Critical speed and critical power
Evidence: strong
Time to exhaustion falls as a hyperbolic function of speed. Critical speed is the asymptote of that curve: the highest intensity with a metabolic steady state, and a sharp boundary between sustainable and unsustainable work.
For any intensity hard enough to drive someone to exhaustion, the time they can hold it falls as a predictable hyperbolic function of how hard they go (Jones et al. 2010). Plot speed against time to exhaustion and the curve flattens towards a horizontal line it never crosses. That asymptote is the critical speed, or in cycling the critical power. It is not a statistical artefact: the same two-parameter relationship holds across species and forms of exercise, which is why it is treated as a real physiological threshold rather than a curve-fitting convenience (Poole et al. 2016).
The boundary of the steady state
Critical speed (CS) marks the line between the heavy and severe intensity domains. Below it, the body can stabilise: oxygen uptake, blood lactate and muscle metabolites settle at an elevated but constant level, and the effort can be held for a long time. Above it, nothing stabilises. Oxygen uptake drifts upward until it reaches VO₂max, lactate and muscle metabolites accumulate without limit, and exhaustion follows in a time fixed by how far above CS the effort sits (Poole et al. 2016). CS is therefore the highest intensity with a genuine metabolic steady state, defined as the greatest rate of oxidative ATP production sustainable without continuously drawing on a finite reserve (Jones et al. 2010).
W’, the reserve above the line
That reserve is the second parameter of the relationship: W’ (W-prime, written D’ for distance when speed is the variable). It is a fixed quantity of work, in kilojoules, that can be done above CS before exhaustion, drawn partly from anaerobic sources (Jones et al. 2010). One way to picture it: CS is the rate at which the tank refills, W’ is the size of the tank. Any effort above CS spends W’ at a rate set by how far above CS it is, and exhaustion arrives when W’ is gone. This links directly to anaerobic capacity and speed reserve, which describes the same finite top-end capacity from the pace side. W’ is reconstituted during recovery below CS, exponentially, and faster the further below CS the recovery sits (Skiba et al. 2012).
Relation to the lactate threshold
CS sits close to, but is not the same as, the second lactate threshold and the maximal lactate steady state (MLSS). Both aim at the same idea, the highest sustainable intensity, but reach it differently: MLSS from constant-pace runs that hold blood lactate steady, CS from the mathematics of time to exhaustion. The two land near each other and CS often sits slightly above MLSS, partly because protocols and definitions of MLSS themselves disagree (Faude et al. 2009). The practical reading is that CS gives a sharply defined boundary from a few maximal efforts, where the lactate approach needs several constant-pace tests on separate days.
Practical use
CS and W’ can be estimated from a handful of maximal time-trials. A validated field protocol is three all-out runs on a track, longest first, over distances giving completion times of roughly three to twelve minutes; fitting the distance-time line yields CS and D’, and the values agree well with a laboratory treadmill protocol (Galbraith et al. 2014). From there, CS anchors pacing: hold goal pace below CS for events meant to be steady, and treat CS as the floor for threshold work. For intervals, the W’ balance model gives a principled way to set rep speed and recovery, since each rep above CS spends W’ and each recovery below it refills the tank (Skiba et al. 2012). This is the determinant a beginner meets informally as the pace they can just hold, covered plainly in the basics.
Limitations
The model assumes CS and W’ are fixed, which they are not over a long effort. Critical power can decay by around 10% after prolonged exercise, which is the mechanism behind durability: a pace that sat safely below CS early can cross a fallen CS late on and tip into the unsustainable domain (Maunder et al. 2021). The two-parameter fit is also sensitive to test protocol: the choice of trial distances, whether efforts are truly maximal, and how complete recovery between them is all shift the estimate, so a CS figure is only as good as the trials behind it (Galbraith et al. 2014).