The momentum transfer during take-off in birds*

Taking off is a critical step before flying for birds. Birds jump using hindlimb muscles and leave the ground before extending their wings. The kinematics of take-off is widely applied to jumping robots. Numerous studies have examined the kinematics of take-off, but the contribution of hindlimb muscles to the whole process remains unknown. In this study, we recorded high-speed videos of birds at the zoo and derived a theoretical model across body size. The relationship between body mass and time can be represented by the following function: T=116M^0.07 (ms), spanning from a 3.2-g hummingbird to a 5-kg goose (N=45). We calculated the momentum change within the take-off time caused by the ground reaction force exerted by the hindlimbs. When hindlimbs muscles contract, the joints rotate and transfer force to the ground. The theoretical prediction of the take-off time is T=72M^0.09 (ms), which is half of the value from observation.  With the high similarity between avians’ take-off and human hopping locomotion, this research may also help diagnose lower limb rehabilitation problems and inspire designs of lower limb training systems.