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Tethered Swimming

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  • Tethered Swimming

    Dear Biomch-L,

    There has been continued interest in the Tethered Swimming problem.
    I have further comments on the matter and have been encouraged by
    one of the list moderators to post them on Biomch-L.

    The concepts introduced so far in the tethered swimming discussion
    have been said to be taught in 1st and 2nd year Physics courses.
    However, learning the definition of a concept and learning how to
    apply a concept can be two completely different things. The same
    concept applied different ways and on different levels can provide
    information that may or not be useful to the original problem. With
    this in mind, I have introduced a few more points.

    1. The original problem is stated as: What is the work done during
    tethered swimming?. This problem can be approached several ways.
    Ideally it is best to choose the approach that gives the greatest
    understanding of the concept of tethered swimming.

    2. Tethered swimming is a system. Work done on or by a system is a
    thermodynamic problem. Problems that occur in the biomechanical
    field use concepts developed in other fields. Dismissing a problem
    just because it requires concepts developed in another filed will not
    bring you closer to understanding the original problem.

    3. The system and the initial and final states of interest has to be
    defined clearly. This is because work is a form of energy that is
    transferred across the defined system's boundary between the two states.
    Note that heat is also a form of energy that is transferred across
    the system boundary between two states. This follows the first law
    of thermodynamics:

    dE = dW + dQ

    dE is the change in energy of a system
    dW is the work transferred across the system boundary
    dQ is the heat transferred across the system boundary

    4. The common equation W = F x is related to the above concepts.
    This is best shown from a section in Fundamentals of Classical
    Thermodynamics: SI Version 2e (1978) by G.J. Wylen and R.E. Sonntag
    on page 61-62:


    "Work is usually defined as a force F acting through a displacement x,
    the displacement being in the direction of the force. That is,

    W=(integral from state 1 to 2)F dx

    This is a very useful relationship because it enables us to find the
    work require to raise a weight, to stretch a wire, or to move a charged
    particle through a magnetic field.

    However, when treating thermodynamics from a macroscopic point of view,
    it is advantageous to tie in the definition of work with the concepts of
    systems, properties, and processes. We therefore define work as follows:
    work is done by a system if the sole effect on the surroundings
    (everything external to the system) could be the raising of a weight.
    Notice that the raising of a weight is in effect a force acting through a
    distance. Notice, also, that our definition does not state that a weight
    was actually raised, or that a force actually acted through a given
    distance but that the sole effect external to the system could be the
    raising of the weight. Work done by a system is considered positive
    work done on a system is considered negative. The symbol W designates
    the work done on a system.

    In general, we will speak of work as a form of energy. No attempt will
    be made to give a rigorous definition of energy. Rather, since the concept
    is familiar, the term energy will be used as appropriate, and various
    forms of energy will be identified, Work is a form of energy that fulfils
    the definition above."

    End of Quote.

    5. In the tethered swimming problem, the system of interest can be
    stated as being the swimmer. In this case the boundary would be the
    surface of the swimmer. Over each cycle, assuming the body temperature
    remains relatively constant, the change in energy of the system, dE,
    would be negative and would equal to the energy loss in chemical bonds
    (respiration). The energy lost would equal the heat loss, dQ, to the water
    and air and the work done, dW, on the water. The work done would be the
    force applied to the water over the distance applied. From the force
    analysis point of view, the net force and direction on the water would
    be equal in magnitude and opposite in sense to the tension on the tether.

    The water is not included in this system and thus the effect on the water,
    such as change in kinetic energy, cannot be calculated at this point.

    6. The system of interest can also be redefined to include the pool water
    and possibly the pool wall and weight apparatus. The energy change of
    the system would have to include any internal thermal energy increases
    (reflected by temperature rise) of the water etc as well as the change in
    the swimmer's chemical energy (assuming the kinetic and potential energy
    remains relatively constant). The heat loss would include any heat lost
    to the environment, which my be considerable because water can be
    an excellent conductor. And finally, any work done would be any work
    done on the environment or could be done to the environment.

    Note, since in this case the environment does not move, work is not
    being done on the environment. However, this does not eliminate the
    possibility that work can be done on the environment. In other words,
    "that the sole effect external to the system could be the raising of the
    weight" (excerpt from the above quote).

    7. I believe the approach used in point 6 gains a greater understanding
    of the tethered swimming problem. The approach in point 5 just calculates
    the effort to "push" something over a distance. Everybody knows that
    a person who pushes something over a distance has the potential to do
    work. A greater understanding of the problem would only be achieved if
    the effect was considered on relevant components in the environment.
    For example, I believe there is a significant difference between the
    case of a weight lifter lifting up and dropping the same weight repeatedly
    and the case of a weight lifter raising a series of identical weights
    to a given height. The approach in point 5 would not distinguish
    between the two cases. From the point of view of the weight lifter,
    the same work is being done.

    However, considering the effect on the weights, there is a
    distinguishable (and measurable) difference between the to cases.
    In the first case, the only effect on the environment is the release of
    heat energy. In the second case, the lifted weights can lift other weights
    (using a lever apparatus) in the environment and return to their initial
    position. Thus "the sole effect external to the system could be the raising
    of the weight". This shows that in the second case work has been done.

    In the problem of the tethered swimmer, the approach in point 5 would
    not distinguish between a swimmer held in place or a swimmer moving
    forward at a constant velocity (and possibly lifting a tethered weight).
    All that is learned is that the person can fight a resistance by pushing

    8. Point 6 gains a greater understanding of the problem because it
    includes the pool water, a relevant component of the swimmer's
    environment. The energy flow within the system can be studied
    including the swimmer and the interacting water. The analysis can be
    done as follows: The swimmer's hand creates a pressure gradient in
    the water. This pressure gradient causes the water to move back and
    gain momentum. The water eventually slows down loses its energy
    as heat and imparts its momentum on the water or directly on the wall
    as a impulse wave. The question "What is the work done during
    tethered swimming?" can be looking at the possibility of doing work
    with the water momentum before it is lost as heat. Rephrased another
    way: can useful energy (work) be transferred out of the tethered swimming
    system without affecting the swimmer? I think that this is a more
    rewarding approach to the tethered swimming question.

    ------------Peter Davidson----------- *********
    Doctorate Student, Biomechanics .:***********>*****
    Health Sciences *:@*************>****
    Universiy of Otago *** ******>****
    PO Box 913, Dunedin ** *********
    New Zealand * I I ~ ~