Critical Power and Intervals: A Spanish Study of 27 Runners Fixes the Cycling Models
Critical power can be used to plan interval sessions with a running power meter, and a Spanish study of 27 runners has just shown that the models used to predict how many reps you can complete, borrowed from cycling, do not work for running. The authors, from the universities of Granada, Cádiz, Castilla-La Mancha, Alicante, Innsbruck and La Frontera (Chile), propose a simpler formula with a single coefficient per runner. The paper came out in October in Physiological Reports.
What critical power and W’ are
Critical power (CP) is the highest power you can hold in a metabolic steady state. It marks the line between hard efforts you can sustain for a long time and severe ones that wear you out sooner or later, depending on how far above it you go. Above CP you have a limited reserve of work, called W’ (W prime) and measured in joules. Every second above CP spends W’, and dropping below it lets W’ refill.
In cycling, “W’ balance” models track that reserve second by second to predict how many intervals you can complete at a given power. With foot pods such as Stryd the same idea applies to running, but it had barely been tested. A 2015 study had already found that one of these models missed on a treadmill with active recovery.
How the study worked
The group was 25 men and 2 women aged 19 to 39, with 8 years of running on average and about 35 km a week, recruited from local clubs and training groups. Everything took place on a 325 m outdoor track, with a Stryd NextGen on the right shoe paired to a Garmin Forerunner 965.
On day one they did the 9/3 test: two time trials of 9 and 3 minutes, 30 minutes apart, covering as much distance as possible. That gave each runner a critical power and a W’.
| 9/3 test (mean) | 9 minutes | 3 minutes |
|---|---|---|
| Distance | 2,487 m | 923 m |
| Pace | 3:37/km | 3:15/km |
| Power | 344 W | 380 W |
Mean critical power was 327 W (4.76 W/kg) and mean W’ was 9,550 joules, with large differences between runners.
On two more days they ran intervals at 108% of critical power, the intensity the authors link to VO2max, until they could not go on. Recovery was standing rest, half as long as the rep. In one session each rep used 40% of W’ (about 2:30 of running and 1:15 of rest on average), and in the other 60% (about 3:50 and 1:55). For a refresher on that intensity, see what is VO2 max.
Results: the cycling models miss badly
Runners completed 9.6 reps on average in the 40% session and 5.5 in the 60% session. The four classic models, used as published, overshot by a wide margin:
| Model | Mean error (reps) |
|---|---|
| Morton and Billat linear | 72.4 |
| W’bal integral (Skiba 2012) | 63.1 |
| W’bal differential (Skiba 2015) | 72.4 |
| Caen biexponential | 26.4 |
| Modified linear, coefficient 1 | 4.85 |
| Modified linear, group coefficient (1.63) | 2.85 |
| Modified linear, individual coefficient | 0.55 |
The models refill W’ too fast. With these runners’ critical power and W’, the linear and differential models treated W’ as almost fully restored after about 30 seconds of rest, so they predicted endless reps. The authors capped the simulation at 80, and both models hit that cap in all 54 sessions. The integral model hit it in 46.
The formula they propose
The new model keeps the linear idea: during a rep you spend W’ according to how far you are above CP, and during rest you get it back at R times that same excess. With R equal to 1 and rests half as long as the rep, you recover half of what you spent. With the group value of 1.63 you recover a little over 80%, and the small loss on each rep eventually empties the reserve.
Fitted to each runner, the coefficient averaged 1.54 and changed little between the two sessions (coefficient of variation 9.9%). With that individual value, the model predicted the number of reps to within about half a rep on average. What the number reflects physiologically is still open, and the authors treat it as a calibration value.
What you can do with your critical power
If you train with Stryd or another sensor that reports power, the 9/3 test is easy to repeat on a track: warm up well, run 9 minutes all out, rest half an hour, then run 3 minutes all out. With the two average powers:
- Critical power = (9-min power × 540 − 3-min power × 180) / 360
- W’ = (3-min power − critical power) × 180
Using the study means, that gives about 326 W and about 9,700 joules, very close to the published values. From there you can set the length of long reps at 108% of CP, log how many you complete in each session and work out your own coefficient. To fit these sessions into your week, see 10K interval workouts and threshold training.
Power numbers differ from one device to another, so always compare readings from the same sensor. If you do not have one yet, the GPS running watch guide can help you choose. Two of the authors, Felipe García-Pinillos and Diego Jaén-Carrillo, also used Stryd in the running durability study of trail runners.
Limitations
The model has only been tested at 108% of critical power, with standing rest and a 2:1 work to rest ratio, in trained runners. The 1.63 coefficient should not be used for recreational or elite runners, or with jogging recoveries, without calibrating it first. The 2.85 and 0.55 rep errors were also measured on the same sessions used to fit the coefficient, so a third session is still needed to confirm them. The authors received no specific funding and report no conflicts of interest. The paper is open access on the journal website and the abstract is on PubMed.
Frequently asked questions
What is critical power in running?
It is the highest power you can hold in a metabolic steady state. Above it you draw on a limited reserve, W’, and the further above it you go, the sooner it runs out.
How do you calculate critical power?
With a 9/3 test: two maximal efforts of 9 and 3 minutes with half an hour of rest between them. The two average powers give you critical power and W’.
Do cycling W’ balance models work for running?
Not as published, according to this study: with standing rest they overshot by 26 to 72 reps on average. A linear model with a coefficient fitted to each runner was off by about half a rep.
