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Hey, guys, didn't Capt. Sumner take one sight of the sun around 10
a.m. and then ASSUME three different LATITUDES (not longitudes) to
plug into a time-sight formula?  HS

On 11/13/09, P H  wrote:
>
> Since LOPs are one-dimensional objects, you need precisely one parameter to
> characterize them.  It is this parametrization that amounts to "calculating
> the LOP directly" (answer to Geoffrey Kolbe's question).  Sumner used
> longitude as the parameter.  The parameter doesn't have to be longitude and
> in the case of LOP=meridian, it is in fact unsuitable.
>
> The LOP is what it is, based on the Ho and GP, independent of any AP.  As I
> said in an earlier post, you need to have a coordinate system to do anything
> practical.  The AP is the origin of such a convenient local coordinate
> system.  We have some freedom in choosing where to place this AP=origin.
> The computed intercept distance then tells us how far the chosen AP is from
> the LOP, and the computed azimuth tells us the orientation/direction.  That
> is what the solution of the celestial triangle AP-GP-Pole is about; it gives
> the relative position of the (independently existing and fixed) LOP and our
> arbitrarily chosen AP.  In practice St. Hilaire proceeds in reverse; we
> choose the AP first, solve the triangle, and then we construct the LOP at
> the appropriate distance from the AP and orientation with respect to true
> North.
>
> On a Mercator plotting chart LOPs look like straight lines (for not too high
> Hs's).  A straight line lying in a plane can be defined by two points, or by
> one point and one direction.  Sumner uses the former; St. Hilaire uses the
> latter.  St. Hilaire is less work because one detail regarding the direction
> part is automatic; it is the angle between the LOP and the azimuth line
> toward the GP, which is always 90 degrees.  We can therefore plot the LOP at
> the right angle to the azimuth line (at the intercept distance) because
> Mercator mapping used in plotting charts is conformal, i.e. it preserves
> angles.
>
>
> Peter Hakel
>
>
> ________________________________
> From: John Karl 
> To: NavList 
> Sent: Fri, November 13, 2009 12:33:27 PM
> Subject: [NavList 10635] Re: AP terminology, WAS: 2-Body Fix -- take three
>
>
> No one has addressed my question of why the St Hilaire method
> calculates an altitude at a location our ship is NOT at, when we've
> just measured the altitude where our ship IS at.  (For politically
> correct reasons, I'm not using the name of this location.)
>
> Now lets go back to Sumner's 1837 calculation, where he picked three
> different longitudes and calculated three points on the circular LOP.
> This calculation is exact, and the equation for each point is the same
> as the one of the two necessary in the St Hilaire method (thus each
> Sumner point is half the work of a St Hilaire reduction).  And he
> could calculate as many exact points as he wished.
>
> So I'll put my question yet another way:  Why is the St Hilaire method
> superior to Sumner's and consequently the only one used today??
>
> I claim that the answer to this question has been made confusing
> because of the conventional name (names?) used for the location of the
> St Hilaire altitude calculation.  As evidence of this confusion I note
> that some authors write that we need to assume some point because the
> distance between the GP and the LOP is too great to plot, that there's
> insufficient information to plot the LOP, or that iterations are
> required to get exact points on the LOP.  The Sumner calculation
> demonstrates that none of this is correct.
>
> JK
>
>
>
>
>  >
>

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