Reed Lunars Method Test Cases
Last updated: February 15, 2018
Slightly different results between Versions 1 and 2.
Version 1 results shown below.
Version 1
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Ho for moon and body are input but Nautical Almanac correction
for the Ha->Ho is required and input with opposite sign.
Worth comparing technique with Letcher which requies the
fewest inputs.
Comments on NA Altitude Corrections:
The Sun correction table includes refraction, parallax, and semi-
diameter. The Stars and Planets table is refraction only, but the
Additional Correction for Venus and Mars takes care of parallax.
This applies to the A2 and A3 tables. The Moon tables in the back
of the Almanac include refraction, parallax, semi-diameter, and
augmentation. Stan Klein comments 10/8/2017
Version 2
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This version computes altitude corrections and reversed signs.
The moon's Horrizontal Parallax is input.
Letcher's and Bowditch-Thompson test cases can be used as-is.
TimeDiff/4 = min' longitude error
Reed Test Cases
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Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13
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Moon Moon
HoMoon 46°39.5' 28°20.8' 52°54.0' 13°38.3' 19°51.2' 16°39'25" 53°11.3' 37°50.1' 41°52.6' 14°11'24 16°39'25" 36°52'00" 27°50'00" HoMoon corrected for UL/LL, semi-diameter
Alt Cor -36.6' -46.72' -34.9' -47.8'?? -48.5' -49'17" -33.2' -42.3' -40.6' -52'25 -55'43" -45'35" -50'25" Alt Cor Fron NA, correction for SD and refraction, use opposite sign
HP for V2 54.7' 55.0' 55.18' 55.91' 60'33" 52'24" HP for V2
Body Sun Star Sun Sun Sun Body
HoBody 47°12.0' 48°26.82' 32°48.4' 30°05.0' 75°42.3' 13°38'28" 42°35.0' 36°10.7' 54°46.4 33°20'30 13°38'28" 47°31'00" 50°44'00" HoBody corrected for UL/LL
Alt Cor 00.9' 00.72' 01.4' 01.5' 00.2' 01'00" 01.1' 01.4' 00.7 01'31 04'11" 00'47" 00'47" Alt Cor From NA, correction for SD and refraction, use opposite sign
LDpc 80°39.3' 83°57.55' 63°14.55' 78°58.38' 55°48.4' 57°03'46" 70°11.1' 95°38.6' 73°59.6 44°31'18 57°03'46" 48°20'29" 93°09'59" LDpc Note that effect of Ho and AltCor is how much bodies were
displaced by Ha to Ho that changed the LDo to LDpc
>A %m 0.9090 0.7980 0.3392 0.4782 1.000 0.0995 0.7189 0.8278 0.8842 0.5514 0.0995 0.5666 0.9059 >A %m
>B %b 0.9070 0.6004 0.7377 0.1647 -1.004 0.1942 0.8246 0.8358 0.7977 -0.2505 0.1942 0.2175 0.8062 >B %b
>Q 1.701E-6 0.0031 2.415E-5 0.0073 4.644E-6 0.0095 0.0021 -2.473E-6 4.586E- 0.0001 0.0001 0.0001 -1.155E-6 >Q
>LDc 80°06.9' 83°20.9' 63°03.7' 78°35.73' 54°59.7' 56°59'38"[6] 69°48.3' 95°04.8' 73°24.26 44°00'22" 56°59'03" 47°54'50" 92°24'04" >LDc
>%Change -0.7000 -0.728 -0.3000 -0.478 -1.500 -0.100 -0.500 -0.600 -0.800 -1.200 -0.100 -0.900 -0.800 >%Change
>delZcos -0.7960 -0.0869 -0.6276 0.7140 0.5114 0.4113 -0.7441 >delZcos cosine of RBA angle
>delZ 142.8° 115.4° 88.0° 85.0° NA 59.2° 117.4° 136.2° 128.9° 44.4° 59.2° ° 65.7° ° 138.1° >delZ Relative Bearing Angle between moon-body vertical circles
NA usually means angle is 0, bodies are vertically aligned on same VC
Time Time
LDo 20:16:37 14:43:55 16:35:20 00:55:00 00:27:06 00:05:54 LDo
LDc 20:16:57 14:43:55 16:35:36 00:27:29 00:05:50.69 23:36:5 LDc
Dif 20 0 16 00:00:23 00:00:03.43 Dif
Lon err 05.0' 0 04.0' 05.8' 00.9' 00.4' Lon err
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Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13
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Longitude error (in mins) = time seconds error / 4
Case References:
1) Example taken from "Lunars are Easy" paper by Frank Reed
reednavigation.com/lunars/easylun.html, Thompson-
Bowditch check compares very well. See those test cases.
2) ?
3) Reversed engineered to get pure Reed example LDa=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
4) Mystic Seaport Workshop, Lunars exercise, November 15, 2014, Popko's best sight #4
5) NavList, A Lunar Example: Sun and Moon Vertically Aligned",
fer3.com/arc/m2.aspx/Lunar-Example-Sun-Moon-vertically-aligned-FrankReed-dec-2017-g40943
6) Example from astronavigatiiondemystified.com/lunar-distance, Geocentric LD 56°59'22"
7) KP=28°411'N 082°18.2'W Dec 26, 2017 moon-Aldabaran (far) LDgc 69°48.5'
8) Extremely good KP=28°41.1'N 082°18.2'W Dec 24, 2017 moon-Aldabaran (far) LDgc 95°04.8'
9) Sight #3, Inverness Series, January 21, 2018, Moon-Aldebaran
10) Lunar-distance observations form by Robert Bishop, Sept 5, 1767, LDc source 44°00'22"
cudl.lib.cam.ac.uk/view/MS-G-00298-00001-00003/1
11) Jack Case, "Astro Navigation Demystified", https://astronavigationdemystified.com/lunar-distance/,
Geocentric lunar published 56°59'22"
12) Henry Raper, "The Practice of Navigation and Nautical Astronomy", Nautical Astronomy, Ex.1, p.288
Published LD cleared = 47°54'59"
https://books.google.com/books?id=iMRNAAAAMAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
12) Henry Raper, "The Practice of Navigation and Nautical Astronomy", Nautical Astronomy, Ex.3, p.288
Published LD cleared = 92°24'04", perfect agreement!
https://books.google.com/books?id=iMRNAAAAMAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
References:
1) Frank Reed, Lunars Workshop, Mystic Seaport, Nov 15-16, class notes.
2) "Longitude by Lunars" by Frank Reed, reednavigation.com/lunars
3) "Lunars are Easy" paper by Frank Reed, reednavigation.com/lunars/easylun.html
4) "Angular Distances between two celestial objects and Lunar Calculation"
www.tecepe.com.br/nav/DistTwoObjects.htm
5) Navigator Light PC program by Omar Reis, www.tecepe.com.br/nav
6) "Elements of Plane and Spherical Trigonometry: With Its Applications to the Principles
of Navigation and Nautical Astronomy; with Logarithmic and Trigonometrical Tables" by
John Radford Young, Thomas Stephens Davies, London, 1833. Lunars example page 173.