New modeling approach for bounding flight in birds.

A new modeling approach is presented which accounts for the unsteady motion features and dynamics characteristics of bounding flight. For this purpose, a realistic mathematical model is developed to describe the flight dynamics of a bird with regard to a motion which comprises flapping and bound phases involving acceleration and deceleration as well as, simultaneously, pull-up and push-down maneuvers. Furthermore, a mathematical optimization method is used for determining that bounding flight mode which yields the minimum energy expenditure per range. Thus, it can be shown to what extent bounding flight is aerodynamically superior to continuous flapping flight, yielding a reduction in the energy expenditure in the speed range practically above the maximum range speed. Moreover, the role of the body lift for the efficiency of bounding flight is identified and quantified. Introducing an appropriate non-dimensionalization of the relations describing the bird's flight dynamics, results of generally valid nature are derived for the addressed items.