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The Flight of An Arrow

As compared with a high velocity bullet which has a sensibly flat trajectory up to several hundred yards, an arrow is slow-moving indeed, so that even at short ranges there is a large effect of gravitational force on the trajectory. Consideration of the flight of an arrow, particularly of one shot to achieve maximum distance, must take into account this large gravitational effect as well as that of air resistance. Thus far no work has been published, specifically relating to air resistance, that is thoroughly rigorous or entirely valid. The air resistance varies approximately as the square of the arrow velocity. If the proportionality constant for a particular velocity were known, it would be feasible to compute with fair accuracy the trajectory of an arrow having known initial velocity and angle of departure. It could be done by the method of short sections, by which the position, angle and velocity of the arrow at the end of the section are found, assuming constant resistance over the entire short distance. Each section is treated successively in the same way, with the initial conditions established by the computation of the preceding section. Equations for this method have been worked out but have not been applied or checked experimentally. The Didion-Bernoulli method[6] is also applicable. If reliable data on resistance can be obtained—and this is feasible by several methods—we should be able to predict accurately the elements of the trajectory of any kind of arrow shot from a bow of known available energy and virtual mass.

All arrows for target and hunting have stabilizing vanes, usually made of turkey feathers. Since the air resistance to such vanes is quite high, flight arrows during the past several years have had very small stabilizing vanes of Pyralin. Many flight shooters follow the practice of rubbing the arrows to a high gloss and then, before the shot, giving them an extra polishing with graphite. for target shooting this is not necessary since the ranges are relatively short. Good flight shooters today are achieving distances in the neighborhood of 500 yd., and some free-style shooting in tournament competition has exceeded 600 yd.

Hunting arrows usually have fairly large broadhead points, sharpened to a keen edge for penetration. It is difficult to affix these to the shaft so that they are perfectly true and symmetrical, and consequently there may be a slight steering effect by the broadhead. This is usually counteracted by using three and sometimes four large vanes, symmetrically placed on the shaft with great care. In most cases they are attached at a slight angle, to accentuate spinning of the shaft as it flies. To be sure, this dissipates energy at the expense of range; but the hunting bow is much stronger than the target bow and there is energy to spare for the distance at which the hunter may expect to make a successful shot. This distance for a skilful archer may, on the average, be 60 yd. or less.