NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Kent Nordström
Date: 2008 Jun 8, 20:32 +0200
In an
earlier e-mail I promised to provide my owm views on accuracies for LDs.
Unfortunatley I have not been succesful to connect to NavList probably beause of my bad e-mail. Frank
Reed has kindly helped to setup my
new account. Anyway here are my comments. If you find my writing below clumsy
pls accept that I am neither English nor American :
Firstly: My comments are all related to the way old
navigators did the lunars, that is roughly in the time span l760-1860.
Secondly: In order to smooth measurement errors the
method I have applied requires
measurements of altitudes of the body, then the moon,
then three distances, then altitude of the moon and finally altitude of the
body. Hence all measurements will be normalized to the mean time of distance
measurements.
Thirdly: I have assumed that there is no GPS onboard and
no chronometer/other accurate time piece
available.
Forthly: The reckoned position is not very accurate as it
was in the old days.
When
the altitudes of the moon and the other body are reduced some uncertainties are
introduced even if corection tables are
used:
- the
moons altitude has be corrected for
augmentation
-
altitudes of the moon and the sun (if used) have to be corrected for the
differencies in refraction between the measured egde and the geocentre of the
body.
Corrections taken from tables provide average values,
hence by using table values some small errors are
introduced.
Refraction, in particular for low altitudes, are always
uncertain. Refraction data and corrections for deviation in air pressure and
temperature from normal taken from most tables are coarse and may (if you are
lucky) represent the actual situation.
The moons true local altitude has to compensated for
earth flatness. The size and sign of this correction is dependant of the azimuth
to the moon. If the azimuth is less than 90 degrees than a negative correction
must be introduced, otherwise the correction is positive. The difficulty here is
that azimuth must be estimated (not calculated because no other ephemeris data
are available this early in the
calculation).
The moons HP has to be corrected for earth flatness
before calculating the local parallax.
Correct reduced altitudes have implications on the
calculation of the LD and consequently on the GMT, however errors in altitudes
have much less implication on the GMT than an erronous LD.
The observed distance has to compensated for the moons
augmentation. This is tricky because the angle between the distance line and the
vertical line through the moon (and sun if used) has to be observed (which in
old times was the normal way to do). This estimation will in practice be rather
un-precise (if ephemeris data are available these angles can of course be
calculated).
Finally. the earth flatness will also have implications
on the final LD. A correction for the moons parallax in azimuth due to earth
flatness is needed before reaching the calculated true
distance.
As you can see from above there are many sources of
errors in each step of the calculation of the
LD.
To this we have the classical difficulties for
navigators:
- how accurate are
measurements of altitudes and distance(s)?
- How accurate are the
readouts of the sextant?
- How accurate is the
index error?
But for finding what we are searching for, i.e. the
longitude, there are more difficulties.
Assuming that LDs are tabulated for the navigator (as in
the old NAs) and that the calculated true distance will provide a first GMT
then the next to consider is the correction for 2nd differencies,
which is a way to compensate for un-regular movements of the moon. The longer
interval between the tbulated true LDs the more need there is for this
correction. Then a final GMT is obtained.
The local time (Mean Time=MT) has to be found as well.
When the sun is used obtaining MT is rather trivial because the sunss LHA
represents apparent time, which corrected with the time equation, gives the
local time. If the other body is a star or a planet it is a little more
complicated to find the MT (the moon is not recommended due to un-regular
movements). What is needed here is to find the difference in sideral time
between the reference point in time=Aries passage of the upper meridian (where
an opinion of the longitude is needed, we have here some kind of Catch 22
situation) and the calculated sideral time at the observation, which is
=LHA+Ascensio Recta. In this case
accuracies in altitude, declination and latitude as well as the GHA of Aries
will all have implications on the accuracy because they all depend on the final
GMT.
The difference in sideral time has to be converted to MT
and thereafter we can do the longitude calculation as MT-GMT or vice
verse.
It is of course possible to try to quantify errors as per
above and calculate a final error using the method of Gaussian normal
distribution. I am not going to do that but instead stating my personal opinion
based on my own knowledge and the brief analysis above: Longitude can be found
typically within 15-20 nautical miles from correct longitude. A very well
trained observer may sometimes obtain 5-10 nautical miles. All measured on the
equator.
By this answer I have hopefully answered Franks question
about LD accuracies some weeks back.
Kent
N
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