Tests were made on Yew, Osage and Lemonwood as a matter of interest. The spine rating number of course does not give the rating of bow woods.
The last column of Table No. 1 gives the diameters of the dowels for a fixed deflection of 1.2". In selecting a material for arrows, this diameter has to be considered since the greater the diameter the greater the air resistance and effect of paradox. These factors become important in flight arrows. Due to the length of an arrow however, the diameter probably has only a small influence on the air resistance. As soon as Professor G. J. Higgins of the University of Detroit publishes the results of his studies on the air resistance of arrows, and if we can obtain the shape of the efficiency curve of flight bows from Mr. Klopsteg or Mr. Hickman, the relationship between weight and diameter for maximum flight can be worked out accurately.
Since the spine rating number "N" as defined above is comparative only for static bending machines having the same distance between supports and using the same loads, it is suggested that a universal spine number be used defined as follows:
Where S = a universal spine number.
E is the modulus of elasticity.
Wc is the weight in pounds per cu. ft. of the material.
The factor 100,000 is used to bring the spine designation into full numbers. The smaller "S" the better the spine. The weight per cu. ft. can be readily determined from the length, diameter, and weight of the specimen tested.
The modulus of elasticity E can be computed from a transposition of equation (2) as follows:
Where E is the modulus of elasticity.
P is the load in pounds on the dowel, half way between the supports.
l is the distance in inches between the supports.
D is the measured deflection in inches, half way between supports due to the load P.
d is the diameter of the dowel in inches.
The dowel must be round, solid and of constant diameter, and should not be footed or feathered, nor should the pile be attached.
For any one static bending machine Pl3/2.35 is a constant and need be computed only once for that particular machine.
If we let K = Pl3/2.35 then
The universal spine number S as computed above could be used to compare tests made in any part of the country, on any of the static bending machines. This would answer the plea of various archers for a uniform designation of spine.