## 20 April, 2014

### On marathons and ultramarathons

Many years ago I had drawn the mean velocity for the track world records as a function of the race distance. The part of the curve that was interesting me at that time was the one corresponding to the transition between anaerobic and aerobic processes. However, instead of limiting the graphic to relatively short races, say of up to 5 km, and since I had the world records for all distances at hand I decided to draw the curve all the way to the longest, 1000 km, ultramarathons. I was not able to find that graphic in my archives but it was a matter of a few minutes to draw it again, based on today’s records. The feature that had  attracted my attention the first time was obviously there.

In the figure above  we distinguish three regions: one from 800 m to the marathon, one from 100 km to 24 h events and one for longer events. I have also drawn a thin curve which corresponds to the best fit for velocity vs. distance for races from 800 m to the marathon and which could, in principle, be used in order to extrapolate towards the velocities of races longer than the marathon. However these longer events do not agree with the extrapolation. Two discontinuities are clearly visible. The first is the interesting one. I remember that, back in the days when I was running marathons, the dreaded moment was “hitting the wall” while approaching 3 h of race. All of a sudden it was impossible to keep the same pace. The reason for this is that the glycogen reserves of the organism are depleted and from then onwards one has to burn lipids. Since the rate at which energy is produced through this mechanism is slower than the one of metabolising glycogen, one cannot sustain the same speed as before. (The second, concerning very long races, is very easy to explain: those are multi-day events and the runners must take some time off in order to sleep).

Marathon champions do not slow down during their races. In fact there exist many examples of record marathons where the second half is run faster than the first.  Top level athletes can sustain a marathon record pace for more than two hours. However a rough extrapolation from the graphic at hand shows that past some distance, around 60 km, an appreciable slow-down occurs. Of course, one can argue that there is substantially less interest in ultramarathons than in shorter races. This is all the more true for the marathon which is meeting with an incredible popularity over the past 20-25 years. A consequence of this is that the best runners do not venture beyond the 42 km races. However I believe that, record-wise, the recent progress in the marathon does not modify the conclusions based on metabolic data. To put it in a nutshell: even the biggest marathon champions would bonk at some point should they attack longer races without the adequate preparation.