Karl Lunars Test Cases Last updated: December 2, 2017 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Case 1 Karl Case 2 Bowditch Case 3 Bowditch Case 4 Reed Case 5 Bowditch Case 6 Bowditch Case 7 Bowditch Case 8 Bowditch --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- INPUTS Moon Observation April January January April Moon Observation U/L Height 30°21.3'LL 28°03'25"UL 26°22'07"LL 47°13.8'UL 45°19'00"LL 70°31'00"LL 34°39'00"LL 44°19'00"LL U/L Height UL/LL 1 (LL) 0 (UL) 1 (LL) 0 (UL) 1 (LL) 1 (LL) 1 (LL) 1 (LL) SD 14.9' 15'25" 14'53" 14.9' 16'00" 14'50" 15'06" 16'00" SD NA Main +58.8' 59'42" 1 00'18" +49.0' 50'12" 29'36" 56'42" 50'54" NA Main NA U/L +01.3'LL 02'48"UL 01'12"LL +02.3'UL 05'54"LL 03'06"LL 02'24"LL 05'54"LL NA U/L LD 51°52.3' 46°05'59" 111°34'50" 80°08.3' 61°04'00" 47°48'53" 68°36'00" 61°04'00" LD LD Limb 1 Near 1 Near 1 Near 1 Near 2 Far 2 Far 2 Far 2 Far LD Limb HP 54.36' imputed 56'35" 54.7' 58'42" 54'22" 55'24" 58'07" HP Thompson 3rd 01'06" Sun Observation Sun Observation U/L Height 38°23.9'LL 39°39'09"LL 24°50'51"LL 47°12.0'LL 68°25'00" Antares 50°31'00" Antares 32°10'00" Aldebaraes 68°25'00" Antares U/L Height SD 15.9' 15'51" 16'09" 15.9' 00'00" 00'00" 00'00" 00'00" SD NA Corr +14.8' 14'48" 14'12" +15.1' -00'24" -00'48" -01'30" -00'24" NA Corr --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- OUTPUTS >hSD 30°36.2' 27°48'00" 26°37'00" 46°58.9' 45°35'00" 70°45'50" 34°54'06" 44°35'00" >hSD Moon's height >HSD 38°39.8' 39°55'00" 25°07'00" 47°27.9' 68°25'00" 50°31'00" 32°10'00" 68°25'00" >HSD Sun's height >Aug 00.1' 00'08" 00'07" 00.2' 00'12" 00'15" 00'09" 00'11" >Aug Moon's augmentation >LDpc 52°23.2' 46°37'23" 112°05'59" 80°39.3' 60°47'48" 47°33'48" 68°20'45" 60°47'49" >LDpc Pre-cleared LD >ho 31°21.4' 28°35'55" 27°23'37" 47°35.2' 46°15'06" 71°03'42" 35°38'06" 45°15'48" >ho Moon's corrected height >Ho 38°38.7' 39°53'57" 25°05'03" 47°27.1' 68°24'36" 50°30'12" 32°08'30" 68°24'36" >Ho Sun's corrected height >%Ch LDpc->LDc -0.6% -0.8% -0.5% -0.7% -1.0% -0.3% -0.4% -1.0% >%Ch LDpc->LDc >LDc 52°02.8' 46°13'44" 111°33'59" 80°06.8' 60°09'59" 47°24'39" 68°03'02" 60°09'35" >LDc Cleared LD >RBA 64°13.3' 55°09'59" 134°24'07" 144°41.4' 133°12'45" 104°55'17" 84°40'42" 128°58'59" >RBA Relative Bearing Angle between Moon/Body vertical circles Publushed LDc 50°02.8' 46°13'41" 111°33'53" 80°06.8' 60°09'54" 47°24'49" 68°03'00" 68°09'54" --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Data Source: 1) Example from "Celestial Navigation in the GPS Age" by John Karl, Revised and expanded edition, Arcata, CA, Paradise Cay Publications, Inc., 2011, Ch 8, pp.107-123. 2) Bowditch, "1839_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example IV, p.235 Bowdith result LDpc=47°37'00" LDc=46°13'41". Bowdith uses 12/20 rule of thumb thus moon/sun's eye height plus limb reverse engineered to remove IE of ship component to rule. Altitudes corrected with NA tables, final LDc almost perfect agreement. Bowditch rounds off LDpc seconds and reduces only degrees and minutes. Calculator carries full precision. 3) Bowditch, "1851_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example III. p.234 Bowditch results LDpc=111°06'00" LDc=111°33'53". Excellent agreement! 4) Example taken from "Lunars are Easy" paper by Frank Reed http://reednavigation.com/lunars/easylun.html, 5) Bowditch, "1864_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example II. p.233 Bowdith results LDpc=60°47'49" LDc=60°09'54". Excellent agreement! 6) Bowditch, "1826_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example I. p.169 Bowdith results LDpc=47°33'48" LDc=47°24'49". Excellent agreement! 7) Bowditch, "1855_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example I. p.232 Bowdith results LDpc=68°20'45 LDc=68°03'00". Excellent agreement! 7) Bowditch, "1844_Bowditch_The_new_American_practical_navigator.pdf", Lunar Observations, Example II. p.233 Bowdith results LDpc=60°47'49 LDc=60°47'49". Exact agreement!