Ancient throwing machines: A method to calculate their performance

The main aim of this paper is to propose a method to measure the performance of ancient throwing machines powered by torsional motors. This could be achieved using a model of torsional motor that allowed evaluating the torsional spring(s) elastic energy and by describing the machine kinematics; thus, the speed of the projectile was calculated from the moment the trigger was pulled to the instant in which the projectile left the machine. Since the ratio between the dimensions of the main parts of the ancient throwing machines was constant (they were designed on a modulus), once the size of one part of the machine (e.g. a remain) was known, the performance of the whole machine could be predicted. Finally, calculation examples are presented for a ballista designed according to Vitruviusʹ reports and for a repeating catapult; the results obtained show that those “ancient artillery devices” thrust the projectile with considerable energy.