# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Position lines, crossing.**

**From:**Dave Walden

**Date:**2006 Dec 19, 15:00 -0800

The previous post answers were based on a Monte-Carlo result. There's no doubt, that Monte-Carlo methods are a powerful tool. But I feel sometimes they're "too powerful." They make is so easy to get to a numerical result, one can "stop thinking" about the problem too soon. After producing the result above, I felt sure the results were "in the equations" somewhere, if I just looked hard enough. Indeed, as expected, thats true. The below compact FORTRAN program reproduces the average distance results for various numbers of equally spaced lines of position based on analytics. (Well, some numerics, since the exponetial integrals involved have no closed form solutions.) No comments/clues are provided so you can enjoy the chase yourself. Details if there's interest. pi=4.*atan(1.) print*,"number of average distance error" print*,"equally spaced LOP's (SD obs error 0.5)" do 10 ilop=3,8 dx=0. do 9 jj=1,ilop dx=dx+((ilop/2.)/(ilop/2.)**2*sin((-75.+jj*360./ilop)*pi/180.))**2 9 continue sd=sqrt(dx*.5*.5) sum=0. do 1 i=-300,300,5 do 1 j=-300,300,5 x=i/100. y=j/100. sum=sum+1./sqrt(2.)*sqrt(x**2+y**2)*1./(sqrt(2.*PI)*SD)*EXP(-X**2/(2*SD**2)) . *1./(SQRT(2.*PI)*SD)*EXP(-Y**2/(2.*SD**2)) 1 continue print*,' ',ilop,' ',sum*.05**2*sqrt(2.) 10 continue end knoppix@ttyp0[knoppix]$ g77 big.f -obig.exe knoppix@ttyp0[knoppix]$ ./big.exe nunmber of average distance error equally spaced LOP's (SD obs error 0.5) 3 0.511632323 4 0.443074971 5 0.396285892 6 0.361745924 7 0.334897667 8 0.313253939 knoppix@ttyp0[knoppix]$ knoppix@ttyp0[knoppix]$ --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---