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First published online September 9, 2003

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Sensitivity analysis of kinematic approximations in dynamic medusan swimming models

John O. Dabiri^* and Morteza Gharib

Option of Bioengineering and Graduate Aeronautical Laboratories, California Institute of Technology, Mail Code 138-78, Pasadena, CA 91125, USA

View larger version (55K): [in a new window]   Fig. 1. (A) Video image frame with half-spline overlay. (B) Three-dimensional bell reconstruction generated by revolution of half-spline around axis of revolution.

View larger version (39K): [in a new window]   Fig. 2. (A) Measured volume versus time. Thick black line, curve fit; thin black line, uncertainty boundaries; gray line, approximate V(t). (B) Measured aperture area versus time. Thick black line, curve fit; thin black line, uncertainty boundaries; gray line, approximate A(t). Values are normalized by maximum in the plot.

View larger version (33K): [in a new window]   Fig. 3. Dynamical model of (A) acceleration versus time, (B) velocity versus time and (C) position versus time. Horizontal bars, mVmA; open diamonds, mVaA; solid black line, aVmA; +, aVaA (see Table 1). Values are normalized by maximum in the plot.

View larger version (14K): [in a new window]   Fig. 4. Fineness ratio. Gray line, direct measurement; black line, values computed from bell volume and aperture measurements using hemiellipsoid approximation.

View larger version (26K): [in a new window]   Fig. 5. Modeled swimming dynamics against time of (A) acceleration, (B) velocity and (C) position, from fineness ratio measurement inputs. Gray line, fineness ratio result; black line, mVmA baseline data set. Values are normalized by maximum in the plot.

View larger version (10K): [in a new window]   Fig. 6. Ratio of diameter for exact fineness-hemiellipsoid model to bell aperture diameter. Solid black line, diameter ratio; gray circles, maximum bell diameter at maximum expansion; open circles, maximum bell diameter at maximum contraction.