The sight I chose for this issue is probably not used enough. Basically three shots of the sun will give an accurate latitude, longitude fix. The downside of the shot is that it does require a certain amount of time, which means that if the sky becomes cloudy, the results will be less accurate.
The shot, as I learned it years ago, is getting longitude by doubling the altitude. Basically about one hour before noon the navigator takes a sun sight, marks the time of the shot and records the Hs. About an hour or so after LAN, when the sun reaches the same Hs as it had on the ascent, the time is recorded. The two times are then added and divided by 2 to get the exact time of LAN. By getting the exact time of LAN, the navigator can convert GHA into longitude and get both a latitude and longitude. Technically this shot is best done on an east/west passage when the declination of the sun will remain constant.
Let’s see how it is done:
The DR of the time of the sights was 49 degrees 20 minutes N by 27 degrees 30 minutes W. The day in question is July 2. The Height of Eye is 9 feet, and there is no Index Error or Chronometer Error. Capt. Nutting is shooting a Lower Limb of the sun.
At 12 hours 54 minutes 35 seconds GMT, the Hs of the sun is 61 degrees 11.2 minutes. The next time the sun is at that exact altitude is at 14 hours 53 minutes 26 seconds GMT.
For the first question, we want to calculate the time of LAN in GMT.
Instead of consulting the time of Meridian Passage in the Nautical Almanac, what we do in this instance is take the two times of the sun shots, add them and then divide by 2:
12 hours 54 minutes 35 seconds
+14 hours 53 minutes 26 seconds
27 hours 48 minutes 01 second divide by 2
13 hours 54 minutes 00 seconds
This is the time of the sun’s crossing the navigator’s meridian. If you want to check the accuracy of this time, use the standard procedure for finding time for Meridian Passage at navigator’s longitude.
The next thing we wish to find is the calculated longitude from the sight. First we must understand the nature of a noon sight; at the time of LAN the sun is on the exact meridian of the observer. Therefore, GHA must equal longitude.
We go into the daily pages of the 2005 NA and find that the GHA of the sun at 1300 hours is 13 degrees 59.3 minutes. To this we add the corrections for 54 minutes of time and that converts using the Arc /Time table into 13 degrees 30.0 minutes. We add these numbers and get a longitude of 27 degrees 29.3 minutes W.
The next objective is to find the latitude based on the time of LAN at 13 hours 54 minutes. The Hs at the time of this sight is 63 degrees 27.4 minutes.
First we reduce the Hs to HO using the standard procedure of correcting for Height of Eye, Index Error and 3rd correction for parallax, semidiameter and refraction.
Hs 63 degrees 27.4 minutes
– dip 2.9 minutes
Ha 63 degrees 24.5 minutes
3rd + 15.5 minutes
Ho 63 degrees 40.0 minutes
Next we have to find the Declination for the time of the sight. At 1300 hours the Declination of the sun is 23 degrees 00.4 minutes N. The d correction is 0.2, and by inspection we see that it is subtracted. We go to the back tables for 54 minutes and see that the Declination has changed 0.2 nm in that time. We subtract that from the Declination and get 23 degrees 00.2 minutes N.
We now apply the formula that will yield latitude:
Lat = 90 degrees – Ho = ZD +/- Dec
90 degrees – 63 degrees 40 minutes = 26 degrees 20 minutes + 23 degrees = 49 degrees 20 minutes N.
For more information on this sight see Bowditch or Mixter.