The forces and power needed for propelling at constant speed an actively swimming flexible fish-like body are calculated. A vortex-lattice method based on a linearized theory is employed and the results are compared against slender body theory predictions, as well as experimental data from an eight-link robotic instrument, the RoboTuna. Qualitative agreement is found between our method and slender body theory; with quantitative agreement over certain parametric ranges and disagreement for other ranges of practical interest. The present linearized vortex lattice calculations predict the power needed for propelling the RoboTuna with less than 20 percent error in most experiments conducted. [S0098-2202(00)01202-5]

1.
Lighthill
,
M. J.
,
1960
, “
Note on the Swimming of Slender Fish
,”
J. Fluid Mech.
,
9
, pp.
305
317
.
2.
Lighthill, M. J., 1975, Mathematical Biofluiddynamics, Society for Industrial and Applied Mechanics, Philadelphia, PA.
3.
Wu
,
T. Y.
,
1961
, “
Swimming of a Waving Plate
,”
J. Fluid Mech.
,
10
, pp.
321
344
.
4.
Wu
,
T. Y.
,
1971
, “
Hydromechanics of Swimming Propulsion. Part 3. Swimming and Optimum Movements of Slender Fish with Side Fins
,”
J. Fluid Mech.
,
46
, pp.
545
568
.
5.
Newman
,
J. N.
, and
Wu
,
T. Y.
,
1973
, “
A Generalized Slender-Body Theory for Fish-Like Forms
,”
J. Fluid Mech.
,
57
, No.
4
, pp.
673
693
.
6.
Newman
,
J. N.
,
1973
, “
The Force on a Slender Fish-Like Body
,”
J. Fluid Mech.
,
58
, No.
4
, pp.
689
702
.
7.
Chopra
,
M.
,
1974
, “
Hydromechanics of Lunate-Tail Swimming Propulsion
,”
J. Fluid Mech.
,
64
, pp.
375
391
.
8.
Chopra
,
M.
, and
Kambe
,
T.
,
1977
, “
Hydromechanics of Lunate-Tail Swimming Propulsion. Part 2.
J. Fluid Mech.
,
79
, pp.
49
69
.
9.
Chopra
,
M.
,
1976
, “
Large-Amplitude Lunate-Tail Theory of Fish Locomotion
,”
J. Fluid Mech.
,
74
, pp.
161
182
.
10.
Katz
,
J.
, and
Weihs
,
D.
,
1978
, “
Hydrodynamic Propulsion by Large Amplitude Oscillation of an Airfoil with Chordwise Flexibility
,”
J. Fluid Mech.
,
88
, No.
3
, pp.
485
497
.
11.
Katz
,
J.
, and
Weihs
,
D.
,
1979
, “
Large Amplitude Unsteady Motion of a Flexible Slender Propulsor
,”
J. Fluid Mech.
,
90
, No.
4
, pp.
713
723
.
12.
Bose
,
N.
, and
Lien
,
J.
,
1989
, “
Propulsion of a Fin Whale (Balaenoptera Physalus): Why the Whale is a Fast Swimmer
,”
Proc. R. Soc. London, Ser. B
,
237
, pp.
175
200
.
13.
Bose
,
N.
, and
Lien
,
J.
,
1990
, “
Energy Absorption from Ocean Waves: A Free Ride for Cetaceans
,”
Proc. R. Soc. London, Ser. B
,
240
, pp.
591
605
.
14.
Katz, J., and Plotkin, A., 1991, Low-Speed Aerodynamics: From Wing Theory to Panel Methods, McGraw-Hill, Series in Aeronautical and Aerospace Engineering, New York, NY.
15.
Greeley
,
D. S.
, and
Kerwin
,
J. E.
,
1982
, “
Numerical Methods for Propeller Design and Analysis in Steady Flow
,”
Trans. Soc. Naval Arch. Marine Eng.
,
90
, pp.
415
453
.
16.
Lan
,
C. E.
,
1974
, “
A Quasi-Vortex-Lattice Method in Thin Wing Theory
,”
J. Aircraft
,
11
, pp.
518
527
.
17.
Lan
,
C. E.
,
1979
, “
The Unsteady Quasi-Vortex-Lattice Method with Applications to Animal Propulsion
,”
J. Fluid Mech.
,
93
, pp.
747
765
.
18.
Cheng
,
J. Y.
,
Zhuang
,
L. X.
, and
Tong
,
B. G.
,
1991
, “
Analysis of Swimming Three-Dimensional Waving Plates
,”
J. Fluid Mech.
,
232
, pp.
341
355
.
19.
Sverdrup, P., 1997, “Analysis of Harmonically Flapping Wing in a Steady Stream,” Sivilingenior thesis, Department of Marine Hydrodynamics, Norwegian University of Science and Technology and the Massachusetts Institute of Technology, Trondheim, Norway.
20.
Liu, P., 1996, “A Time Domain Panel Method for Oscillating Propulsors with both Chordwise and Spanwise Flexibility,” Ph.D. thesis, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, Newfoundland.
21.
Wolfgang, M. J., 1999, “Hydrodynamics of Flexible-Body Swimming Motions,” Ph.D. thesis, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.
22.
Wolfgang
,
M. J.
,
Yue
,
D. K. P.
, and
Triantafyllou
,
M. S.
,
1999
, “
Visualization of Complex Near-Body Transport Processes in Flexible-Body Propulsion
,”
J. Flow Visualization
,
2
, No.
2
, pp.
143
151
.
23.
Liu
,
H.
,
Wassenberg
,
R.
, and
Kawachi
,
K.
,
1997
, “
The Three-Dimensional Hydrodynamics of Tadpole Swimming
,”
J. Exp. Biol.
,
200
, pp.
2807
2819
.
24.
Liu
,
H.
,
Ellington
,
C.
,
Kawachi
,
K.
,
van den Berg
,
C.
, and
Willmott
,
A.
,
1998
, “
A Computational Fluid Dynamic Study of Hawkmoth Hovering
,”
J. Exp. Biol.
,
201
, pp.
461
477
.
25.
Carling
,
J.
,
Williams
,
T.
, and
Bowtell
,
G.
,
1998
, “
Self-Propelled Anguilliform Swimming: Simultaneous Solution of the Two-Dimensional Navier-Stokes Equations and Newton’s Laws of Motion
,”
J. Exp. Biol.
,
201
, pp.
3143
3166
.
26.
Barrett
,
D. S.
,
Triantafyllou
,
M. S.
,
Yue
,
D. K. P.
,
Grosenbaugh
,
M. A.
, and
Wolfgang
,
M. J.
,
1999
, “
Drag Reduction in Fish-Like Locomotion
,”
J. Fluid Mech.
,
392
, pp.
183
212
.
27.
Kagemoto
,
H.
,
1997
, “
Design of an Artificial Fish
,”
Department of Ocean Engineering Technical Report, Massachusetts Institute of Technology, Cambridge, MA.
28.
Kagemoto, H., Yue, D. K. P., and Triantafyllou, M. S., 1997, “Optimization of a Fish-Like Swimming Body,” 50th Annual Meeting of the Division of Fluid Dynamics, American Physical Society, Nov. 23–25, San Francisco, CA.
29.
Weihs, D., and Webb, P., 1983, “Optimization of Locomotion,” Praeger Special Series Fish Biomechanics, P. Webb and D. Weihs, eds., Chapter 11, pp. 339–371, Praeger, New York, NY.
30.
Triantafyllou
,
G. S.
,
Triantafyllou
,
M. S.
, and
Grosenbaugh
,
M. A.
,
1993
, “
Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion
,”
J. Fluids Struct.
,
7
, pp.
205
224
.
31.
Goldberg, D., 1989, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, MA.
32.
Barrett, D. S., 1996, “Forces and Efficiency of a Flexible Hull Vehicle,” Ph.D. thesis, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.
33.
Barrett, D. S., 1994, “The Design of a Flexible Hull Undersea Vehicle Propelled by an Oscillating Foil,” M. S. thesis, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.
34.
Triantafyllou
,
M. S.
, and
Triantafyllou
,
G. S.
,
1995
, “
An Efficient Swimming Machine
,”
Sci. Am.
,
272
, No.
3
, pp.
64
70
.
35.
Triantafyllou
,
M. S.
,
Barrett
,
D. S.
,
Yue
,
D. K. P.
,
Anderson
,
J. M.
,
Grosenbaugh
,
M. A.
,
Streitlien
,
K.
, and
Triantafyllou
,
G. S.
,
1996
, “
A New Paradigm of Propulsion and Maneuvering for Marine Vehicles
,”
Trans. Soc. Naval Arch. Marine Eng.
,
104
, pp.
81
100
.
36.
Konstadinopoulos, P., Mook, D. T., and Nayfeh, A. H., 1981, “A Numerical Method for General, Unsteady Aerodynamics,” AIAA paper 81–1877.
37.
Anderson
,
J. M.
,
Streitlien
,
K.
,
Barrett
,
D. S.
, and
Triantafyllou
,
M. S.
,
1998
, “
Oscillating Foils of High Propulsive Efficiency
,”
J. Fluid Mech.
,
360
, pp.
41
72
.
38.
Videler, J., 1993, Fish Swimming, Chapman and Hall, London, U.K.
39.
Gray, J., 1968, Animal Locomotion, Weidenfeld & Nicolson, London.
40.
Wolfgang
,
M. J.
,
Anderson
,
J. M.
,
Grosenbaugh
,
M. A.
,
Yue
,
D. K. P.
, and
Triantafyliou
,
M. S.
,
1999
, “
Near-Body Flow Dynamics in Swimming Fish
,”
J. Exp. Biol.
,
202
, pp.
2303
2327
.
41.
Hoerner, S. F., 1965, Fluid-Dynamic Drag, Hoerner Fluid Dynamics, Vancouver, WA.
42.
Liu
,
P.
, and
Bose
,
N.
,
1993
, “
Propulsive Performance of Three Naturally-Occurring Oscillating Propeller Planforms
,”
Ocean Eng.
,
20
, No.
1
, pp.
55
75
.
43.
Hoerner, S. F., 1985, Fluid-Dynamic Lift, Hoerner Fluid Dynamics, Vancouver, WA.
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