The question of the proper height of bracing a bow has long been a subject for discussion among archers. Many rules have been given, but each archer has his own preference.
It is believed that a theoretical treatment of this subject, together with some experimental data, may assist the archer in selecting the proper bracing height for his particular bow.
We may proceed as indicated in the preceding articles to obtain the string tension and the drawing force as functions of the draw.
If we obtain values of these variables for various bracing heights of the bow string, we may plot curves which will enable us to make some interesting conclusions.
Let us consider a six foot bow which has a middle section of eight inches length that does not bend.
These values will depend upon the bracing height of the bow string, H0. Let us determine these values for four different values of HO; HO = 0; HO = 3.0", HO = 6.0", and HO = 9.0".
Graph 3, shows the values of T and F for the four conditions. Each curve is labeled with the initial bracing height of the bow string. HO.
For HO= 0, the value of T rises very rapidly from zero to about 32 and then increases slowly to about 37, for a 28 inch draw.
For HO = 3", the value of T drops rapidly on the first half of the draw. And then increases during the last half of the draw.
For larger values of HO, the curves for T are more symmetrical, decreasing during the first half of the draw and increasing in the last half of the draw.
If we study the curves for F we discover a very interesting fact that apparently has not been observed by archers. The force F, for a full draw, is practically independent of the bracing height of the string. In other words, all of the curves almost merge into one, for draws of over 20 inches.
This means that a bow braced high does not require much more strength to hold, when fully drawn, than if it were braced low. This was discovered several years ago through some mathematical equations. At first this did not seem reasonable and it was thought that some mathematical mistake had been made. To check over the mathematical development would have taken considerable time, so rather than do this, a bow was tested and it was found that the equations were checked by experimental results. Since then many bows have been tested and for all practical bracing heights, the force-draw curves merge into one common curve near the end of a full draw. Any archer may readily test this with his own bow. It should be remembered, however that the stress in the bow fibers goes up with increase in bracing height so that it is not wise to brace it too high for, it may break on full draw.
In a previous article, attention was called to the fact that the tension in the string does not change a great deal with increase in the draw. In fact the tension at full draw is seldom as great as when at rest. This feature was observed by Pope and is probably familiar to many archers. The curves of Graph 3 show all of these interesting features.