On the mechanics of the arrow: Archer's Paradox

Abstract

In ancient bows the grip of the bow was in the way of the arrow. The arrow needed to get round the bow while being accelerated; this phenomenon is called the ‘Archer's Paradox’. In the forties it was observed experimentally with high-speed cameras that the arrow vibrates in a horizontal plane perpendicular to the vertical median plane of the bow. These movements are started and controlled by the movements of the two points of contact with the bow, viz. the middle of the string in contact with the rear end of the arrow and the grip where the arrow slides along the bow. The latter contact imposes a moving-boundary condition. The numerically obtained results are satisfactorily in agreement with experimental data. The model can be used to estimate the drawing force of ancient bows of which only the contemporary arrows are available and also for the design of new archery equipment.