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    Re: Error ellipse proportions
    From: Frank Reed
    Date: 2017 Jun 9, 16:15 -0700

    I wrote previously:

    Turns out there's a relatively simple formula for it, which can be derived from the usual rules for a statistical fix (details in PS). It is
      b/a = tan(dZ/2).
    There is a very nice fast approximation for this: the ratio is dZ/114 when dZ is in degrees. So if you have two sights separated in azimuth by about one compass point (11.25°), the ratio of the length of the ellipse to the width is just about 10-to-1. If the sights are separated by two compass points then the ratio is about 5-to-1. And so on.

    I'm attaching a quick photo of the derivation of this. It's nothing complicated. You can assume zero intercepts. Then "without loss of generality" assume the first LOP has Z=0 and the second has some angle to it. Crunch through the calculation of the quantities A-G in the statistical fix. Then calculate X and a/b. Throw in a few trig identities, and you're done. Sorry about my handwriting. This wasn't intended for publication! 

    Frank Reed


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