In a previous article August 2000 we discussed how to estimate your latitude based on the observation of the sun’s altitude at local noon, i.e., at the time when the sun crosses the boat’s meridian.

We found that the exercise involves six steps:

1) On the basis of your dead reckoning position, estimate from the Nautical Almanac the approximate time of local noon in your location. To avoid mistakes in making these calculations, you may wish to refer always to Coordinated Universal Time ( UTC , also known as Greenwich Mean Time or Zulu Time).

2) Take sextant sights approximately every minute for about ten minutes before and after local noon noting altitudes and times (in minutes and seconds).

3) Average the three highest altitudes and correct the average thus obtained for index, dip and altitude errors to get the "corrected sextant altitude" (H°)- dip and altitude tables are in the Nautical Almanac and the index error comes with a certificate provided by the sextant manufacturer.

4) Determine the sun’s declination at local noon by using the daily tables in the Nautical Almanac.

5) Calculate the zenith distance by subtracting the corrected sextant altitude (H°) from 90°.

6) Estimate your latitude by adding the sun’s declination to the zenith distance in spring and summer (when the sun’s declination is north) or subtracting it in autumn and winter (when the sun’s declination is south).

The nice thing about the noon sight is that with the same data you collected to estimate your latitude you can also estimate your longitude. All you need is an accurate watch and a bit of additional calculations.

The watch need not be a marine chronometer; nowadays, most electronic wrist watches are accurate enough for celestial navigation and in any case can be easily synchronized to time signals from atomic clocks which can be received on the radio all over the world. As for the calculations, there are essentially two methods used by the US Navy (see The American Practical Navigator, 1995 edition, para 2010):

1) The graphical method requires you to plot all the sun’s altitudes you observed on a simple diagram where the altitudes are measured on the vertical axis and the time ( in minutes and seconds) is measured on the horizontal axis. If you have done a good job taking your sightings, you should be able to draw a symmetrical curve through the plotted data showing a gradual increase in sun’s altitude before local noon followed by a gradual decline (if some data are clearly outside the curve, chances are that you made a mistake in measuring the sun’s altitude; perhaps the boat was rolling or the sextant was not perfectly vertical or whatever; in any case, you should discard the anomalous data).
Next, draw at least 3 horizontal lines across the curve, making sure that there is sufficient vertical separation among them. The points where each of these lines crosses the curve identify two different times when the sun’s altitude was equal (one time when the sun was ascending and the other time when the sun was descending). For each line, average the two times when the line intersects the curve.
Then average the three resulting averages to obtain your best estimate of the time of local noon.
For instance, if the sextant altitude was 70° 27’.5 at 11h 36 min. 00 sec. UTC and at 11h 44 min. 00 sec. UTC, the average for the first line will be 11h 40 min. 00 sec. UTC. If the averages for the second and third line were 11h 40 min. 04 sec. UTC and 11 h 40 min. 05 sec. UTC, respectively, the average of the averages will be 11h 40 min. 03 sec. UTC.
This represents your best estimate of the time when the sun crossed your local meridian.
At this point, go back to the Nautical Almanac and determine the sun’s Greenwich Hour Angle (GHA) at 11h 40 min. 03 sec. UTC. If you are in the Western Hemisphere, this will be your longitude. If you are east of Greenwich, subtract the sun’s GHA from 360° and you will get your longitude.

2) The arithmetic method is in fact quite similar to the graphical method. First, you measure and record the sun’s altitudes as the sun is ascending to its maximum altitude. As the sun begins to descend, set your sextant to correspond to one altitude already recorded (e.g. 2 minutes before the sun reached its maximum altitude). Keep sighting the sun until the sun reaches that particular altitude. Note the precise time when this occurs and then average the two times when the sun was at the same altitude.
Repeat this procedure with at least two other altitudes recorded, say, 4 and 6 minutes before local noon, each time presetting the sextant to those altitudes and recording the corresponding time when the sun, now in its descent, passes through those altitudes. Average the corresponding times and then take an average of the three averages.
The result will be your best estimate of the time of the sun’s meridian passage.
Based on this estimate, you can then get from the Nautical Almanac the sun’s GHA and your longitude.
One should keep in mind that the noon sight is a more reliable approach to estimate latitude than to estimate longitude. As the sun appears to "hang on" at roughly the same altitude for two or three minutes during meridian passage, you have a window of 2-3 minutes during which any good sighting will produce a fairly accurate estimate of the latitude.
An accurate estimate of longitude, on the other hand, depends on the precise determination of the exact moment when the sun crosses your meridian. This is never easy because while the sun appears to hang on at local noon, it is in fact moving quite rapidly east to west: remember that in its apparent movement around the earth, the sun covers 360° in 24 hours, i.e. 1° or 60 nautical miles every 4 minutes. It follows that the estimation of longitude based on local noon sights is inherently less accurate than the estimation of latitude, all other things being equal.
If you want more accurate estimates of longitude, you need to go through a full exercise of sight reduction, including comparisons of computed and observed altitudes and the plotting of lines of position.

The advantage of the noon sight is that it is simple, quick and when complemented by good dead reckoning will produce readily available and very useful data for safer offshore navigation.