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

Previous work has shown that the scaling of mechanical behaviour in bending of the metathoracic tibiae of the African desert locust (Schistocerca gregaria) is not predicted by the scaling of external dimensions. The flexural stiffness of the tibia scales to (body mass)1.53, which is similar to the predictions of the elastic similarity model of scaling. The external dimensions, however, scale in a manner that produces relatively more elongate limb segments ­ an observation that differs from the predictions of any existing scaling model. In this paper, we examined two alternative hypotheses to explain this uncoupling of morphology and mechanics: (1) that the load-bearing cuticular material is distributed in the legs in a manner that is not indicated by changes in external dimensions, or (2) that the stiffness of the cuticular material is altered to produce the observed scaling of flexural stiffness. The second moment of area (I) scaled to (body mass)1.19, which was similar to scaling I to (tibial radius)4. This indicates that the relationship between the external dimensions of the tibiae and the specific distribution of load-bearing material is conserved independently of scale. Therefore, the locust achieves the observed scaling of flexural stiffness by altering the modulus of the load-bearing cuticular material. 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 with increases in body size.