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    Re: How good is St. Hilaire?
    From: John Karl
    Date: 2010 Mar 4, 10:23 -0800

    There's several points that can be made concerning the accuracy of St. Hilaire. Many of the recent posts are on the accuracy of fixes made from St. Hilaire. Geoffrey's is on the question of the straight-line approximation.

    I'll made a third observation -- about the PLOP: The point at the end of the intercept distance is EXACTLY on the circular LOP for all practical navigation purposes and cases. The only approximation here is plotting the intercept as a rhumb line rather than a great circle arc. And this error is negligible for all intercept distances and chart scales used in practice (exercice 3.5 in my book). So let's call this point PLOP for a Point on the Line of Position. This PLOP is exactly on the LOP independent of the AP, DR, which tables are used, or if a calculator or a computer is used.

    If you want to plot a segment of the LOP exactly, you could pick another AP, calculate a new PLOP, and you now have another point exactly on the celestial LOP. Do it as many times as you wish -- you're plotting the LOP exactly. (This is merely instructive, not the most efficient way to plot the LOP exactly.)

    The only error that comes into St. Hilaire (not considering fixes which are a different matter) is drawing the straight-line approximation through the PLOP. The distance between this straight line and the true curved LOP is called the offset in H.O. 229, where a table gives the offset vs the altitude and distance along the straight-line from the PLOP. For example in agreement with Geoffrey for a 50d altitude, the table gives an error of 0.3' at 45nm along the straight-line from the PLOP. (These offsets are easy to calculate using plane geometry.)

    JK
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