A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2018 Mar 22, 19:19 +0100
Coincidentally in a few weeks I have been consulted several times about the same topic, which came from members of NavList. Coincidences of time and space… J. I usually tell them it is better to start a new topic and talk about it in common, but.
It is about how to correct the change in position of the observed body, and also, in some cases about how to correct the change in position of the observer.
Let me explain it!
If SOG is the modulus of the observer’s velocity vector and Δt is the difference in time between the observations, one have:
Some recent publications use only the term fix, so using classic lexicon, these different cases are:
· Fix - 1, 2, 3
· Running Fix - 4
· Stationary observer – 1, 2
With the hypothesis that the speed in constant, SOG = cte, the mathematical basis is that in the differential equation of motion the partial derivatives en case 1, 2 & 3are cancelled.
Should the Nautical Almanac is used in order to obtain at the time of each sight the declination and the GHA of the observed body, the motion of the body is automatically corrected. But it is absolutely necessary to correct the effect of movement of theobserver.
What does “PUB. NO. 249 - SIGHT REDUCTION TABLES FOR AIR NAVIGATION” say?
Motion of the observer (MOO). If it is desired to get a fix from two or more observations, the resulting position lines must be reduced to a common time, usually the time of one of them. This may be done in two ways: the position lines of observations made earlier or later than this time may be transferred on the plotting chart by the motion of the aircraft in the time-interval concerned, or the corrected sextant altitudes (or intercepts) may be adjusted to allow for the motion of the aircraft.
Motion of the body (MOB). If the time of observation differs from that used to obtain the tabular value of LHA, the entry may still be used if a correction for the motion of the body (due to the rotation of the Earth) in the time interval is applied to the altitude (or intercept). Table 2, on page (i), provides for this correction. It enables observations made at different times to be reduced and plotted as if they were made simultaneously, and it thus facilitates precomputation from the Air Almanac. Since the time used for reduction is normally the time at which the fix is desired, it is convenient to combine the corrections for motion of the body with those for the motion of the observer, as the time intervals are the same.