Ok here goes, the original posting with regards tethered swimming is
reproduced below, and following that I've appended selected responses, up to
the point where the discussion became more general and turned work in cyclic
activities (over to you Paolo).

Thanks to all who took the time to respond. Part of the reason for posting
was to demonstrate to my students (who I've been encouraging to become
internet literate) the value of the Biomech list. That end was certainly
achieved, even if the specific students concerned didn't get the answer they
wanted to hear!

Robin Burgess-Limerick

________Original Posting________________

On Wed, 23 Aug 1995, Robin Burgess-Limerick wrote:

> G'day all,
> An undergraduate student has mailed me the following question regarding
> to estimate the amount of work done during tethered swimming. I have
> appended my best response after the request, but I guess I'm not
> Anyone care to comment, point out my error, suggest a better way?
> Thanks,
> Robin Burgess-Limerick
> Student's question:
> i am currently involved in a directed study (hm315) which requires me to
> determine the amount of work done during tethered swimming. I have been
> considering this question for quite a while and have also talked to a
> couple of lecturers. No conclusions have been found!
> The actual proposed study will involve comparing on-land weights training
> to training with this specific tether. I wish to compare the effects of
> the two types of training on 50m sprint performance in the pool, so i
> need to equate the work done under the two conditions.
> The tether simply consists of a harrness strapped to the swimmers waist
> and a rope attached to this and through a pulley at the end of the pool
> at water level, up to a second pulley suspended from the roof. weights
> can be added to the end of the rope. the swimmer is required to perform
> skulling actions to hold a stationary position in the water and the
> weight in the air.
> Do you have any clues on how to calculate work performed during these
> skulling actions???????
> Any advice would be greatly appreciated.
> thanks!
> Robin's response:
> The only idea that comes to mind is to make an estimate of the rate at
> work must be being done by the swimmer on the water to maintain constant
> position then multiplying by the time the activity is performed. I think
> estimate could be made by having the stationary swimmer initially tethered
> from the front as well, release the swimmer, and measure the distance the
> load falls in some small time period. The work done by the load on the
> swimmer during that small time is then m.g.d where d is the distance the
> load falls, and by my, perhaps faulty, logic the work that would be done
> the swimmer on the water in the same time period to remain stationary. I
> think this might be a good question to refer to the wider biomech
> via biomech-l and see if there are any better ideas.

_______________Selected responses_____________________

From: p.sinclair@cchs.su.edu.au (Peter Sinclair)

I gave a lecture on swimming mechanics just last night so I will try and get
it out while it's fresh.

The problem is that swimmers do work not only to drive the body forward
against resistance but also work done to impart kinetic energy to water
pushed backwards by the hand. The ratio of useful work (ie driving the
swimmer forward) to total work is propelling efficiency (See Toussaint and
Beek, Biomechanics of front crawl swimming in Sports Medicine 13(1): 8-24,
1992 for a review). Without knowing how much work is done propelling water
it is impossible to determine the work load of a moving swimmer, let alone a
tethered one (who has an efficiency of zero if the tether is a simple rope).

See Toussaint, Differences in propelling efficiency between competittive and
triathlon swimmers in Medicine and Science in Sports and Exercise 22:
409-415, 1990 for a method to calculate propelling efficiency. Unfortunately
this involves complicated equipment.

Cappaert et al in Journal of Applied Biomechanics 11(1): 103-112 used 3D
cinematography to estimate work done by swimmers. There were lots of
assumptions made in the calculations and the method seems to complicated for
the purposes of your swimmer anyway.

Sorry to give you a negative reply. I hope someone else is more inventive
than I and can recommend a method. Keep us informed.


Peter Sinclair

Division of Biomechanics E-mail: p.sinclair@cchs.su.edu.au
Faculty of Health Sciences Phone: (02) 646 6137
The University of Sydney Fax: (02) 646 6520
East St
Lidcombe NSW 2141


From: Oyvind Stavdahl

We're talking about _the mechanical work done on the water by the
swimmer_, since a weight with constant height has constant potential
energy and no (and thus constant) kinetic energy (relative to the place
on the planet Tellus where the study is being made :-).

I do not think the solution proposed by Robin will give a
right estimate of this work, because there is no reason why the average
"drag resistance" between the swimmer and the water should be the same
when the swimmer is "dragging" the weight as when the weight is
dragging the swimmer (due to the very nonlinear relationships between
speed and force etc.).

The total mechanical work done by the swimmer's body on the water is
given by some product between force and moved distance, integrated over
the whole body surface and then integrated over the appropriate time
period. This integral can be expressed mathematically, but hardly
evaluated by integrating physical measurements.

The only method that I can think of, would be to utilize the water's
heat capacity; mechanical work excerted on the water will produce a
raise in the water temperature proportional to the amount of work.

A direct heat transfer will also take place between the swimer's body
and the water; this has to be taken into account (unless it is
negligible compared to the mechanically induced temperature change).
Also, heat transfer betweeen the water and the surroundings will give
measurement "noise". However, if the effect of these factors can be
reduced or modelled the work in question can be derived from a
temperature measurement.

Just to summarize the idea:
* assume the swimming pool is small enough for a "sufficient"
temperature rise to take place (the smaller the better - depending on
the equipment used for measureing the temperature).
* assume no temperature gradients in the swimming pool.
* assume heat transfer between the water and all other objects
(swimmer's body and surroundings) is reduced to a negligible value or

* The amount of work done by the swimmer during the tethered swimming
will then be implicitly given by the equation

T = (W + H) * C*V


T = rise in the water temperature during the exercise [K]
W = the work we want to measure/estimate [J]
H = the energy added to the water by direct heat transfer [J]
(from swimmer's body, the walls of the pool and the
air above the water)
C = water's heat capacity [K/(J*m^3)]
V = volume of water in swiming pool [m^3]

I emphasize that i DO NOT KNOW whether this method is practically
usable, it might require a specially designed (thermally isolated)
swimming pool and/or some mathematical modelling.

Comments are strongly welcomed.

Oyvind Stavdahl

Oyvind Stavdahl (Siv.ing., Dr.ing. student)

Dept. of Engineering Cybernetics Direct line: +47 73 59 43 77
O. Bragstads plass 8 Switchboard: +47 73 59 43 76
N-7034 TRONDHEIM Fax: +47 73 59 43 99
NORWAY Email: stavdahl@itk.unit.no


From: Dale Knochenmuss

The methods discussed which use external weights would ignore the
substantial work the swimmer performs on the water but which serves only to
churn the water and overcome drag. Stavdahl's suggestion would address the
total work, but implementation would be dauntingly difficult.

I believe measurements of oxygen consumption are used to estimate the work
involved in performing various industrial tasks on dry land. Such a
technique might be adapted to work with tethered swimmers.
Dale R. Knochenmuss
University of Cincinnati
Noyes-Giannestras Biomechanics Laboratories


From: l.abraham@mail.utexas.edu (Larry Abraham)

Your query about measuring work during tethered swimming is indeed a
difficult problem. Previous respondents have made some good and some weak
(I feel) points. I agree that your first guess would serve only to measure
the drag of the weights on the swimmer and would not be related to the work
of active swimming. The best suggestion you have received, I believe, is
to look into measuring oxygen consumption. This has been done before by my
colleague Ed Coyle. If you can't find a reference I'll be glad to ask him
for one. However this will still require quite a bit of estimation and
result in a rather imprecise error. I wonder if you might not be better
off redefining the question. From the standpoint of swimming efficacy,
could your concerns be addressed by assessing propulsive force while
swimming? If so, you could then use a strain gauge in line with the tether
and either weights or a fixed tether point (if the intention is to have the
swimmer stay in place, a fixed anchor might be easier and better than
weights?). The biggest problem then might be that the testing situation
doesn't exactly match true swimming, but at least you should be able to
make accurate measurements of an important dynamic output variable. You
could also integrate the force with respect to time to determine the
propulsive impulse per stroke.

Larry Abraham, EdD
Kinesiology & Health Education
The University of Texas at Austin
Austin, TX 78712 USA
(512)471-1273 FAX (512)471-8914


From: "Paolo de Leva - Sport Biomechanics, Rome, Italy"

After Robin Burgess-Limerick posted his message asking
how to estimate the amount of work done during tethered swimming, some
answers have been given which were based on bad applications of
the laws of physics.

I agree with Dale R. Knochenmuss, when he says that:

> The methods discussed which use external weights would ignore the
> substantial work the swimmer performs on the water [...]

I also totally agree with Dale about the following:

> I believe measurements of oxygen consumption are used to estimate the work
> involved in performing various industrial tasks on dry land. Such a
> technique might be adapted to work with tethered swimmers.

Some other answers were misleading, and I believe it is
important to explain why. It is well known thet, generally, the concept of
work should be always clearly and explicitly referred
(1) to a specific system that DOES work, and
(2) to the specific object ON WHICH the work is done.
This implies that the formula w=F.d refers always ONLY to the force
done by the system (1) on the object (2), and to the distance covered by the
CM of the object (1) in the direction of the force.
It should be also clear that in the meantime the system (1)
itself may also be displaced by a DIFFERENT distance (d2 not equal to d!),
and other systems may exert other forces (F2, F3...) on the same object!
Work might be done on the same object by several systems. On the
other hand, a system may apply work on several objects. I just would like to
point out that the concept of total work is not as simple as it
seems, especially if non-rigid systems as the human body or the water are
In this case, the total work done by the swimmer (ON WHAT?) while
performing thetered swimming DEPENDS also on the amount of load, but it
is neither equal nor proportional to the work done ON THE LOAD!.
In fact, the work done ON THE LOAD is ZERO, when the load is held
at a constant height, as described.
And if somebody has any doubts, he should perhaps try asking the
swimmer whether he agrees that the work he did was ZERO!
surrounding WATER (and air). It cannot be computed directly.
Dale R. Knochenmuss suggested a good indirect method
(see above) to compute something different: the work done by the swimmer's

It must be extremely clear that this is the SUM of the works

(=total work) done by several different systems (the muscles, not the
on several different objects (bones, fat, even OTHER MSCLES, and water).

This is one of the uncorrect answers:

> [...] I think an
> estimate could be made by having the stationary swimmer initially tethered
> from the front as well, release the swimmer, and measure the distance the
> load falls in some small time period. The work done by the load on the
> swimmer during that small time is then m.g.d where d is the distance the
> load fell, and by my, perhaps faulty, logic the work that would be done by
> the swimmer on the water in the same time period to remain stationary.

This is such a rich collection of misunderstandings that it needs
quite a bit of time to identify them all. Of course the
subscriber who wrote them is excused because he explicitly stated he was not
sure about that.
The proposed method does NOT MEASURE THE WORK BY THE LOAD ON THE
On the contrary, it is quite evident that m.g.d is simply the
work done by the (1) GRAVITATIONAL FORCE on (2) THE LOAD!!! In fact, m.g is
(1) GRAVITATIONAL FORCE acting (2) ON THE LOAD, and d is the vertical
covered by (2) THE LOAD. (I assumed that m is the mass OF THE LOAD, not the
of the swimmer). The swimmer has nothing to do with this work, and this is
even the TOTAL work done on the load. The gravitational force is not
the only force acting on the load. The load is also acted upon
(through the pulleys) by the swimmer's pull. The net force applied on the
load produces an acceleration a that is not equal to g!
The (negative) work done by the SWIMMER ON THE LOAD can be computed,
for instance, using a load cell above the load, to measure the tension of
rope (or using the inverse dynamics approach: acceleration of the load is
estimated from position/time daetc.).
However, the work BY THE SWIMMER ON THE LOAD, which in this
example is different from zero, is only a part of the total work done by the
swimmer, as Dale R. Knochenmuss pointed out.
Also, here it would be useful to distinguish, theoretically, between
work done actively by the swimmer, by means of muscle contraction, and work
done passively by its body. In the situation explained above, for example,
the swimmer is moving backward in the water, and this elicits water
resistance forces, that contribute PASSIVELY to the total force exerted by
swimmer on the load!
The only true thing implied in the above statements is that
IN THIS CASE the work done by the swimmer on the load is equal
and opposite to the work done by the LOAD ON THE SWIMMER. (This is not
the general rule. It happens only because swimmer and load
undergo the same displacement. Usually two free bodies that make equal
and opposite forces on each other cover different distances, depending
on their masses, and their initial velocity)

Somebody else wrote to BIOMCH-L:

> the amount of work done is the force times the distance it is moved.

Let's say this is acceptable, although not very precise

> In this case, the force is the weights being suspended by the pulley.

Not at all. See above. The same subscriber continued as follows
(and here absurdity reaches its historical climax):

> The distance can be chosen from any arbitrary datum, i.e. the surface
> of the water or bottom of the pool. However, in this case I would choose
> it to be the swimmers waist where the rope is secured.

That's totally crazy. The distance is always the distance covered
by the object during the considered period of time. It cannot be any
arbitrary distance between the object and something else, at a given
instant! Here, we are talking about work, not potential energy.
Let me underline that the concepts of work and energy need a
deep study to be FULLY understood and used .
Otherwise, they can only be "FOOLLY" used!
There was another "eretic" statement, in the same message.
We might say that absurdity had two peaks in that posting. Here
is the second one:

> m.g.d is the amount of potential energy in the weights
> and it is the amount of energy, or work, required of the swimmer to keep
> those weights in that position.

First of all, the work done to keep an object in a constant
position is ZERO, whatever is its weight!!!!!!
Secondly, potential energy and work are TWO DIFFERENT THINGS.
Mainly, potential energy is a property of an object at a given instant,
whilst work is something that an object "receives" during a period of
time while it is moving in a given direction...
Third, work may (IN SOME CASES, NOT ALWAYS) change potential
energy: IT HAPPENS, for example, that the gravitational potential
energy of a weight with respect to an arbitrary horizontal plane
is equal in magnitude to the work needed to move (lift) the weight
FROM THAT PLANE to the given height d.
This is the our adventurous friend's conclusion:

> I have used a basic physics argument.

Uncorrect. You have misused complex physics concepts, that have to
be chewed and digested before they can be applied properly.

> [...] Yes, to see how much work is being done by the swimmer while
> have the swimmer stop and when the weights stop moving, measure the
> CHANGE in distance the weights move. Then multiply the weight of the
> weights (mg) by this change in distance. This is the amount of work
> being done by the swimmer WHILE swimmming.

Uncorrect, as explained above!

With regards,

__________ _________ ___________~___ ________ _________________~___
/ ~ ~ ~ ~ \
/______________~______~__________ _______~_____~______________~_____~_____\
| Paolo de Leva ~ \ Tel.+ FAX: (39-6) 575.40.81
| Istituto Superiore di Educazione Fisica > other FAX: (39-6) 361.30.65
| Biomechanics Lab /
| Via di Villa Pepoli, 4 < INTERNET e-mail address:
| 00153 ROME - ITALY \ deLEVA@RISCcics.Ing.UniRoma1.IT
|_____________________~________~__________________ __________________
challenging entropy :-)


End of responses on tethered swimming, discussion then became more general.

Robin B-L

__________________________________________________ ______

Robin Burgess-Limerick robin@hms01.hms.uq.oz.au

Department of Human Movement Studies
The University of Queensland 4072

Ph. +61 7 3365 4718 Fax +61 7 3365 6877
__________________________________________________ _______