So much for the static stresses existing when the bow is at rest in the braced position or is being drawn. During the discharge of the arrow there appears a dynamic stress which reaches a maximum as the string becomes taut. The flight shooter doesn't worry about this as he can afford to break a string every shot. However the target shooter or the hunter must build his string to withstand this dynamic stress. The magnitude of this stress is affected by several factors, particularly the cast of the bow and the weight of the arrow. By gradually decreasing the size of the string to the breaking point, knowing accurately the strength of these various sized strings as made up by my particular method of manufacture, I have found that the dynamic stress is usually about twice the maximum static stress as indicated by the diagram Fig. 1. This factor of two is in line with the practice of some flight shooters to load flight bow strings about twice as heavy as target bow strings.
With the above guide as to the strength required in a bow string we may proceed to the next question of how to supply this strength. For this, one must have knowledge of the strength of the material from which he constructs the string.
In making a bow string it is important to use a material which has great strength for its weight. In order to compare bow string material it is necessary to reduce tensile strength data to some standard basis. Suppose we arbitrarily agree that the strength coefficient (S.C.) by which a string material shall be judged be
where S is the strength in lbs./sq. in. or
with P the force in pounds and A the cross section in sq. in. Specific gravity (Sp. Gr.) referred to water equals
where W is the weight in grams and V the volume in cubic centimeters.
V in cubic centimeters equals
cubic inches. If L is the length in inches then
If one determines the weight per foot of material, W/f, then
If the weight per foot of material is expressed in grains, W/fg, then
Thus, to determine the value of a material for making bowstrings it is only necessary to measure the strength of the material in pounds, multiply by 3040 and divide by the weight in grains of one foot of the material.