A few years back I published a post entitled "On marathons and ultramarathons". The main aim of that post was to present the dependence of the mean velocity of a race on the distance. In that presentation I was focusing particularly on the transition between long and super-long races.
Recently I was discussing with my friend and collaborator G. Purdy and he pointed out that (many years ago) he had published an article where he was presenting this dependence together with a best fit by a simple analytical expression.
I have always believed that there are different regimes in the running performance depending on the biomechanical and physiological processes involved and thus one should better separate the various ranges of distances. So I decided to revisit the question of the mean velocity as a function of the distance of the race. The figures below are all based on the current men's world records but similar results are obtained with the women's ones.
The first figure shows the mean velocity for distances from 50 to 1000 m. Distances up to 400 m are the sprint events. Here one observes first a purely biomechanical effect. The athlete must accelerate over a certain distance before reaching his maximum velocity. Once this velocity is attained it can be maintained for a short time before deceleration appears.
For races not exceeding 800 m there is a complicated interplay between the various energy production mechanisms, but beyond this distance the main energy source is the aerobic mechanism. However an athlete cannot cover the total distance producing the maximum possible power under the aerobic mechanism. The main reason for this is that despite the aerobic character of the effort there is always a significant quantity of lactate produced which limits the aerobic power and thus the mean velocity. (I am aware that I am over-simplifying things here).
Once one reaches races where the duration exceeds 2-2.30 hours another physiological change appears: the glycogen stored in the muscles is depleted. So the athlete can pursue his effort only by burning lipids. The consequence of this is that the maximal aerobic power that can be sustained for these super-long races is diminished. Hence the transition observed in the figure above where one sees that the mean velocity for races from 50 to 300 km follows a curve different from the one obtained in the middle and long distance regime.
The curve above shows the mean velocities of ultra-long, multi-day, events. Here, although the mechanism is physiological it has not to do with energy production. In multi-day events the athlete must take time to sleep, eat and take care of other bodily functions. This has a direct impact on the mean velocity. It is in fact interesting to remark that the lower curve, when back-extrapolated crosses the upper one at around the 12-hour performance. This means that for races with a duration above 12 hours a non-negligible amount of time would normally be devoted to non-running moments. The fact that despite this the 24-hour record follows the upper curve means that the athletes minimise these pauses for the sake of the record. However as the race duration becomes longer this is no more possible hence the transition to the lower curve.
The last curve is the analogue of Purdy's curve, now extended over the whole spectrum of distances. One can distinguish the four regimes identified above. And it is interesting to notice that the records of the Marathon and, to a lesser degree, that of the 100 km are better that what one would have expected by drawing naïvely a continuous curve. This is due to the fact that the former is a most popular distance while the latter is the longest distance over which a world record is homologated by World Athletics.
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