The archer's paradox

Abstract

The archer's paradox is the fact that an arrow does not fly to its mark along the line represented by its axis. The explanation of the archer's paradox was found by means of high speed spark photography which P. E. Klopsteg undertook in order to secure direct evidence of what an arrow does as it leaves the bow [1]. The impulse normal to the axis of the arrow, caused by the release of the fingers from the string, as well as the column-like force of the string on the arrow during its acceleration, results in a significant bending of the arrow shaft as it transits the bow. This allows the arrow to undulate around the bow handle and follow a straight course towards its target without striking the bow handle. P. E. Klopsteg explained this paradox and provided a qualitative understanding of the reasons for matching arrows to a given bow and archer combination [2]. The objective of our study is to develop the mathematical methods of the archer's paradox.