A self-propelling clapping body

Abstract

We report an experimental study of the motion of a clapping body consisting of two flat plates pivoted at the leading edge by a torsion spring. Clapping motion and forward propulsion of the body are initiated by the sudden release of the plates, initially held apart at an angle $2\theta _o$ . Results are presented for the clapping and forward motions, and for the wake flow field for 24 cases, where depth-to-length ratio ( $d^* = 1.5,1\text { and }0.5$ ), spring stiffness per unit depth ( $Kt$ ), body mass ( $m_b$ ) and initial separation angle ( $2\theta _o = 45^{\circ }\text { and }60^{\circ }$ ) are varied. The body initially accelerates rapidly forward, then slowly retards to nearly zero velocity. Whereas the acceleration phase involves a complex interaction between plate and fluid motions, the retardation phase is simply fluid dynamic drag slowing the body. The wake consists of either a single axis-switching elliptical vortex loop (for $d^* = 1\text { and }1.5$ ) or multiple vortex loops (for $d^* = 0.5$ ). The body motion is nearly independent of $d^*$ and most affected by variation in $\theta _o$ and $Kt$ . Using conservation of linear momentum and conversion of spring strain energy into kinetic energy in the fluid and body, we obtain a relation for the translation velocity of the body in terms of the various parameters. Approximately 80 % of the initial stored energy is transferred to the fluid, only 20 % to the body. The experimentally obtained cost of transport lies between 2 and $8\ \mathrm {J}\ \mathrm {kg}^{-1}\ \mathrm {m}^{-1}$ .