# NavList:

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

**Poor St. Hilaire**

**From:**John Karl

**Date:**2007 Oct 15, 08:29 -0700

To all criminals against GPS, Have you noticed Poor St Hilaire? It seems that he is misunderstood by most CN navigators, even the authors of CN books. Of the more than 20 authors I've read, I think none has it correct. Now recent postings on the List have reminded me of the St. Hilaire discussion in my recent book, "Celestial Navigation in the GPS Age." It goes back to Capt. Marcq himself. In my English translation of his 1873 publication, he refers to the "estimated position" when explaining his intercept method. This unfortunate terminology has guided many CN students to a Sea of Mystery engulfing the DR position and the confusing concept of "assumed position". The confusion even dates back to Sumner. I'm sure most List members are familiar with his 1837 calculation of a points on the ship's LOP by calculating its longitudes from its stipulated latitudes. Sumner called these "assumed" latitudes. At first he thought he was using unreliable latitudes. But after plotting three such "trial" positions, he had an epiphanic realization that his calculations actually gave exact locations of points on his celestial LOP. Two such calculations give two exact points on the LOP. The straight line connecting these two points has an error between the points that depends on several factors, such as the LOP's curvature and the chart's projection. Hilaire's intercept method invites further confusion. First, we observe that the altitude observation and the knowledge of the body's GP completely determines the celestial LOP. Therefore no sight reduction method uses estimations or assumptions. Again, it's the terminology that screws up the concepts. There are several ways to determine the exact LOP by directly computing and plotting latitudes and longitudes of as many points as we wish (Sumner's being one such method). But St. Hilaire is different -- it doesn't compute Lats and Lons at all. Rather, it specifies a point's latitude and longitude which I'll call the reference point, RP, even though conventionally it's called the "assumed" position -- a misnomer. St. Hilaire calculates the great- circle distance and azimuth from this RP to the nearest point on the LOP. This point is exactly on the LOP; let's call it the St. Hilaire point (SHP). Both the great-circle distance and the azimuth to the SHP are exact. No errors. Even if we use inspection tables (such as HO 214, 249, or 229) with their whole-degree limitation, the SHP is located exactly on the LOP within the table's accuracy. (HO 229 states a max altitude error of 0.3'; and for altitudes less than 86 degrees, the max azimuth error is 0.2'.) If we use a $12 calculator we get 10-digit accuracy. However, unlike the Sumner method that calculates Lats and Lons directly, the St Hilaire method produces errors when the LOP is plotted. On a gnomonic chart the intercept distance is correct, but the azimuth is in error. On a Mercator chart it's the reverse. This statement is true no matter what RP is used, using whole degrees of latitude and LHA with inspection tables, or not. In common practice at sea, we use a Mercator projection where the intercept's azimuth is correct and its intercept distance has negligible error when approximated by a rhumb line (error less than 0.3 nm for a 300 nm intercept, unless in polar latitudes). Therefore, in practical terms, several SHPs can be calculated with inspection tables (or other means), tracing out the LOP exactly. This method uses no iterations, no estimations, and no assumptions. However as List members know, these multiple SHPs are seldom calculated because drawing a straight line through the SHP perpendicular to the azimuth is usually an acceptable approximation to the curved LOP at altitudes below about 75 degrees. If the LOP's curvature deviates unacceptably from the straight-line approximation, another (or even a different) calculation can be made. But in any case, with an 75 degree observed altitude, a point along the straight- line LOP 40 nm from the SHP is offset from the true curved LOP by 0.9 nm. So at lower altitudes, the whole-degree limitation of inspection tables would never contribute significant error. My book also discusses why the St. Hilaire method is superior to other methods even though (1) it requires exactly the same amount of calculation as other methods, (2) it doesn't give latitudes & longitudes directly, (3) it has plotting inconveniences, and (4) it's only approximate. I'm new to the NavList; so I apologize if members find this all verbose, irrelevant, or old hat. John Karl --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---