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Arrow design
Part 4 of 6

Arrow Design:

Having selected a material suitable for use in arrows, by means of the above spine testers, formulas, or tables, let us stick out our necks by venturing into the field of arrow design. Since spine has been defined as a measure of suitable arrow material, let us now drop this word and use "stiffness", as be­ing a measure of the resistance of an arrow to bending. How­ever, since the deflection of an arrow as measured in a spine testing machine is a measure of the stiffness, and since most archers are more familiar with the term deflection, we will use this latter designation in the following.

In designing an arrow, the question then is, what deflec­tion shall the arrow have for best flight and greatest accuracy? Also, how will the correct deflection vary with the weight of the arrow and the weight of the bow?

In June 1933, Dr. Paul E. Klopsteg wrote a letter revising his discussion of spine in the June 1933 archery review. This letter was never published, but it checks the author's views on arrow design.

Still more recent work by the authors indicates that for any given bow and shooter, deflection of all arrows should be constant, regardless of arrow weight. This has checked out in practice on the shooting machine and is derived mathe­matically from the following consideration:

The natural vibrating time of an arrow depends upon its weight and deflection according to the following relation­ship.

formula35 (1K)

K equals a constant.
W equals weight of the arrow.
D equals deflection of the arrow.

The time it requires an arrow to go from full draw to delivery is approximately:

formula36 (1K)

C equals a constant.
W equals weight of the arrow.

The most reasonable explanation of the "paradox" lies in that the arrow bends first concave to the left under the push of the string and then concave to the right, and if this latter position coincides with the passing of the rear end of the ar­row from the bow, there is no slap or side-kick. If the deflec­tion is too small, the arrow will return towards the bow before it has passed and there will be slap. If the deflection is too great, its first end will be so far away from the bow and so slow in reversing that although there may be no slap, the arrow will flirt after it has left the bow. Proper deflection will, therefore, insure proper delivery without slap or displacement. It then follows that if the relationship between T and T1 is constant, their quotient will be constant and the arrow will be delivered properly.

formula37 (1K)

It will be noted that the weight of the arrow cancels out. This is obvious because the heavier the arrow, the lower its velocity, and similarly its vibrating time, both in the same power; therefore, the deflection of the arrow should be con­stant for any particular bow. This deflection should be de­creased for heavier bows and increased for lighter bows.

To arrive at some standard method of comparison, the authors again suggest that a standard method of measuring the deflection of an arrow be adopted. The arrow deflection can quite readily be measured in the spine testers described above and it is again suggested that the standard for compari­son be its deflection in inches, when supported on 26" centers and loaded with a two-pound weight in the middle. This would certainly simplify the studying, building, or filling of orders for arrows.

If it is desired to include shorter arrows with the supports, say 25" or 24" apart, the deflection obtained with a two-pound weight can be multiplied by a constant factor for compari­son with the standard 26" supports. The correct factors are as follows:

1. For 25" supports, multiply the deflection obtained by 1.12 for comparison with 26" support deflections.

2. For 24" supports, multiply the deflection obtained by 1.27 for comparison with 26" support deflections.

Note that the smaller the distance between supports, the smaller the deflection, since it varies as the cube of the dis­tance between the supports.