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Muscles and Hydrodynamics

 

An artificial fish moves as a real fish does: by contracting its muscles. If tex2html_wrap_inline2344 is a muscle, it is contracted by decreasing its rest length tex2html_wrap_inline2472 . The characteristic undulation of the fish tail can be achieved by periodically contracting the swimming segment muscles on one side of the body while relaxing their counterparts on the other side. We will develop the motor controllers that produce this muscle coordination in Section gif.

When the fish tail swings, it sets in motion a volume of water. The inertia of the displaced water produces a reaction force normal to the fish's body and proportional to the volume of water displaced per unit time, which propels the fish forward (Fig. gif).

  figure522

Assuming irrotational, incompressible and not very viscid fluid, the instantaneous hydrodynamic force on the surface S of a body due to the fluid is approximately proportional to

displaymath2468

where tex2html_wrap_inline2488 is the unit outward normal function over the surface and tex2html_wrap_inline2490 is the relative velocity function between the surface and the fluid [Massey1983]. For efficiency, we triangulate the faces of the fish model between the nodes. For each triangle, we approximate the hydrodynamic force as

  equation537

where tex2html_wrap_inline2492 is the viscosity of the fluid medium, A is the area of the triangle, tex2html_wrap_inline2488 is its normal, and tex2html_wrap_inline2490 is its velocity relative to the water.gif The external forces tex2html_wrap_inline2414 (see Eq. gif) at each of the three nodes of the triangle are incremented by tex2html_wrap_inline2508 .


next up previous contents
Next: Numerical Solution Up: Biomechanical Fish Model and Locomotion Previous: Biomechanical Properties
Xiaoyuan TuJanuary 1996