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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.
> ================================================================

   

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