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    Re: Understanding a 1902 Sumner
    From: David C
    Date: 2017 Jan 23, 13:31 -0800

    Here is the next instalment.........

    The difference between the intercept method and CoP app positions is partly due to errors in the azimuth plotted on Google Earth. I decided to eliminate this error by using Sumner's chord (two point) method. It is easy to plot accurate positions on google earth and draw lines between them. I have attached a revised plot. The sumner method position includes rounding errors so is not a perfect match to the CoP position. As would be expected the sumner and intercept position lines are parallel  -  it is satisfying to demonstrate this.

    The position lines are approximations of a circle of position. The error can be determined by stringlining a curve. See the attached 2009 photo which shows measurements being taken without the ubiquitous GPS receiver on a pole. For details of the method see

    https://en.wikipedia.org/wiki/Hallade_method

    v = approx  L2/(8R)

    where v =versine

               L = chord length

               R = radius

    All values in the same units. I will use nm.

    T Alt approx = 44°

    ZD = 46° so radius = 46 X 60 nm

    Chord length = 1.91nm  (measured on Google Earth)

    From which v = 0.000165 nm

                          =  .01"

    Clearly in this case the assumption that the CoP can be approximated by a straight line is valid.



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