NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2008 Jun 12, 14:53 +0200
The average in this case is incorrect, see the Hs graph:
-----Mensaje original-----
De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de George
Huxtable
Enviado el: sábado, 07 de junio de 2008 15:57
Para: NavList@fer3.com
Asunto: [NavList 5360] Re: Exercise #12 Daylight Sun/Moon Fix
I suspect that there are many more unposted attempts at Jeremy's
exercises,
behind the scenes, than actually turn up on Navlist.
Here's my go at #12.
Date 28 May 08
Start with a position line for the Sun. Without a 2008 almanac, I have
to
rely on my pocket calculator. Its Sun predictions should be good, and
should
correspond to the Almanac's. Someone please tell me if they don't.
at UT 21h 06m 15s, I get Sun dec +21º 37.5', GHA 137º 13.2', semidiam
15.8'
corrected altitude from Sun LL is obtained from-
16º 43.1 Sun sextant altitude
- 9.9' dip from
- 3.2 refraction
+ 15.8 semidiameter
+ 0.1 parallax
======
16º45.9 corrected altitude.
Without having alt-az tables for that latitude band, I have to
calculate the
Sun altitude using a program which gives me great-circle course and
distance
in miles from A to B. From an assumed position of N 14º 37.9' and long
of E
145º 18.6, to Sun at N 21º 37.5', W 137º 13.2', I get a course (= Sun
azimuth) of 71.4º, and a great-circle distance of
corresponding to 73º15' zenith distance, or 16º 45' altitude, to
compare
with 16º 45.9' corrected altitude. At the moment of the Sun sight,
then, the
Sun was actually 0.9' higher in the sky, and therefore
the Sun's GP, than was assumed. So it's on a position line, displaced
from
that assumed position by
being drawn at right angles to that displacement.
The Sun was on that line at 21h 06m 15s, but with its course due East
at
14.3 knots, then at 21h 00m it was
that position line bodily sideways by
Now for the Moon. Averaging the 8 observations, I get the mean altitude
of
72º 26.0', at a mean time of 21h 01m 57s. Hope others agree.
For that moment, my pocket calculator predicts Moon dec = -3º 05.2',
GHA
214º58.6. It's less precise, for the Moon, than it is for the Sun, so I
wonder what others get. In this exercise, the geometry is such that only
the
dec matters, not the GHA.
Working from the same Assumed Position as before, and using the same
technique as for the Sun, I get the calculated Moon altitude to be 72º
16.9
at an aziimuth of 179.8º. So the Moon is very nearly due South, and
what we
are finding from it is simply our latitude.
We need to compare that altitude with the sextant altitude, after all
corrections have been made, so the next step is to make those
corrections.
72º 26.0' Moon sextant altitude.
- 9.9' Dip from
- 0.3' refraction
- 15.5' semidiameter Moon (using UL)
+ 17.6' parallax taking HP = 57.6 and calculating HPcos alt.
==========
72º 17.9' corrected Moon altitude. This is just
altitude we calculated from the AP, so therefore we are just
to the Moon's position, or 1 arc-minute further South, which puts us on
an
E-W position line at N 14º 36.9. In this case, because that position
line
runs E-W, and the ship travels due East, the position line doesn't
shift: it
was in the same place at 21 h, near as dammit. And a bit of rough
sketching
gives a final longitude just
So we can congratulate the people in
job in the GPS positions they are puttting out.
Jeremy says "the latitude is consistently off", but it's only
a mile out
from GPS, according to me, so nothing to be ashamed of there. Indeed,
it's
well within the margin of error that can be caused by natural changes
in the
refractive part of the dip. Rather more interesting, to me, is the
scatter
in those Moon altitudes. I wonder why. Was the sea state good, at that
time?
Often, with a high Moon, contrast can be low, especially if the sky is
a
touch milky. That gets worse if you use an all-over horizon mirror,
rather
than a half-and-half split job. If Jeremy had recorded a number of
altitudes
for the Sun, as he did for the Moon, I wonder whether thet, too, might
have
shown scatter. What's his experience?
I didn't really need to do all those hand-corrections, but could have
left
the lot to my calculator software instead. However, that inflexibly
chooses
a height-of-eye appropriate to the "bridge" of my little
craft, at 6ft above
sea level, rather than to Jeremy's
subtracting 7.6' from them first, then it gives the same answer.
George.
contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from
or at
================================
Exercise #12 Daylight Sun/Moon fix.
This exercise is for our math friends. It is a series of Moon lines
taken near meridian transit, crossed with an early AM sunline.
Plotting these lines, you will notice an averaged Moon line giving a
decent position with lines within 5 degrees of the horizontal. The
sun line will be nearly vertical and gives a good Longitude line as a
cross.
In this case, my calculations show that Latitude is consistently off,
but the Longitude is within a couple of tenths. I am guessing that my
I wasn’t seeing the actual limb of the moon and therefore was off with
the sextant observations by better than a minute of arc. The moon is
a strange mistress to try and shoot with the sextant.
----------------------------------
UTC date is 28 May 2008. The 21h 00m UTC GPS fix was Latitude 14deg
090 at 14.3 knots. Height of eye is
and 1010 MB. Index error is 0.0. The following observations were
made (times in UTC):
Sun (LL): Hs 16deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Moon (UL) Hs 72deg
Determine a fix at 21h 00 UTC (07h 00m Local)
Jeremy
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