NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Haversine formula
From: Frank Reed
Date: 2008 Apr 08, 22:28 -0400
From: Frank Reed
Date: 2008 Apr 08, 22:28 -0400
There's also a much older application of a formula sometimes called the "haversine formula". In the 1790s, both Mendoza Rios (first) and Bowditch (probably independently) realized that the number of "cases" in a series solution of a lunar distance calculation could be reduced by replacing the standard cosine formula for the corner angle in a spherical triangle with a formula for the haversine. The latter was entirely multiplicative, so well-suited to logarithmic calculation, and there no problems with the signs of the arguments. The historical "cases" were what we understand today as the algebraic signs of the factors. The calculation is slightly longer when you use the haversine formula, but since there are no cases, it's apparently less prone to error. Those of you who attended the Navigation Weekend at Mystic Seaport in June, 2006 heard me talk all about this (this was the chalkboard presentation on the second day). For the few people who are new to the list in the past few months, you're welcome to attend the next Navigation Weekend in Mystic in June of this year. It's shaping up very nicely, and I think it's going to be very successful. There's a web page describing it here: www.fer3.com/Mystic2008 . -FER www.HistoricalAtlas.com/lunars --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---