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 the models which have ever 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 and aerodynamic force and torque generated by the butterfly model using the immersed boundary–lattice Boltzmann method． As a result, the butterfly generates the horizontal and vertical vortex rings as well as the aerodynamic lift and thrust forces during the downstroke and upstroke, respectively. 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.

We conducted measurements of a butterfly's motion in forward flight and numerical simulations using a computawith fore and hind parts). Furthermore, we calculated the flow field and aerodynamic force and torque generated by the butterfly model using the immersed boundary-lattice Boltzmann method. In this simulation, we considered two types of periodic motions corresponding to slightly-descending and ascending forward flights. As a result, we found that the wing-tip and leading-edge vortices are formed on the wings and then released backward and downward in both flights. The major difference between the two flights is the flapping amplitude, indicating that the butterfly changes the flapping amplitude for each period and increases it to ascend. In addition, we considered a chimera model whose motion is based on the slightly-descending flight but partly given by the ascending flight. As a result, we found that the pitching angle and the angle of attack determine the traveling direction, but simply changing these angles does not achieve the ascending flight due to insufficient lift force. Thus, the butterfly should adjust the flapping and lead-lag angles in response to the pitching angle and the angle of attack to change the flight mode.