# NavList:

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

**Re: Latitude of prime vertical sight**

**From:**Gary LaPook

**Date:**2007 Aug 01, 10:08 -0700

Gary writes: Remember, "the sun rises in the east" that you learned as a child. Of course we then learn that it doesn't rise exactly due east but sometimes north and sometimes to the south depending on the season. At 44� of latitude the azimuth at sunrise varies from 56� to 124� which is never more than 34� from due east. At lower latitudes the azimuth changes even less, at the equator its maximum difference form due east is only 23.5�, the maximum declination of the sun. So advancing an LOP derived from a sunrise observation would provide a maximum angle of cut of about 30� or less which we know will at least double the possible error in the latitude determined. Figure in the error due to variable refraction of a low altitude sight and you end up with what would only be a very approximate latitude. George Huxtable wrote: >Paul Lee asked- > >| Hi everyone, >| I'm new to navigation, and am doing some work on the usage of prime >| vertical sights. I know it gives longitude, but if you knew the time >| of sunrise, is it possible to obtain a value for lattitude too? > >Later, he added- > >"The local sunrise had been determined in retrospect by an astronomical >program. >The prime vertical sight would be taken about this time." > >=================== > >Reply from George. > >No, it's not possible. > >The comments about unpredictable low-level refraction, though true in >themselves, are missing the point. (True, I might add, except for Bill's >lower limit of 30 degrees, which would exclude half the sky, and most >observations. Lower limits of 5 or 10 degrees are more appropriate, >depending on the level of precision that's sought) > >You are only making one measurement, presumably an altitude of the Sun, at a >moment when you have calculated (not observed), that it will be exactly to >your East. You are not observing the time of local sunrise, simply taking it >from some program, which will have asked for both latitude and longitude >before predicting that time. Your longitude could have been derived from the >prime vertical observation, but how did you provide the latitude, to feed >into the program? If you have had to tell it the latitude, you can't then >expect a prediction that it provides to tell you the latitude. > >As a a general rule, if you have two quantities to find (such as latitude >and longitude) you have to make two independent observations to do so. >Calculating the time of sunrise, from a program, is not observing it. IF you >could allow precisely for the low-level refraction (which you can't, because >it's so variable), you could TIME the moment when (say) the Sun just peeped >over the horizon, and then due to refraction, its centre would be at an >altitude of about 50' below the true horizon. If you timed that moment, it >would be just like measuring a sextant altitude at a particular moment, and >from it, and an almanac for the Sun, you could derive a position line at >that moment. Then you could cross that with a North-South position line from >the prime vertical observation, and where these lines meet is where you are, >in lat and long. > >But beware; even that would not work well in the circumstances you describe, >when you say "The prime vertical sight would be taken about this time." >Unless the Sun's azimuth has had plenty of time to change, between sunrise >and your prime vertical observation, then the two resulting position lines >would not have a decent angle between them, and latitude of the crossing >would be found very imprecisely. That would exclude such a procedure at >dates anywhere near the equinox. Of course, prime vertical observations of >the Sun are themselves impossible throughout the Winter half of the year. > >If both the azimuth and the altitude of the Sun (or any other body) could be >precisely measured at sea, at the same instant, they would comprise the two >independent observations that are called for, to determine latitude and >longitude, in one go. That's true at the moment of prime vertical, or any >other moment. So if you could observe (not predict) that the Sun really was >exactly on the prime meridian, to your East, and simultaneously measure its >altitude, you could get both latitude and longitude. That's possible for a >surveyor on land, with a firmly-planted theodolite, knowing his direction of >due North, but not for a mariner at sea, who has only his compass. > >I am puzzled, though, why Paul is interested in prime vertical observations. >Is it for historical studies? When the Sumner method came in, improved by St >Hilaire in the mid 19th century, a position line could be determined from an >observation of any body at any time. Two such observations provide two >position lines. Where they cross is where you are. Simple as that. It's a >method which applies everywhere, at all times. Then, such special-cases as >prime-vertical became irrelevant, though noon sights lingered on, because of >their arithmetic simplicity. > >Prime vertical observations are no more than a special case of a Sumner >line, providing a North-South position line (longitude), which has to be >crossed with a different observation (often, near noon) to provide a >position in lat and long. > >George. > >contact George Huxtable at george---.u-net.com >or at +44 1865 820222 (from UK, 01865 820222) >or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. > > > >> > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---