SCALING MODULUS AS A DEGREE-OF-FREEDOM IN THE DESIGN OF LOCUST LEGS

Previous work has shown that the scaling of mechanical behaviour in be nding of the metathoracic tibiae of the African desert locust (Schisto cerca gregaria) is not predicted by the scaling of external dimensions . The flexural stiffness of the tibia scales to (body mass)(l.53), whi ch is similar to the predictions of the elastic similarity model of sc aling. The external dimensions, however, scale in a manner that produc es relatively more elongate limb segments - an observation that differ s from the predictions of any existing scaling model. In this paper, w e examined two alternative hypotheses to explain this uncoupling of mo rphology and mechanics: (1) that the load-bearing cuticular material i s distributed in the legs in a manner that is not indicated by changes in external dimensions, or (2) that the stiffness of the cuticular ma terial is altered to produce the observed scaling of flexural stiffnes s. The second moment of area (1) scaled to (body mass)(1.19), which wa s similar to scaling I to (tibial radius)(4). This indicates that the relationship between the external dimensions of the tibiae and the spe cific distribution of load-bearing material is conserved independently of scale. Therefore, the locust achieves the observed scaling of flex ural stiffness by altering the modulus of the load-bearing cuticular m aterial. In fact, the time-dependent modulus (E') scales to (body mass )(0.311). In essence, the scaled material stiffness provides a degree of freedom in design in addition to external morphological dimensions in accommodating the changing demands placed on a skeletal structure w ith increases in body size.