# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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----- > From: Navigation Mailing List > [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of Trevor J. > Kenchington > Sent: Sunday, December 21, 2003 06:44 > To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM > 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 >