This is a summary of my thesis. I have some copies left for people who are
interested. (the thesis is on HUMAN swimming).


Huub M Toussaint

In swimming some of the power output generated by the swimmer is necessarily
expended in giving water a kinetic energy change, since the propelling
thrust is made against masses of water that acquire a backward
momentum. Hence the power output (Po) is apportioned between that part
used to overcome drag (Pd) and that part which gives water a kinetic
energy change (Pk). Hence

Po = Pd + Pk (1)

It will be obvious that the latter component Pk is rather difficult to
measure. However, the apportionment of Po into Pd and Pk could be an
important determinant of swimming performance. This idea is given
expression in the concept of propelling efficiency ep (Toussaint et al

ep = Pd/Po = Pd/(Pd + Pk) (2)

The measurement of the component powers of the total mechanical power
produced by the swimmer was made possible by the development of the
system to measure active drag (MAD-system, Hollander et al, 1986). With
suitable instrumentation this system allows active drag to be directly
measured for the first time.

Active drag related to velocity

The drag force on the swimmer while swimming the front crawl is related
to the swimming velocity raised to the power 2.12 1 0.2 (males) or 2.28 1
0.35 (females). Most subjects (29) showed rather constant values of
Fd/v2, but 12 subjects gave significantly (p < 0.01) stronger or weaker
quadratic relationships. Differences in drag force and coefficient of drag
between males and females (drag at 1 m/s 28.9 1 5.1 N, 20.4 1 1.9 N,
drag coefficient: 0.64 1 0.09, 0.54 1 0.07 respectively) are especially
apparent at the lowest swimming velocity (1 m/s), which becomes less
at higher swimming velocities.

Mechanical efficiency of swimming

Mechanical efficiency can be defined as the ratio of the power output to
the power input. The power output was assessed by use of the MAD system.
The estimation of power input from steady state oxygen uptake
measurements does not present major problems, provided that the
respiratory apparatus does not increase body drag.

A respiratory valve was developed whereby the inspiratory and expiratory
tubing was arranged in-line and moulded over the swimmers head. Using
the MAD system the effect on total body drag due to the addition of the
respiratory apparatus was evaluated to be negligible. This apparatus was
applied in the determination of mechanical efficiency in a group of male (N
= 6) and female (N = 4) competitive swimmers. The mechanical efficiency
ranged from 5 - 9.5%. At equal swimming speed the male competitive
swimmers demonstrated a higher mechanical efficiency. However, this
was due to the higher power output required by the male swimmers at a
given speed. At the same power output the values for the mechanical
efficiency do not differ between the male and female competitive

Propelling efficiency of swimming

To determine the propelling efficiency of swimming it is necessary to
measure Pk. This can be done by comparing at the same velocity the Pi
swimming free, where Pi reflects Pd + Pk, with the Pi obtained while
swimming on the MAD system (Pk = 0, since the push off is made against a
fixed point). For the four top class swimmers studied the propelling
efficiency was found to range from 46 - 77%.

To evaluate the significance of the propelling efficiency as a performance
determining factor, the ep of 6 competitive swimmers was compared to
the ep of 5 triathletes. Using regression equations the data was
interpolated and the groups were compared at equal rates (900 Watt) of
energy expenditure. The groups did not differ in mechanical efficiency,
stroke frequency, and work per stroke. There was a difference in distance
per stroke (1.28 m vs 0.99 m), and mean swimming velocity (1.11 m/s vs
0.90 m/s). The difference in swimming speed between the two groups
can be explained by the fact that the competitive swimmers can use a
much higher proportion of their power output to overcome drag (44 W vs
30 W). At the same time the competitive swimmers expend less power in
moving water backwards (28 W vs 39 W). This difference in
apportionnement of the power output can be characterized as the
propelling efficiency. Mean (1SD) propelling efficiency for the competitive
swimmers was 62 1 6% but only 44 1 4% for the triathletes.

Since propelling efficiency was shown to be an important determinant of
swimming performance the influence of contributing factors was
considered. One of them, the artificial enlargement of the propelling
surfaces of the hand, resulted at a given velocity in a decrease in energy
expenditure (6%), power output (7.6%) and work per unit distance (7.5%). At
the same time increases were seen in propelling efficiency (7.8%) and
work per stroke (7%). The increase in distance per stroke and the decrease
in stroke frequency could be explained by the increase of the propulsive

Future directions

It is obvious that the technique of the swimmer determines the level of
propelling efficiency. However, the present method employed to determine
the propelling efficiency does not relate technique to it directly. For a
more thorough understanding of swimming it seems imperative to develop
methods that relate the movement pattern of the swimmer to their
propelling efficiency.


Hollander, A.P., G. de Groot, G.J. van Ingen Schenau, H.M. Toussaint, H. de
Best, W. Peeters, A. Meulemans, and A.W. Schreurs. Measurement of active
drag during crawl arm stroke swimming. J. Sport Sci. 4, 21-30, 1986.

Toussaint, H.M., F.C.T. van der Helm, J.R. Elzerman, A.P. Hollander, G. de
Groot, and G.J. van Ingen Schenau. A power balance applied to swimming. In:
A.P. Hollander, P.A. Huijing and G. de Groot (Eds.), Biomechanics and
Medicine in Swimming. Champaign, IL, Human Kinetics Publishers, pp.
165-172, 1983.

Parts of the present thesis are published:

Toussaint, H.M., G. de Groot, H.H.C.M. Savelberg, K. Vervoorn, A.P. Hollander,
and G.J. van Ingen Schenau. Active drag related to velocity in male and
female swimmers. J. Biomechanics 21, 435-438, 1988.

Toussaint, H.M., A. Meulemans, G. de Groot, A.P. Hollander, A.W. Schreurs,
and K. Vervoorn. Respiratory valve for oxygen uptake measurements during
swimming. Eur. J. Appl. Physiol. 56, 363-366, 1987.

Toussaint, H.M., A. Beelen, A. Rodenburg, A.J. Sargeant, G. de Groot, A.P.
Hollander, and G.J. van Ingen Schenau. Propelling efficiency of front crawl
swimming. J. Appl. Physiol. 65, ...-..., 1988.

The following parts of the present thesis have been submitted for

Toussaint, H.M., W. Knops, G. de Groot and A.P. Hollander. The mechanical
efficiency of front crawl swimming. submitted to: Medicine and Science in
Sports and Exercises.

Toussaint, H.M. Differences in propelling efficiency between competitive
and triathlon swimmers. submitted to: Medicine and Science in Sports and

Toussaint, H.M., T. Janssen, and M. Kluft. Effect of propelling surfaces size
on the mechanics and energetics of front crawl swimming. submitted to: J.
Applied Physiology.

Huub Toussaint
Faculty of Human Movement Sciences
Dept Exercise Physiology and Health
Meibergdreef 15 (AMC)
1105 AZ Amsterdam
The Netherlands