A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: h.a.c. van Asten
Date: 2013 Apr 28, 06:18 -0700
Appreciated Opponent ,
I refer to your link to the TIGHAR forum , where you pin a sunrise local hour angle miscalculation on me , with the remark that I should not necessarily demonstrate how to compute such angle , since navigators (your words : "who do understand celestial navigation")know how to do that themselves with their almanacs . For 150 SM off Howland westwards your algorithm for the hour angle of the sun at sunrise U.L. ends up at 87-45.7 , U.L. in the local horizon ,sea level , time 1754:53 GMT , which is all good . Excellent . However , I do NOT fly with you to Howland , especially if for an assessment of our position you refer to the rising sun , like mr.Noonan possibly did when nearing the island in 1937 .
If you observe sun´s upper limb in the horizon by no matter what medium , the marine sextant , binoculars , or the unarmed eye , you do not look at the mean sun . You look at the true , apparent sun which on July 2nd is 3m50s slow on the mean sun for the 1700-1800 GMT time window . Your comparison Lapook-to- Asten local hour angle , 87-45.7 versus 88-43.2 accounts for 0-57´.5 . Multiply by 15 deg/hr and find 3m50s time point difference , exactly covering the equation of time since the sun´s rising time was 3m50s identically for 13.8 arcmin velocity per minute of time (*) . From any western point on the 500 SM radius about Howland-chart circle our distance made good is (1754:53 - 1540:00) x 150 MPH = 337 SM . However , the distance to our precomputed sun-up coordinates is 348 SM : we are 11 miles short and not 150 , but 161(**) miles off destination . Proceeding for the offset lane and turn-off point by DR (***) will bring us on a 157-337 position line 3m50s x 150 MPH = 9.6 miles westwards of Howland-chart , 14.6 miles westwards of Howland-true .
We wil not run the destination in sight , head-on on our APL , since when passing at ETA over its latitude the island is 14.6 miles , 23.5 km on the port bow .
. Therefore , not to offend you , I stay home and let you travel alone , for which the reason is that you did not follow the advise : If you observe sunset by the bubble sextant (true , apparent sun´s centre in the horizon) , KEEP TO THE BUBBLE SEXTANT for next morning sunrise but if not , you artificially shorten your night time window and as a result you undershoot destination . Mr. Noonan should have waited for (1754:53 + 3m50s) GMT = 1758:43 GMT to plot his DR offset for Howland . The mechanism is dealt with in EJN-July 2008 , p.27 , figures 3 & 4 .
Eventually , you disqualify my on the subject articles series by stating that they are littered with errors , thereby bringing into discussion the theory´s consistency . It is true that for the relevance there is up to now no proof , but no complaint about consistency , the articles having been meanwhile gone through by many readers the world over , has been brought to my attention ,
sincerely yours ,
(*) Vr/min = 15´sin 67 . cos 00-09
(**) R.Con.Nesbit in Aeroplane Monthly , Feb. 1989 , p.71 ,without further calculation , gives "approximately 160 miles off" , at sunrise .
(***) P.Mantz remembering F.Noonan´s "Find the Island" fashion (Mantz biography ´Hollywood Pilot´ , interview) .
It may for members of this forum be of interest to solve for the sunrise time-distance-coordinates group from sunset the evening before . It can be made for any pair of locations , here executed for the Earhart New Guinea to Howland flight , July 2 , 1937 , departure 0000 GMT from Lae . Sunset 159-07-E / 04-33.5-S . Sunrise next morning 150 SM off Howland-chart . For one single day you can delete the Equation of Time difference and work with apparent time .
159-07-E to 178-47- W Diff.Long. due east 22-06
LHA at central sunset bubble 88-03
LHA at visible sun U.L. 90-04
Subtract from 360-00
Travel of true sun during (partial) trip 157-47
Divide by 15 deg / hr flight time 10h39m08s
Add to GAT of sunset 07 15 45
GMT of sunrise U.L. unarmed eye 17 54 53
Note that at 1754:53 GMT the visual sun´s U.L. (any instrument , not bubble) is in the horizon . For the specific event the Equation of Time covered the rise time of the sun , both figured 3m50s . Note that sun´s centre (bubble sextant)is in the horizon at 1754:53 + 3m50s = 1758:43 GMT . GAT of sunrise was 1751:03 .
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