If all bows were made of a homogenous material such as steel, it would be possible to construct them according to theoretical computations. The proper dimensions for any desired bending form could be obtained by relatively simple mathematical computations.
Most bows, however, are made of wood and the wood varies not only from limb to limb, but within the same limb. These variations are due to many factors, such as grain, knots, curing, moisture content, cell size, etc. There is not only a variation in the strength of the wood but a considerable variation in the amount of set that the wood will take.
Long years of experience are usually required in mastering the technique and judgment necessary to construct a bow out of any billet. Any archer who has ever made a bow will admit that his first bows were far from ideal, although they would of course shoot an arrow.
It is impossible to write out instructions for making a bow of wood so that a beginner can make a perfect bow. There are a number of good books on the subject and most of them tell about as much as possible.
The master bowyer can give much valuable advice but he can not give his instructions so well that a beginner can make as good a bow from a billet as the master bowyer could make from the same billet.
The beginner in bow making should thoroughly understand that he can not copy dimensions from another bow and expect his bow to bend in the same form or to be as good as the one he is attempting to copy. In fact, it is quite possible that his bow may be worthless, even though all dimensions are identical with those of a fine bow.
As was stated in the beginning, if bows were made of homogeneous materials, exact dimensions could be given and followed. While it is not possible to give a set of dimensions for a bow made of most woods, nevertheless an understanding of some of the laws of bending should be of great value to anyone making a bow.
It is not the intention to recommend in this paper the shape of a bow nor its cross sectional dimensions. However, a treatment of the effect of thickness and width on the form of bending may be of some assistance to archers who are interested in bow making, and may lead to a radical change in bow construction.
We shall therefore consider some specific cases which are of fundamental importance. It is hoped that those archers, who do not readily follow mathematical developments, will obtain some information from the drawings and text of this article. There are a great number of archers who do follow mathematical developments and who have shown interest in previous articles. It is hoped that they will obtain some value from this treatment.