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Daily paper · 2026-10-17 · athlete

The wall is at 76% of VO₂max, and eating moves it

A marathon is a constrained optimisation. The constraint is grams of carbohydrate, and it decides the fastest pace a runner can hold before arithmetic rather than willpower ends the race.

athleticsphysiologypacing
In the legs
305 g
muscle glycogen, plus about 90 g in the liver
Eating nothing
2:46:34
the wall at 76% of VO₂max
Eating 60 g an hour
2:20:39
limit at 90%
Worth
26 min
the difference the feed zone makes

The arithmetic

Running costs about 1 kcal per kilogram per kilometre. The share of that coming from carbohydrate rises with intensity, so the faster the pace the more carbohydrate each kilometre costs. Muscle glycogen, liver glycogen and what is eaten on the way are the supply. Where need crosses supply is the wall.

What it does not say

It gives a ceiling, not a prediction. Plenty of runners slow for reasons that have nothing to do with glycogen: heat, pacing errors, a lack of specific endurance. The model says only that above this pace the fuel runs out, whatever else does.

Method

Rapoport's formulation with literature constants for glycogen density and the carbohydrate share of energy by intensity, and Keller's two-equation runner for the pacing profile.

Caveat

Constants fitted to a population do not transfer to a person. Gut tolerance for 60 g an hour is itself trained, and not everyone has it.

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Carbohydrate needed against carbohydrate on board015030045060050%60%70%80%90%intensity, fraction of VO₂maxgrams of carbohydrateneeded at this paceon boardthe limit
Two curves and their crossing. Where they meet is the fastest pace the store can pay for.
Keller's optimal 1500 m: full force to the cruise, hold it, and arrive with the anaerobicstore empty · 3:39.5024680306090120150180210time, sspeed, m/scruise 6.85 m/sanaerobic store, scaledstore emptyspeedwhat is left of the anaerobic store
The optimal way to spend a finite engine over a fixed distance.