Abstract
The power required by flapping and fixed wing vehicles in level flight is determined and compared. Based on a new modelling approach, the effects of flapping on the induced drag in flapping wing vehicles are mathematically described. It is shown that flapping causes a significant increase in the induced drag when compared with a non-flapping, fixed wing vehicle. There are two effects for that induced drag increase; one is due to tilting of the lift vector caused by flapping the wings and the other results from changes in the amount of the lift vector during flapping. The induced drag increase yields a significant contribution to the power required by flapping wing vehicles. Furthermore, the power characteristics of fixed wing vehicles are dealt with. It is shown that, for this vehicle type, the propeller efficiency plays a major role. This is because there are considerable differences in the propeller efficiency when taking the size of vehicles into account. Comparing flapping and fixed wing vehicles, the conditions are shown where flapping wing vehicles have a lower power demand and where fixed wing vehicles are superior regarding the required power. There is a tendency such that fixed wing vehicles have an advantage in the case of larger size vehicles and flapping wing vehicles have an advantage in the case of smaller size ones.
Highlights
Vehicles with flapping wings that enable simultaneous lift and thrust generation have gained significant interest as an alternative flight possibility when compared with fixed wing vehicles [1,2,3].Flapping wing vehicles show a variety of aerodynamic configurational designs and constructional solutions for flapping the wings
The size of flapping wing vehicles ranges from large-scale, ornithopter-type aircraft powered by an engine or by the muscles of the pilot to small- and even micro-scale air vehicles
To expand the relation describing the engine power required by fixed wing vehicles, Equation (4), reference is made to the quadratic drag polar, Equations (17) and (18), which holds for fixed wing vehicles
Summary
Vehicles with flapping wings that enable simultaneous lift and thrust generation have gained significant interest as an alternative flight possibility when compared with fixed wing vehicles [1,2,3]. With respect to the efficiency of flapping wings and the achievable flight performance, there are differing results. One relates to unsteady effects, considered to provide advantages over comparable fixed wing designs Another example are separated flow aspects which are assumed to enhance lift and thrust, and efficiency effects unique for micro-sized vehicles. Such effects will not be addressed because they are beyond the scope of this paper. The question, which is subject of this paper, is how the flight mechanical performance of flapping wing vehicles can be modelled and what are the mathematical relations describing the performance characteristics, in particular those describing the engine or muscle power necessary for level flight and the associated minimum. The findings are considered to properly describe the essentials of the performance topics under consideration
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