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Dear Biomch-L,
There have been plenty of thoughtful discussions on the work
done by the tethered swimmer. I agree with Paolo de Leva and some
others, the work done by the tethered swimmer on water per cycle
is not equal to zero and is positive generally. The work can be
calculated, as we often did in the studies of aquatic animal
locomotion, if you know hydrodynamic forces acting on the swimmer
(basically the fluid pressure field near the swimmer) at any
instant. Multiplying the distributive hydrodynamic force by
the corresponding differential displacement, and summerizing
(integrating) it over the whole body surface and over one cycle
give a value, negative of which is the work done by the swimmer
on surrounding fluid and is supplied by the mechanical energy
produced by muscle contraction. But this method probably won't
help much in solving the problem posted by the originator of
the debate. The reason is that, I believe, little about the
fluiddynamics of human swimming has been known. I would expect
that the fluid flow around a normal adult human swimmer is
associated with large or middle Reynolds numbers (during swimming).
Thus the hydrodynamic forces acting on the body or body parts at
any instant is path dependent and even history dependent
(we need to know complete kinematics in order to obtain
the hydrodynamic forces).
I would say that many arguments about the fluid flow in
previous posting are wrong, but this can be excused as those
people probably have not much backgroud in the mechanics
of continuous media.
For those of you interested in swimming, I have listed below
some of our work on aquatic animal swimming. These studies
include hydrodynamics, swimming mechanics, and dynamics of
locomotor system. We can quantify the mechanical energy
generated by muscle contraction, and its partition into
water for propulsion, to deform internal soft tissues,
and maintaining cyclic motions of the body parts.
Cheng J-Y., Zhuang L-X., Tong B-G., Analysis of swimming three-dimensional
waving plates, J. Fluid Mech., Vol .232: 341-355, 1991
Blickhan R. & Cheng J-Y., Energy storage by elastic mechanisms in the
tail of large swimmers-- a re-evaluation, J. Theor. Biol., Vol.168:315-321,
1994
Cheng, J-Y & Blickhan R., Bending moment distribution along swimming
fish, J. Theor. Biol., Vol.168:337-348, 1994
Cheng, J-Y & Blickhan R., Note on the calculation of propeller
efficiency using elongated body theory, J. Experimental Biology, Vol.192:
p169-177, 1994
Cheng, J-Y., DeMont, M.E., Jet propelled swimming in scallops:
swimming mechanics and ontogenic scaling, Canadian Journal of Zoology
(submitted)
Cheng, J-Y., DeMont, M.E., Hydrodynamics of scallop locomotion:
unsteady fluid force acting on clapping shells, J. Fluid Mech.
(submitted)
Cheng, J-Y., Davison, I & DeMont, M.E., Dynamics and energetics
of scallop swimming, J. Experimental Biology, (submitted)
Regards!
Jianyu Cheng
Biology Dept, STFX University, Canada
There have been plenty of thoughtful discussions on the work
done by the tethered swimmer. I agree with Paolo de Leva and some
others, the work done by the tethered swimmer on water per cycle
is not equal to zero and is positive generally. The work can be
calculated, as we often did in the studies of aquatic animal
locomotion, if you know hydrodynamic forces acting on the swimmer
(basically the fluid pressure field near the swimmer) at any
instant. Multiplying the distributive hydrodynamic force by
the corresponding differential displacement, and summerizing
(integrating) it over the whole body surface and over one cycle
give a value, negative of which is the work done by the swimmer
on surrounding fluid and is supplied by the mechanical energy
produced by muscle contraction. But this method probably won't
help much in solving the problem posted by the originator of
the debate. The reason is that, I believe, little about the
fluiddynamics of human swimming has been known. I would expect
that the fluid flow around a normal adult human swimmer is
associated with large or middle Reynolds numbers (during swimming).
Thus the hydrodynamic forces acting on the body or body parts at
any instant is path dependent and even history dependent
(we need to know complete kinematics in order to obtain
the hydrodynamic forces).
I would say that many arguments about the fluid flow in
previous posting are wrong, but this can be excused as those
people probably have not much backgroud in the mechanics
of continuous media.
For those of you interested in swimming, I have listed below
some of our work on aquatic animal swimming. These studies
include hydrodynamics, swimming mechanics, and dynamics of
locomotor system. We can quantify the mechanical energy
generated by muscle contraction, and its partition into
water for propulsion, to deform internal soft tissues,
and maintaining cyclic motions of the body parts.
Cheng J-Y., Zhuang L-X., Tong B-G., Analysis of swimming three-dimensional
waving plates, J. Fluid Mech., Vol .232: 341-355, 1991
Blickhan R. & Cheng J-Y., Energy storage by elastic mechanisms in the
tail of large swimmers-- a re-evaluation, J. Theor. Biol., Vol.168:315-321,
1994
Cheng, J-Y & Blickhan R., Bending moment distribution along swimming
fish, J. Theor. Biol., Vol.168:337-348, 1994
Cheng, J-Y & Blickhan R., Note on the calculation of propeller
efficiency using elongated body theory, J. Experimental Biology, Vol.192:
p169-177, 1994
Cheng, J-Y., DeMont, M.E., Jet propelled swimming in scallops:
swimming mechanics and ontogenic scaling, Canadian Journal of Zoology
(submitted)
Cheng, J-Y., DeMont, M.E., Hydrodynamics of scallop locomotion:
unsteady fluid force acting on clapping shells, J. Fluid Mech.
(submitted)
Cheng, J-Y., Davison, I & DeMont, M.E., Dynamics and energetics
of scallop swimming, J. Experimental Biology, (submitted)
Regards!
Jianyu Cheng
Biology Dept, STFX University, Canada