Archer's paradox

Settled in 1943 by Paul E. Klopsteg.

Archers long noticed that an arrow resting against the side of a bow, seemingly pointed off-target, nonetheless flies straight to the mark, a puzzle dubbed the 'archer's paradox.' Paul Klopsteg used high-speed spark photography in the early 1940s to directly capture an arrow's motion as it left the bowstring, showing the shaft flexes and oscillates around the bow's riser in a way precisely timed to the launch, so that by the time it clears the bow it is traveling straight along the intended line. His 1943 American Journal of Physics paper established that matching an arrow's bending-mode period ('arrow spine') to the bow's draw characteristics is essential for accurate flight, a principle still used in modern archery equipment design. The paradox is now a standard example in classical mechanics courses on beam flexure and resonance.

An arrow visibly pointed off-target at the moment of release still hits the bullseye, because its own elastic wobble is precisely tuned to cancel out just as it clears the bow.

Explanations that circulated

• The mistaken folk belief that skilled archers must consciously aim to the side of the target to compensate for the bow's obstruction, rather than the arrow self-correcting through its own elastic bending oscillation as it leaves the bow

References

• Physics of Bows and Arrows, Paul E. Klopsteg, American Journal of Physics, 1943