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

```Doug,

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.

Thanks,

Fred

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-----
> [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
> 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
> 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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