Maximum bow force revisited for the cello—Instrumentation with a precision pendulum

Schelleng (1971), Askenfelt (1989), Schumacher (1993), and Schoonderwaldt et al. (2008) formulated—in slightly different ways—how the maximum bow force relates to bow velocity, bow-bridge distance, string impedance, and friction coefficients. Related measurements at the respective transitions between Helmholtz und bifurcation regimes cover a diverse scenario of bowing machines and stringed instruments. So far, the empirical data does not clearly support either of the theories in a general way. A bowing pendulum of virtually infinite radius has been constructed to allow precise measurement of relevant bowing parameters. Two cellos are measured across all strings for three different bow-bridge distances. The empirical data suggest that linear relations predict the maximum bow force sufficiently well and a more distinct general model can be drawn. Furthermore, the pendulum employs an adaptive bow driving mechanism instead of a motor or engine. Such adaptive bowing discloses that mentioned regimes are stable and transitions between them sometimes require a hysteresis on force and speed variations. This explains some of the uncertainties in earlier studies and in this study. To confirm the findings the friction coefficients are measured separately by means of the same pendulum construction.