Revisiting the flight dynamics of take-off of a butterfly: experiments and CFD simulations for a cabbage white butterfly.

We conducted measurements of the taking-off motion of a butterfly (Pieris rapae) and numerical simulations using a computational model reflecting its motion. The computational butterfly model is composed of a thorax, an abdomen, and four wings (left and right wings with fore and hind parts), i.e. a six-link, rigid-body system. The present model is more sophisticated than any models that have ever been constructed in existing studies. In the butterfly model, the body trajectory and thoracic pitching angle can be calculated from the equations of motion, whereas the abdominal angle and wings' joint angles are prescribed by the measured data. We calculated the flow field, aerodynamic force and torque generated by the butterfly model using the immersed boundary-lattice Boltzmann method. As a result, the butterfly generates the horizontal vortex ring and aerodynamic lift force during the downstroke, while it generates the vertical vortex ring and aerodynamic thrust force during the upstroke. The leg impulsion is essential in the upward motion of the taking-off butterfly rather than the aerodynamic lift force by the flapping wings. The inertial forces of the abdomen and wings are comparable in magnitude with the aerodynamic forces, but the net influence of the inertial forces on the position of the butterfly is not significant due to the offsetting of the body and wing inertia. The net aerodynamic and gravitational torques raise the thorax of the butterfly, and the net inertial torques suppress the rise of the thorax.