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Exterior Ballistics of Bows and Arrows
by J. W. Rheingans
Part 1 of 10

Exterior Ballistics of Bows and Arrows deals with the flight of an arrow after it leaves the bow. This article is concerned primarily with the maximum range that can be obtained with arrows of various designs, and with various initial velocities.

When an arrow is shot from a bow, the distance that it will fly depends upon the following:

1. —The velocity with which it leaves the bow, called the "Initial Velocity" ;
2. —The angle of departure;
3. —The weight of the arrow;
4. —The resistance or friction or drag of the arrow in air;
5. —Velocity and direction of wind.

The velocity with which an arrow leaves the bow depends upon the force of the bow, the efficiency of the bow, and the mass of the arrow. This article will not deal with the relationship between these factors, which is called "Interior Ballistics", but will simply assume a given initial velocity when calculating the effect of arrow design on maximum range.

The angle of departure for maximum range is approximately 45 degrees with the horizontal. The actual angle of departure for maximum range will be calculated below.

Since the effect of wind on the maximum range is variable and hard to determine, no attempt will be made to evaluate its effects.

The resistance to motion of an arrow during its flight thru the air considerably reduces its range. Since this resistance depends upon the design of an arrow, the first step in determining the effects of arrow design on maximum range will be to determine this resistance.

Resistance varies with velocity. The higher the velocity the greater the resistance. It has been found in wind tunnel tests, and by the firing of a large number of projectiles, that the resistance varies as the square of the velocity for velocities below 800 feet per second.