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Physics of Bows and Arrows
by Paul E. Klopsteg

There is presumably no sport that may not in some of its aspects be subjected to physical analysis or experiment, particularly so when certain specialized instruments are used in its pursuit. Golf, baseball, tennis, lawn bowling and boomerang throwing are examples. In each of them a physicist may find plenty of scope for "recreational physics," the application of physics for his own recreation. No sport to my knowledge affords greater opportunity for the exercise of recreational or hobby physics than does archery. For a decade and more it has from time to time provided me with hobby material of several kinds. One of them is the outdoor recreation of target shooting and bow-and-arrow hunting. Another is the collecting of old books and prints. Scientific study and experiment constitute a third. Still another is the application of results of the third to improvement in design, and the exercise of craftsmanship in fashioning better weapons and missiles.

Although much that is interesting could be written on the first two aspects of the hobby, this is not the place to attempt such an undertaking. This is an article for physicists written by one who has experienced great satisfaction in the joining of his vocation with his avocation. In it he hopes to convey some idea of what he has experienced and to present certain material that may prove interesting to them and to their students, whether or not they are archers.

The bow is one of the earliest man-made machines with which it is possible to store energy slowly, and at will transform it into the kinetic energy of a missile that is being projected at a more or less distant object. Muscular effort provides the energy for propulsion; coordination of mind and muscle directs that energy. Although the bow is one of the most ancient weapons, the bow and arrow are as modern as they are ancient. They are with us today in greater numbers than ever and are gaining devotees at a rapidly increasing rate. An explanation of the persistence of interest in archery may be the fascination of seeing the arrow fly or in hearing its "thunk" as it strikes. Possibly love of the bow, like affection for one's dog, or love of an open fire, is an inheritance passed along through generations of ancestors for whom the bow meant subsistence and protection.

It hardly needs saying that the toy archery set procurable in the dime store is not representative of the bows and arrows that we are considering. These are by no means toys. They are implements capable of storing and converting large amounts of energy. Even the smaller sizes, for childrens' use, can cause injury and damage if carelessly handled, and their use should be permitted only under adult supervision. The larger sizes, as used in hunting, constitute a powerful, lethal weapon. There are many thousands of bow-and-arrow hunters; of these, large numbers have discarded the rifle for the bow. They have discovered that, although the bag is necessarily limited by the smaller range and accuracy of the bow, there is incomparable compensation in the thrill of a successful stalk—an art not called for in rifle shooting—and in seeing the arrow miss by the narrowest of margins. I have had no greater fun in hunting than to see a broadhead arrow, at 50 yd., overtake a fleeing jackrabbit and pass directly between his ears.

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Fig. 1. A 42-lb. yew bow held at full draw while the arrow is being aimed.