NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Exercise #6, Lunars at sea
From: Frank Reed
Date: 2008 Jun 04, 10:02 -0400
From: Frank Reed
Date: 2008 Jun 04, 10:02 -0400
Jeremy, on averaging a set of lunars, you asked: "What is the traditional means of averaging? Do you average the time and then the LDs and just do one reduction?" Yes, exactly. If you shoot the altitudes, you can usually do them by averaging, too. A good sequence is: body altitude, Moon altitude, four lunar distances, Moon altitude, body altitude. When you average the bracketing altitudes, you often find that their average time falls very close to the average time of the observed lunar distances. If they're not quite right, it's very easy to adjust them a little to bring them to the correct time. If you don't shoot the altitudes (which is the way almost everyone uses my online clearing tool), you just average the times, average the LDs, and clear them as if it's a single sight. With a set of four, this typically doubles the accuracy. The rule is that random error is reduced in proportion to the square root of the number of sights. So you cut the error in half with four sights. To cut it in half again, you need a total of 16 sights (this applies to random observational error, not systematic error). And regarding getting an LOP from a lunar you wrote: "I would like to try this, but am not sure how you do it." It's remarkably easy (again we're assuming GMT is known here, as it always is for a modern navigator). Try this: take that set of Moon-Jupiter lunars you posted. Go ahead and average the times and the distances. Now go to my online calculator and try different DR points scattered about your known position. You will discover that the "error" in the sight goes to zero along a narrow path. That's your LOP. If you want to be a little more systematic, pick four points around your DR in a square, each offset by one degree in latitude and longitude. Suppose we determine the error in the lunar at each corner of the square. For some example numbers, suppose the error at the northwest corner is 0.5', at the northeast 1.0', at the southwest, -1.0', at the southeast -0.5'. I'm sure you can see that there must be a line across the middle of this square where the error is zero. It should run across the square from a point approximately one-third of the way down the west side to a point apprximately two-thirds of the way down the east side ("down" here is north biased). Anywhere along that line, our lunar observation would be 'true', so that's the line of position. And again, if the horizon is lost in thick haze, you can often still see the Moon clearly. If you take two lunars separated by a few hours, you can cross those "lunar LOPs" and get a fix. This is a rough fix. An error of 0.1 minutes of arc in the LD yields a 6 n.m. error in the LOP. If you have a bubble sextant (which also requires no visible horizon) you could get this sort of accuracy without even trying very hard. Then again, I could just turn on the GPS and be done with it. :-) -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---