeve about the calculation of LAN. In all examples I have seen it appears to have been calculated by converting longitude to time and then adding or subtracting a whole number of minutes obtained the listed “Mer. Pass.” entry for the day. I produced my result by interpolating the “Eqn. of Time” which is available in the NA to the nearest second at 12 hour intervals. Of course a few seconds are neither here nor there for the noon sight but it does grate on me that answer is quoted to a misleading level of accuracy. Glad to hear from Stan that this has been addressed in the latest edition.
    Given the ON answers above you can work backwards to find what value of the Sun’s declination of the must have been used. This comes out be 8d55.9’N which is exactly the declination listed in the Almanac for 12h GMT. Coincidence?
    Unfortunately over the limited period that I have been subscribing to Ocean Navigator errors of one type or another don’t appear to be very uncommon. The November/December 2012 edition contains a problem in which a value of Hs of 38d28.8’ yields a value for Ho of 21d46.7’.
    I also have doubts about some others. October 2012 has a nice LOP problem using Mars and H.O.249 asking for Ho, the intercept and EP. I agree reasonably well with the EP but cannot reproduce the quoted intercept. I get 6.7nm towards vs. ON’s 12.7nm towards. March/April 2012 also has an LOP problem for which I get an intercept of 17.2nm towards. The ON answer is 16.2nm towards. Maybe they are typos or maybe I just screwed up.
    If I had a point it would be that I find it rather sad that one of the few readily available sources Celnav problems can be have these sorts of issues. It must be discouraging for those trying to use them to learn the practice.
    Robin Stuart
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