A kamal is a celestial navigation device that determines latitude. The invention of the kamal allowed for the earliest known latitude sailing, and was thus the earliest step towards the use of quantitative methods in navigation. It originated with Arab navigators of the late 9th century, and was employed in the Indian Ocean from the 10th century. It was adopted by Indian navigators soon after, and then adopted by Chinese navigators some time before the 16th century.
The kamal consists of a rectangular wooden card about 2 by 1 inch (5.1 by 2.5 cm), to which a string with several equally spaced knots is attached through a hole in the middle of the card. The kamal is used by placing one end of the string in the teeth while the other end is held away from the body roughly parallel to the ground. The card is then moved along the string, positioned so the lower edge is even with the horizon, and the upper edge is occluding a target star, typically Polaris because its angle to the horizon does not change with longitude or time. The angle can then be measured by counting the number of knots from the teeth to the card, or a particular knot can be tied into the string if travelling to a known latitude.
The knots were typically tied to measure angles of one finger-width. When held at arm's length, the width of a finger measures an angle that remains fairly similar from person to person. This was widely used (and still is today) for rough angle measurements, an angle known as issabah in Arabic, or a chih in Chinese. By modern measure, this is about 1 degree, 36 minutes, and 25 seconds, or just over 1.5 degrees. It is equal to the arcsine of the ratio of the width of the finger to the length of the arm.
Due to the limited width of the card, the kamal was only really useful for measuring Polaris in equatorial latitudes, where Polaris remains close to the horizon. This fact may explain why it was not common in Europe. For these higher-latitude needs somewhat more complex devices based on the same principle were used, notably the cross-staff and backstaff.
where D = distance to the object observed
S= size of object observed
d= distance from kamal to the observer's eye
s= apparent size of object observed, at apparent distance
Around this time (of the Discoveries) the Arabs were using a very ingenious instrument in the Mediterranean Sea that allowed them to know latitude. It was called al-kamal – the guiding line. It was simply a small wooden board with a notch made on top and in the middle of it and a piece of string that was attached to the centre of the board; it could only be operated at night. To find where they were, an operator would adjust the distance of the piece of wood closer or farther away from his eyes in order to have the bottom of the plank levelled with the horizon and the North Star placed inside the notch. The operator would then tie a knot in the string on the point where it touched his nose, and a celestial location was then marked. There were no angles to measure and record or complicated mathematical formulas to consider. From then on the navigator knew that every time the horizon was levelled with the bottom of the board, the North Star was inside the notch, and the distance measured in the string was the same as marked, he was in a place that had the same latitude as the one where he had made those measurements. Portugal had to wait for Vasco da Gama to bring it from India on the first voyage he made there in 1498.
- (McGrail 2004, p. 316)
- (McGrail 2004, p. 393)
- (McGrail 2004, pp. 85–6)
- Raju, C. K. (2007), Cultural Foundations of Mathematics: The Nature of Mathematical Proof and Transmission of the Calculus From India to Europe in the 16th c. CE, Delhi: Pearson Longman, pp. 240–59, ISBN 81-317-0871-3, retrieved 10 September 2008
- Burch, David, Fundamentals of Kayak Navigation, 2nd edition, The Globe Pequot Press, 1993, ISBN 1-56440-155-3
- Carlos B. Carreiro, Portugal's Golden Years, The Life and Times of Prince Henry "The Navigator". Dorrance Publishing Co., p. 84