Stability analysis of gliding flight of a swallowtail butterfly Papilio xuthus

Abstract

Preliminary observation of the flights of swallowtail butterfly Papilio xuthus revealed that its dihedral angle is larger than 30° and that the section of its left hind wing close to its body and the counterpart of its right hind wing actually clap and form a “vertical tail”. In this study, the effects of these two features on the lateral-directional dynamic flight stability of these butterflies were analyzed theoretically and revealed the following: (a) when the dihedral angle is larger than 30°, the lateral-directional motion of the swallowtail becomes stable; (b) the vertical tail stabilizes the dutch roll mode; (c) the effects of the dihedral angle on the roll and spiral modes of a swallowtail are qualitatively the same as those of a meter-sized airplane; and (d) with increasing dihedral angle, the stability of the dutch roll mode decreases for a meter-sized airplane with vertical and horizontal tails but increases for the swallowtail. A possible explanation for the latter effect is the smaller Reynolds number of the insect that causes the drag coefficient of the swallowtail wings to increase more rapidly with an increasing angle of attack compared to a large airplane.