## 16 March, 2014

### On race-walking

I do not like race-walking. I find it both inefficient and non-aesthetic. And while “non-aesthetic” is a matter of personal taste the inefficiency of race-walking is something we can establish in a simple way.

Let us start with some very simple physical model of both walking and running. (In what follows I shall borrow from the presentation of J.C. Sprott ). The basic assumption is that the energy consumed in raising the centre of mass of the body at each step is not recovered when the centre of mass is lowered. In the case of running we assume that we are in the presence of successive leaps propelling the body along a parabolic trajectory. Making the additional simplification that the angle at the origin of the parabola is of 45° we find for the energy per unit time for running at velocity v, the expression

$$P={1\over4}mgv$$

where m is the mass of the body and g the acceleration due to gravity. In the case of walking we assume that legs are stiff and that each foot leaves contact with the ground at the instant the other touches the ground. Moreover a leg swings at its natural period, as if it were a pendulum. (Moreover we neglect any energy spent in flexing the knee, since this is only useful in avoiding contact with the ground while the leg swings forward). The energy per unit time in this case is given by

$$P={mg\sqrt{3gL}\over\pi\sqrt2}\left(1-\sqrt{1-{\pi^2\over6gL}v^2}\right)$$
where L is the length of the leg. The model is admittedly a very naïve one but the important result is that, while the energetic cost of running increases linearly with velocity, that of walking is a quadratic function of speed.
As a result while walking is advantageous at low speeds, running is more economical when speed increases. The transition velocity depends of course on the precise model but the fact that if one wishes to go fast one has to run is undeniable. It is perhaps interesting to see what physiological measurements have to say concerning walking versus running. The figure below is borrowed from di Prampero’s excellent monograph “La locomozione umana”.
One can see readily that at slow speeds up to roughly 2.5 m/s walking is advantageous but its energetic cost increases in agreement with a quadratic law (curve m). Above the transition speed we have two possibilities: either running (curve c) or race-walking (curve m*). Both show a linear dependence of energetic cost on velocity with the cost of walking being higher than that of running.

So, while the simple model for the energetic cost of walking versus running is in agreement with the findings of physiology we have a problem with race-walking. How come the energy per unit time spent by race-walkers increases linearly with velocity? My answer to this is that race-walkers use an irregular style as often as they can get away with it.
The rules stipulate that race-walking is a progression of steps so taken that the walker makes contact with the ground, so that no visible, to the human eye, loss of contact occurs. The advancing leg must be straightened, i.e. not bent at the knee, from the moment of first contact with the ground until the vertical upright position. Curiously there are no recent experimental data concerning the maximum speed one can attain by walking regularly. The only data I could find goes back to 1920 when E. Anthoine performed an experiment on the grounds of the Ecole Nationale de Joinville (now Institut National des Sports). He was filmed under control of time-keepers and the movies were analysed afterwards in slow motion so as to establish the maximum speed without loss of contact with the ground and with straight legs. It turned out that the maximal speed sustained over 200 m was of the order of 20 km/h. Starting from this data one can extrapolate to a realistic situation of a walking race of, say, 20 km. (The argument that follows is to be taken with a huge grain of salt but I believe that at least it shows that a problem does exist). For running, the ratio of maximal velocities over 20 km and 200 m is close to 0.6. If we apply the same ratio to the 20 km/h speed found by E. Anthoine we obtain a maximal velocity for a 20 km walk of 12 km/h to be compared to a velocity of close to 16 km/h attained by the elite race-walkers. Where does this extra speed come from? I think that it is obtained through subtle rule violations, “running” interludes wisely interspersed in a walking race.

Now, these critiques, and the fact that I do not particularly like race-walking should not be interpreted as a lack for respect for race-walkers. They are great athletes who train very hard. Many great champions have honoured this discipline. The greatest among them, to my eyes, is Robert Korzeniowski, three times gold-medal winner at the 50 km race at the Olympics and the first athlete to win both the short, 20 km, and the long, 50 km, race in the same olympiad.
However, even the great Korzeniowski, has had his collection of disqualifications in major championships. For instance I am not sure that in the photo above he has contact with the ground (in fact I think that he does not).

Is there anything to be done? My opinion is that, if we wish to maintain this discipline in major championships, we should use top-class technology, like high-speed cameras, that will compensate for the shortcomings of the human eye and the subjectiveness of human judges. This will look unfair to athletes competing most of the time in minor competitions with less stringent controls but it is the only way to save the credibility of race-walking. Apart from this measure, I believe that race-walking should move away from the short races and concentrate on the longer ones without olympic events and perhaps world championships over 100 km. However, race-walking finds its true raison d’être in races like the famous Paris-Strasbourg, a 500 km race created by the same E. Anthoine we referred to above. The Paris-Strasbourg race, survives to this date transformed into a Paris-Colmar, and slightly shorter, one. (In fact E. Anthoine was the one who campaigned for the inclusion of race-walking in the Olympic Games, but his proposal was in favour of a 100 km race). One expects that in ultra-walking races the walking style violations will be so rare as to have negligible impact on the outcome of the race; this will bestow increased credibility upon the discipline. (The “non-aesthetic” argument will of course remain, but as I said at the beginning of this post, this is a matter of personal taste and in no way a decisive one).

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