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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

View larger version (12K): [in a new window]   Fig. 1. Schematic representation of a basalar muscle and its third order lever system. FWf indicates the position of the wing fulcrum, FW represents forewing length and Ba indicates the position of the apodeme of the basalar muscle. The basalar muscle (yellow) produces force Fdyn, which is then transmitted through d1, the distance between the basalar apodeme and wing fulcrum, and d2, the second moment of wing area where the mean aerodynamic force acts.

View larger version (23K): [in a new window]   Fig. 2. Example of raw data obtained during a workloop experiment. The sinusoidal length cycles are shown in red, the timing of stimulation is shown in blue, and resulting tension developed by the basalar muscle is shown in green. Tension data from the fourth cycle were used for further analyses.

View larger version (44K): [in a new window]   Fig. 3. Detailed ventral view of the internal surface of the Anax junius dorsal thorax at the base of the forewing, showing the location of the basalar muscle apodeme (Ba) and the wing fulcrum (Wf) of the forewing (FW). The distance between these two structures is the muscle apodeme-to-wing fulcrum lever arm length (d1). All muscle tissue has been removed. Scale bar, 1 mm. A portion of the wing is drawn to orient the reader; this wing is not to scale.

View larger version (17K): [in a new window]   Fig. 4. (A) Maximum lifting force (Flift) as a function of thorax mass (mthor). log10Flift=1.682+1.035log10mthor (r2=0.99; S.E.slope=0.036; N=10). (B) Maximum isometric force (Fstat) as a function of basalar muscle mass (mbas). log10Fstat=2.863+0.670log10mbas (r2=0.96; S.E.slope=0.050; N=10). The datapoint marked `Teneral' indicates a newly emerged and therefore physiologically immature T. lacerata. This point was excluded from the regression analysis.

View larger version (19K): [in a new window]   Fig. 5. (A) Effective lever arm length (d2) as a function of basalar muscle mass (mbas). log10d2=–0.143+0.307log10mbas (r2=0.72; S.E.slope=0.027; N=51). Symbols are as in B. (B) Internal lever arm length (d1) as a function of mbas. log10d1=–0.710+0.540log10mbas (r2=0.77; S.E.slope=0.042; N=52).

View larger version (18K): [in a new window]   Fig. 6. Examples of workloops for each species. Basalar muscle length (l), mass (m) and contraction frequency (f) are given for each specimen.

View larger version (14K): [in a new window]   Fig. 7. (A) Mean dynamic force output (Fdyn) as a function of basalar muscle mass (mbas). log10Fdyn=3.020+0.834log10mbas (r2=0.76; S.E.slope=0.086; N=33). (B) Force output during one maximal-effort muscle contraction cycle at the output end of the lever system (Find) as a function of mbas. log10 Find=2.304+1.036log10mbas (r2=0.83; S.E.slope=0.086; N=33). Symbols are as in Fig. 5B.

View larger version (23K): [in a new window]   Fig. 8. Maximum force output as a function of motor mass for `Group 2 motors' and single muscles (Marden and Allen, 2002). The upper and lower (grey) linear regression equations are log10Max. force output=2.95+0.667log10Muscle mass and log10Max. force output= 1.74+0.999log10Motor mass, respectively. Blue graphs a, b, c and d represent data and scaling equations obtained in this study. `Motor mass' is synonymous to thorax mass (mthor) for Flift data. Basalar muscle mass (mbas) is used for Fstat, Fdyn and Find data.

View larger version (13K): [in a new window]   Fig. 9. (A) Mass-specific power (Pm) as a function of basalar mass (mbas). log10Pm=3.147+0.237log10mbas (r2=0.18; S.E.slope=0.09; N=33). (B) Mass-specific work (Wm) as a function of mbas. log10Wm=2.530+0.433log10mbas (r2=0.39; S.E.slope=0.10; N=33). Symbols are as in Fig. 5B.