NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Still on LOP's
From: Michael Wescott
Date: 2002 May 6, 11:44 -0400
From: Michael Wescott
Date: 2002 May 6, 11:44 -0400
Bill Murdoch wrote: > I am still having a hard time with the 25% of the time you are inside > the cocked hat rule. It just does not 'feel right'. I have played > around with the Excel spreadsheet map that I mentioned a week or so > ago, and I can not get the calculations to work like I think they > should. > We have been discussing LOPs in two-dimensional (surface) navigation. > I have what may be a simpler question. What rule applies in > one-dimensional navigation? Let's say you are a tightrope walker, > getting nervous, and want to know exactly where you are on the rope. > You whip out your sextant and with a little skill and calculation plot > two POPs (points of position). The two POPs are not in the same spot > (naturally). What is the chance that you are between the two POPs? > What is the chance that you are to one side of both? What is the > chance that you are on the other side of both? Answers: .5, .25, .25 Usual assumptions apply: no "systemic errors", equally probable that error is + or -. If both are plus, they're both on one side of you. If both are - then they're both on the other side of you. If #1 is + and #2 is - then one is one each side. Likewise, if #1 is - and #2 is +. Four equiprobable possibilities and 2 of the four have you between the POPs: 50% and 1 in four (25%) for each of the other two possiblities. -- Mike Wescott Wescott_Mike@EMC.COM