Conductance-Domain In Situ Single-Point Calibration for an FSR Array Embedded Inside a Handball

Abstract

Embedding a multichannel force-sensitive resistor (FSR) array inside a sports ball creates a calibration challenge with no precedent in the existing literature: every sensor is permanently sandwiched between the outer leather cover and the inner rubber bladder, subjecting each channel to a structural preload that varies channel-by-channel due to stitching tension and cover-bladder assembly tolerances. Prior FSR calibration practice either eliminates preloads before calibration or treats them as a source of error. This letter shows instead that performing calibration in situ, after full ball assembly in the preloaded state, is not merely acceptable but advantageous. Converting the voltage-divider output to conductance and normalizing by a single 30-N in situ reference measurement causes the structural preload, the pull-down conductance, and the per-channel sensitivity factor to cancel simultaneously in one algebraic step. Applied to a custom 36-channel FSR array (Type A: 30 trapezoidal channels; Type B: Six circular channels, one at the center of each pentagonal panel), this normalization reduces interchannel sensitivity variation substantially for loads of 20 N and above. The normalized conductance exhibits a semilogarithmic linearity with force ($r = 0.975$), consistent with Hertzian contact mechanics and percolation-driven transport, which supports a type-specific two-parameter log-space formula achieving mean absolute percentage error (MAPE) $= 6.3\%$, recovering 89% of the accuracy gain of full per-channel five-load calibration (MAPE $= 3.5\%$) from a single 30-N in situ measurement per channel.