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Re: Timed Noon sights for position
From: Joel Jacobs
Date: 2004 Jan 23, 08:55 -0500
From: Joel Jacobs
Date: 2004 Jan 23, 08:55 -0500
George, I will be out much of our morning, but before leaving, I want to compliment you on a thorough and well crafted article on Noon Sight Navigation. Nothing was left unsaid. Joel Jacobs ----- Original Message ----- From: "George Huxtable"To: Sent: Friday, January 23, 2004 8:34 AM Subject: Re: Timed Noon sights for position > Fred Hebard recommended Bob Young to visit my earlier posting on the > accuracy of trying to measure longitude from an around-noon Sun > observertion. > > That actually comprised two postings in the thread " Lat. and Lon at LAN" > on 8th Jan 2004, the second correcting a big numerical error that Fred had > uncovered in the first. Sorry about that. > > Because of that error, perhaps it's best if I post an amended (and somewhat > expanded) version of that earlier message. Note that it reflects the > discussion that had taken place up to that date, 8th Jan, and not more > recent postings, which I have been reading but not analysing closely. > > TIMED NOON SIGHTS FOR POSITION. > > There are two problems in determining the longitude.. > > 1. Accuracy in determining the time of maximum altitude. > > Doug said, in a posting sent on on 7 Jan via Dick Savage- > >If the sight taker timed the noon sight within a few secounds of LAN(the > >Sun appears to >hang for 20-30 sec at LAN but still moves in that time > >frame to greater than 180* or less >than 360*)the sight taker has the > >vessel's longitude. > > But the Sun doesn't simply "hang for 20-30 seconds", it hangs near its > unchanging maximum altitude for MUCH longer than that. Take, as an example. > a winter-solstice Sun observation from my own latitude of 51deg North. > Local Apparent Noon (LAN) is at 11h 57m 53sec GMT, when the Sun altitude is > at 15deg 33.7'. The Sun doesn't drop by 0.5' from that value until it is 5 > minutes (in time) away from LAN, before or after. > > How little a change of altitude can Doug reliably detect before he can say, > with confidence, that it's past the maximum and has started to descend > again? Perhaps, as an experienced observer, he might claim to detect that > 0.5' change, but it would require a > crystal-sharp horizon to do so, I suspect. Perhaps he can do even better, > but it takes about two minutes before or after LAN for the Sun to drop by a > mere 0.1', and nobody is going to claim to improve on that. > > So there's no way for an observer to time the noon sight within a few > seconds, as Doug claims. If the time of LAN could be determined within 5 > minutes, then it would establish longitude within about 75 arc-minutes. Not > a great result. In the unlikely event of a timing precision to 2 minutes, a > longitude determination to 30 arc-minutes would result. > > An observer can do much better by timing an altitude sometime before noon, > and timing the same altitude after noon, and splitting the difference > between those times. This is the age-old method of determining LAN by > equal-altitudes. And the more widespread that these two times depart from > Noon, the more accurate such a measurement will be. At noon itself is the > very worst moment to try to determine when LAN occurs. If the Sun appears > only at the moment of noon, and no other, it would be best to rely on > whatever DR information exists, rather than fool yourself by presuming you > can determine longitude at noon. > > 2. Time difference between moment of maximum altitude and LAN on a moving ship. > > This second problem affects Doug's big-ships more than it does the small > vessels that most of us sail. I don't know the speed of Doug's ships, but > let's choose 20 knots as a round number. Let's say that he is steaming > South at 20 knots, toward the Sun, from 51deg N, at the exact LAN of 11 h > 57m 53s GMT. A stationary observer with a sextant, on a raft that he > passes, will indeed see the Sun "hanging" with a constant maximum altitude > at that time. On his bridge, however, Doug WON'T see the Sun's altitude as > stationary, he will see it as increasing at 20' per hour, because he is > steaming toward the Sun at 20 knots, or 20' per hour. To him, the Sun won't > appear to "hang" in the sky until somewhat later, when it's real altitude > (to the man in the raft) is falling by 20' per hour, but on Doug's vessel, > just matches the rise that's caused by his own speed. > > So his LAN will appear to be too late, because what he takes for local > apparent noon isn't LAN at all, it's just the moment of maximum altitude. > > How big will that error be? Charles H Cotter (in A History of Nautical > Astronomy) deals with the matter on pages 264 to 266, but gets very > confused. > > The moment of maximum altitude will be delayed on LAN by 15.3 (tan lat - > tan dec) * v seconds of time, where v is the Southerly component of the > speed in knots, and lat and dec are positive if North, negative if South. > If lat = +51deg and dec = -23.5deg, this works out at 511 sec, or all of > 8.5 minutes late. Unless allowed for, this will give rise to an error (not > an uncertainty this time, but an actual error) of 128' in the longitude! > > Note that the moment of maximum altitude is delayed after LAN, if the > vessel has a Southward component of speed, and the Sun is to her South, as > in the case referred to above. If sailing toward the Sun when the Sun is to > her North, the delay is the same way. If the Sun has a direction that's aft > of her beam, so her course is to some extent away from the Sun, then the > maximum altitude is correspondingly before LAN. > > ================= > Effect of Sun declination changing. > > Even in the case of the man in the raft (whose latitude isn't changing), he > will see a displacement between the times of max. altitude and LAN of the > Sun, even though he has no motion toward or away from it, because the Sun > can have a North-South motion toward or away from him. Not at a solstice > (which is why I chose that example) but at the equinoxes, when the Sun's > declination is changing fastest. At the Spring equinox, the Sun is moving > toward him at about 1 arc-minute per hour, so that can be thought of quite > simply as the Sun having a Northerly speed of 1 knot. Even for the > stationary observer on the raft, then, there can be a time-difference > between the maximum altitude of the Sun and the true LAN, which unless > corrected will give rise to an error in longitude of 6 arc-minutes. > > This correction, for the time-difference due to changing declination of the > Sun, is referred to as the Equation of Equal Amplitudes, and can be found > under this heading in older editions of Norie or Raper. It was important > for accurate determination of longitudes of harbours from on-land > observations. > > It's one of the factors that makes meridian altitudes of the Moon so > complicated, because its declination can change over 35 x faster than the > Sun's. > > Except at the solstices, that North-South motion of the Sun needs to be > taken into account, even for the observer on a moving vessel, and added to > his own speed.. > > ============ > > For slow-moving vessels, determining LATITUDE by a Sun meridian altitude > won't be badly affected by measuring max-altitude at the wrong moment in > time, away from LAN by (say) a couple of minutes, because altitude hovers > so steady for so long. But for faster vessels (20 knots North or South > affecting the timing by over 8 minutes) the resulting errors in latitude > can become rather significant. Correction methods exist (e.g. Raper, 1864, > par. 798-800). Or a mariner can ignore the maximum altitude reading (and > its time) and instead measure the altitude at the true moment of LAN, > predicted from his chronometer and the equation of time: but to do that his > longitude needs to be known, at least approximately. Did Doug Royer depend > on such a prediction for choosing the appropriate time to measure his Sun > altitude, I wonder? > > But that was just for latitude. Determining LONGITUDE from a noon sight is, > as we have seen above, fraught with very serious error. > > There's little hope of using such a technique to make an improvement on a > previous DR longitude, unless that DR was very dodgy indeed. So I think > it's dangerous to encourage novice navigators to presume that they can > deduce a longitude from their LAN, when that just ain't so; not with any > accuracy that's worthwhile. > > George. > > > ================================================================ > contact George Huxtable by email at george@huxtable.u-net.com, by phone at > 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy > Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. > ================================================================