# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: AP terminology, WAS: 2-Body Fix -- take three**

**From:**Tom Sult

**Date:**2009 Nov 13, 19:57 -0600

Thanks... I think that is what I tried to say a few days ago ; ) Thomas A. Sult, MD IntegraCare Clinic www.icareclinics.com tsult---.com On Nov 13, 2009, at 7:05 PM, douglas.denny{at}btopenworld.com wrote: > > I'll attempt an answer to this question: > > " ....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...." > --------- > > Answer: Because you are not comparing altitudes with the St Hilaire > method but you are comparing zenith distances. > > You -do- know your zenith distance to an astronomical body because > you have just measured it with a sextant, but you do not have enough > information to work out the other parameters you want i.e. lat or > long from that alone. > > What you can do however is imagine you are at position you _do_ know > and work out a zenith distance for that position. Then you can > compare the difference between them because they will be close > together in value. > > If you go back to basics and consider what you DO know and what do > NOT know, and what you have available and not available with the PZX > spherical triangle, it should be clearer,(see diagrams). > > You have: > > The geographical position of the body from the almanac. Hence:- > > 1) co-declination of the body (from Dec in the almanac:-i.e. 90-dec). > and > 2)the GHA of the body. (This not enough to know the local hour > angle in the PZX triangle because you do not know your longitude). > > You also have from your sextant sight the altitude of the body to > your local horizon, which means you have immediately:- > 3) the 'true' zenith distance from yourself to the body. (i.e. the > side ZX of PZX). > > And therein lies the problem. You do not have enough information > about the PZX triangle to solve it. > Consider: > > a)If you knew the longitude accurately you would know what the angle > ZPX is (i.e.the local hour angle) and could work out the latitude > accurately. > > b)If you knew the latitude accurately, you would know the side PZ > accurately - the co-latitude and you could work out the local hour > angle and hence longitude. > > But you do not have either. > > Sumner stumbled on the position line principle by making an > assumption as if he did know the latitude and worked out a > longitude. He did this three times with three different latitudes > and suddenly realised that what he had was a line of position where > the sun could have been along that line found with the three results > at that instant of the time of the sight - it was the line of equal > altitude from the body, and a certain fixed zenith distance from > the body to the position line is implied, it is an equal zenith > distance - a circle surrounding the geographical position of the > body. (see diagram "position line X at pole). > > St Hilare's brilliance is in the realisation that it is not > necessary to know either either lat or long singly with precision to > solve the pzx triangle, as you can work out an accurate zenith > distance if you use an _assumed position_ (this is the correct use > of this term here) which is _near_ where you are, and using an > exact lat and long for that assumed position. > > .... and then compare the accurate (or 'true') zenith distance you > have measured with your sextant with the calculated zenith distance > for the assumed position nearby (which must be similar in value to > your sextant sight value) - and close by as the assumed position is > close by. And hence find the difference. > > That difference (the intercept) is easily marked off on the chart > from the assumed position. You then have a position line along where > you must lie. (neglecting errors). > > In other words you are supplying yourself with the (accurate) > necessary information of latitude and longitude to work out the PZX > triangle that you cannot work out normally with insufficiently > accurate informaation, then using a comparison method with your > sextant (measured) information you do have in terms of zenith > distance. > > That in a nutshell is the Mark St Hilaire's (or intercept) method. > > Douglas Denny. > Chichester. England. > > > ===================== > Original Posting:- > > 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 > > > > > --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavList+unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---