Thompson-Bowditch Lunars Test Cases
Last updated: November 28, 2017
LDc times are computed by interpolating between geocentric LD's that bracket the observation time.
The resulting LDc sight time is then compared to the computed LDc time to determine the time error.
Frank Reed says an LDc within 30" of GMT is a very good sight. A Longitude error (in mins) = seconds error / 4
LD Sextant error resulting time error
1.0' = 2 minutes error
0.5' = 1 minute error
0.1' = 12 secs error
Longitude Error - difference between GMT actual and computed in seconds divided by 4.
Thompson-Bowditch Lunars Test Cases
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Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
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Moon Waning Waning Waning Waning NP NP Waning NP Waning Waning NP NP NP Waning NP Waning NP Moon
Ho 26°42.7' 64°37.6' 13°22.7' 46°39.5' 31°05.2' 66°38'00" 46°42.7' 49°43'28" 27°40.7' 36°11.8' 15°00.0' 27°48'00" 42°35'00" 53°18.5' 70°44'00" 52°54.0' 30°36.2' Ho
HP 59.6' 58.2' 54.3' 54.7' 54.8' 55'47" 57.8' 54'19.4" 56.69' 58.2' 57.5' 56'03" 59'47" 59.6' 59'15" 58.2' 54.4' HP
LDo 111°15.0' 58°52.4' 78°27.0' 80°08.3' 77°58.2' 85°54'45" 74°42.7' 43°52'10" 74°36.9' 93°13.7' 35°00.0' 46°05'59" 45°31'31" 69°27.2' 103°30'08" 62°42.3' 51°52.3' LDo
Near/Far Near Near Near Near Near Near Near Near Near Near Far Near Near Near LDpc Near Near Near/Far
3rdCorr 02.7' 02.2' 02.1' 01.5' 01.85' 00'10" 01.40' 07'54" 01.7' 01.9' 02.7' 01'12" 01'12" 01.3' 03'24" 01.3' 01.2' 3rdCorr
Other Body Other Body
Ho 36°14.1' 19°46.9' 29°48.9' 47°12.0' 16°28.5' 26°03'00" 38°45.8' 5°38'42" 53°50.7' 42°02.4' 45°00.0' 39°55'00" 28°21'00" 45°00.7' 18°59'30" 32°48.4' 38°39.8' Ho
SD 15.8' 15.8' 16.2' 15.9' 16.3' 16'12" 15.9' 15'55" 15.9' 15.7' 16.0' 15'51" 16'13" 15.8' 16'00" 16.1' 15.9' SD
>P1 -0.1785 0.5182 0.0408 0.1091 0.0960 0.0531 0.1847 0.7057 0.1165 -0.0376 0.3542 0.4117 0.6495 0.2901 -0.2238 0.3903 0.3554 >P1
>P2 0.6323 0.3814 0.4584 0.6779 0.2643 0.4091 0.6237 0.1273 0.7893 0.6510 1.1813 0.8247 0.6570 0.7475 0.3305 0.5889 0.7145 >P2
>P=P1-P2 -0.8108 0.1368 -0.4176 -0.5688 -0.1683 -0.3560 -0.4390 0.5784 -0.6728 -0.6886 -0.8271 -0.4130 -0.0075 -0.4575 -0.5543 -0.1986 -0.3592 >P=P1-P2
>SDm 16.24' 15.86' 14.79' 14.9' 14.9' 15'12" 15.8' 14'48" 15.45' 15.86' 15.67' 15'16" 16'17" 16.24' 16'09" 15.86' 14.81' >SDm
>AGm 00.13' 00.27' 00.07' 0.2' 0.15' 00'17" 0.22' 00'14" 0.14' 0.18' 0.08' 00'08" 00'12" 00.24' 00'17" 0.24' 0.15' >AGm
>LDpc 111°47.17' 59°24.33' 78°58.06' 80°39.3' 78°29.6' 86°26'25" 75°14.6' 44°23'07" 75°08.38' 93°45.43' 35°00.26' 46°37'15" 46°04'13" 69°59.48' 103°30'08" 63°14.45' 52°23.16' >LDpc
>LDcorr -0°45.95' +0°10.46' -0°22.90' -0°32.6' -0°08.3' -21'12" -0°24.9' +42'36" -0°38.67' -0°39.41' -0°46.93' -23'35" 00'45" -26.15' -29'52" -0°10.61' -0°20.35' >LDcorr
-------- -------- -------- -------- -------- ------- -------- ------- -------- -------- ------- ------- ------- ------- ------- ------- -------
>LDc 111°01.23' 59°34.74' 78°35.11' 80°06.7' 78°21.3' 86°05'13" 74°49.6' 45°05'43" 74°29.7' 93°06.0' 34°13.3' 46°13'40" 46°04'59" 69°33.33' 103°00'16" 63°03.9' 52°02.8' >LDc
>%LD Change -0.7% +0.3% -0.5% -0.7% -0.2% -0.4% -0.6% +1.6% -0.9% -0.7% -2.2% -0.8% 0.0% -0.6% -0.3% -0.6% >%ld Change LDpc->LDc
>RBA 152°06.8' 59°44.7' 84°48.7' 142°45.6' 86°17.7' 163°09'54" 112°05.2' 6°10'00" 113°07.2' 140°16.8' 21°21.7' 55°09.5' 54°54.54" 122°10.7' 87°57.2' 64°13.2' >RBA
Source Book Ans 45°04'45" 34°13.1' 46°13'41" 46°04'55" 103°00'16" 63°04.0' 34°02.8' Source
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LDc Time 13:36:22 12:08:42 16:36:11 20:16:44 14:25:32 14:43:51 16:26:13 13:35:10 14:19:24 LDc Time
Sight Time 13:36:02 12:09:16 16:35:20 20:16:37 14:25:14 NP 14:43:19 NP 16:26:58 13:34:49 NP NP NP 14:19:15 NP 14:43:55 NP Sight Time
Time error 00:00:20 -00:00:34 00:00:51 -00:00:07 00:00:18 00:00:32 -00:00:45 00:00:21 00:00:09 Time error
Longitude 05.0' 08.5' 12.7' 01.8' 04.5' 08.0' 11.3' 05.3' 02.3' Longitude Error
Error
Agreement Excellent V Good Good Excellent Excellent w/ book V Good Same as book OK Excellent LDc agree LDc agree Excellent w/ book Excellent Agreement
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Case Sources and Comments NP=Not Published
1) KP="28 West" Lat 42°00.2'N Lon 074°07.5'W August 23, 2016 GMT 13:36:02 Sight #18
2) KP="28 West" Lat 42°00.2'N Lon 074°07.5'W August 27, 2016 GMT 12:09:16 Sight #35
3) KP=Mystic Seaport November 15, 2014 GMT 16:35:20 Sight #4 Lunars Workshop field trial
4) "Lunars are Easy" by Frank Reed April 27, 2004 GMT 20:16:37, LDc is 20:16:31 6" difference
5) KP="28 West" Lat 42°00.2'N Lon 074°07.5'W December 15, 2014 GMT 14:25:14 Sight #4
6) "Lunar and Horary Tables.." 1845 Boulter Bell Example II, p.11 https://books.google.com/books?id=phsEAAAAQAAJ
LD observed was listed, thus subtracted moon and sun SDb to simulate sextant LD. Perfect agreement with book is probably a fluke.
7) KP="28 West" Lat 42°00.2'N Lon 074°07.5'W September 23, 2016, 14:43:19 Sight 73, Series #9
8) September 7, 1855, "New method of correcting lunar distances, and Improved method ..." Chauvenet, William, 1820-1870. Example 1 p. 10
https://babel.hathitrust.org/cgi/pt?id=uc2.ark:/13960/t4jm2513s;view=1up;seq=17;size=75
9) KP="28 West" Lat 42°00.2'N Lon 074°07.5'W Sept 6, 2015, Sight #1, Moon age 22.7 waning
10) KP="28 West" Lat 42°00.2'N Lon 074°07.5'W July 16, 2017, Sight #4, Moon age 22.7 waning
11) Bowditch-Thompson Method example with round numbers by Frank Reed, Lunars Workshop, November 15, 2014. GMT not given
12) Bowditch, "1837_2_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example IV, p. 235
13) Bowditch, "1837_2_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example V, p. 236
14) KP="28 West" Lat 42°00.2'N Lon 74°07.5'W August 16, 2017, Sight #2, Moon age 23.4 waning
15) Example from Moore "The Method of Finding" Example III, p. 52 (seem Image Library\Lunars)
16) Reversed engineered to get pure Reed example LDo=62°42.25' KP=42°00.2'N 074°07.5'W Oct 14, 2017 GMT14:43:55
LDpc=62°42.25'+16.1'+16.0'+00.2'=63°14.55' SDs and augmentation
17) From "Celestial Navigation in the GPS Age" by John Karl, Revised and expanded edition, Arcata, CA,
Paradise Cay Publications, Inc., Lunar-Observation complete example, 2011, Ch 8, pp.107-123.