This study successfully described the mechanics of flapping hovering flight within the framework of conventional aerodynamics. Additionally, the theory proposed and supported by this research provides an entirely new way of looking at animal flapping flight. The mechanisms of biological flight are not well understood, and researchers have not been able to describe them using conventional aerodynamic forces. This study proposed that natural flapping flight can be broken down into a simplest model, that this model can then be used to develop a mathematical representation of flapping hovering flight, and finally, that the model can be successfully refined and compared to biological flapping data. This paper proposed a unique theory that the lift of a flapping animal is primarily the result of velocity across the cambered span of the wing. A force analysis was developed using centripetal acceleration to define an acceleration profile that would lead to a spanwise velocity profile. The force produced by the spanwise velocity profile was determined using a computational fluid dynamics analysis of flow on the simplified wing model. The overall forces on the model were found to produce more than twice the lift required for hovering flight. In addition, spanwise lift was shown to generate induced drag on the wing. Induced drag increased both the model wing's lift and drag. The model allowed the development of a mathematical representation that could be refined to account for insect hovering characteristics and that could predict expected physical attributes of the fluid flow. This computational representation resulted in a profile of lift and drag production that corresponds to known force profiles for insect flight. The model of flapping flight was shown to produce results similar to biological observation and experiment, and these results can potentially be applied to the study of other flapping animals. This work provides a foundation on which to base further exploration and hypotheses regarding flapping flight.
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