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First published online December 14, 2005
Journal of Experimental Biology 209, 66-77 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01969

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Take-off and landing forces in jumping frogs

Sandra Nauwelaerts^1,* and Peter Aerts^1,2

¹ Department of Biology, University of Antwerp (UIA), Universiteitsplein 1, B-2610 Wilrijk, Antwerpen, Belgium
² Department of Movement and Sports Sciences, University of Ghent, Watersportlaan 2, B-9000 Gent, Belgium

View larger version (22K): [in a new window]   Fig. 1. Examples of force, power and work profiles of type I (A) and type II (B). Type I is defined as a profile in which the arms intercept the major force peak, while in type II profiles the timing of body contact with the force plate is prior to the timing of the peak forces. Vertical lines indicate timing of body contact with the force plate.

View larger version (10K): [in a new window]   Fig. 2. An example of the angle profile of the GRF during propulsion p,r and landing l,r.

View larger version (23K): [in a new window]   Fig. 3. Timing of body posture and angle p,r and magnitude of Fp,r during propulsion. Note the fact that around halfway through the propulsion phase the direction of the GRF (red arrows) runs behind the centre of gravity (which lies for a fully extended frog close to the hip). Red arrow at the bottom of the figure indicates 1N.

View larger version (42K): [in a new window]   Fig. 4. Timing of body posture and angle l,r and magnitude of l,r during landing. The scale of the magnitude of the force is half the size of that for the propulsion phase. Red arrows indicate direction of GRF. Horizontal arrow at bottom of figure indicates 1N. Note that the scale differs between Fig. 3 and Fig. 4.

View larger version (16K): [in a new window]   Fig. 5. Lateral view of the displacements of the COM, from touchdown (red circle) until the COM is situated 1 cm above the ground surface (body contact), resulting from the simulations of the spring-dashpot model. The time difference between two circles is 0.005 s. (A) A simulation for the real sequence, where the arm angle at touchdown is 125°, resulting in the spring-dashpot becoming shorter and rotating to a vertical position during landing. (B) The arms are put further forward, at an angle of 140°, which results in the arms stretched forward at the moment of body contact. (C) When the arm angle is decreased to 110°, the arms rotate over the vertical position during landing and the frog will land with its front limbs stretched backwards.

View larger version (21K): [in a new window]   Fig. 6. (A) Vertical (solid lines) and horizontal (broken lines) velocity squared (v2) at the moment of body contact against arm angle at touchdown. The effect of a change in height h of the jump becomes visible in the difference between the colours. Optimal arm angle is defined as the arm angle for which both v2 are minimal (at the intersection of the solid and the broken lines) and is shown for each height as a full circle. From this graph we could determine the relationship between optimal angle and height, which we used to verify our predictions. (B) The relationship between optimal angle and height is shown as a solid line on top of a scatterplot showing the observed arm angles at touchdown against the height of the jump. Regression equation, angle= -77xheight+142.5; units for v2, m2 s-2.

View larger version (20K): [in a new window]   Fig. 7. (A) Vertical (solid lines) and horizontal (broken lines) velocity squared (v2) at the moment of body contact against arm angle at touchdown. The effect of a change in horizontal velocity of the jump becomes visible in the difference between the colours. Optimal arm angle is defined as the arm angle for which both v2 are minimal (in the crossing of the solid and the broken lines) and is shown for each horizontal flight velocity as a full circle. From this graph we could determine the relationship between optimal angle and horizontal velocity, which we used to verify our predictions. (B) The relationship between optimal angle and horizontal velocity is shown as a solid line on top of a scatterplot showing the observed arm angles at touchdown against the horizontal velocity of the jump. Regression equation, angle=18xhorizontal velocity+100.5; units for v2, m2 s-2.