At a DR position of 27° 10’ south by 09° 50’ west in a deep, low pressure system, the ship was struck by a particularly large sea, and sank. The men launched the 13-foot lifeboat, grabbed the sextant, chronometer and two tins of turnips.
Dudley and Stephens navigated by finding latitude and longitude from a noon sight. They relied on their sextant and chronometer. Let us join them before the sinking as they cross the equator. They believe that their DR at the time of the sight is 0° 25’ N by 22° 15’ W. The day in question is June 30, the height of eye is 10 feet and there is no sextant error and no chronometer error. They will take an upper limb sun shot at LAN and try to use the one sight to get a fix of both latitude and longitude. The time of the shot is 13 hours 33 minutes 10 seconds GMT. The Hs of the shot is 66° 44.4’ We know this is not the most accurate method of finding longitude but if the ship is traveling on an easterly or westerly heading, it can be reasonably effective. We will use the 2007 Nautical Almanac.
B. What is the latitude?
C. What is the longitude?
By David Berson
We are looking at a noon solution to both latitude and longitude in this problem. As was noted in the last Ocean Navigator newsletter, this method, is not as accurate as obtaining a three-star fix or a sun/moon fix. There are times, though, when circumstances make it necessary to make do. The goal of the navigator is to get as much information as possible under whatever conditions might exist. In a perfect world the sky would always be cloudless, the sun would always be shining, and the stars would always be bright. Unfortunately, those conditions usually exist just in the imagination.
Theoretically, obtaining a longitude line from a noon sight should be pretty simple. Noon or meridian passage is defined as when the LHA equals 0°. Thus when the GHA of the sun is equal to the longitude, the LHA is 0°. So it would be easy to conclude that at the time of LAN the GHA of the sun is the same as the longitude of the observer. Well, yes and no. In reality the noon sight is bit trickier than it seems. First off, the time of exact LAN is difficult to accurately time as the sun “hangs” for a few moments when it reaches the meridian of the observer. The other problem is that if the vessel is on a north/south course line the declination is changing during the time of the sight; perhaps not much but enough to make the accuracy of obtaining longitude questionable. There are methods described in Bowditch that allow for a much more accurate timed sight of the meridian passage. That method, however, requires a great deal of time. There are just occasions when one has to strike when the iron is hot and hope for the best. This problem exemplifies one of those times.
Dudley and crew were in the lifeboat at a DR of 0° 25’ N by 22° 15’ W. The day is June 30, and the height of the eye is 10 feet. There is no sextant or chronometer error. Dudley shoots an upper limb shot of the sun at LAN. The time of the shot is 13 hrs 33 min 10 sec GMT. The Hs of the shot is 66° 44.4’. We are using the 2007 Nautical Almanac to solve this problem.
The first thing we require is the Ho from the Hs. We find this in the standard way.
Hs 66° 44.4’
Ha 66° 41.3’
3rd corr -16.3’
Ho 66° 25’
The most important point to pay attention to is the fact that the shot is an upper limb so the 3rd correction is subtracted from the Ha.
Next we want to find the latitude of the observer at the time of LAN. To do this we employ the standard formula: Latitude = 90° – Ho = Zenith Distance ±dec. Let’s see what we have:
90 ° 00’
23° 35’= Zenith Distance (ZD)
Now we have to figure if we add the declination or subtract it. There are formulas to help with this but common sense makes the formulas unnecessary. The navigator knows that the DR is about 0°. Therefore by inspection he know that the declination has to be subtracted from the ZD in order to get a latitude close to this number. Remember we always have some idea of where we are! We go to the Nautical Almanac to the daily sun pages for June 30. At 13 hours GMT the declination of the sun is N 23° 10.5’. Even though the shot was taken at 33 minutes after the hour the d correction is so small (0.1’ or one-tenth of a nautical mile) that I have in this instance ignored it.
ZD= 23° 35’
-dec 23° 10.4’
Lat= 0° 24.6’N
Now we are ready to see if we can nail the longitude. We go to the daily pages of the Nautical Almanac for June 30 and find that the GHA of the sun at 13 hrs GMT is 14° 05.9’ Our shot time, however, is 33 minutes and 10 seconds. Beyond that so we go into the increments and corrections table and find that in 33 minutes and 10 seconds the GHA has increased by 8° 17.5’. We add this number to the GHA of 14° 05.9’ and we get the following:
13 hrs GHA 14° 05.9’
+33min 10 sec 8° 17.5’
Longitude= 22° 23.4’W
Now this information is not ironclad but it is considerably more precise that the DR. Hopefully the numbers correspond enough to give the navigator the confidence to know that he has predicted the set, drift, and speed of the vessel.