# NavList:

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

**Re: Latitude by Lunar Distance**

**From:**Lars Bergman

**Date:**2006 Oct 18, 08:59 +0200

Some comments on George's "adding together 14 numbers, each varying randomly in the range between -.05' and +.05' ", in [NavList 1433]. As the variation in each number is due to rounding error, we can assume a uniform distribution for each variable. The standard deviation of a uniform distribution is the interval length divided by sqrt(12), i.e. in this case 0.1'/sqrt(12)=0.03'. Adding 14 such distributions results in a nearly normal distribution with standard deviation 0.03'*sqrt(14)=0.1'. In such a normal distribution, the probability of an error in excess of 0.19' is 6%, and 68% for an error less than 0.1'. This corresponds pretty well with George's brute-force simulations, as it should. With Frank's assumed distance measurements within 0.1', no timing errors and presumably negligible almanac data errors, furthermore assuming a "good cut" between the lines; we get a resulting standard deviation of say 0.08'. Using a "positional error multiplier" of 60 gives us a "less than 6 miles error" with about 80% probability, less than 9 miles with 95%. So I think Frank's claim is reasonable, given the stated preconditions. Frank could also claim that although there is 20% probability to have an error above 6 miles, there is as well a 20% probability that the error is less than 1.2 miles! Lars 59N 18E --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---