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Subject: Grenadine Lunar Distances
From: Arthur Pearson (arthurpearson@XXX.XXX)
Date: Fri Jan 31 2003 - 11:47:33 EST
Ladies and Gentlemen:
In early January I had the opportunity to take two sets of lunar
distance observations while on a 40' bareboat charter in the Grenadines
in the southeastern Caribbean. Having only taken lunars on land
previously, it was a great fun wrestling with the practical
considerations of taking lunars more or less at sea. This posting will
share the data for those who would like to work with them and offer some
comments on the practicalities.
FIRST SET
My first observations composed a complete series intended to find
latitude and longitude by the "1800 method". I took a local apparent
noon sight (LAN) for latitude. About 3 hours later, I took sun and moon
altitudes before and after a series of 7 lunar distances. The first sun
sight was used to determine local apparent time (LAT) which was
converted to local mean time (LMT). I graphed the lunars and selected
the fourth for solution. Interpolating the altitudes to the time of the
selected lunar, I cleared the lunar and solved for GMT per lunar. The
difference between GMT and LMT was converted to longitude per lunar.
Having GMT and exact position from a handheld GPS, we have a gauge to
judge my accuracy. The data and my solutions are as follows:
Date: Jan. 7, 2003
Index Correction: -1.1'
LAN Sight:
Height of Eye: 10 feet
Hs LAN: 54° 37.3'
Latitude per LAN: 12° 49.0'N
Altitudes Before Lunar:
Height of Eye: 8 feet
GMT Hs
Sun 19:18.00 32° 15.0' Lower limb
Moon 19:21:21 63° 24.0' Upper limb
GMT Ds
19:33:27 59° 33.2'
19:35:08 59° 34.0'
19:40:22 59° 34.8'
19:42:04 59° 35.4' (after graphing all 7, I used this one)
19:45:17 59° 36.6'
19:48:07 59° 36.0'
19:50:24 59° 37.5'
Altitudes After Lunar:
GMT Hs
Sun 19:52.39 25° 27.2' Lower limb, dip short at 0.3 nautical miles
Moon 19:55:15 66° 18.6' Lower limb
"DR" Latitude of Lunar: 12° 37.2'N (see explanation below)
LMT of Lunar per 1st sun sight: 15:36:22 (=LMT sun sight + time elapsed to
lunar)
GMT per Lunar: 19:44:55
Longitude per lunar: 62° 8.2'W
Time Error of Lunar: 2m 51sec fast
Distance Error of Lunar: 1.3' too long
Longitude Error: 47' too far west
Total Error in position: 46 nm including 1 mile error in latitude
Position per GPS:
12° 38.2'N
61° 21.2'W
COMMENTS
This LAN sight was taken on a broad reach in 20-25 knots in six foot
seas, common conditions between the islands of the Grenadines at this
time of year. The error was 1 nm compared to GPS. In the course of the
afternoon we took a varied course around and between islands to our
anchorage behind the reef of the Tobago Cays. A strict DR was not
practical, so for the "DR" latitude for the lunar, I simply applied the
1nm error in my LAN sight to the latitude per GPS of my lunar
observations.
The lunar was taken in the very rolly anchorage behind the reef. Not
open ocean, but definitely a lot of motion. The moon happened to be
nearing its highest point, providing several challenges. It was very
difficult to get the sun over to the moon, and the high altitude made
for a very awkward posture when I did. This sight was a prolonged
struggle; I tried several postures but found nothing comfortable. The
first moon altitude used the upper limb, the second one used the lower
limb because that looked best at the time (a mistake; I latter
calculated that the moon had not yet reached the meridian by the second
lunar). This made interpolating between the moon altitudes cumbersome
and may have introduced error by measuring an incomplete limb. Finally,
the second sun sight came down against one of the Cays, so I had to
correct for dip short for HOE 8ft, distance of 0.3 nm, which I calculate
to be 15.2'.
The high moon also brought George's parallactic retardation into play; I
calculated the hourly change in apparent distance as only 14.5' which is
quite slow. All in all, I am pleased with how well it came out given
the difficulties. I also solved this lunar using the "Lewis & Clark"
method by which I calculated the altitudes based on latitude per LAN, an
assumed longitude, and the LHA of the bodies based on the afternoon sun
sight. This method came in only 31' too far west, an improvement of
16'. As I used the same distance observation, the difference can only be
attributed to using different altitudes to clear the distance
(calculated vs. observed). Perhaps I made errors in the unusual
corrections that were needed for the observed altitudes. In any case, it
is another demonstration of the robustness and efficiency of the "Lewis &
Clark" methodology.
SECOND SET
The second set of observations was a series of lunar distances alone. I
cleared and reduced to GMT based on calculated altitudes that were in
turn based on known GMT and position. There is no point to this process
other than improving one's lunar technique. This set was taken hard on the
wind in 25 knots and 6 foot seas just south of Bequia. My data and
results are as follows:
Date: Jan. 10, 2003
Index correction: -1.1'
GMT Ds
18:29:25 92° 28.4'
18:32:31 92° 29.0'
18:36:06 92° 30.8'
18:38:47 92° 31.1' (after graphing, I used this one)
18:43:44 92° 33.8'
18:46:13 92° 33.4'
Position per GPS at time of selected distance:
12° 56.9' N
61° 16.7' W
GMT per Lunar: 18:42:59
Time error of lunar: 5m 12sec fast
Distance error of lunar: 2.3' too long
COMMENTS
With a much lower moon (Hs~17°) and thus a much faster rate of change in
apparent distance (21' per hour), this was a better time to take a
distance than the high moon of the first set. Although a longer
distance, the posture was much more comfortable. I was braced solidly
in the companion way and could pivot comfortably from the waste up.
However, the motion of the boat had the sun and moon dancing
boisterously around in the scope. I felt I got a good look at a couple
of the contacts but struggled with the others. The graph of the
observations is more consistent than I would have guessed although I ended
up pretty far off. I would guess that had I worked the longitude as I did
with the first set, I'd be off by over 80 miles. Practice, practice,
practice... I suppose I'll just have to spend more time in the
Caribbean!
Had I been depending on these lunars at the end of a transatlantic
passage to the Grenadines, the practical consequence would be a landfall
7 to 15 hours later than anticipated. Late landfall might mean after
dark when one was planning for daylight. More unsettling would be
arriving early in the dark had the error gone the other way. Clearly a
broad margin of error and extreme caution are required when depending on
these techniques. On the other hand, I would love to know the
satisfaction of leaving the Canaries, crossing an ocean, and arriving
within a few hours of ETA using only sun, moon and a sextant.
Regards,
Arthur
arthurpearson@XXX.XXX
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