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Exterior Ballistics of Bows and Arrows
Part 2 of 10

In archery, we deal with velocities well below this value, and a simple equation for resistance can be written as follows:

Rf - KV2 (1)
Where  Rf  = the resistance in pounds
K  = a coefficient depending upon arrow design.
V  = velocity in feet per second.

The coefficient K applies to only one design of arrow. If the value of K is measured for a given arrow, any change in design, such as a change in length, diameter, or size of feathers, would require a new wind tunnel test to determine the new value of "K". To obviate an infinite number of wind tunnel tests, the separate factors in arrow design affecting the resistance coefficient can be evaluated, making it possible to calculate "K" for any design of arrow.

The resistance of arrow is made up of the following:

1.—The head-on resistance, which includes the rear end drag. This resistance depends upon the head-on area of the arrow, and will therefore vary as the square of the diameter. The head-on resistance will also vary in accordance with the shape of the head of the arrow, an ogival shaped head giving considerably less resistance than a blunt head.
2.—Skin friction of the arrow shaft. This varies with the surface area of the shaft and therefore varies with the length and diameter of the shaft.
3.—Skin friction of the feather. This will vary with the total area of both sides of the feathers. The above can be expressed in terms of an equation as follows:
K = K1 BD2 + K11 LD + K111 F (2)
Where K, K1, K11 and K111 are coefficients.
B is a coefficient of form for the head of the arrow.
D is the diameter of the arrow in inches.
L is the length of the arrow in inches.
F is the area of both sides of the feathers in square inches.

By determining the coefficients K1, K11 and K111 in equation (2), the value of K for any design of arrow can be calculated. One way to determine these values accurately is by wind tunnel tests.