Understanding Optimal Cadence Dynamics: A Systematic Analysis of the Power–Velocity Relationship in Track Cyclists
¹ Institute for Applied Training Science, Dept. of Endurance Sports, Leipzig, Germany
² German Cycling Federation, Frankfurt, Germany
³ Magdeburg-Stendal University of Applied Sciences, Dept. of Engineering and Industrial Design, Germany
⁴ Institute for Applied Training Science, Dept. of Biomechanics, Leipzig, Germany
Abstract
This study aimed to investigate the changes in force-velocity (F/v) and power-velocity (P/v) relationships with increasing work rate up to maximal oxygen uptake and to assess the resulting alterations in optimal cadence, particularly at characteristic metabolic states.
Fourteen professional track cyclists (9 sprinters, 5 endurance athletes) performed submaximal incremental tests, high-intensity cycling trials, and maximal sprints at varied cadences (60, 90, 120 rpm) on an SRM bicycle ergometer. Linear and non-linear regression analyses were used to assess the relationship between heart rate, oxygen uptake (V̇O₂), blood lactate concentration and power output at each pedaling rate. Work rates linked to various cardiopulmonary and metabolic states, including lactate threshold (LT1), maximal fat combustion (FATmax), maximal lactate steady-state (MLSS) and maximal oxygen uptake (V̇O₂max), were determined using cadence-specific inverse functions. These data were used to calculate state-specific F/v and P/v profiles, from which state-specific optimal cadences were derived. Additionally, fatigue-free profiles were generated from sprint data to illustrate the entire F/v and P/v continuum.
HR, V̇O₂ demonstrated linear relationships, while BLC exhibited an exponential relationship with work rate, influenced by cadence (p < 0.05, η² ≥ 0.655). Optimal cadence increased sigmoidally across all parameters, ranging from 66.18 ± 3.00 rpm at LT1, 76.01 ± 3.36 rpm at FATmax, 82.24 ± 2.59 rpm at MLSS, culminating at 84.49 ± 2.66 rpm at V̇O₂max (p < 0.01, η² = 0.936 | Very large effect | Explains 94% of variance). A fatigue-free optimal cadence of 135 ± 11 rpm was identified. Sprinters and endurance athletes showed no differences in optimal cadences, except for the fatigue-free optimum (p < 0.001, d = 2.215).
Optimal cadence increases sigmoidally with exercise intensity up to maximal aerobic power, irrespective of the athlete's physical condition or discipline. Threshold-specific changes in optimal cadence suggest a shift in muscle fiber type recruitment toward faster types beyond these thresholds. Moreover, the results indicate the need to integrate movement velocity into Henneman's hierarchical size principle and the critical power curve. Consequently, intensity zones should be presented as a function of movement velocity rather than in absolute terms.
Cadence is not a "one-size-fits-all" variable — it should be scaled with metabolic demand. The present findings establish that optimal pedaling rate follows a sigmoidal trajectory from ≈45 rpm at rest to ≈85 rpm at V̇O₂max, with discrete step-changes at LT1 (~66 rpm), FATmax (~76 rpm), and MLSS (~82 rpm). Each transition is interpreted as the recruitment ceiling of a distinct motor-unit pool: slow-twitch type I fibers dominate at LT1, oxidative-glycolytic type IIa fibers are progressively engaged beyond FATmax, and fast-twitch glycolytic IIx fibers are required for fatigue-free sprinting at ~135 rpm. Practically, cyclists and coaches should abandon fixed cadence targets and instead match cadence to the prevailing metabolic state — riding ~65 rpm during aerobic base work, ~82 rpm at MLSS, ~85 rpm near maximal aerobic power, and >120 rpm only in fully fresh maximal sprint efforts. Furthermore, training intensity zones must be re-defined as a function of movement velocity (not absolute power alone), because identical wattage at 60 vs. 120 rpm recruits different fiber populations and produces different metabolic costs. Integrating velocity into Henneman's size principle and the critical power curve will refine pacing strategy, improve the diagnostic accuracy of performance tests, and allow fiber-type-specific training stimuli to be prescribed with greater precision.
1 · Introduction
The velocity of movement is a critical determinant of various aspects of physical performance in sports. Cadence, measured in pedal revolutions per minute (rpm), is a key factor influencing metabolic responses during cycling across varying exercise intensities (Michaelis and Müller, 1942); (Gaesser and Brooks, 1975); (Zoladz et al., 2000); (Beneke et al., 2018). At lower exercise intensities, a higher cadence is associated with elevated blood lactate concentration (BLC), increased cardiac, and respiratory measures (Chavarren and Calbet, 1999); (Zoladz et al., 2000).
Simultaneously, cadence-dependent oxygen uptake and carbon dioxide expiration kinetics tend to converge at maximal aerobic power (PV̇O₂max) (Zoladz et al., 2000). This leads to reduced performance at higher cadences (90–100 rpm) compared to lower cadences (40–60 rpm) across various submaximal physiological states, including BLC of 2 mmol L⁻¹ and 4 mmol L⁻¹ (Buchanan and Weltman, 1985); (Beneke and Leithäuser, 2017), highlighting intensity-dependent cadence effects on gross efficiency (Hughes et al., 1982).
These cadence-dependent metabolic differences have been linked to specific muscle fiber activation patterns, particularly the premature recruitment of fast-twitch muscle fibers at higher cadences during lower exercise intensities (Macintosh et al., 2000); (Sanderson et al., 2006). These patterns occur due to the distinct biomechanical and metabolic properties of muscle fiber types (I, IIa, IIx), including contraction velocity, myosin ATPase activity, and the content of anaerobic glycolytic enzymes (Essén-Gustavsson and Henriksson, 1984); (Sargeant, 1994).
The precise impact of cadence on optimal cycling performance remains debated, with preferences among professional and elite cyclists varying widely (Lucia et al., 2001); (Vogt et al., 2008). Generally, the relationships between force, power, and pedaling rate in cycling mirror those observed within an isolated muscle, with established linear and parabolic relationships between maximal mean pedal force, pedaling rate, and maximal power output (Dorel et al., 2005); (Dunst et al., 2022).
Parabolic functions have also been established to describe the relationship between metabolic or cardio-pulmonary state and cadence at a given work rate (Böning et al., 1984); (Zoladz et al., 2000), indicating an inverted U-shaped relationship between power and velocity even at submaximal intensities. This allows the use of inverse functions of the underlying linear force-velocity relationships to determine the maximal power output and its corresponding optimal cadence within a specific physical state.
A systematic increase in optimal cadence with rising work intensity, potentially indicating the recruitment of faster-twitching muscle fibers in the propulsive muscles during cycling. This hypothesis combines Henneman's size principle (Henneman and Mendell, 1981) with fiber type-specific force-velocity and power-velocity properties (Sargeant, 2007).
2 · Materials and Methods
2.1 Participants
Fourteen male professional track cyclists (9 sprinters, 5 endurance athletes) were included in this study.
Only those athletes were selected who had shown a close linear F/v profile (R² > 0.95) in previous tests and who had demonstrated consistently high performance over all races per day in a track cycling event at international championships. The study was approved by the Institute's Ethics Committee (ER_2022.02.06_20) and conducted in accordance with the Declaration of Helsinki.
2.2 Exercise Protocol
Each participant completed a single day of laboratory testing, which included:
All tests were performed on an SRM cycle ergometer (Schoberer Radmesstechnik GmbH, Jülich/Germany) with settings reflecting actual individual competition conditions. Participants used their own cycling shoes and pedals.
2.3 – 2.5 Test Procedures
Incremental test: Work rates from 100–300 W at pedaling rates of 60, 90, 120 rpm. Starting at 100 W, participants exercised 9 min at each work rate, changing cadence every 3 min. Work rate increased by 40 W until BLC > 4 mmol L⁻¹ or RER ≥ 1.0.
Ramp test: Power increased by 10 W every 10 s from 140 W baseline; performed at 90 rpm; ended when cadence fell below 60 rpm despite maximal voluntary effort.
Sprints + HI cycling: Three sets of 6-s maximal sprint followed by 4-min high-intensity cycling (≥90% PV̇O₂max) at constant pedaling rates of 60, 90, 120 rpm (randomized). 15-min passive rest between sets.
2.6 Data Collection
An SRM power meter continuously monitored crank torque and angular velocity at an internal sampling rate of 500 Hz, sampled at 10 Hz. Heart rate and respiratory data were measured continuously using a Polar heart rate monitor and a breath-by-breath portable gas analyzer (Metamax 3B, Cortex). Blood lactate concentration was measured immediately before and after exercise, and at 1, 3, 5, 7, 10 min post-test, by collecting 20 µL capillary blood from the hyperemic earlobe (Biosen, EKF Diagnostics).
2.7 Data Processing
Steady-state measurements were determined as the average values over the last 30 s of each trial. Linear and non-linear regression analyses were performed for each pedaling rate separately:
P(V̇O₂i) = (V̇O₂i − V̇O₂i,Base) / CEV̇O₂,i
P(BLCi) = ln[(BLCi − Ci) / Ai] / τi
2.8 Statistical Analyses
Data checked for normality (Shapiro-Wilk); two-factorial ANOVA with discipline as within-factor and pedaling rates as independent factors. Effect sizes reported as partial eta-squared (η²): ≥0.01 small, ≥0.06 moderate, ≥0.14 large. Bonferroni post hoc tests. Standardized mean differences (SMD): trivial d<0.2, small 0.2≤d<0.5, moderate 0.5≤d<0.8, large d≥0.8. Alpha < 0.05. Software: IBM SPSS v24, Excel 2016, MATLAB 9.10.0 R2021a.
3 · Results
3.1 Cardiopulmonary & Metabolic Response
Heart rate and oxygen uptake increased linearly with power output at each pedaling rate. Blood lactate concentration increased exponentially. Significant differences between pedaling rates were observed for HR (F=30.131, p<0.001, η²=0.733), V̇O₂ (F=12.144, p<0.001, η²=0.503), and BLC baseline (F=6.856, p=0.004, η²=0.364).
| Parameter | Stage | 60 rpm (M±SD) | 90 rpm (M±SD) | 120 rpm (M±SD) | η² |
|---|---|---|---|---|---|
| HR (bpm) | 100 W | 105.6 ± 12.4 | 114.4 ± 12.5 | 131.7 ± 12.4 | 0.962 |
| 140 W | 122.3 ± 12.6 | 131.2 ± 13.5 | 144.6 ± 11.2 | 0.963 | |
| 180 W | 137.4 ± 12.7 | 146.0 ± 13.3 | 158.8 ± 11.8 | 0.942 | |
| 220 W | 152.8 ± 13.5 | 160.3 ± 13.0 | 172.1 ± 10.9 | 0.913 | |
| 260 W | 168.2 ± 15.3 | 174.4 ± 14.3 | 182.9 ± 11.5 | 0.872 | |
| 300 W | 176.1 ± 12.7 | 183.7 ± 10.8 | 188.2 ± 12.2 | 0.929 | |
| V̇O₂ (L/min) | 100 W | 0.82 ± 0.25 | 0.88 ± 0.28 | 1.20 ± 0.39 | 0.957 |
| 140 W | 1.06 ± 0.41 | 1.07 ± 0.45 | 1.49 ± 0.54 | 0.956 | |
| 180 W | 1.25 ± 0.58 | 1.49 ± 0.67 | 2.02 ± 0.87 | 0.962 | |
| 220 W | 1.90 ± 0.84 | 2.33 ± 1.16 | 3.09 ± 1.29 | 0.955 | |
| 260 W | 2.59 ± 0.80 | 2.89 ± 0.97 | 4.07 ± 1.17 | 0.896 | |
| 300 W | 3.94 ± 0.16 | 4.12 ± 0.18 | 4.64 ± 0.25 | 0.969 |
3.2 Optimal Pedaling Rate at Different States
Non-linear regression analysis revealed a sigmoidal relationship between work rate and optimal pedaling rate for HR and V̇O₂, while BLC exhibited a tri-component sigmoidal relationship. Derived functions exhibited high goodness of fit (R² > 0.996).
Across all parameters, optimal pedaling rate exhibited a consistent exponential rise with intensity, ranging from approximately 45 rpm at individual minimal intensity to 85 rpm at maximum, without statistically significant differences between parameters.
A thorough examination of optimal cadence as influenced by blood lactate concentration unveiled three statistically significant components (FC: fast, MC: medium, SC: slow) across all athletes. Limit values: 66.22 ± 4.96 rpm, 75.29 ± 2.83 rpm, and 84.86 ± 2.39 rpm (F ≥ 47.483, p < 0.001, η² ≥ 0.798).
3.3 F/v and P/v Profiles at Metabolic Thresholds
Test-specific maximal oxygen uptake averaged 62.6 ± 9.4 mL·kg⁻¹·min⁻¹, with maximal blood lactate accumulation rate of 0.80 ± 0.20 mmol·L⁻¹·s⁻¹. The fatigue-free F/v profile revealed mean maximal force of 1,282 ± 188 N, average calculated maximal crank velocity of 270 ± 21 rpm, peak power output of 1,523 ± 282 W at optimal pedaling rate of 135 ± 11 rpm.
A statistically significant increase in optimal cadence was observed with the intensity of the corresponding metabolic threshold (F = 176.039, p < 0.01, η² = 0.936 | Very large effect | Explains 94% of variance). Significant differences between sprinters and endurance athletes were observed in Fmax (p<0.001; d=3.092), Pmax (p<0.001; d=3.342), PRmax (p<0.001; d=2.215), and V̇O₂max (p<0.001; d=−1.997).
4 · Discussion
4.1 Cardiopulmonary & Metabolic Response
Consistent with previous findings, oxygen uptake and heart rate increased linearly with work rate and converged with small differences at maximum (Chavarren and Calbet, 1999); (Zoladz et al., 2000). Higher absolute values at equivalent intensities at 120 rpm can be attributed to higher baseline levels, indicating greater metabolic cost associated with leg movement (internal work) (Francescato et al., 1995).
4.2 Changes in Optimal Pedaling Rate
Our study identified a systematic sigmoidal increase in optimal pedaling rate from ≈45 rpm at minimal intensity to ≈85 rpm at maximal aerobic effort — consistent with research indicating the most efficient pedaling rate is within 40–85 rpm (Hagberg et al., 1981); (Foss and Hallén, 2004). Some studies report a preference for higher cadence (90–105 rpm) during prolonged intense efforts, attributed to reduced neuromuscular fatigue (Sarre and Lepers, 2005).
4.3 Optimal Pedaling Rate at Metabolic States
Optimal utilization of oxidative metabolism without substantial glycolytic activity (LT1) occurs at ≈65 rpm — consistent with Buśko (2004) who found lowest BLC at 60 rpm. The tri-exponential increase in optimal cadence with BLC suggests at least two different muscle fiber types with specific optimal and maximal movement velocities. Slow-twitch type I fibers exhibit optimal rate ≈65 rpm; predominantly glycolytic type IIa fibers raise the optimum to ≈85 rpm at maximal aerobic power.
Theoretical maximum pedaling rate of fast-twitch glycolytic IIx fibers is approximately 4× higher than slow-twitch fibers. Maximum power of IIx fibers exceeds type IIa by 5× and type I by 12× — consistent with in vitro observations (Bottinelli et al., 1999); (Plomgaard et al., 2006).
4.4 Practical Applications
Intensity-specific optima can serve as useful references for exercise programming. Intensity zones should be presented as a function of movement velocity rather than absolute terms. The critical power model needs expansion to incorporate movement velocity. Heart rate, oxygen uptake, and BLC vary with cadence at the same work rate, making them inadequate as the only control parameters.
4.5 Limitations
The model equates velocity to crank angular velocity from a macroscopic perspective. Mathematical modeling simplifies interrelationships; quality decreases as extrapolation extent increases. The 3-min period for steady state during incremental test remains debatable. Performing all tests on a single day may have influenced high-intensity test results. Non-randomized cadence setting may have introduced an order effect.
4.6 Conclusion
Optimal cycling cadence increases systematically and sigmoidally with intensity, from 45 rpm at very low intensity to 85 rpm at maximal aerobic effort. At characteristic metabolic states, PRopt increases from 65 rpm at LT1 to 85 rpm at V̇O₂max, with no significant inter-individual variations. State-specific changing points suggest increased recruitment of faster muscle fiber types. The previously postulated two-dimensional metabolic profiles lack accuracy as they neglect the dimension of movement velocity.
Interactive Figures
Hover over data points and lines for details. Click legend chips to toggle visibility. Use the expand icon in the top right of each chart for a fullscreen view or the PDF icon on the left to save. Abbreviations in text are bolded with interactive definitions.
Optimal Pedaling Rate vs. Exercise Intensity
Sigmoidal rise of PRopt across HR, V̇O₂, BLC, and metabolic work rate.
Heart Rate vs. Power Output
Linear HR-P relationship at three pedaling rates (60, 90, 120 rpm).
Blood Lactate Concentration vs. Power
Mono-exponential BLC-P relationship at three pedaling rates.
Force-Velocity & Power-Velocity Profiles at Metabolic Thresholds
From LT1 through PV̇O₂max to fatigue-free maxima. Vertical markers indicate PRopt.
Three Components of PRopt vs. Blood Lactate
Fast (FC), medium (MC), and slow (SC) components with fiber-type interpretation.
Fiber-Type Specific F/v & P/v Profiles
Cumulative maxima and individual fiber-type contributions (I, IIa, IIx).
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