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First published online March 31, 2005
Journal of Experimental Biology 208, 1435-1443 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01509

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Propulsive force calculations in swimming frogs I. A momentum–impulse approach

Sandra Nauwelaerts^1,*, Eize J. Stamhuis² and Peter Aerts¹

¹ Department of Biology, University of Antwerp, campus drie eiken, Universiteitsplein 1, B-2610 Wilrijk (Antwerpen), Belgium
² Department of Marine Biology, University of Groningen, Biologisch centrum, Haren, The Netherlands

View larger version (12K): [in a new window]   Fig. 1. An ellipsoid body, representing the water mass around the foot, is characterised by three axes, A, B and C. During the DPIV experiments, we used two sheet orientations (V, vertical; H, horizontal), which cut through the ellipsoid, creating a section with the shape of an ellipse characterised by two axes. Axis B belongs to both ellipses.

View larger version (21K): [in a new window]   Fig. 2. Dorsal (A) and lateral (B) view on the stick figure (ankle–mid-foot–toe) of the leg of a swimming frog during leg extension. The blue circles show the joint positions at the start of the kick, the red ones represent the end of the kick. The time increment between two successive sticks is 0.004 s.

View larger version (108K): [in a new window]   Fig. 3. Vector diagram of the flow around a swimming frog in two perpendicular views. Each vector shows the direction and relative magnitude of the velocity of the local flow. Maximal velocity is colour coded red, minimal velocity (around zero) is shown in blue. The top sequence results from a DPIV analysis of a sequence with a horizontal laser sheet orientation, the bottom sequence with a vertical laser sheet orientation. From each sequence, six images distributed equally over the whole kick are shown.

View larger version (17K): [in a new window]   Fig. 4. Force profile in N on the feet of a swimming frog through time in % of total extension time. Average force profile is shown as a solid line; dotted lines indicate ± S.D. (A) Calculated based on the displacements of the centre of mass (COM) of the frog with and without drag. (B) Measured using an impulse–momentum approach based on the DPIV data. (C) Measured using a force plate.

View larger version (5K): [in a new window]   Fig. 5. Schematic diagram of the time lag between propulsion and extension. Extension duration is expressed in percentages, from 0 to 100. Propulsion is expressed as a fraction of total extension time and starts at 42±8% (mean ± S.D.) before extension and ends at 71±15% of extension.

View larger version (94K): [in a new window]   Fig. 6. Vector diagram of the flow around a swimming Rana esculenta results from a digital particle image velocimetry (DPIV) analysis. Each vector shows the direction and relative magnitude of the velocity of the local flow. Maximal velocity is colour coded red, minimal velocity is shown in blue. Extension is not yet initiated and thrust is obtained by slowing down the flow coming towards the frog. This flow is generated during recovery, i.e. flexing the hind limbs behind the frog's body.