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    Cosine Method Revisited
    From: OH Jacobson
    Date: 1996 Dec 15, 11:09 EST

    Hi guys, it's your armchair navigator again.
    1. A couple of msgs back, someone corrected LOP to COP in horizontal
    angle fixes. My Webster's Ninth Collegiate Dictionary says:
    Line, n, 8: a straight or curved geometric element that is generated by a
    moving point and that has extension only along the path of the point :
    I take this to mean that a COP is an LOP.
    2. This leads to the business of No DR or AP. The standard linear LOP
    resulting from Zn and a, a Sumner line if you will, is nothing more than
    a linear approximation to the great circle with the GP as the center.
    Whereas it would be impossible to plot such a huge circle on any normal
    chart, it is reasonable to generate this LOP (COP?) in a computer, and
    with two more like it, even resolve the ambiguity of only two LOPs.
    Additional sights allow averaging to get an even better Fix. Nothing
    mysterious about no DR or AP.
    As to the ambiguity of inverse trig functions: Note that the hc comes
    from an arcsin. A calculator will give a positive value between 0 and 90
    deg. But so is hc! Unless you took a back sight. So there should be no
    problem there. Also note that the Zn comes from the arccos which gives a
    positive value of Zc between 0 and 180 deg. Then, based on LHA, there is
    the minor calculation for getting Zn from Zc.
    Conclusion: There is no trigonometric ambiguity problem with the Cosine
    Method. The thrust of my msg seems to have been lost. People seem to want
    to compare it with a computer solution for which there is no comparison.
    The method is only a possible replacement for the Tables. But what if you
    lose your computer due to computer failure or power failure. Then you
    have to go to the Tables or ... Certainly a calculator can fail and if it
    is only battery powered it can surely fail. But a solar powered
    calculator can be used any time there is light, either emergency or
    Anyway, so as not to belabor the point, it is offered as a possible
    solution to a possible problem.
    Lt/C Ollie Jacobson, FC
    SEO, Redondo Beach PS (CA)

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