SCHILDER, R.J.; MARDEN, J.H.: Workloop Force and Lever Arm Length Allometry in Dragonfly Flight Motors

Maximum isometric muscle force production scales as muscle mass^2/3, whereas maximum net force output by flying animals scales isometrically with total flight muscle mass. What causes this transition between the two scaling relations? We examined this question by subjecting dragonfly flight muscles to contraction regimes (workloops) that simulated working conditions of the muscle during maximum load lifting. Our hypothesis is that a combination of allometric (rather than isometric) scaling of average net muscle force output and the ratio of lever arm lengths (i.e. mechanical advantage) in the muscle-to-wingtip mechanical linkage is sufficient to account for the observed transition from muscle mass^2/3 scaling to the isometric scaling. We found that 1) maximum isometric force scales as muscle mass^0.67, 2) maximum net force production during load lifting (F₂) scales as total flight muscle mass^1.067 (M^1.067), 3) workloop average net force output (F₁) scales as muscle mass^0.86 (M^0.86), 4) muscle fulcrum – lever arm length (d₁) scales as muscle mass^0.54 (M^0.54), and 5) fulcrum – wingtip length (d₂) scales as muscle mass^0.33 (M^0.33). Since moments are conserved on either side of a fulcrum (F₁*d₁ = F₂*d₂), maximum net force output by the muscle-wing system (F₂) should scale as: M^0.86 * (M^0.54/M^0.33) = M^1.07, which agrees well with the observed scaling (M^1.067) in this study and previous load lifting experiments on dragonflies and other flying animals.