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    Re: Latitude of prime vertical sight
    From: Paul Lee
    Date: 2007 Aug 12, 15:22 -0700

    Thanks for your interesting replies, they have helped a lot. From
    what's been said, it
    doesn't look a prime vertical sight can give a lat and long value for
    a certain time, which
    is a shame. However, can it give values with a certain error margin?
    On 1 Aug, 18:08, Gary LaPook  wrote:
    > 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 geo...@huxtable.u-net.com
    > >or at +44 1865 820222 (from UK, 01865 820222)
    > >or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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