Next message: Peter Fogg: "FW: Latitude and Longitude by "Noon Sun""
And as long as you are looking for maximum precision don't forget the
second differences corections in HO 229.
Gary LaPook
George Huxtable wrote:
>Lu Abel wrote-
>
>
>
>>I don't know how many on this list have actually taken a noon sight. I
>>have.
>>
>>
>
>But from on-land, it seems, when he says later "I also freely confess this
>sight was taken on dry land, so I wasn't dealing with trying to bring down
>the sun on a heaving ship's deck."
>
>It's quite a lot harder, and less accurate, when you observe a Sun altitude
>in real-life, at sea, above a real sea-horizon. Is an observation from
>on-land considered adequate by the US Power Squadron?
>
>
>
>>A noon sight is part of the requirements for US Power Squadron's
>>Navigation course (advanced celestial nav) which I have taken. I found
>>(at ~40N Lat, sight taken during the early summer) that not only did I
>>get a spot-on latitude value, but by graphing a series of sights over
>>about 10 minutes (5 min on either side of LAN) I got quite an excellent
>>value for longitude.
>>
>>
>
>I would expect a "spot-on" latitude value, just as Lu claims. But notice,
>he doesn't quote any actual figures for his "quite an excellent value" for
>longitude. I hope he will dig out his observation log and give us some real
>numbers.
>
>I have recalculated what Lu's observations should have been, taking an
>observer at 40 deg North, 0 deg West, and as an example of "early Summer",
>today's date of 4 June 05. The following altitudes include no correction
>for refraction, dip, semidiameter.
>
>Noon-by-the Sun occurred at 11h 58m 18s, when Sun alt. was at its maximum
>of 72deg 28.6'
>
>5 minutes earlier, and also 5 minutes later, the Sun alt was 1.9' less, at
>72deg 26.7'
>
>At those two times, 10 minutes apart, for which Lu will have to split the
>difference to find his moment-of-noon, the Sun is first rising, then
>falling, at 0.75 arc-minutes for each minute of time.
>
>How accurate are Lu's altitudes going to be, if measured in real-life at
>sea? I wonder if any one of us can put his hand on his heart and claim to
>be able to measure the altitude of a real Sun above a real horizon AT SEA
>within a scatter of, say, ±1 arc-minute. Here, I am referring to the
>small-craft situation; I accept that on a big-ship, in millpond conditions,
>somewhat less scatter than that might perhaps be achievable.
>
>If the altitude is changing at only 0.75 arc-minutes, each minute of time,
>at the extremes of Lu's time-range, and with a presumed scatter of ± 1
>minute in each observation, I really can't see how, with the most careful
>graph-plotting over those 10 minutes, a navigator will find the
>centre-of-symmetry of the resulting curve to better than, say ±1 minute of
>time. Not a very precise result then, when he might expect his chronometer
>to be good to a second. A scatter of ±1 minute of time corresponds to a
>longitude error of ±15'.
>
>Those error estimates seem fair to me, but I would be happy to argue the
>matter out if anyone thinks otherwise.
>
>Compare that with a time-sight measurement made several hours away from
>noon. If the Sun is on a path to pass overhead, then its altitude will
>change by 15 arc-minutes for every minute of time. From higher latitudes,
>the rate of rise will be less, but a properly chosen moment for a
>time-sight will normally involve the altitude changing by at least 7.5
>arc-minutes per time-minute (except in arctic latitudes). This is ten times
>faster than the rate-of-change that Lu observed, so given the same accuracy
>in observing altitude, the scatter in deduced time will be reduced by a
>factor of 10, to be 6 seconds of time. And that would correspond to a
>longitude error of 1.5 miles, not 15 miles: a substantial improvement,
>obtained by using the traditional time-sight technique.
>
>So if Lu really did get his unspecified "quite excellent value for
>longitude", I wonder if it was perhaps obtained by some sort of fluke.
>
>I don't deny that a noon Sun longitude can be made to work, to some extent.
>One distinct improvement would be to extend the period of observation, to
>be significantly longer than the 10 minutes around noon that Lu allowed
>himself. But if the time interval between the rising Sun and the falling
>Sun becomes great enough, the question then arises: can you call it a "noon
>observation" any more?
>
>Of course, from a moving ship, with any Northing or Southing in her course,
>there's another factor to consider, that didn't come into Lu's on-land
>observations. That motion gives rise to a displacement in time between the
>moment of maximum altitude (which is what's observed) and the moment of the
>Sun's meridian passage (which is what's needed). It isn't hard to correct
>for, but that correction should not be neglected. There's an additional,
>smaller, correction to make to allow for the Sun's changing declination,
>being greatest near the equinoxes, but that's usually small enough to
>neglect.
>
>George.
>
>================================================================
>contact George Huxtable by email at , by phone at
>01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
>Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
>================================================================
>
>
>
>
