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    Re: Poor St. Hilaire
    From: George Huxtable
    Date: 2007 Oct 18, 01:34 +0100

    |
    | Ok, one last try on Poor St. Hilaire, using a different approach:
    |
    | We can say that the St. Hilaire intercept method is a process
    | (containing both computational and graphic components), perhaps
    | thinking of it as a machine.  It has inputs and outputs:  We feed in x
    | and y, the latitude and longitude of a point, let's call it the RP
    | (the reference point).  For every x and y that's input to the process,
    | out comes another pair of coordinates, the lat and lon of a point on
    | the celestial LOP.  Let's call this point SHP (St. Hilaire point) for
    | convenience of discussion.  The SHP is the unique point closest to the
    | RP that is exactly on the LOP.
    |
    | Some List members will recognize that the above descrinption is close
    | to mathematical phraseology:  The St. Hilaire method is a function
    | F(x,y) with inputs (independent variables) x and y.  You feed in these
    | coordinates of the RP.  Out comes the coordinates of a point exactly
    | on the LOP, which we're labeling the SHP.  You can find as many points
    | on the LOP as you like, tracing out the LOP - exactly.
    |
    | Now for comparison, consider the hull speed of a displacement boat, Hs
    | = 1.34 sqrt(Lw), where Lw is the waterline length (in feet) and Hs is
    | the hull speed (in knots), and sqrt means take the square root.  This
    | also represents a function, a process, or a machine, however you want
    | to look at it.  You input Lw, out comes Hs.
    |
    | Now the major point:  If we wanted to plot the hull speed versa the
    | waterline length, would we call the waterline length an estimate?
    | Would we call it an assumed Lw??  NO.  It's called an independent
    | variable,  meaning we can specify any Lw we like and we get the
    | corresponding Hs.  There is no estimation, no uncertain reckoning, no
    | assumptions in specifying Lw.  The same is true for the specifying St.
    | Hilaire's RP.
    
    John Karl has had another go, and to be honest, I am little the wiser, which
    may well be my problem rather than his. Let me summarise, mostly to check
    whether I am following him correctly.He argues, at some length, that for any
    arbitrary position that you specify, (call it the RP) and a defined GP and
    altitude of a body, the St Hilaire process will generate another position
    (call it the SHP), on the corresponding position circle around the body, as
    close as you can get to the RP, and will do so exactly. And I agree. So
    what?
    
    That is only a part of the St Hilaire process. The next step is to draw a
    tangent to the position circle through that point, knowing the azimuth
    direction. And the next step is to do the whole thing again for another
    body, and find the position where those tangents intersect.Only then is the
    process completed. And it's those parts of the operation that are affected
    by any errors in choosing the RP, divergent from the true position.
    
    and John goes on to say-
    
    | 2.  A List member has stated that the accuracy of the St. Hilaire
    | result depends on how good the initial estimated position is.
    
    I wonder if that was me? Whether or not it was, I think that it's true.
    
    | 3. And therefore the St. Hilaire method is really an iterative method.
    
    And I think that is true also. And indeed, so does St Hilaire. See his
    comments on page B2- 368, in which he writes "It seems to us necessary to
    determine, at least roughly, the approximations that one obtains by the
    calculations and thus to know if it is necessary to make a second
    calculation to obtain a more correct position". And on page B2-375 he works
    an example in which the error from the true position after one calculation
    is 16 miles, which after a second iteration has reduced to 0.2 miles. I
    admit that I've made no attempt to follow these sections in detail, however.
    
    | We've just seen that all of this is wrong.
    
    I've seen nothing of the kind. I remain unconvinced, as yet. What am I
    missing?
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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