# NavList:

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

**St. Hilaire -- My Take**

**From:**John Karl

**Date:**2009 Nov 15, 19:08 -0800

Here's my answers to several questions from the recent 2-body post. I'm starting a new post since these are unrelated to the 2-body question (although they've been somewhat addressed in much early posts). A. DIRECT CALCULATION: By direct calculation I mean computing the Lats and Lons of points on the celestial LOP from some an equation, or equations. These points trace out the LOP in Lats & Lons, just as one would make an x-y plot of Sin A versus the angle A, by evaluating Sin A and plotting the result versus A. For a CN example, we can find LHA from the single equation Cos LHA = (Sin Ho - Sin Lat Sin dec)/ Cos Lat Cos dec, getting the longitude of a LOP point that has latitude Lat (from Lon = LHA - GHA). This is an example of a direct calculation of the Lats & Lons of the LOP's coordinates. Also tables could be easily constructed to give the LHA in terms of entries of Dec, Lat, and Ho. (The navigator then takes LHA - GHA to get longitude.) B. PLOTTING VARIABLES: I think (not sure) that the discussion on the List about parameters is what I would call plotting variables. In the above, the plotting variable is the latitude. Sumner used the longitude as a plotting variable to plot three points on his LOP. Another plotting variable is the true bearing from the GP to the LOP point (that is, the angle at the GP between the coH side and the coDec side of the nav triangle). This is convenient in computer applications. (These bearing-angle equations are discussed in Exercise 1.22 in my book.) In high altitude sights using a drafting compass with its point on the GP, its distance equal to the observed coH, and striking an arc on a chart, we are mechanically using the bearing angle as the plotting variable. C. ST. HILAIRE: The St. Hilaire method uses two equations to plot a point on the LOP, the altitude and azimuths equations. The point at the end of the intercept, at the computed azimuth, is exactly on the LOP, just as in the above examples. (In all practical applications the difference between the rhumb line and great-circle distances is negligible. Moreover, the great circle intercept distance is indeed exact, just as the Lats & Lons are from the direct method. So chart projections are irrelevant in this whole discussion.) If desired, many other APs can be used to compute many other points exactly on the LOP. Thus St. Hilaire can be used to trace out the LOP -- exactly. D. ST. HILAIRE & DIRECT: Both methods compute points on the LOP exactly. There are no assumptions, no estimates, no iterations. These computations might be done with calculators, computers, logarithms, Bygrave slide rules, or tabulated results (which are the results of someone else doing the same math). The means of calculating has no bearing on this topic. And forget whole degrees -- they have nothing to do with this discussion. (Also BTW, they are sometimes used in log calculations and calculator applications for convenience, the same reason they're used in tables.) Both methods provide straight line approximations to the circular LOP. In the direct calculation, two points on the LOP are connected with a cord, giving a approximation similar to St. Hilaire's, and in some cases even better. E. ST. HILAIRE vs. DIRECT: At first it seems that St. Hilaire is inferior to direct calculation for two reasons: It requires two trig equations for each LOP point, and it requires plotting because it doesn't give Lats & Lons directly. But St. Hilaire has a trump card: IT'S ROBUST (i.e., it's not fussy, works the same in all cases, has no gotcha's). But the direct calculation isn't robust. For example, in calculating a Lon corresponding to a selected Lat, a nearly east-west LOP can yield a Lon that's too far away. Worse yet, the LOP might not even intersect the parallel of latitude. Likewise, specifying Lons and calculating Lats gives the same problem with nearly north-south LOPs. The essential point is that the St. Hilaire method completely avoids these problems by using a completely different approach to specifying which section of the LOP we wish to plot. It specifies a point by both Lats & Lons to identify our area of interest. It says that we want the section of the LOP that is closest to this point. This point is a reference point, a locator point, usually abbreviated "AP" (doesn't "AP" stand for A locator Point?). There is no assumption, no estimation, only a decision. We need to decide where we want to plot the LOP. We must decide this before plotting any celestial LOP by any method (unless we wish to plot the whole circle). Once we have the point on the LOP closest to our area of interest, a straight line drawn perpendicular to the azimuth to the GP gives an approximation suitable for all but very high altitude cases. This is similar to the direct-calculation straight-line approximation. F. TERMINOLOGY: Some list members have pointed out that our terminology may depend on our background: how, where, and when we learned celestial. Yes, this is true of many words, but from what I've read by members, we have pretty good agreement on DR and EP. However, I was surprised to see a member write that the term "LOP" means a straight line. Not in my book. There are many LOPs that are not straight: a range LOP from a lighthouse's height, the double horizontal-angles LOP from two objects, a LORAN LOP, and a bathometric contour, just to name a few. An LOP is simply any line of position, no matter what shape. As some member's know by now, "AP" is nomenclature that really irks me, for two reasons: First we don't assume anything when we pick an AP, we just decide where we want to plot a section of the LOP. We select it -- we don't assume anything. It's like deciding to plot Sin A between 45 and 63 degrees. We're deciding, not assuming. The 2002 edition of Bowditch also lists CHOSEN POSITION for the term, which matches well with what I'm saying. Second, if you think this is putting too fine a point on terminology, let me say that every CN book I've seen either doesn't explain why we're using an AP, or if they attempt to explain it, they either have it wrong, or give the wrong implication. I believe the term "assumed position" contributes to this confusion. G. Someone asked where, or how, I learned CN. Well, when I was about 8 or 9-yrs old in Flint MI, I purchased a new 1945 edition of Bowditch since we were all sailors in my family. While it was hard going for me, I think I learned a lot from it, but with no sextant and no horizon, wasn't able to practice sights. Then in 1960, while a physics undergrad at M.I.T., I stumbled upon a sextant in a Chelsea pawn shop. I bought this Hezzanith for $18, went home and pulled Bowditch off the self, and started taking sights looking at the sky and ocean from near my home, then in Marblehead. In those days I used logs from Bowditch, and later, tables from H.O. 211. Many years later, when I was invited to teach CN aboard the S/V Denis Sullivan on a Milwaukee-Montreal leg, I become interested in teaching this stuff. So I wrote a couple of books, a course manual, a PowerPoint presentation, and now teach on land or sea whenever I get the chance. JK --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavList+unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---