NavList:

   

Reply

George Huxtable wrote � I don't see what Sun's apparent time has to do with 
the matter, or MT, or longitude. The aim of a lunar is to establish GMT, to 
set a local clock
right; nothing more than that. Steven's web page of lunar predictions is 
marked as being for UT (= GMT), unlike the early almanacs, which until 1834
were based on Greenwich Apparent Time. Kent's predictions must also be for 
GMT, so I suggest he is bringing in complications that don't exist...�



I don�t know if I complicate things or not, that was certainly not my 
intention. My own view is that finding the GMT is of course interesting, 
whatever means are used, but even more interesting is it to be able to find 
own ship�s position in Lat. and Long. Finding a ship�s position at any time 
is indeed the very objective for navigation. It was therefore I commented 
not only the GMT but also the corresponding position in longitude (only) by 
using the apparent time of the sun etc. My predictions of GMT incl. The 
correction for 2.nd differencies are based on GMT while my predictions of MT 
are based on sideral time converted to MT.



Georg Huxtable wrote� I've had a go at working that lunar in my own way; 
which means that I like to get out of those damned sexagesimals and into 
decimals, so I can use my calculator properly. I will spell it all out in 
more detail than if I were just calculating for myself.�



I would like to comment this and also Geroge�s calculations. Firstly I hope 
we agree that it is the mean time for the LD observation that has to be used 
as reference for calculating altitudes of (in this case) the moon and the 
sun. The mean time for LD observation was 06-22-59 (type of time still not 
completely clear to me). If I then refer the moon�s and the suns� altitude 
to this time I get the following:



Moon:

2.nd obs.       06-26-28               61d 49,2m

1.st obs.        06-20-13               60d 36,8m

Difference      00-06-15 (375 s)   1d 12,4m (72,4m)

Elapsed time 1.st obs to mean LD= 2m 46s=166s

Moon�s altitude 60d 36,8m+72,4*166/375=61d 08m 24s (George 61d 05m 16s)

My data stated before was 61d 19m 18s. Wrongly calculated by me. Sorry for 
any inconveniance caused.

Sun:

2.nd obs.       06-25-19               32d 35,8

1.st obs         06-19-13               33d 58,5

Difference      00-06-06 (366 s)   -1d 22,7 (82,7m)

Elapsed time 1.st obs to mean LD=3m 46s=226s

Sun�s altitude 33d 58,3m+82,7*226/366=33d 7m 24s (George same)



Furhermore some comments and comparisons to George�s data:

Moon:

Dip -10m 11s (George -0,1667 =10m)

Refr -29,5m (George -0,083=4m 58,8s)

It is not clear to me how George�s refraction has been calculated.

SD -15m 25s (George -(0,2606-0,0035)=15m 25,6s)

Augmentation   -13,34s (George � 0,0035= -12,6s) 
A

Corr for refr. Edge-centre -0,34s (George none)

Parallax +27m 30s (George +0,4622=27m 36,7s)

I wonder if George�s calculation of the moon�s parallax considers earth 
flattening. I do not follow the correction of -0,002 =-7,2s, however with 
this included we reach the same parallax.

Altitude 61d 10m 11,6s (George 61 06m 51,5s)

For the sun it seems that we have reached the same altitude, anyway I don�t 
understand George�s data on refraction (seems to be the same as for the 
moon). My refraction for the sun is -1m 21,02s.



Calculated d= 86d 41m 28,1s. Nearest edges used. (George 86,1698 =86d 10m 
11,3s)



Calculated D=86d 15m 00,3s (George 85,7384 =85d 44m 18,2s)



GMT 07-26-52,9 (George 06-24-53). This difference depends of course on how 
the LD�s were measured. However the method for measurement by �overlapping� 
edges does not convince me. It seems to be a construction afterwards.



2nd diff 00-00-5,6s (George none)



Corrected GMT 07-26-47,3

Kent N
----- Original Message ----- 
From: "George Huxtable" 
To: 
Sent: Friday, June 20, 2008 12:30 PM
Subject: [NavList 5530] Re: Lunar trouble, need help



Since my last Navlist posting, I've had a short spell in hospital, and my
pocket calculator came with me. Now I'm back out again, I can report back on
some findings, to show my time there wasn't entirely wasted.

Jeremy wrote, in 5413-

"Here is my data around 0620 on 10 June 2008.

1) Sun LL: Hs 33deg 58.5� @ 06h 19m 13s UTC
2) Moon UL:  60deg 36.8� @ 06h 20m 44s
3) LD1: 86deg 10.3� @ 06h 21m 40s
4) LD2: 86deg 10.0� @06h 22m 20s
5) LD3: 86deg 10.2� @06h 22m 52s
6) LD4: 86deg 10.6� @06h 23m 24s
7) LD5: 86deg 10.6� @06h 24m 39s
8) Sun LL: 32deg 35.8� @ 06h 25m 19s
9) Moon UL: 61deg 49.2� @ 06h 26m 28s

DR (didn�t take a fix) Latitude was 15deg 14.0�N and Longitude was
144-04�E.  Ship was on course 270 at 12.0 knots.  IE was 0.0 T/P was
98deg F and 1010MB.  Height of eye is 106 feet.

I averaged the two sun lines to get 33deg 17.2� at 06h 22m 15s, then
the two moon altitudes to get 61deg 13.0� at 06h 23m 37s.  Finally the
5 LD�s averaged to 86deg 10.34� at 06h 22m 59s."

=======================
Those numbers didn't "add up", and Frank surmised (correctly, in my view)
that overlapping, rather than the usual side-by-side, views of the Moon and
Sun limbs had been taken.

I've had a go at working that lunar in my own way; which means that I like
to get out of those damned sexagesimals and into decimals, so I can use my
calculator properly. I will spell it all out in more detail than if I were
just calculating for myself.

I agree with Jeremy and with Kent that the mean lunar distance is 86.1717�
at a mean time of 6.3831hrs (give or take 2 or 3 arc-seconds, which between
friends are not worth arguing about).

That needs correcting for the two semidiameters, in this (odd) case by
adding the Moon's semidiameter, of 0.2606� (which includes "augmentation" of
0.0035�), and (unusually) subtracting the Sun's, of 0.2625�.

so observed lunar distance between centres = 86.1698�   (this is d)

Then we have to take a weighted-mean of the two Sun observations so that
it's the same as if it had been taken at that same moment, which gives-
Sun LL altitude at 6.3831 h = 33.1231�, which agrees pretty well with Kent's
figure.
Similarly,
Moon UL altitude at 6.3831 h = 61.0879�, which disagrees a bit with Kent.

Now for some corrections for the Moon
61.0879 UL observed sextant alt Moon
 -.1667 dip
--------
60.9212 alt. above true horizon
 -.0083 refraction
-------
60.9129
 -.2606 less semidiameter Moon from UL obs.
-------
60.6523 alt Moon centre
 +.4622 parallax (=HP cos alt), where Moon HP = .9433�
-.0002 reduction of parallax
-------
61.1143 =M, corrected altitude of Moon centre
60.6606 =m, altitude of Moon centre before correction for parallax and
refraction.
========================
Similarly for the Sun
33.1231 LL observed sextant alt Sun
 -.1667 dip
-------
32.9564 alt above true horizon
 -.0083 refraction
--------
32.9314
 +.2625 add semidiameter Sun to LL obs.
--------
33.1939
 +.0020 sun parallax based on Sun HP = .0024�
--------
33.1959 = S, corrected altitude of Sun centre.
33.2189 = s, altitude of Sun centre before correction for parallax and
refraction.

Next we have to "clear" the observed lunar distance d of the effects of
parallax and refraction, to arrive at the true lunar distance D.

s and m are the altitudes of Sun and Moon corrected for everything except
parallax and refraction.
S and M are the altitudes of Sun and Moon corrected for everything including
parallax and refraction.

I use the formula-
D = arc cos[(cos d - sin s sin m) cos S cos M /(cos s cos m) +Sin S sin M]
and I get D= 85.7384�. This is the corrected lunar distance, that has to be
compared with prediction.

I've taken the predictions quoted by Kent (who may have "rolled his own",
and they agree, within an arc-second with those you can get from Steven
Wepster's website, at http://www.math.uu.nl/people/wepster/tables.html) and
converted to decimal degrees, these are, for 10 June 08-

GMT 0600, D = 85.5331�
GMT 0900, D = 87.0181�
and to deduce the time of the observation, we have to do a
reverse-interpolation between them.

The result I get is 06h 24m 53s as the final result for the GMT of the
observation.

This has to be compared with Jeremy's averaged chronometer time of 06h 22m
59s for his lunar distances. So my conclusion is that his chronometer was
slow by 1 minute 54 seconds. Or, perhaps more realistically, that his
chronometer was correct and his lunar-derived GMT was in error by 1 minute
54 seconds. That isn't a bad result, for a lunar. It would have put his
deduced longitudes out by about 28.5 arc-minutes, which would have (but only
just) qualified Jeremy for the Longitude Prize, if he had been observing
around 240 years ago. The total error in angle in the whole process was less
than an arc-minute, which for a first-shot at a lunar, is creditable work
indeed.

If anyone is bothered to check my numbers, and finds anything to question,
or any step hard to follow, I hope he will let me know.

That compares pretty well with what Kent Nordstrom deduced, in [5476], when
he wrote-

"By using my average time for the LD observations 06-22-59 the corresponding
true LD from a NA is 85d 23m 43s. If I ,without paying attention to the GMT
06-22-59 but only use this distance in my calculations I get a GMT of
06-23-43."  I disagree (but only marginally), with that GMT, but it comes
even closer to the time of Jeremy's observation than does my calculation;
within a minute, indeed.

However, I do NOT understand Kent when he continues-

"At this time the sun�s apparent time is 16-59-47.5. The TE is +31.5 s,
which gives the MT of 15-59-47.5 + 00-00-31,5=16-00-19.


The difference between MT and GMT, that is 16-00-19 � 06-23-43=09-36-36 or
corresponding to the long. E 144d 09m.



So it seems to me that Jeremy�s distances are not correct."



I don't see what Sun's apparent time has to do with the matter, or MT, or
longitude. The aim of a lunar is to establish GMT, to set a local clock
right; nothing more than that. Steven's web page of lunar predictions is
marked as being for UT (= GMT), unlike the early almanacs, which until 1834
were based on Greenwich Apparent Time. Kent's predictions must also be for
GMT, so I suggest he is bringing in complications that don't exist.



Armed, now, with a figure for GMT (if we ignore what the chronometer was
saying), it's easy to deduce, from the Almanac, a position for the Sun (or
the Moon, for that matter, or both) and from the observed altitude, generate
position lines in the familiar way, which should provide a good longitude,
but (from the way they cut) not a good latitude, which deserves another
observation at a different time.



==========================================



Jeremy wrote, in [5469]-



"I will also say that getting lunars at sea will be inherently more
inaccurate then land.  Roll alone can change my height of eye several feet
and ship's vibration also make it more difficult to get a steady platform
(it pretty much forces you to shoot while standing.)  I am actually quite
happy with about 1' of error for sea lunars.  Sitting on a beach, I'd expect
a bit better however...."

Changing height of eye will have little affect on a lunar, being no more
than a correction to a correction.

 Adding "... I don't have logs, but I was wondering how accurate old time
sailors got with their lunars at sea?"

I doubt if that's an easy question to answer. Trouble is, only recently have
navigators known REALLY where they were when out in the ocean. Lunar
distance navigation loses its point once land is in sight. So it's only when
taking lunars for training and for practice that they would be taken from
well-known positions, and then the results would seldom be logged.
Comparisons of lunars with chronometers could be informative, if at the end
of a voyage a chronometer had been shown to have kept good time overall, but
I don't know of any retrospective study that has ever been made.

Mariners usually had log trig tables available with sufficient decimal
places (5 or 6) so as not to contribute significant error, together with
familiarity in using them (though without much understanding of what they
were doing, in general, I suspect).

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.











--~--~---------~--~----~------------~-------~--~----~
Navigation List archive: www.fer3.com/arc
To post, email NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply