Maximum bow force revisited

Schelleng [J. Acoust. Soc. Am. 53, 26-41 (1973)], Askenfelt [J. Acoust. Soc. Am. 86, 503-516 (1989)], Schumacher [J. Acoust. Soc. Am. 96, 1985-1998 (1994)], and Schoonderwaldt, Guettler, and Askenfelt [Acta Acust. Acust. 94, 604-622 (2008)] formulated-in different ways-how the maximum bow force relates to bow velocity, bow-bridge distance, string impedance, and friction coefficients. Issues of uncertainty are how to account for friction or for the rotational admittance of the strings. Related measurements at the respective transitions between regimes of Helmholtz motion and non-Helmholtz motion employ a variety of bowing machines and stringed instruments. The related findings include all necessary parameters except the friction coefficients, leaving the underlying models unconfirmed. Here, a bowing pendulum has been constructed which allows precise measurement of relevant bowing parameters, including the friction coefficients. Two cellos are measured across all strings for three different bow-bridge distances. The empirical data suggest that-taking the diverse elements of existing models as options-Schelleng's model combined with Schumacher's velocity term yields the best fit. Furthermore, the pendulum employs a bow driving mechanism with adaptive impedance which discloses that mentioned regimes are stable and transitions between them sometimes require a hysteresis on related parameters.