Abstract—A model of vortex wake is suggested to determine the induced power during animal hovering flight. The wake is modeled by a series of equi-spaced rigid rectangular vortex plates, positioned horizontally and moving vertically downwards with identical speeds; each plate is generated during powering of the functionally wing stroke. The vortex representation of the wake considered in the current theory allows a considerable loss of momentum to occur. The current approach accords well with the nature of the wingbeat since it considers the unsteadiness in the wake as an important fluid dynamical characteristic. Induced power in hovering is calculated as the aerodynamic power required to generate the vortex wake system. Specific mean induced power to mean wing tip velocity ratio is determined by solely the normal spacing parameter (f) for a given wing stroke amplitude. The current theory gives much higher specific induced power estimate than anticipated by classical methods. Keywords—vortex theory, hovering flight, induced power, Prandlt’s tip theory. I. INTRODUCTION OVERING phenomenon is aerodynamically an extreme mode of flying that necessitates a tremendous energy expenditure since all downward movement of air requisite to neutralize the effect of gravity on the hovering animal for the duration of the wing beat must be supplied by the beating wings. The mechanical power input is expected to be unobtainable especially for animals which are not characteristically suited to utilize hovering flight as a locomotion means during their life cycle since their power budget can not tolerate such massive amount of power consumption. The flow field produced during hovering animal flight is extraordinarily difficult to treat mathematically and the associated wing kinematics is of great complexity to perceive. The resulting flow pattern is periodically-generated nearly equally spaced twisted vortex sheets. The complexity of this flow requires a more elaborate modeling of its structure to obtain an accurate computation of the induced velocity developed at the wing disk. Numerical methods are the outcome of most flight models and the accompanying computing time is normally astronomical. However, the vortex lattice illustration of the wake utilized in present theory is computationally the most economical. Early quantitative approaches introduced drastic simplifications to the wake structure such as neglecting the Khaled M. S. Faqih is with the Information Systems Department, Al al- Bayt University, Jordan (e-mail: km_faqih@aabu.edu.jo). unsteadiness of the wake by assuming that vorticity is distributed throughout the wake volume rather than in a discrete pattern. These methods can only describe the general airflow characteristic and it does not require any detailed knowledge of the internal process within the fluid. Most of the early studies on hovering flight adopted the actuator disk and its associated momentum jet. These methods assume that the flapping motion imparts continuous momentum to the air, and the lift force is generated as a result of accelerating the air vertically downwards. The momentum jet theory assumes that no flow passes through the boundary of the wake, and that both mass and momentum are conserved in the body of the wake. The classical methods are elegant in their simplicities and can reduce the complexity of the mathematical treatment enormously. In fact, animal flight produces a very complex wake structure which sequentially generates a highly complicated airflow pattern over the wings and around the resulting vortex sheets. Also the vorticity generation during hovering activity is discontinuous, consequently there can be a flow through the boundary of the wake which violates strongly the continuity requirement assumed by the conventional aerodynamic analysis. The validity of these assumptions in application to animal flight is therefore limited. Apparently these discrepancies can not be disregarded and should be sufficiently adequate to dispense with the utilizing of momentum jet theory in animal flight analysis [1], [2], [3], [4], [5]. The blade element theory of propellers has been widely used to study the animal flight. This theory assumes that the wing is operating under quasi-steady aerofoil states. The aerodynamic effects of wing motion are calculated by assuming that the aerodynamic forces produced by each element of the wing are identical to those that would be produced by such element traveling at the same steady velocity and angle of attack. [6] derived the general equations that apply to flapping flight. This type of analysis nevertheless requires a knowledge of lift and drag coefficients. The classical studies of flapping flight composed of a blade element theory which provides the lift and drag forces and a momentum theory that gives the induced velocity at the wing disk [7], [8], [9], [10]. Theoretical and experimental predictions for the force coefficients contain numerous ‘gray areas’ of uncertainty which force the employment of a number of simplifying assumptions to obtain approximate estimates to them. It is evident that conventional aerodynamic analysis is incapable of providing a detailed knowledge of the flow field and can not fully tackle the animal flight problem. However, Khaled. M. Faqih A Vortex Plate Theory of Hovering Animal Flight H World Academy of Science, Engineering and Technology International Journal of Aerospace and Mechanical Engineering Vol:4, No:9, 2010 841 International Scholarly and Scientific Research & Innovation 4(9) 2010 scholar.waset.org/1307-6892/662 International Science Index, Aerospace and Mechanical Engineering Vol:4, No:9, 2010 waset.org/Publication/662