NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Irregular Quadrilateral Center
From: Tom Sult
Date: 2015 Feb 05, 08:18 -0600
From: Tom Sult
Date: 2015 Feb 05, 08:18 -0600
Generally speaking the cocked hat is 1 to 3 miles per side. Given that at sea a very good site is going to place you within 1 mile of your GPS position, any place inside is a reasonable approximation of your position. Unless your sites are composed of multiple sites with averaging it seems to me that we're talking about insignificant figures by placing too much emphasis on the precise center of the cocked hat. Celestial navigation is for mid ocean navigation and having your position fit underneath the tip of your finger is pretty darn good.
Thoughts from a generally lazy and certainly not academic celestial navigator.
By the way I always take multiple sites. I just don't have the confidence to take two sites and call it good. So perhaps I should add generally lazy, gently chicken and certainly not academic.
Tom Sult
Tom Sult
Sent from my iPhone
Greg,
The procedure for finding the centre of a quadrilateral or other figure is described in the Nautical Almanac. I don't have the page number with me but the formulas involve sums of sines and cosines of azimuths. The formulas are derived by a least squares fit to the observations. If you apply the formulas to 3 observations you'll get the symmedian point of the cocked hat that has been discussed here extensively. The formulas in the NA assume that any constant offset (such as an unknown Index Error) is zero. It is a fairly easy matter to extend the method to perform the least squares fit incorporating an unknown constant and actually produce a value for it.
Robin Stuart
