Abstract
Jumping take-off in birds is an explosive behaviour with the goal of providing a rapid transition from ground to airborne locomotion. An effective jump is predicated on the need to maintain dynamic stability through the acceleration phase. The present study concerns understanding how birds retain control of body attitude and trajectory during take-off. Cursory observation suggests that stability is achieved with relatively little cost. However, analysis of the problem shows that the stability margins during jumping are actually very small and that stability considerations play a significant role in the selection of appropriate jumping kinematics. We use theoretical models to understand stability in prehensile take-off (from a perch) and also in non-prehensile take-off (from the ground). The primary instability is tipping, defined as rotation of the centre of gravity about the ground contact point. Tipping occurs when the centre of pressure falls outside the functional foot. A contribution of the paper is the development of graphical tipping stability margins for both centre of gravity location and acceleration angle. We show that the nose-up angular acceleration extends stability bounds forward and is hence helpful in achieving shallow take-offs. The stability margins are used to interrogate simulated take-offs of real birds using published experimental kinematic data from a guinea fowl (ground take-off) and a diamond dove (perch take-off). For the guinea fowl, the initial part of the jump is stable; however, simulations exhibit a stuttering instability not observed experimentally that is probably due to the absence of compliance in the idealized joints. The diamond dove model confirms that the foot provides an active torque reaction during take-off, extending the range of stable jump angles by around 45°.
Highlights
Take-off is the most energetically demanding phase of flight, where the highest accelerations are imposed on the body
The horizontal ground reaction force becomes negative at t/Tt-off 0.7, which is not believed to be representative of the biological system, and occurs here due to the model neglecting the disengagement of the toes from the perch; later it will be shown that the ground model predicts the reaction force reasonably closely to the experimental measurements when the foot is fully engaged with the ground
The ground reaction force increases to zero at t/Tt-off 0.07, and continues to increase to a peak of Fy/mg 2. This body acceleration is modest in comparison with previously recorded vertical jumping accelerations of over 5g in guinea fowl [2], 4g in starlings [1] and almost 8g in quails [1], but is plausible for diamond doves which have previously been recorded to have take-off 12 accelerations of 2 –3g [33]
Summary
Take-off is the most energetically demanding phase of flight, where the highest accelerations are imposed on the body. It is well understood that a leg-driven jump is advantageous for accelerating into flight [1,2,3]. The energetic cost of jumping using ground reaction of muscle forces is much less than the energetic cost of using aerodynamic reaction in flapping flight, and the maximum available force is higher [4,5]. Jumping is both more efficient and more effective than flapping wings as a means of propulsion. The effectiveness benefit of using legs to achieve high acceleration applies well to flights of all durations
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