Solution to ‘Gallant Ship, Brace Men’

Because this problem deals with star sights, it is a tad more difficult than the latitude noon sight. The difficulty lies in using the tables — they can be confusing at first, but with some practice they become quite familiar. I assume that if any of you are using celestial navigation at sea, you probably employ a computer program or a dedicated computer like the Celesticomp. The Celesticomp is a great tool and makes reducing multiple sights almost painless. For the sake of our exercises, though, I still use the sight reduction tables — just to stay in practice. While at sea I always carry two Celesticomps as well as the Nautical Almanac, three volumes of H.O. 249, and universal plotting sheets. No point in being under prepared!

Before we begin, I would like to explain how I arrive at the creation of these problems. I base all the problems on historically accurate events. Since I cannot use the same sights the authors of the books used, I work backwards from a DR position mentioned in the story and use the Rude star finder to see what stars would be available for a fix this year. It takes some time to precalculate, but usually after the eighth cup of coffee I�ve zeroed in on stars that will give a good cut.

Problem:

The facts are: It is April 19, and the ship is at 31 degrees 20 minutes S by 40 degrees 20 minutes E. Height of eye is 30 feet and there is no Index Correction. The time of the first star shot of Procyon is 15 hours 33 minutes 10 seconds, and the Hs is 53 degrees 29.0 minutes. We are using the 2004 Nautical Almanac and Vol. 2 of H.O. 249.

What is the Ho?

This is a basic reduction with a slight twist. Because stars are so far away, there is a different 3rd correction than that used for the sun. Look under Stars and Planets in the front cover of the Nautical Almanac.

Hs 53 degrees 29.0 minutes

– Dip 5.3 minutes

Ha 53 degrees 23.7 minutes

– App Alt 0.7 minutes

Ho 53 degrees 23.0 minutes

What is the Hc?

To answer this, we have to crunch some numbers, but it�s no problem. Star sights are actually easier to work than sun sights once you get used to them, and they yield a lot more information.

The first thing we have to do is find the GHA (Greenwich hour angle) of Procyon for the time that we took the shot, at 15 hours 33 minutes 10 seconds GMT. To find the GHA of the star, we use the formula GHA Aries + SHA (sidereal hour angle) of the star = GHA star. For more information about these terms, see Bowditch.

We go to the daily pages of the Nautical Almanac for April 19 and look under the column for GHA Aries. At 15 hrs GMT, the GHA of Aries is 73 degrees 02.8 minutes. We need to add the 33 minutes and 10 seconds of time to this, so we go to the rear of the Nautical Almanac to Increments and Corrections under 33 minutes 10 seconds. Make sure you use the column labeled Aries. The correction is 8 degrees 18.9 minutes. We add that to the 73 degrees 02.8 minutes and get the GHA of Aries at the time of the sight as 81 degrees 21.7 minutes

Now we need to find the SHA of the star. Go to the right-hand column of the same page, where the 57 navigational stars are listed. The SHA of Procyon is 245 degrees 07.3 minutes and the Dec, is N5 degrees 12.9 minutes We now add the GHA of Aries and the SHA of the star to get:

81 degrees 21.7 minutes

+245 degrees 07.3 minutes

326 degrees 29.0 minutes GHA

We still need to find the LHA of the star, so we use the formula LHA = GHA + East Longitude. We add, based on the DR longitude 40 degrees 31 minutes because we need a whole number of degrees, no minutes or tenths, to use the tables:

326 degrees 29 minutes

+Ass long 40 degrees 31 minutes

367 degrees = 7 degrees LHA

We are now ready to enter the H.O. 249 sight reduction tables. We have an assumed latitude of 31 degrees S, an LHA of 7 degrees, and the dec of 5 degrees 29 minutes N. We enter Vol. 2 at 31 degrees Latitude Contrary because we are in south latitude with a north declination. We go to 7 degrees LHA to column 5 degrees Declination and extract the Hc, d and z. They are Hc 53 degrees 23 minutes, d -59, and Z 168 degrees. We now go to Table 5 to get the minutes of declination, which is 12.9 minutes (round off to 13 minutes). That is subtracted from the Hc because we can tell by inspection that the 59 minutes of the d corr is minus. We have the following:

Hc 53 degrees 23 minutes

– 13 minutes

HC 53 degrees 10 minutes

Ho 53 degrees 23 minutes

Intercept 13 nm Toward

We are not quite done, though, because we still have to refine the Z or direction. At the bottom of the page we are told that if we are in southern latitude and LHA is less than 180 degrees, then Zn = 180 degrees +Z. So we have 168 degrees + 180 degrees = 348 degrees. If we were to plot this, that would be the direction of the star. The assumed position would be 31 degrees S by 40 degrees 31 minutes E, 13 miles in the direction of 348 degrees T.

We would follow the same procedure for the next star. Spica.