Wednesday, January 6, 2010

Latitude for the Common Man

A post or two ago I wrote "The determination of latitude is simple; in less than an hour anyone can be taught how to use a sextant to measure the sun's height above the horizon in degrees at "high noon" (local apparent noon), and how to correct that "altitude" for time of year (declination), height of eye, refraction, and error of sextant. The result of this "noon sight" is latitude, accurate to a mile or so if the sextant work is good, and no clock needed."

Here goes. Using a table in your Nautical Almanac, look up the approximate time local noon will occur at roughly your longitude on your date. A few minutes before that time, take your sextant, put the appropriate sun shade on, and make yourself comfortable on the bridge wing or wedge yourself into the companionway of your yacht. Sight the sun through your sextant. The sextant shows you two superimposed images: one of the horizon, and one of the sun or other body. Move the sextant arm until the sun is brought down to the horizon. Rock the sextant back and forth slightly, and the sun will describe an arc that should just touch the horizon. You will observe the sun to climb, and you will adjust the sextant accordingly, to keep the sun just kissing the horizon in its arc. In a short while the sun will pause, and then begin to come down; local apparent noon has occurred. Read and record the highest altitude the sun achieved.

Now correct your sextant reading for instrument error, height of your eye ("dip"), refraction, and semi-diameter of the sun (16 minutes, usually, and always added). Instrument error is read from a table in the sextant case. Dip and refraction are from simple tables in the Nautical Almanac. Each is either added to or subtracted from your sextant reading, as indicated. The corrected result of your sextant reading is the sun's observed altitude, or "Ho".

Subtract the Ho from 90 degrees to get the "zenith distance."

Again using the Almanac, look up the sun's declination for that date. Declination is the sun's "latitude" on the celestial sphere. For example, you learned in fifth grade that on the winter solstice the declination is 23.5 degrees south, and that on the equinoxes, it is zero degrees, or right over the equator. But you don't really have to know this to reduce a noon sight: you just have to know how to look up declination for a given date.

Add the declination to your zenith distance, if the delination is the same name as your latitude. That is, if you are in the northern hemisphere, and declination is north, add the zenith distance and the declination. If you are in the northern hemisphere and the declination is south, subtract the declination from your zenith distance.

The result is your latitude!

An example. Suppose you are eight days out from Boston headed for Ireland. You consult your Almanac, determine the approximate time of local noon for your date and approximate longitude, take a good noon sight, and correct it for dip, index error, refraction and semi-diameter of the sun. The result - 47.23 degrees in this example - is your Ho. Then:

               90.00 degrees
minus       47.23 degrees Ho
Result:      43.37 degrees Zenith distance

You consult the Almanac again, and find that for the date the sun's declination is 06.04 degrees north. So:
               43.37 Zenith distance
plus          06.04 declination

Result:     49.41 north latitude.

It is just that simple. Sights other than the noon sight are harder, but it's all just adding, subtracting and tables, and, for other than noon sights and Polaris, time. And it is way, way cool.

Tomorrow's post is about a great, unsung American, the man who taught the cook and the boatswain how to navigate by the stars.

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