Meeting Abstract

74.1  Tuesday, Jan. 6  An inverted pendulum model for underwater walking ELLERS, O*; YOSHIMURA, K; MOTOKAWA, T; JOHNSON, A.S.; Bowdoin College, Maine; Tokyo Institute of Technology; Tokyo Institute of Technology; Bowdoin College, Maine olafellers@suscom-maine.net

The inverted pendulum is a common model for terrestrial locomotion but a corresponding model for underwater walking has not been explicitly enunciated. We present an underwater version of the Froude number that is modified to account for buoyancy, acceleration reaction and drag. We use standard damped oscillator theory to model the motion of underwater pendulums and, via the inverted pendulum, to model underwater walking. An underwater pendulum’s frequency is strongly affected by its density relative to the fluid density and somewhat influenced by the added mass coefficient. Higher frequencies result from shorter strings, lower added mass and higher bob densities. Drag tends to damp motion and slightly decreases frequency with increasing drag. The damping effect of drag is greater for smaller diameter bobs, and damping is slightly increased by increasing added mass. Reasonable values of drag coefficient and added mass can produce damping that is large enough that nearly all of the swing amplitude is lost each cycle (critical damping). This model should apply to many underwater walkers such as bipedal octopuses, crabs and sea urchins. The urchin Diadema setosum moves rapidly, speed-walking on its spines when alarmed. We tested the pendulum-like characteristics of this urchin by swinging it with and without spines to measure the added mass and damping due to drag. Both the added mass and high drag damping of this urchin mean that with spines, this urchin is nearly critically damped. Thus, walking rapidly must be energetically costly and therefore reasonable only for escape locomotion. We will further develop the inverted pendulum model and apply it to filmed walking kinematics.