Nav Problem Solution to ‘Battling winter storms on U-boat patrol’

May/June 2004

This issue’s problem takes us back into the realm of sun sights. Familiar ground for many of you, but territory worth covering again. A note here: I know many of you come up with slightly different answers than I do. Some of you use different sight reduction methods, computers or different tables than I do. Even if our answers differ slightly, it is the process that we are attempting to teach — the step-by-step methodology of solving a celestial navigation problem.

It is Dec. 7, 1942. We will, of course, use the 2004 Nautical Almanac for the solution. DR of Zaida is 41 degrees 10 minutes N by 71 degrees 50 minutes W. Height of Eye is 10 feet. The Index Error on the sextant is 3 minutes Off the Arc. The time of the Lower Limb sight of the sun is 14:10:20 GMT. The Hs was 17 degrees 13 minutes. Calculate the Ho and the Intercept.

Sight Reduction:

Hs 17 degrees 13 minutes

+IC 3.0 minutes

-Dip 3.1 minutes

App Alt 17 degrees 12.9 minutes

3rd corr+ 13.2 minutes

Ho 17 degrees 26.1 minutes

GHA for 14 hours 32 degrees 04.8 minutes

Declination S 22 degrees 41.1 minutes (d)+ 0.3 minutes

+ 0.1 minutes

10 min 20 sec

2 degrees 35.0 minutes

S 22 degrees 41.2 minutes

GHA 34 degrees 39.8 minutes

+360 degrees

GHA 394 degrees 39.8 minutes

-Assumed Long 71 degrees 39.8 minutes

LHA 323 degrees

From H.O. 249 vol. 3 p. 19: Declination Contrary to Latitude

Hc 18 degrees 15 minutes

d -53

Z 144 degrees

Table 5 -36 minutes

Hc 17 degrees 39 minutes

Ho 17 degrees 26.1 minutes

Intercept 12.9 miles away

There should be nothing too difficult about reducing this sight. It is a matter of following procedure and paying attention to the entry of the numbers. In this case, pay attention to the southern declination and the fact that the (d) correction is added to the declination, since the sun at this time of year is still going south and will be until the winter solstice, on or around the Dec. 21.

Also, I add 360 degrees to the GHA so that when I subtract the Assumed Longitude I get a positive number. This is a legitimate thing to do, by the way; the addition of 360 degrees to find LHA when the Assumed Longitude is greater than the calculated GHA. The only other thing that can trip you up is the entry of Table 5 for the corrected minutes of Declination that you have to — in this case subtract from the Hc — find in H.O. 249. We have 41 minutes of declination, and this correction is subtracted. I know this by the inspection of the d tables in H.O. 249. There is a minus sign as one looks up the column.

Again we have a sun sight, but this time we are shooting an Upper Limb shot of the sun. Sometimes this is necessary if cloud covers the lower limb. Most navigators prefer shooting the lower limb of the sun, but either limb, if shot correctly, will provide a Line of Position. The time of the second shot is 18:35:17 GMT. The Hs is 20 degrees 59.1 minutes.

Hs 20 degrees 59.1 minutes

Index err + 3.0 minutes

Dip – 3.1 minutes

App alt 20 degrees 59.0 minutes

3rd corr – 18.5 minutes

Ho 20 degrees 40.5 minutes

GHA 18 hours 92 degrees 03.8 minutes

Declination S 22 degrees 42.2 minutes (d)+ 0.3 minutes

35 min 17 sec + 8 degrees 49.3 minutes

+ 0.2 minutes

Declination S 22 degrees 42.4 minutes

GHA 100 degrees 53.1 minutes

Assumed Long – 71 degrees 53.1 minutes

LHA 29 degrees

H.O. 249 p. 19

Hc 21 degrees 29 minutes

d -55 minutes

Z (Zn) 151 degrees (209 degrees)

Table 5 for 42 minutes declination -38 minutes

Hc 20 degrees 51 minutes

Ho 20 degrees 40.5 minutes

Intercept 10.5 minutes Away

The important thing to remember in this problem is to SUBTRACT the third correction when reducing the Hs to Ho. This is because we are taking an upper limb shot of the sun. Everything else should be pretty clear, in terms of the procedure. Again we are adding to the declination because the sun is still moving south at the time of the shot.

I hope you all enjoy the exercise, and I thank you for allowing me the privilege.

— David Berson

By Ocean Navigator