Making a Kamal

A kamal is an Arab navigation device from the 9th century -- basically a stick with markings on it attached to a string with a knot in the end. You hold the knot in your teeth, and then place the top edge of the kamal on the center of your celestial object. If you have a ruler you can use, great. A retractable tape measure will also serve you.

If your celestial object is the sun, put the top edge of your kamal directly over the top of the sun so you don't damage your eye, and then subtract 1/4° to compensate for sighting the top edge. The sun's diameter is 32'. So its radius is 16', or pretty close to the 1/4° figure we will use for the kamal.

If you are shooting the moon, you can sight for the moon's top (or bottom) edge, then you can subtract (or add) 1/4° to its altitude. The moon has a radius of 1/4°, just like the sun. (This is, by the way, why a "total eclipse" can be total. Both the moon and the sun have the same diameter as seen from the earth.)

Put your thumb down even with the horizon...and then read the altitude of your celestial object.

In my first try using this particular kamal, I got an altitude of 10 1/4° for the object I sighted, or 10° 15'. My Tamaya sextant gave me an altitude of 10° 03'. So I was within 15'.

There are mathematical reasons why a kamal is accurate only up to 15°. So then, if you have lost or damaged your sextant and are using a kamal, you will be taking early day and late day sun shots, plus planet/star shots during twightlight before dawn and after sunset, and the moon whenever you can get it. You will be selecting your objects that are no more than 15° above the horizon. But if suitable objects are available in your location, at your time of year, you can get reasonably accurate fixes.

You can make a kamal just like mine, with a comfortable string length of 18.0" (45.8 cm), by downloading this graphic and taping it to a short length of 1x2 lumber.

Because of several unknowns, e.g. how much the string will stretch, whether the knot you are holding in your teeth is at the same vertical plane as the retina of your eye, I don't obsess too much over fractional differences in string length.

I did, however, attach the strings in such a way to make my kamal hang horizontally when suspended, which means that it will be easier to keep it vertical when using it.

Improvising a Kamal at Sea

You have just dropped your sextant overboard. "Next time," you say, "I will put that lanyard around my neck." You look for something straight that you can conveniently hold, and mark with lengths. You want to be able to sight the sun, so you want your "something straight" to be opaque so you don't blind yourself. Your clear plastic parallel rules are out. You don't have a "stick" on board, and you don't have a string, and you may not even have a ruler.

No matter. You can even use the edge of a book, like your Nautical Almanac. Hold it out in front of you with one or both hands. Calibrate it by looking at the night sky. The distance between Merak and Megrez in the Big Dipper is 10.0 degrees. Hold your improvised kamal up and put the top of edge on one of those stars, and your thumb on the kamal opposite the other. Then mark that distance off as 10°. Subtract half that length to mark 5° and add that same amount to get 15°.

A second measure you can use is to look at Castor and Pollux, with a separation of 4.5°.

After you have 5, 10 and 15 degrees marked off...and you have 4.5° marked off, by observing the 0.5° difference between the 4.5° and 5° marks, you have the wherewithall to finish marking increments on your improvised kamal.

You will want to use the dip and main correction for sights, just as you would with your sextant. Index error, of course, is irrelevant.

The Mathematical Fine Print

Read this section only if you are mathematically curious.

The trigonometry equation for solving the angle of one corner of a right triangle when you know the length of the adjacent side and the opposite side is:

tan(θ) = LengthOpposite ÷ LengthAdjacent

So then, if you want to have a vertical scale of centimeters (which with 1° = 1 cm is convenient to make) you can calculate the length of string you need with

LengthAdjacent = 1 cm ÷ tan(1°)

...which gives you a string length of 57.3 cm.

Using a string this long is just a little longer than I can comfortably manage with my arm length. So I went with:

LengthAdjacent = 0.8 cm ÷ tan(1°)

...which gave me a very nice string length of 45.8 cm, or 18.0 inches. I would never use such a string length if I were improvising a kamal from a ruler in an emergency. You would be unlikely to get accurate altitudes on the fly trying to use a conventional ruler at 0.8 cm per degree. But with a computer and printer available, I used the Inkscape vector drawing program to space my lines precisely 0.8 cm apart.

If your arm is long enough to manage a 57 cm string, then use that. Actually, if your arm is 57 cm long, you don't need to use a string at all. Just hold a ruler out. You will get acceptable accuracy at 1.0 cm per degree. However, if your arm is more like mine, you can download a PDF of my graphic with the 0.8 cm per degree by clicking here.

As indicated above, a kamal is only useful for angles of 15° or less. This is because a kamal has a fixed string length. But you know from using a universal plotting sheet that as your angle increases, the base of your triangle needs to shorten up to keep your degree sizes consistent. But for low angles, you get acceptable accuracy with a single string length.