NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Certaine Errors in Navigation Corrected
From: Gary LaPook
Date: 2007 Dec 04, 01:18 -0800
From: Gary LaPook
Date: 2007 Dec 04, 01:18 -0800
Gary J. LaPook wrote:
It is not surprising that nobody ever noticed this before (considering that Wright published in 1599 almost 300 years prior to Marc St. Hilaire) that Wright's method of calculating the great circle distance on the earth using only a strait edge and a compass could just as easily be used to calculate the altitude of a celestial body. The great circle distance is simply 60 NM times the number of degrees of the great circle between two points and this is exactly the same as the zenith distance to a body having the geographical position represented by the second point. The formula is 90º minus zenith distance equals altitude.
Wright's example of calculation of the great circle distance between London and Jerusalem resulted in his calculated distance of 2325 NM and a modern digital calculator comes up with 2316.8 NM a difference of only 8.2 NM or minutes of zenith distance or of computed altitude for those coordinates! Using his method Wright could compute altitudes to a precision of 8.2'. It is surprising in light of the many devices invented later in an attempt to find a mechanical method for this calculation that none (that I am aware of) attempted to use Wright's method, a method that would seem easily adapted to a mechanical device and that could provide much greater accuracy using a larger scale and precise machining of the parts.
I would really like it if someone could explain why Wright's method works since I have not been able to find such an explanation anywhere. I am attaching pages 45-52 of "Certaine Errors" in which he lays out his method. I am also including the errata sheet showing that the corrections of typos I identified in my previous posts were correct.
gl
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It is not surprising that nobody ever noticed this before (considering that Wright published in 1599 almost 300 years prior to Marc St. Hilaire) that Wright's method of calculating the great circle distance on the earth using only a strait edge and a compass could just as easily be used to calculate the altitude of a celestial body. The great circle distance is simply 60 NM times the number of degrees of the great circle between two points and this is exactly the same as the zenith distance to a body having the geographical position represented by the second point. The formula is 90º minus zenith distance equals altitude.
Wright's example of calculation of the great circle distance between London and Jerusalem resulted in his calculated distance of 2325 NM and a modern digital calculator comes up with 2316.8 NM a difference of only 8.2 NM or minutes of zenith distance or of computed altitude for those coordinates! Using his method Wright could compute altitudes to a precision of 8.2'. It is surprising in light of the many devices invented later in an attempt to find a mechanical method for this calculation that none (that I am aware of) attempted to use Wright's method, a method that would seem easily adapted to a mechanical device and that could provide much greater accuracy using a larger scale and precise machining of the parts.
I would really like it if someone could explain why Wright's method works since I have not been able to find such an explanation anywhere. I am attaching pages 45-52 of "Certaine Errors" in which he lays out his method. I am also including the errata sheet showing that the corrections of typos I identified in my previous posts were correct.
gl
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to NavList@fer3.com
To , send email to NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---