Solution to: “Like a duck on the waves”

This is the second time in as many issues that I have drawn upon my sailing experience to replicate a navigation problem. Those readers who actually read the problems may perceive a pattern developing; it appears as though the problems I am writing about have to do with being caught in storms and the abilities of the vessels that I was on to heave-to in those situations. This is no accident. I am a great believer in the technique of heaving-to and on more than one occasion this technique has, if not actually, saved a crew from disaster and mitigated the severe effects of stormy weather. Unfortunately, heaving-to has fallen out of popularity; either as a result of modern sailing ships being unable to, due to design, heave-to effectively or the lack of understanding of many sailors as to the specifics involved in the procedure. Whatever the reasons, every sailor should have as part of his vocabulary the skills required to heave-to if that becomes necessary. Even for the coastal sailor, who might need a few minutes to get his bearings, heaving-to is an excellent technique. I have also found that it is very simple to heave a boat-to when taking sextant sights. This could mean nothing more than sheeting in the main, backwinding the headsail and putting the wheel to windward, or conversely, the tiller to leeward. The boat basically stops and it is very easy to get a steady footing on deck and take a shot.

Now the problem we have is a basic sunsight. Our DR position was 34 degrees 20 minutes N by 65 degrees 40 minutes W. The Height of Eye is 10 feet and the sextant has no error. The time of the upper limb shot of the sun is 18 hours, 22 minutes and 25 seconds GMT. The day is Nov. 4 and we will use the 2006 NA. The Hs of the sun is 30 degrees 55.4 minutes. For those who don’t have the tables in HO 249, the information is as follows:

Hc = 31 degrees 17 minutes

d = – 51 minutes

Z = 141 degrees

Table 5 yields a correction of – 26 minutes

I: What is the Ho?

Ans: This is a standard reduction factoring in the dip correction, the 3rd correction for semi-diameter, parallax, refraction and Index Error (should there be any) to find the Ho or observed altitude of the sun. The only misstep here is that we are using an upper limb shot of the sun, so pay attention when entering the tables.

Hs = 30 degrees 55.4 minutes

-Dip = 3.1 minutes

Ha = 30 degrees 52.1 minutes

3rd cor = – 17.7 minutes

Ho = 30 degrees 34.6 minutes

Next we go to the daily sun pages in the NA to find GHA and declination of the sun at the time of the shot.

GHA sun at 18 hours = 94 degrees 06.3 minutes

Inc and corr = 5 degrees 36.3 minutes

GHA = 99 degrees 42.6 minutes

-Assumed longitude = 65 degrees 42.6 minutes

LHA = 34 degrees

Dec at 18 hours = 15 degrees 29.5 minutes S (d = 0.8 minutes) + .3 minutes

Dec at time of sight = 15 degrees 29.8 minutes S. (Round off to 30 minutes declination for Table 5)

The only thing to watch here is the fact that the declination is increasing so the d correction is added. This is found by seeing the direction that the declination is taking as the hours of the day increase. Also, common sense will tell you that the sun is moving further south until it reaches solstice on or around Dec. 21.

The last bit of information we need is the assumed latitude, which we will make at 34 degrees N. This is based on the DR latitude of 34 degrees 20 minutes N.

We now enter HO 249 to solve the celestial triangle.

Hc = 31 degrees 17 minutes

d = – 51 minutes

Z = 141 degrees

We go to Table 5 to solve for the minutes of declination, which is 30 minutes, and come up with 26 minutes. This is subtracted from the Hc to give us a final Hc of 30 degrees 51 minutes. From this we subtract the Ho to give us our intercept.

Hc = 30 degrees 51 minutes

Ho = 30 degrees 34.6 minutes

Intercept = 16.4 nm away

We know that it is away because in this instance the Hc is greater than the Ho.

One last point: According to the directions in HO 249, if LHA is less than 180 degrees Z has to be subtracted from 360 degrees in order to find ZN. Thus the bearing of the sun at the time of the sight is 219 degrees. This makes sense as the shot is taken after meridian passage and the sun is no longer in the east but in the west.

Once you have these numbers you should make the effort to plot the positions. If you do, you will find that the EP of the ship is at 34 degrees 25 minutes N by 65 degrees 34 minutes W. Thanks for your time and good luck.