# 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:**Frank Reed

**Date:**2009 Nov 13, 14:29 -0800

I wrote previously, "Well, you can do that today. Historically it was prohibitively inefficient in terms of computation cost. But today if I observe Venus 4d 12.5' above the horizon, I can easily calculate every spot on the Earth where this would be the observed altitude." And John you wrote in a later message, "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." Followed later by, "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??" My reply above did address your question, I think, and the answer to your latest version is the same. It's computationally "cheaper" to do it by St Hilaire. This mattered a great deal 25 to 100 years ago and the increase in computational efficiency eventually (very slowly!) made these methods almost the only ones used in the latter half of the 20th century, but that compuational efficiency matters much less today. In fact there are quite a few people who use the Sumner method to plot points today when the calculations are done by computer. Of course, the traditional Sumner approach of picking a couple of points and drawing a straight line through them is still only an approximation. With the astounding amount of computation power available even on tiny devices like cell phones today, it's quite possible to go way beyond the original Sumner approach and calculate everything at every single point on Earth (at some grid spacing, e.g., every 0.1' of lat, lon) and figure out the apparent altitude at every point with all the small details like oblateness handled correctly in a direct calculation. You could even get really crazy with this and include variations in temperature and pressure from weather service data. Then our plots would really be telling us the locations where the observed altitudes would be most closely matched by reality on the globe. Wouldn't that be fun?! Finally, I think all this focus on how to calculate LOPs is fundamentally historical. If I take several sights, the plotted result of my observations should be some sort of error ellipse, or several ellipses with different levels of confidence, taking into account all of the sights statistically. Naturally we can include the LOPs in such a plot (and they provide an important check for gross errors), but the error ellipse should be the primary result. And here we can take a lesson from the software in many GPS receivers. When they display the position as a dot, they usually put a shaded circle around it indicating the degree of accuracy you should expect from the satellite fix. When fewer satellites are available, the error circle is larger. More satellites, smaller circle. Of course there are plenty of software packages available for celestial navigation sights that do exactly this, too. Whether there's any convenient way to accommodate such statistical indicators in paper plots with purely manual calculations is a more open issue. The beginning of any such procedure is to locate the center of the error ellipse from three or more LOPs. There is a long-established algorithm for this. Herbert Prinz demonstrated a proof of a clever "straight-edge and dividers" method for finding that point during the Navigation Weekend in Mystic in 2008 (www.fer3.com/Mystic2008) without doing any trig or using any software. -FER --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavList+unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---