Mechanics of the Contact Area Between a Violin Bow and a String. Part III: Parameter Dependence

This paper explores aspects of the simulation model of a string bowed by a bow of finite width developed in the companions [1, 2] to this paper. In particular we study the details of the stick-slip transitions, the flattening effect, and the influence of changing bow-hair compliance and string bending stiffness. Modelling of the finite width changes markedly the region of the player's control-parameter space in which musically acceptable waveforms are obtained. It is clearly important to allow for finite-width effects in future systematic studies of bowed-string dynamics. It is shown that one can go some way towards doing this by defining an "equivalent point-bow model" in which use is made of the finite-width results to modify the friction model used in point-bow simulations.