# NavList:

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

**Re: It works - within limits.**

**From:**Arthur Pearson

**Date:**2002 Apr 11, 21:41 -0400

Gentlemen, This has been a great thread but I must make a request for some remedial education. I am generally familiar with St. Hilaire technique as the method by which I calculate an intercept and azimuth from by assumed position and use them to plot an LOP from a sight. I get the feeling from this thread that the formulas for a calculated fix solution given in the back of the Nautical Almanac are an extension of this methodology, but I am unsure where St. Hilaire begins and ends, and whether least squares was part of his contribution. Could someone make a short statement of the essence of his technique for the uninitiated? Also, Herbert states below that "When starting from a wildly wrong DR position, St. Hilaire will get you the right fix, albeit only after 2 or 3 iterations. That's not surprising, because direct methods will not even need a DR." What are the "direct methods". Apologies to those of you for whom this is old hat, my introduction to celestial was less theoretical than the discussion here so I am playing catch baseball (or cricket?). Thanks, Arthur -----Original Message----- From: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM] On Behalf Of Herbert Prinz Sent: Thursday, April 11, 2002 9:18 PM To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM Subject: It works - within limits. To find GMT and our position simultaneously we need the observation of the altitude of any two celestial bodies, the distance of the Moon from any suitable body, and the time intervals between these three observations. The simplest case from a mathematical point of view is to measure the altitudes of the Moon and second body themselves (because they are needed anyway for clearing the distance), and to measure all three quantities at exactly the same moment. One can cheat a little on the latter by bracketing the distance observation with the altitude observations and subsequent averaging. While it's true that the required altitudes can be computed, we also know that there is no free lunch. To use computed altitudes merely means that we have already observed some (other) altitudes at an earlier stage (for the purpose of finding time and latitude). The solution by this method is, therefore, a running fix. Consider the case where double altitudes of the Sun, or some such method is used during the day to establish local time and latitude. If a vessel sailing from New York towards the Azores in and out of the meanders of the Gulf Stream observes Sun altitudes around 10:00 and 14:00 to establish local time and then takes a lunar around 20:00, the dead reckoning of longitude made good between the former and the later observations can easily be off by 10 nm, and hence its local time be off by 40s. So the error in computed Moon altitude could be up to 10' of arc, hence the error of computed parallax up to 10" of arc, which in turn could translate to an error of as much as 20s in GMT or 5nm in longitude for the final fix. This is not much in the scheme of things. Most navigators were and will be happy to get GMT within a minute. I am only emphasizing that this is an additional error that does not appear if altitudes for clearing the distance are measured directly and that cannot possibly be detected or eliminated by any mathematical tricks. Bruce Stark soft-pedals the impact of DR error on the accuracy of the final fix in his message "It works", of April, 2. The reason why it works for Bruce even "when both GMT and longitude are wildly uncertain" is that in his example, he does not depend on measuring local time at all; he computes it from accurate data and only THEN shifts assumed GMT and assumed longitude in sync with each other, so as to not upset their relation (defining local time). Naturally, after 2 iterations, one gets the correct GMT and longitude from the lunar distance. But this is tautological. In the real world, however, local time is only as good as your dead reckoning since the time you established it. The "wildly uncertain" DR does, indeed, not matter up to the moment where we start with the first observation for time. But any subsequent error in dead reckoning will have its inevitable effect on the resulting fix for GMT from the final lunar observation. Of course, there is nothing special about lunars here. This is a general problem with the running fix. Take the standard timed altitude observation of two stars as an example. When starting from a wildly wrong DR position, St. Hilaire will get you the right fix, albeit only after 2 or 3 iterations. That's not surprising, because direct methods will not even need a DR. The same is true for a running fix, if and only if you are absolutely sure about your dead reckoning between observations. But if you screw up on the DR (e.g. by getting into a current) no method will tell you. All of them will result in the same wrong fix. There is another, minor problem with computed altitudes. I am not sure whether this has been mentioned already. They rely on an unverified assumption about there being ideal atmospheric conditions in the direction of the Moon and second object. But if there are unusual circumstances, the effect can result in up to 12s error in GMT for every 0.1' deviation from standard refraction. If one measures the altitudes, this error is automatically eliminated, at the cost of only the corresponding negligible positional error. Using computed altitudes is thus inherently less safe than measuring them. All numbers I gave are worst case scenarios that I could THINK of. I never lost time at sea and never had to depend on a lunar distance. So, I really don't know what I am talking about. All I have ever done were isolated experiments of various kinds. Herbert Prinz