``Playability'' can be defined as the region of a multidimensional space given by the parameters of the model where a good tone is obtained, where by good tone, we usually mean the Helmholtz motion.
The string sticks to the bow for most of the time, slipping
backwards just once per vibration period.
String motion:
Motion of a bowed string during an ideal Helmholtz motion. String velocity at the bowed point and trasverse force exerted by the string on the bridge.