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    Re: Predicting transit using Bowditch section 2010
    From: Trevor Kenchington
    Date: 2003 Dec 21, 14:44 +0000

    You wrote:
    > When I ignored the seconds in Method 2, everything fell into line nicely.
    > But I have two problems with this neat solution to my problem.
    > Transit time occured at 13h 08m 09s (Method 1).
    > http://jimthompson.net/boating/CelestialNav/NoonSunSight.htm
    > 1. My DLo converts to 12m 32s.  So rounding up to the nearest minute should
    > have brought the DLo to 13m, which would produce a predicted transit time of
    > 1156 + 13 min = 1309, not 1308.  If I simply ignore the 32s, then I get
    > 1308, which is in agreement with all the other methods.
    If you round your numbers before making a calculation, you can get
    "rounding errors" (as in this example). That is: approximations entered
    into a calculation will not always give you an answer accurate to the
    precision of the original approximation. The moral is that you should
    never round off your numbers until to get to your final answer. At
    least, you should not round them off as far until you get to the end of
    the calculations (e.g. you could calculate to the nearest second if you
    intend to express your final answer to the nearest minute but if you
    really wanted your answer to be to the nearest second, you should
    calculate using values to the nearest 0.1 or 0.01 of a second).
    > 2. However Bowditch Section 2010 instructs us to add 11h 56 m and 12m 32s
    > for a total of 12h 08m 32s, shown as if accurate to the nearest second.  Why
    > is that?
    > Here is the relevant section from the 2002 version of Bowditch: "2010.
    > Latitude at Meridian Passage.  First, determine the time of meridian passage
    > from the daily pages of the Nautical Almanac. In this case, the meridian
    > passage for May 16, 1995, is 1156. That is, the Sun crosses the central
    > meridian of the time zone at 1156 ZT and the observer's local meridian at
    > 1156 local time. Next, determine the vessel's DR longitude for the time of
    > meridian passage. In this case, the vessel's 1156 DR longitude is 157? 23.0'
    > W. Determine the time zone in which this DR longitude falls and record the
    > longitude of that time zone's central meridian. In this case, the central
    > meridian is 150? W. Enter the Conversion of Arc to Time table in the
    > Nautical Almanac with the difference between the DR longitude and the
    > central meridian longitude. The conversion for 7? of arc is 28 m of time,
    > and the conversion for 23' of arc is 1 m 32 s of time. Sum these two times.
    > If the DR position is west of the central meridian (as it is in this case),
    > add this time to the time of tabulated meridian passage. If the longitude
    > difference is to the east of the central meridian, subtract this time from
    > the tabulated meridian passage. In this case, the DR position is west of the
    > central meridian. Therefore, add 29 minutes and 32 seconds to 1156, the
    > tabulated time of meridian passage. The estimated time of LAN is 12-25-32
    > ZT."
    > My answer is that the time of LAN so determined in Bowditch should be
    > written this way:
    > 12-26 ZT, not 12-25-32 ZT.
    > Is that most correct, and the way that Bowditch should have shown the
    > estimate?
    These are instructions for finding the _latitude_ of a moving object
    whose longitude cannot be known precisely. My guess is that they are
    intended to tell the navigator how to estimate when to step out to the
    bridge wing with his sextant and begin observing, _not_ as a way of
    determining just when the Sun crosses the meridian. That is, the method
    described is only intended to give the clock time of LAN to the nearest
    minute. That would explain why the instructions suggest that the time of
    the Sun's crossing the Greenwich meridian in GMT can be used as the time
      (in LMT) of her crossing any other meridian -- an adequate
    approximation to the nearest minute but clearly not precise to the
    nearest second.
    So why, having set out to calculate to the nearest minute, does Bowditch
    quote an answer to the nearest second? I'd suggest that the authors of
    this section have fallen into a common trap that catches many writers of
    textbooks by seeking to present a degree of theoretical perfection that
    is irrelevant to the real world. In this case, their attempt at
    additional precision actually introduced an error.
    If I am wrong in that, I trust that some member of this list will point
    out my error.
    Trevor Kenchington
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
                         Science Serving the Fisheries

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