Bow-arrow interaction in archery.

A mathematical model of the flight of the arrow during its discharge from a bow was proposed by Pekalski (1990). His description of the model was incomplete. In this paper, I give a full description of the model. Furthermore, I propose some improvements that make his model more consistent with reality. One achievement is the modelling of contact of the arrow and grip; the pressure button is modelled as a unilateral elastic support. The acceleration force acting upon the arrow during the launch is predicted by an advanced mathematical model of bow dynamics. There is a satisfactory conformity of the simulation and experimental results. The new model predicts that the arrow leaves the pressure button before it leaves the string, as reported previously. The ability to model arrow dynamics can be used to improve the adjustment of the bow-arrow system for optimal performance.