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    Re: Predicting transit using Bowditch section 2010
    From: Fred Hebard
    Date: 2003 Dec 22, 14:27 -0500

    Having somebody present these techniques is precisely why I am on this
    list.  If you can, I would appreciate hearing of any you wish to share.
    On Dec 22, 2003, at 1:28 PM, Royer, Doug wrote:
    > Jim,Trevor is correct in his explaination of useing the table.It was
    > used
    > mainly for the purpose of the navigator to calculate the "Watch Time"
    > of LAN
    > on a moveing vessel.In real practice it is as Trevor states:to let the
    > sight
    > taker know when to be on deck or bridge to take the round of noon
    > sights.There are more techniques to do this and I would be happy to
    > show
    > them to you.Contact me off list if interested.
    > -----Original Message-----
    > From: Navigation Mailing List
    > [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of Trevor J.
    > Kenchington
    > Sent: Sunday, December 21, 2003 06:44
    > Subject: Re: Predicting transit using Bowditch section 2010
    > Jim,
    > 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
    >                       http://home.istar.ca/~gadus

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