Linear Estimation of the Rigid-Body Acceleration Field From Point-Acceleration Measurements

Among other applications, accelerometer arrays have been used extensively in crashworthiness to measure the acceleration field of the head of a dummy subjected to impact. As it turns out, most accelerometer arrays proposed in the literature were analyzed on a case-by-case basis, often not knowing what components of the rigid-body acceleration field the sensor allows to estimate. We introduce a general model of accelerometer behavior, which encompasses the features of all acclerometer arrays proposed in the literature, with the purpose of determining their scope and limitations. The model proposed leads to a classification of accelerometer arrays into three types: point-determined; tangentially determined; and radially determined. The conditions that define each type are established, then applied to the three types drawn from the literature. The model proposed lends itself to a symbolic manipulation, which can be readily automated, with the purpose of providing an evaluation tool for any acceleration array, which should be invaluable at the development stage, especially when a rich set of variants is proposed.