A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2016 Oct 16, 22:00 -0700
All this discussion of the pluses and minuses of having a "v" correction for the sun's GHA brings up another topic that I have mentioned from time to time in the past, that being the accuracy of celestial navigation. The current discussion reminds me of the theological arguments about how many angels could dance on the head of a pin. We tend to get into esoteric discussions about all aspects of navigation but sometimes it is good to come back down to earth. Celestial navigation is an enroute navigation method and the achievable accuracy is perfectly adequate for that purpose. It is not accurate enough for entering a narrow, unlit, channel at night. For that you need a more accurate method such as visual observations or radar or GPS. It is a waste of time and effort to try to achieve sub-millimeter accuracy with celestial navigation so the Nautical Almanac's method of providing the GHA of the sun is perfectly adequate for its purpose. Adding a "v" correction would not make it any more accurate since other inputs are less accurate and the accuracy of the result is limited to the accuracy of the LEAST accurate imput.
Look at the process. The final result is the intercept in nautical miles. How do we get there? Using the sun we take out the tabulated GHA to one-tenth of a minute, add the increment for the time, also to one-tenth of a minute, and determine the GHA at the time of the observation. We do the same thing for the declination. At the end of this how accurate is the computed GHA and declination? Since the tabulated values are only to a level of precision of one-tenth of a minute then the actual values can range plus and minus half of one-tenth of a minute from 0.05 to 0.15 minutes and the variation is NOT gaussian, it is a rectangular error, every value in the one-tenth of a minute range is equally likely. So after adding the the tabulated GHA and the increment the computed GHA has a possible error of plus and minus one -tenth of a minute, e.g. if the derived GHA of the sun is 181°15.5' the correct value of the GHA could be anywhere between 181°15.4' and 181°15.6' and the same for the declination so arguing about having a "v" correction for the sun is silly.
Looking at the rest of the process, you start with Hs measured to one-tenth precision; add IC also determined to a precision of one-tenth; then add dip also to a precision of one-tenth; and finally the combined "sun correction" which includes refraction, semidiameter and parallax in altitude, also taken out to the correction table to a precision of one-tenth of a minute. Even if the sextant readings and the table entries have a precision of one-tenth there are likely errors and uncertainties in these numbers, hazy horizon for Hs, error in height of eye for dip, (the ship was rolling); and abnormal refraction. And, built into the sun correction table is an additional error. The table shows two six month periods and assumes a constant semidiameter for those periods but the SD is not constant for six months as refering to the daily SD values on each daily page will clearly show. During the April through September period the table assumes that the SD was a constant of 15.9' when, in fact, it varied from 16.0' down to 15.8' so this introduces a 0.1' error into the derivation of Ho for most of the period. Similarly, the period of October through March assumes a constant SD of 16.1' when it varies from 16.0' up to 16.3' thus introducing an 0.15' error during most of that period. Ignoring those built in errors or uncertainties, doing the normal corrections to Hs introduces a plus and minus 0.2' uncertainty in Ho, e.g. if Ho is determined to be 15°15.5' it could actually be 15°15.3' or 15°15.7' or any place in beteen.
Then we have to compute Hc which also involves adding increments to the tabulated Hc, each of which have a precision of 0.2' if using HO 229 since they consist of two separate parts. So, if the Hc from Ho 229 were 15°17.5' its correct value could be anywhere between 15°17.3' and 15°17.7'. So subtracting Ho from Hc would produce an intercept nominally of 2.0 NM away but the actual intercept could be anywhere between 1.6 NM away and 2.4 NM away, a range of 0.8 NM. And if you are using HO 249 then the tabulated precision of one whole minute swamps out any one-tenth of a minute precision in your computation of of GHA, declination, or Ho.
And this is without looking at the errors of the observation which also swamps out such attempted precision in figuring GHA sun, see: