REF-1192 · Kordi et al., 2018 · European Journal of Applied Physiology · Paper · PubMed

Does leg strength relate to W′?

In 11 elite male cyclists, knee-extensor max torque tracked W′ (r = 0.87; our 95% CI 0.57-0.97), thigh volume borderline (r = 0.60, p = 0.05), CP neither. Correlation only: strength-for-W′ is untested.

Blimited evidenceMeasured on elite athletes

Kordi, Menzies and Parker Simpson asked what in the thigh goes with the two parameters of the power-duration relationship: critical power (CP), the asymptote, and W′, the curvature constant or finite work capacity above CP.

Their premise was that short endurance events lean more on W′, whose mechanism is not fully known, and that both muscle volume and muscle strength may contribute to it.

In 11 elite male cyclists they measured gross thigh volume (TVOL), quadriceps muscle volume (QVOL), vastus lateralis pennation angle (PA) and muscle thickness (MT), and maximal torque production of the knee extensors (FMAX), then correlated each with CP and W′.

W′ correlated very strongly with FMAX (r = 0.87, p < 0.001) and, at the edge of significance, with TVOL (r = 0.60, p = 0.05); QVOL, PA and MT were not related to W′, and CP was not associated with any mechanical or anthropometric measure.

The authors conclude that, in addition to muscle size, the maximal force of a muscle group "appears to be linked" to the size of W′ in elite cyclists.

Our reading: a plausible and strong association in a very small elite sample, with a wide uncertainty (our 95% CI for r = 0.87 runs from about 0.57 to 0.97) and a thigh-volume link that may be no association at all (CI about 0.00 to 0.88). It does not test whether raising strength raises W′.

Protocol

Participants (from the abstract): 11 elite male cyclists. Age, body mass, discipline, training history and performance level are not in the abstract.
Design: cross-sectional; thigh anatomy, knee-extensor torque and the power-duration parameters measured in the same riders; correlations of each thigh measure with CP and with W′ (the abstract reports r and p only and does not name the coefficient; our CIs assume Pearson's r).
Thigh anatomy: gross thigh volume (TVOL), quadriceps muscle volume (QVOL), and vastus lateralis pennation angle (PA) and muscle thickness (MT). The imaging methods are not named in the abstract.
Strength: "maximum torque production of the knee extensors (FMAX)". The abstract does not state the contraction type, joint angles or dynamometer; its conclusion calls it "maximal evocable force".
CP and W′: the abstract does not state how they were derived (number and length of trials, ergometer, model). A secondary summary (not checked against the paper) reports two maximal trials of 3 and 12 min; if so, CP and W′ come from a two-point fit of the two-parameter model, whose limits are in Mechanisms and Limitations.
Not reported in the abstract: mean values of CP, W′ or any thigh measure; whether W′ was absolute (kJ) or scaled to body mass; whether body size was controlled; correction for multiple correlations; confidence intervals; funding and conflicts of interest.
Affiliations (Europe PMC record): English Institute of Sport and Northumbria University (Kordi); University of Bath (Menzies); Scottish Institute of Sport and University of Kent (Parker Simpson). No grants are listed in the record.

Key Results

Pair (n = 11, from the abstract)rpr² (our calculation)95% CI on r (our calculation, Fisher z)
W′ vs knee-extensor maximal torque (FMAX)0.87< 0.0010.760.57 to 0.97
W′ vs gross thigh volume (TVOL)0.600.050.360.00 to 0.88
W′ vs quadriceps volume, VL pennation angle, VL thickness"No other anthropometric characteristics were related to the W′"not given——
CP vs any mechanical or anthropometric measurenot associatednot given——
Borderline thigh-volume result (our calculation): with 11 pairs the smallest r that reaches two-sided p < 0.05 is about 0.602; r = 0.60 gives p ≈ 0.051. The authors call it "large" and "significant"; on these numbers it sits on the threshold, and its CI reaches zero.
Strength result (our calculation): r = 0.87 with n = 11 gives p ≈ 0.0005, consistent with the reported p < 0.001. Read as r², 0.87 is 76% of the variance, but the CI on r of 0.57 to 0.97 puts it anywhere from about 32% to 93%.
Muscle size did not carry it on its own: quadriceps volume, the measure closest to the knee extensors, was not related to W′, while knee-extensor torque was.
CP: no thigh measure went with CP.

Mechanisms

Measured: between riders, higher knee-extensor torque went with a larger W′ (r = 0.87); gross thigh volume went with W′ at r = 0.60 (p = 0.05); quadriceps volume, pennation angle and thickness did not; CP went with none of them.
Authors' interpretation: besides muscle size, the maximal force a muscle (group) can be made to produce appears linked to how large W′ is. This is association language; the study has no intervention and no mediation analysis.
Inference (body size): stronger riders are often bigger riders, and a larger body can produce both more torque and more work above CP in absolute terms. Whether W′ and FMAX were absolute or scaled to body mass, and whether body size was controlled, is not in the abstract, so part of the r = 0.87 may be shared body size.
Inference (what the test measures): if CP and W′ came from 3- and 12-min trials, W′ from two points equals 240 s × (3-min power − 12-min power) (our calculation from P = CP + W′/t). A 5-W error in the 3-min trial then moves W′ by 1.2 kJ and CP by under 2 W, so W′ here is largely "how far a rider's 3-min power sits above their 12-min power". A correlation of strength with that gap is what you would expect if the strongest riders are the best at short, very hard efforts.
Inference (force is not the direct limit): pedalling forces stayed below 54% of maximal dynamic force in every condition up to maximal aerobic power in 11 cyclists (REF-119, B), so a 3-min effort does not call on maximal force directly; maximal torque is more plausibly a marker of what a large W′ needs (muscle mass able to work hard, fibre make-up, energy stores) than the limiter itself. None of these was measured here.
Inference (why CP was not linked): CP is set mainly by aerobic and oxidative capacity, which thigh size and strength do not index; with n = 11 a missing correlation is also not proof of none.

Practical Application

Does leg strength relate to W′? In 11 elite male cyclists, knee-extensor max torque tracked W′ (r = 0.87; our 95% CI 0.57-0.97), thigh volume borderline (r = 0.60, p = 0.05), CP neither. Correlation only: strength-for-W′ is untested.
Read it as a profile clue, not a prediction: in these 11 elite men the riders with the larger W′ had the higher knee-extensor torque (a lab torque test, not a gym lift); a W′-to-CP profile (the pursuiter or sprinter shape in REF-442, the base's composite) was not analysed, and carrying this to other riders is inference. The abstract gives no prediction equation, and with 11 riders a torque test cannot stand in for measuring W′.
"Raise strength to raise W′" is an inference, not a finding. No training was done here.The base's training evidence points the other way on the specific claim: pooled heavy strength trials in cyclists raised anaerobic power (ES 0.56) and performance but did not change anaerobic capacity (REF-743, A, 17 trials, low certainty; anaerobic capacity as that review defined it, not necessarily W′).The base's position stays as in SYNTH-46: promise better short-effort performance, not a bigger W′.
Heavy strength twice a week remains the cyclist's default for its own trial-backed reasons (efficiency, sprint and late-race power: SYNTH-43; isometric half-squat strength and Wingate power in elite cyclists, REF-147; 5-min power after 185 min of riding, REF-146), not because of this correlation. On-bike isometric training raised power per kilogram in elite track sprinters, from the same first author (REF-1182, B, non-randomised), and did not measure W′.
If you track W′ (the base's practice): test it the way the base tests CP, with several maximal efforts in the race position, labelled with the protocol (SYNTH-53, REF-026, REF-201). If you use only a 3-min and a 12-min effort, any error in the 3-min effort lands mostly in W′ (about 1.2 kJ per 5 W, our calculation), so read a W′ change of 1-2 kJ between two tests as noise until it repeats.
Pacing use is unchanged: W′ is the budget above CP for efforts under about 20 min (SYNTH-48); this study changes nothing about how to spend it.

Limitations

Cross-sectional and correlational: association between riders, not cause; no training, so nothing about whether changing strength or thigh size changes W′.
Very small (n = 11), men only, elite only; one correlation at r = 0.87 has a 95% CI of about 0.57 to 0.97 and the other at r = 0.60 has one of about 0.00 to 0.88 (our calculation; the abstract gives no CIs).
Several thigh measures each tested against two outcomes (about ten correlations by the abstract's list) with no correction for multiple tests reported in the abstract; r = 0.60 at p = 0.05 would not survive one.
Body size: the abstract does not say whether W′ and torque were absolute or relative to body mass or whether size was controlled, so shared body size may carry part of the correlation.
CP and W′ method not in the abstract; if from two trials (as a secondary summary reports), the two-parameter line fits the two points exactly, gives no fit error, and puts the error of the shorter trial mostly into W′. W′ is the less precisely estimated of the two parameters: in REF-044 the 3-min test's work above end power agreed with W′ at r = 0.84, against r = 0.99 for end power vs CP.
Read from the abstract only (closed access): contraction type and joint angles of the torque test, imaging methods, group means, funding and conflicts of interest were not checked.
How this entry was checked and changed
Why this level

cross-sectional / correlational, n = 11, from the abstract (the paper is closed access; Europe PMC, OpenAlex and the publisher gave no open copy). The rubric puts a cross-sectional correlational study under 100 participants at B (B+ needs a cross-sectional study of 100 or more); within B this is a weak one: 11 riders, one sex, several thigh measures each correlated with two outcomes, no correction for multiple tests reported in the abstract, no confidence intervals, and the second correlation sits on the significance threshold