The two-parameter critical power (CP) model is a robust mathematical interpretation of the power–duration relationship, with CP being the rate associated with the maximal aerobic steady state, and W′ the fixed amount of tolerable work above CP available without any recovery. The aim of this narrative review is to describe the CP concept and the methodologies used to assess it, and to summarize the research applying it to intermittent cycle training techniques. CP and W′ are traditionally assessed using a number of constant work rate cycling tests spread over several days. Alternatively, both the 3-min all-out and ramp all-out protocols provide valid measurements of CP and W′ from a single test, thereby enhancing their suitability to athletes and likely reducing errors associated with the assumptions of the CP model. As CP represents the physiological landmark that is the boundary between heavy and severe intensity domains, it presents several advantages over the de facto arbitrarily defined functional threshold power as the basis for cycle training prescription at intensities up to CP. For intensities above CP, precise prescription is not possible based solely on aerobic measures; however, the addition of the W′ parameter does facilitate the prescription of individualized training intensities and durations within the severe intensity domain. Modelling of W′ reconstitution extends this application, although more research is needed to identify the individual parameters that govern W′ reconstitution rates and their kinetics.

This study examined the partial reconstitution of the work capacity above critical power (W’) following successive bouts of maximal exercise using a new repeated ramp test (RRT), against which the fit of an existing W’ balance (W’_bal) prediction model was tested. Twenty active adults, consisting of trained cyclists (n = 9; age 43 ± 15 years; V̇O_2max 61.9 ± 8.5 mL∙kg∙min^-1) and untrained (n = 11; age 36 ± 15 years; V̇O_2max 52.4 ± 5.8 mL∙kg∙min^-1) performed two tests 2-4 days apart, consisting of three incremental ramps (20 W∙min^-1) to exhaustion interspersed with 2-min recoveries. Intra-trial differences between recoveries demonstrated significant reductions in the amount of W’ reconstituted for the group and both sub-sets (p < 0.05). The observed minimal detectable changes of 475 J (first recovery) and 368 J (second recovery) can be used to monitor changes in the rate of W’ reconstitution in individual trained cyclists. Inter-trial relative reliability of W’ reconstitution was evaluated by intraclass correlation coefficients for the group (≥ 0.859); trained (≥ 0.940) and untrained (≥ 0.768) sub-sets. Absolute reliability was evaluated with typical error (TE) and coefficient of variation (CV) for the group (TE ≤ 559 J; CV ≤ 9.2%), trained (TE ≤ 301 J; CV ≤ 4.7%), and untrained (TE ≤ 720 J; CV ≤ 12.4%). The reconstitution of W’ is subject to a fatiguing effect hitherto unaccounted for in W’_bal prediction models. Furthermore, the W’_bal model did not provide a good fit for the RRT, which itself proved to be a reliable test protocol.

Purpose: This study examined the relationship of physiological and anthropometric characteristics with parameters of the critical power (CP) model, and in particular the reconstitution of W′ following successive bouts of maximal exercise, amongst trained and untrained cyclists. Methods: Twenty male adults (trained nine; untrained 11; age 39 ± 15 year; mass 74.7 ± 8.7 kg; V̇O_2max 58.0 ± 8.7 mL kg⁻¹ min⁻¹) completed three incremental ramps (20 W min⁻¹) to exhaustion interspersed with 2-min recoveries. Pearson’s correlation coefficients were used to assess relationships for W′ reconstitution after the first recovery (W′_rec1), the delta in W′ reconstituted between recoveries (∆W′_rec)_, CP and W′. Results: CP was strongly related to V̇O_2max for both trained (r = 0.82) and untrained participants (r = 0.71), whereas W′ was related to V̇O_2max when both groups were considered together (r = 0.54). W′_rec1 was strongly related to V̇O_2max for the trained (r = 0.81) but not untrained (r = 0.18); similarly, ∆W′_rec was strongly related to V̇O_2max (r = − 0.85) and CP (r = − 0.71) in the trained group only. Conclusions: Notable physiological relationships between parameters of aerobic fitness and the measurements of W′ reconstitution were observed, which differed among groups. The amount of W′ reconstitution and the maintenance of W′ reconstitution that occurred with repeated bouts of maximal exercise were found to be related to key measures of aerobic fitness such as CP and V̇O_2max. This data demonstrates that trained cyclists wishing to improve their rate of W′ reconstitution following repeated efforts should focus training on improving key aspects of aerobic fitness such as V̇O_2max and CP.

Chorley, A and Lamb, KL. The effects of a cycling warm-up including high-intensity heavy-resistance conditioning contractions on subsequent 4-km time trial performance. J Strength Cond Res 33(1): 57–65, 2019—Previous exercise has been shown to improve subsequent performance through different mechanisms. Sport-specific conditioning contractions can be used to exploit the “post-activation potentiation” (PAP) phenomenon to enhance performance although this has rarely been investigated in short endurance events. The aim of this study was to compare a cycling warm-up with PAP-inducing conditioning contractions (CW) with a moderate-intensity warm-up (MW) on performance and physiological outcomes of a 4-km time trial. Ten well-trained male endurance cyclists ( JOURNAL/jscr/04.03/00124278-201901000-00007/7FFU1/v/2023-08-19T002812Z/r/image-tiff max 65.3 ± 5.6 ml·kg⁻¹·min⁻¹) performed two 4-km cycling time trials after a 5-minute recovery after a warm-up at 60% of JOURNAL/jscr/04.03/00124278-201901000-00007/7FFU1/v/2023-08-19T002812Z/r/image-tiff max for 6.5 minutes (MW), and a warm-up with conditioning contractions (CW) consisting of 5 minutes at 60% of JOURNAL/jscr/04.03/00124278-201901000-00007/7FFU1/v/2023-08-19T002812Z/r/image-tiff max then 3 × 10-second at 70% of peak power interspersed with a 30-second recovery. Blood lactate concentrations were measured before and after time trial. Expired gases were analyzed along with time, power output (PO), and peak forces over each 500 m split. After CW, mean completion time was reduced (1.7 ± 3.5 seconds p > 0.05), PO increased (5.1 ± 10.5 W p > 0.05) as did peak force per pedal stroke (5.7 ± 11 N p > 0.05) when compared with MW. JOURNAL/jscr/04.03/00124278-201901000-00007/7FFU1/v/2023-08-19T002812Z/r/image-tiff increased (1.4 ± 1.6 ml·kg⁻¹·min⁻¹ p ≤ 0.05) after CW, whereas respiratory exchange ratio (RER) decreased (0.05 ± 0.02 p ≤ 0.05). Physiological and performance differences after CW were greatest over the first 1,500 m of the trials. The results suggest that a PAP-inducing warm-up alters JOURNAL/jscr/04.03/00124278-201901000-00007/7FFU1/v/2023-08-19T002812Z/r/image-tiff kinetics and can lead to performance improvements in short endurance cycling but work and recovery durations should be optimized for each athlete.

Purpose: The aim of this study was to investigate the individual $$W^{^{\prime}}$$W ′ reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe $$W^{^{\prime}}$$W ′ reconstitution. Methods: Ten trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; $$\dot{V}{\text{O}}_{2\max }$$V ˙ O 2 max 58.6 ± 7.1 mL kg min⁻¹) completed three incremental ramps (20 W min⁻¹) to the limit of tolerance with varying recovery durations (15–360 s) on 5–9 occasions. $$W^{^{\prime}}$$W ′ reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R² and bias-corrected Akaike information criterion (AICc). Results: A bi-exponential model outperformed the mono-exponential model of $$W^{^{\prime}}$$W ′ reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adjR² = 0.999) for the first recovery when optimised with parameters of fast component (FC) amplitude = 50.67%; slow component (SC) amplitude = 49.33%; time constant (τ)_FC = 21.5 s; τ_SC = 388 s. Following the second recovery, W′ reconstitution reduced by 9.1 ± 7.3%, at 180 s and 8.2 ± 9.8% at 240 s resulting in an increase in the modelled τ_SC to 716 s with τ_FC unchanged. Individual bi-exponential models also fit well (adjR² = 0.978 ± 0.017) with large individual parameter variations (FC amplitude 47.7 ± 17.8%; first recovery: (τ)_FC = 22.0 ± 11.8 s; (τ)_SC = 377 ± 100 s; second recovery: (τ)_FC = 16.3.0 ± 6.6 s; (τ)_SC = 549 ± 226 s). Conclusions: W′ reconstitution kinetics were best described by a bi-exponential model consisting of distinct fast and slow phases. The amplitudes of the FC and SC remained unchanged with repeated bouts, with a slowing of W′ reconstitution confined to an increase in the time constant of the slow component.

The aim of this study was to investigate the effects of different recovery power outputs on the reconstitution of W′ and to develop a dynamic bi‐exponential model of W′ during depletion and reconstitution. Ten trained cyclists (mass 71.7 ± 8.4 kg; V̇O_2max 60.0 ± 6.3 ml·kg⁻¹·min⁻¹) completed three incremental ramps (20 W·min⁻¹) to the limit of tolerance on each of six occasions with recovery durations of 30 and 240 s. Recovery power outputs varied between 50 W (LOW); 60% of critical power (CP) (MOD) and 85% of CP (HVY). W′ reconstitution was measured following each recovery and fitted to a bi‐exponential model. Amplitude and time constant (τ) parameters were then determined via regression analysis accounting for relative intensity and duration to produce a dynamic model of W′. W′ reconstitution slowed disproportionately as recovery power output increased (p < 0.001) and increased with recovery duration (p < 0.001). The amplitudes of each recovery component were strongly correlated to W′ reconstitution after 240 s at HVY (r = 0.95), whilst τ parameters were found to be related to the fractional difference between recovery power and CP. The predictive capacity of the resultant model was assessed against experimental data with no differences found between predicted and experimental values of W′ reconstitution (p > 0.05). The dynamic bi‐exponential model of W′ accounting for varying recovery intensities closely described W′ kinetics in trained cyclists facilitating real‐time decisions about pacing and tactics during competition. The model can be customised for individuals from known CP and W′ and a single additional test session.Highlights A dynamic bi‐exponential model of W′ accounting for both varying power output and duration. Individual customisation of the model can be achieved with a single specific test session. W′ reconstitution slows disproportionally with increasing intensity after repeated bouts.