Specialty sights: getting more from your lines of position
One of the drawbacks to sun-sight celestial navigation is that each sight yields only one LOP. Of course, a running fix is often possible, but that means a wait between sun sights of a couple of hours or more to allow for the azimuth to change significantly. While any single line of position is better than no line of position, and the sun line running fix is certainly an admirable sort of fix, there may be times during the day when the navigator wants more information from the single LOP.
With a little advance planning, a navigator can get a sun LOP that yields cross-track information (a "course" LOP) or speed data (a "speed" line). The key to this method is performing the calculations that tell you the optimum time to take these specialty sights.
A good illustration of getting and using this sort of information is the noon sight; when sailing an east-west course, the noon sight indicates any set to the north or south, and when sailing more north-south, the noon sight indicates progress along the track.
The simple method to use the rest of the day is to simply shoot the sun (or any other body, for that matter) when it is more or less dead ahead or astern to get a speed line. And, when a course or cross-track error line is desired, shoot the sun when it is more or less abeam.
But the knowledgeable navigator with a bit of time on his hands can more exactly determine speed and cross-track measurements by using one of the key pieces of information derived from any sun sight, the azimuth (true bearing to the sun). To use this technique, the navigator must enter the sight-reduction tables and the Nautical Almanac and work backwards. Let's take a look at how this process works.
To set the stage, let's assume that on June 18, 1997, we are on a sailboat crossing the Gulf Stream, heading to Bermuda in the biennial Marion-Bermuda Race. We want to use our sun sights not only for determining an estimated position but also to detect the presence of any current, as well as get a measure of progress down the rhumb line of 135° true. We figure that, if we can calculate the time when a sun sight will yield an azimuth of 135° true, we will be able to draw an LOP perpendicular to the rhumb line, giving us our "down track" progress. Another simple calculation for an azimuth perpendicular to the rhumb line will yield an LOP parallel to the rhumb line, giving us an indication of set.
We'll need a couple of pieces of information to get started. First, a DR position: let's use 38° N, 68° W. Next, the declination of the sun on the day in questionin degrees only. Looking in the Nautical Almanac for the date, we find the declination to be N 23°. Next, let's calculate the azimuth that will set up our desired LOPs. Recall how the sight reduction tables are set up: in the morning, when LHA will be large, the Zn will be equal to the Z (Z is the number printed in the sight reduction table); in the afternoon, when LHA will be small, the Zn will be equal to 360 - Z (for a quick reminder of these formulae, refer to the upper left corner of every page in the sight reduction table). So, a morning sight with a large LHA, taken at the right time, will yield our desired Zn close to our course line, and we will plot the LOP across our course, giving us a measure of progress down the rhumb line. An afternoon sight with a small LHA, again taken at the right time, will yield a Zn perpendicular to the rhumb line, and we will plot the LOP parallel to our course, giving us an indication of set and drift. A bit of math yields the entries we want to look for in the tables:Large LHA (morning): Zn = Z look for Z of 135°, gives Zn of 135°Small LHA (afternoon): Zn = 360° ?
Z look for Z of 135°, gives Zn of 225° Now we're ready to go to work. Open up the sight-reduction tables (Pub. No. 249, volume II) to the appropriate pages for a latitude of 38°, a declination of 23°, same name (since latitude and declination are both north). First, let's find an answer to our progress down the rhumb line, which means searching for a Z close to 135°. Searching down the column for declination of 23°N, we find an entry for 135°, corresponding to an LHA of 345° (don't forget this is a morning sun line, so the LHA must be taken from the right hand column, where the values are large). Jot down the Hc of 70° 15'. Now we have the basic information, but we still need to figure out what time of day will yield this answer. How to do this? All we have to do is work backwards to find the GHA and then the time, which corresponds to an LHA of 345°. We do this by first reversing the calculation for LHA, adding back our west longitude to arrive at GHA: LHA 345°W 413° ?360° GHA 053°Now take the GHA of 053° and match it up with the correct GMT time: open the Nautical Almanac to June 18 and search for a GHA a bit less than 53 (remember to look in the sun column!). We find the nearest value is 44° 43', which corresponds to 15 hrs. Subtract 44° 43' from 53 to find the remaining minutes and seconds of GHA. Then we go to the increments and corrections table in the back of the almanac and scan the GHA values until we find 08° 17'in this case, the correct value is found in the 33 minute box, across from the 08 seconds entry: GHA 53° 00' 15 hrs - 44° 43' 33:08 08° 17' We're done. We now know that if we go up on deck at around 15:33 GMT and shoot a sun line, the plotted LOP will give us a pretty good idea of our progress down the rhumb line. (The sight should be reduced and plotted as a normal sun sight.) For our second problem, how to measure set, or cross-track error, we will use much the same analysis. This time, when searching through the sight-reduction tables we are still looking for a Z of 135°. Why? Because we want to draw an LOP closely parallel to the rhumb line, which requires a Zn of 224°, or 90° from the desired LOP of 135°. Since Zn = 360° - Z, this means that we must find a Z of about 135° again. Going back to the sight-reduction tables, we can go to the same entry. But this time use the smaller LHA value from the left hand column (remember, afternoon sight, small LHA)15°. Doing the same reverse calculations as before, we end up with first the GHA and then the corresponding GMT time: LHA 015° GHA 083° 17 hrs - 74° 42.8' GHA 083° 33:09 08° 17.2' So, if we take a sun sight at about 17:33:09 GMT, reduce, and plot it, the resulting LOP will give a good indication of any set or cross-track error. This can be of use to a navigator trying to gauge the strength or direction of a mid ocean current, or to a sailor just trying to stay on the rhumb line. Note that using either of these two specialty sun lines in a running fix makes the fix even more valuable to the navigator. Of course, a more exact calculation could be done by refining the DR and interpolating for minutes of declination, but in most cases the above rough precalculation is sufficient. The more industrious navigator may want to use these methods for other bodies as well. So, by using just a few carefully preplanned sun sights, the competent navigator can maximize the utility of sun sight celestial navigation. And, of course, you'll also have a lot of fun in the bargain.