Forward flight of a model butterfly: Simulation by equations of motion coupled with the Navier-Stokes equations

The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body oscillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small negative horizontal force, whilst in the upstroke, the body angle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-massspecific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.