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First published online January 27, 2004
Journal of Experimental Biology 207, 767-776 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00817

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A hierarchical analysis of the scaling of force and power production by dragonfly flight motors

Rudolf J. Schilder^* and James H. Marden

208 Mueller Laboratory, Department of Biology, Pennsylvania State University, University Park, PA 16802, USA

^* Author for correspondence (e-mail: rjs360{at}psu.edu)

Accepted 25 November 2003

Maximum isometric force output by single muscles has long been known to be proportional to muscle mass^0.67, i.e to muscle cross-sectional area. However, locomotion often requires a different muscle contraction regime than that used under isometric conditions. Moreover, lever mechanisms generally affect the force outputs of muscle–limb linkages, which is one reason why the scaling of net force output by intact musculoskeletal systems can differ from mass^0.67. Indeed, several studies have demonstrated that force output by intact musculoskeletal systems and non-biological systems is proportional to motor mass^1.0. Here we trace the mechanisms that cause dragonflies to achieve a change from muscle mass^0.67 scaling of maximum force output by single flight muscles to mass^1.0 scaling of dynamic force output by the intact dragonfly flight motor. In eight species of dragonflies, tetanic force output by the basalar muscle during isometric contraction scaled as muscle mass^0.67. Mean force output by the basalar muscle under dynamic conditions (workloops) that simulated in vivo maximum musculoskeletal performance was proportional to muscle mass^0.83, a significant increase in the scaling exponent over that of maximum isometric force output. The dynamic performance of the basalar muscle and the anatomy of its lever, consisting of the second moment of area of the forewing (d₂) and the distance between the muscle apodeme and the wing fulcrum (d₁), were used to analyze net force output by the integrated muscle-lever system (F_ind). The scaling of d₂ conformed closely to the expected value from geometic similarity (proportional to muscle mass^0.31), whereas d₁ scaled as muscle mass^0.54, a significant increase over the expected value from geometric similarity. F_ind scaled as muscle mass^1.036, and this scaling exponent was not significantly different from unity or from the scaling exponent relating maximum load-lifting by flying dragonflies to their thorax mass. Thus, the combined effect of a change in the scaling of force output by the muscle during dynamic contraction compared to that during isometric contraction and the departure from geometric similarity of one of the two lever arm lengths provides an explanation for how mass^1.0 scaling of force output by the intact musculoskeletal system is accomplished. We also show that maximum muscle mass-specific net work and power output available scale as mass^0.43 and mass^0.24, respectively.

Key words: force, work, power, scaling, allometry, dynamic force output, dragonfly, flight motor, lever arm, basalar muscle, work loop, load lifting

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