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    Re: Franklin Piloting
    From: Antoine Couëtte
    Date: 2012 Sep 6, 00:50 -0700

    Dear Byron,

    You have invented a piloting/plotting technique now know known as "Franklin's Piloting/Plotting Technique" in the US Navy and that is definitely a remarkable achievement. Congratulations again for it.

    *******

    The main idea behind your method as I see it could be re-written as follows :

    FIRST : assume that the fix obtained from the 2 closest Navaids is "exact", and

    SECOND : compare with "Compass azimuth" from the 3 rd most remote Navaid to establish Compass Azimuth error. Correct for such error back onto the three observed azimuts in order to refine the observed fix.

    NOTE : In fact, a mathematician would continue refining such new fixes "ad infinitum", with the end result of such mathematician work being a "perfect fix" from which all angular distances between Navaids would exactly match the recorded ones. Nonetheless, and most importantly ... being real life men with limited time we are to consider that your first correction is to treated as "perfect", which is very close from reality.

    THIRD : Use such derived Compass Azimuth error onto all upcoming sets of three bearings so as to refine the next observed points.

    *******

    All in all, you have found an extremely clever method, which definitely seems very powerful to immediately detect and correct for systematic Compass errors.

    Just one question : how does your method perform when facing (significant) random errors, whether reading/recording errors, or random compass errors which can happen on both types of Compasses (swinging errors for Magnetic Compasses, and "repeat" errors for Gyro Compasses) ?

    Thank you for your Kind Attention and Best Regards

    Kermit

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