Wingate Test Research Paper

Citation: Naharudin MN, Yusof A (2013) Fatigue Index and Fatigue Rate during an Anaerobic Performance under Hypohydrations. PLoS ONE 8(10): e77290.

Editor: Alejandro Lucia, Universidad Europea de Madrid, Spain

Received: June 1, 2013; Accepted: August 30, 2013; Published: October 30, 2013

Copyright: © 2013 Naharudin, Yusof. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: The work is supported by University of Malaya's Institute of Research Management and Monitoring research fund (RG367/11HTM). The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.


Hydration status is an important issue to be taken into consideration during sports performance, and athletes are generally urged to be well hydrated prior to competitions. Investigators have studied the effect of hypohydration on anaerobic performance however, there exist discrepancies within the body of literature, some of which show improvement of performance [1], while others demonstrate no change in performance [2], [3], [4], [5], [6], or reduction in performance under states of hypohydration [7], [8], [9], [10], [11]. Strength and power are important determinants of muscle anaerobic performance. Several studies [3], [6], [12] reported no significant difference in peak torque, vertical jump height, peak lower-body power (jump squat), or peak lower-body force (assessed via isometric back squat) during a maximal isometric voluntary contraction or for time to fatigue of knee muscles between dehydration of less than 5% body weight and control. On the contrary, upper and lower body anaerobic muscular power and isometric muscular strength significantly decreased following a hyperthermic (30 min of sauna) dehydration method [5], [12], [13], [14].

Kraft et al. [6] suggested that the equivocal evidence is associated with the variation of hydration levels tested, the mode of inducing hypohydration and testing paradigms. Many have attempted to explain the impairment of muscle anaerobic capacity based on factors such as the cardiovascular strain involved in prolonged anaerobic bouts greater than 30 seconds [3], [12], muscular damage [11], and an increase in lactate concentration [3], [10]. Meanwhile, the increase in performance has been attributed to a lighter body weight to be resisted following hypohydration [1], [3]. To our knowledge, most of the studies reported that anaerobic performance was not affected by hypohydration [3], [5], [15]. The variables measured in those studies, however did not take into account rate of the decline in power output throughout the entire test period.

In measuring anaerobic fatigue during a Wingate test, the fatigue index (FI) is ordinarily applied by taking the percentage of power drop of 2 data points (peak and low power). However, another possible method of measuring fatigue during a Wingate test which has not been reported previously is by using fatigue rate (FR) [16]. Several researchers believe that the inability to maintain power output during a Wingate test may lead to an exponential decline in power throughout the entire duration of the test indicated by the rate of fatigue [17], [18]. By taking every data point (per second) between peak and low power output, the rate of exponential decay could be calculated. Since, most of the studies reported no change in anaerobic peak power (APP) and FI at hypohydration of less than 4% [3], [6], [12], it is believed that greater physiological responses in maintaining power output will occur at levels closer to or at 4% than levels lower (1–2%). By using FR, the kinetics of power decline would reflect the changes in power output throughout the Wingate test. A lower FR would mean greater body responses to maintain the power output throughout testing period, as most study reported no change in APP.

Thus, the purpose of this study is to observe the FI and FR during an anaerobic performance test under different levels of acute hypohydrations with the assumption that there would be no change in the kinetics between the states of hypohydrations.

Materials and Methods

Ethics Statement

Subjects signed a consent form and received briefing on the hydration procedures and test protocols without being given too much detail about the experiment. The study was approved by the Sports Centre, University of Malaya Research Committee.

The descriptive statistics on the demographic characteristics (age, height and BMI) pertaining to all of the subjects are presented in Table 1. The fact that there was no significant difference between the groups indicated that each group was similarly characterized.


We selected thirty two healthy non-smoking male college cyclists (n = 32) who had been involved in at least 3 training sessions (a combination of anaerobic and aerobic) per week for the previous 6 months. Athletes with a mean age of 22±2 years, body weight, 71.45±3.43 kg and height, 173.23±0.04 cm participated in this study. The subjects were among varsity athletes who had never been trained at either high altitudes (low oxygen) or in hot and humid environments. The subjects were matched according to their APP, whereupon they were randomly divided into the 4 groups namely EU (the control group/euhydrated), 2H (2% of hypohydration), 3H (3% of hypohydration) 3H, and 4H (4% of hypohydration).

Experimental Design

Hydration levels served as the independent variables, while anaerobic power performance and anaerobic kinetics of fatigue were the dependent variables. A pre and post-tests research design had been implemented for each group in this study. In order to measure subjects' anaerobic performance (FI and FR), the 30 second Wingate test was used. A week before the pre-test, a brief explanation of the experiment process and several practice sessions of the exercise protocol were given to all subjects (3 to 4 times).

During the pre-test, subjects were asked to consume 2.4 liters of water to reach a state of euhydration (divided into 1.2 liters in the morning, and 1.2 liters several hours before the exercise testing started). While during the post-test on the following day, a similar practice was implemented. Conversely, after consuming 2.4 liters of water, subjects in 2H, 3H and 4H underwent the dehydration process in the sauna. Each subject's body weight reduction after having sweated in moderate heat would indicate the percentage of hypohydration he had undergone.

In this study, in order to achieve factual effect of anaerobic performance under hypohydrations, several potential factors that may leads to inconsistency of the results have been controlled accordingly. Seeing as how the presence of hyperthermia which accompanies hypohydration also holds the potential to independently influence anaerobic exercise performance positively [14] or negatively [15], resting at least 2 hours prior to anaerobic testing following the heat exposure method is recommended [5], [10]. Each subject rested for at least 2 hours until their body temperature return to normal (37°C) at room temperature (22.7°C) with a relative humidity of 50% subsequently the heat exposure to avoid hyperthermia. The subject's core body temperature was determined using a rectal thermistor probe Model 406; Yellow Springs Instruments, Inc. To limit physiological fluctuations, subjects were also asked to abstain from performing any exercises and prohibited from consuming alcohol and caffeine for 36 hours prior to the experiment session [3], [19]. Exercises testing were conducted in an environment of standard room temperature. Similar controls existed for dietary intake during the 2 days prior to pre and post-test experimental sessions. To minimize the potential effect of reduced caloric intake on exercise performance, we encouraged subjects to consume their typical diet throughout the study.

Experimental Procedure

Preliminary Procedure.

Before performing anaerobic exercise testing, the subjects' hydration status was confirmed using the Body Impedance Analyzer (Tanita TBF-300A, USA), while their euhydration status was determined using a Urine Specific Gravity (USG) Refractometer (Atago, Model PAL-10S, Japan).

Dehydration Method.

Acute body weight loss from sweating in a room with controlled heat was used as a method to estimate the subjects' level of hypohydration level in this study [20]. Prior to the process of dehydration, each subject's nude body weight in 2H, 3H and 4H groups was recorded in a state of euhydration. Once weighed, the subjects were exposed to moderate heat in a sauna set at 40°C with 20% humidity. The subjects were dehydrated in the sauna for 15 minutes [21] after which time their body weight (after having been dehydrated) was measured using weighing scales (Seca 876, Brooklyn, New York). In the event that a subject's weight had yet to reach the desired level, he would continue the process (another 15 minutes in the sauna) of dehydration until he reached 2, 3 or 4% of hypohydration accordingly. However, if a subject did not reach the targeted level of hypohydration after a period of more than 60 minutes, no further dehydration process would be allowed in order to offset any possible deleterious effects. Subjects who were unable to achieve the desired hypohydration level were asked to undergo these procedures on another day. The control group (EU) did not follow the dehydration procedures. The hypohydration level was calculated using the method of Montain et al. [21], as follows:

Wingate Anaerobic Performance Test.

To measure the anaerobic capacity, each subject was required to perform a 30 second supramaximal anaerobic cycling test using the cycle ergometer (Monark 818E, Vansbro, Sweden). The ergometer was calibrated before each testing, as recommended by the manufacturer. Each subject was required to perform a pre (euhydrated) and post (hypohydrated) Wingate Anaerobic Test [22]. Test with the load resistance of the flywheel calculated based on 0.075 kg of a subject's current body weight [5]. Verbal encouragement was given during the test to ensure that the subjects performed at their maximal cycling capacity. Subject's workout intensity was measured using the Borg Scale Rating of Perceived Exertion (RPE). A scale ranging from 6 to 20 (no exertion to maximal exertion) was quantified to determine the subjects' perceived level of strenuousness after performing the testing. The subjects' heart rate (HR) responses were measured using a Polar heart rate monitor (Polar CS100 Cycling Heart Rate Monitor).

Measures of APP ALP, TWD, FI and FR

The APP, ALP (anaerobic low power) and TWD (total work done) were calculated using Monark Anaerobic Test software (Sports Medicine Industries, Inc., St. Cloud, MN). During the anaerobic test, a sharp rise in APP was observed within the first 10 seconds of cycling [4], [5], [22], [23]. The subjects' power output showed an exponential decline in the remaining 20 seconds. To measure the level of fatiguing during the anaerobic test, the FI and FR were calculated [4], [16]. FI was determined by taking the percentage difference between maximal and minimal anaerobic performance along 30 second [24].

Meanwhile, FR was determined using rate constant (k) of the exponential decline of power output [4]. Similarly, the highest and lowest points of anaerobic power were established during the highest and lowest 5 seconds, respectively.Where;

Statistical Analyses

All statistical analysis was performed using the Statistical Package for the Social Science version 19.0′ (SPSS, Inc, Chicago, IL). A 4×2 (group × time) two-way analysis of variance (ANOVA) with repeated measure was used independently to analyze the main group (EU, 2H, 3H and 4H) and time (pre and post-test) effects on APP, ALP, TWD, FI and FR. A paired sample t-test was used to compare between pre and post-tests. Bonferroni post-hoc test was used to determine the significant pair wise difference. The Shapiro Wilk normality test was carried out to determine the homogeneity of the sample. The test of normality verified that all of the data produced was normally distributed (p>0.05). Statistical significance was set at p<0.05.



The means of the APP, ALP and TWD for each group are displayed in Table 2. The APP, ALP and TWD in this study elucidated that there were no significant main effects (group and time) among the 32 subjects. There were no significant differences in these three variables during the pre-test among any of the groups, with similar results obtained during the post-test.

Body Weight, USG, HR and RPE

All of the subjects became considerably dehydrated during the sauna due to the changes in their body weight. The body weight of the subjects was shown to have significantly decreased in 2H, 3H and 4H (p<0.05) compared to their pre-test values. Similarly, these groups also showed significant differences (p<0.05) in USG values. In HR and RPE, although there were increments in 2H, 3H and 4H, analyses showed no significant differences between and within groups.

FI and FR

The values of FI showed no significant effect in between and within groups in both pre and post-test. While for FR, no within group effects were observed in both pre and post-tests. However, a main effect between group of FR was observed (F4, 30 = 6.45; p<0.05). Although no significant differences were observed in 2H compared to the control EU group, Bonferroni post-hoc test showed a significant difference in FR between EU vs. 3H (p<0.05) and EU vs. 4H (p<0.05) as shown in Figure 1. It was also observed that FR in 3H and 4H at post-test were significantly lower (p<0.05) than pre-test (Figure 2).


Despite the fact that plethora of studies have examined on the effect of anaerobic performance under hypohydrations, the findings remain equivocal. Thus, it is a need for an analysis using different approaches so as to gain a more profound insight in the kinetics of anaerobic performance under hypohydration [2], [3], [6],[14]. This study was designed in attempt to observe the effect of anaerobic performance using FI and FR at different levels of hypohydrations during a Wingate test. To date there is no study on such measurements has been conducted.

Present study showed body weight reductions in 2H, 3H and 4H by 1.85±0.37%, 2.75±0.47% and 4.03±0.82% respectively, while the USG values for these groups increased significantly following the dehydration procedure. The reduction of each subject's body mass was determined by calculating the percentage from the pre-test body weight in relation to the increase in USG readings [5]. Increased perspiration produces a higher concentration of blood osmolarity, which in turn results in the kidneys acting to retain body fluid, thereby leading to an increase in urine concentration which negatively correlates with the total body water loss. Under heat exposure method of dehydration, undiminished heat may alter the muscles' metabolism, which contributes to heat exhaustion or pre-fatigue. This would add to the difficulty in determining muscle performance alone during hypohydration [21], [25], [26]. If the dehydration procedures used to reduce total body water are not sufficiently controlled, incorrectly performed, or immediately precede performance testing after the sauna exposure, confounding factors such as hyperthermia-induced muscle fatigue, neuromuscular activation deficit and metabolic changes resulted from the elevation of body temperature can affect the results [3], [21], [25], [26]. Thus, an attempt to isolate hypohydration from unwanted thermal effect after being exposed to heat in present study was successfully done. By resting for about 2 hours under room temperature prior to exercise testing, body temperature returned to baseline similar to what has been reported previously [5], [6], [26]. Consequently, it is evidence that the anaerobic peak power was unaltered after the isolation procedure of was employed. Present results strongly support most findings of earlier researchers [3], [4], [5], [6], [26] who suggested that anaerobic power performance was unaltered under mild hypohydration (2–4%). Although it is known that hypohydration leads to several physiological changes that potentially distressed exercise performance (i.e. reduced total plasma volume, increase in submaximal heart rate and decrease maximal cardiac output) [19], [21], it is believed that brief anaerobic exercise (<30 second) was independent from these changes because, it is largely relies upon stored intramuscular fuel for energy [2], [3], [19], [21], [24]. However in contrast to our findings, Jones et al. [5] reported that active dehydration of 3.1% via exercising in a hot and humid environment has a negative effect on anaerobic power. Reductions in anaerobic capacity and anaerobic power were also demonstrated among dehydrated (4.9%) wrestlers [8]. However, the active hydration implemented in those studies was different from this, where the reduction of anaerobic power could be associated with heat related fatigue and excessive workloads [3], [19].

Present study shows FI did not exhibit any changes in each of the hypohydration group and also between the groups, which means hypohydations of up to 4% did not change the gradient between APP and ALP. In other words, analyses based on FI could not discriminate the changes in power output between the groups under the range of moderate hypohydration. With the results of both APP and ALP showed insignificant differences between and within the groups, the problem has been inherently amplified that FI calculation is just based on the subtraction and division of two low-resolution values as mentioned in the methodology section [16]. Thus, the calculation of FI here might not show the actual pattern of power output throughout the testing and could be the reason behind the unchanged FI in this study.

The kinetics of power output throughout the whole period of the anaerobic test would provide relevant information on the fatiguing performance which could be invariably different from FI. Interestingly, although no significant alterations of APP and FI under hypohydrations, it is found that there were reductions of FR in 3H and 4H compared to EU. It seems that subjects in both the 3H and 4H groups were able to exert their power output (maintaining cycling cadence) better than the control group.

According to Judelson et al., [19], decrease in body mass resulted from hypohydration might offset reduced muscular power for body mass related performance. Thus, if muscular power is unaltered from hypohydration, mechanically, the working muscles will become more efficient in performing task. For example, if hypohydration fails to reduce muscle force or power as evidenced in current study (post-test APP is unchanged when compared to pre-test), number of cycling cadence actually increased as total body mass decreased because subjects resisted lesser flywheel load. In other words, if hypohydration did not reduce muscle power (APP), weight related performance (e.g. vertical jump, cycling, sprinting) should increase as total body water decreases, because the subjects are working with lesser body mass [1], [19].

Although it is not quite clear the underlying physiological mechanism, these findings may possibly be explained by the mechanism earlier proposed by De Luca et al. [27]. As the power output during the 30 second anaerobic test progressively declined in the continuously active muscle, increase excitation is required to keep the muscle output constant. The increased excitation (central drive) produces the recruitment of additional motor units. The higher activation may have influenced the rate either at the beginning of the 30 second anaerobic test [28], [29] or at the end [30]. A study by Judelson et al, [3] suggested possible differences in nervous stimulation of the musculature might occur despite no change in peak force at 2.5 to 5% of hypohydration. Although this argument is somewhat speculative, alterations in central drive seemed to be more evidenced at higher level within the moderate level hypohydration without any perceivable change in RPE.

In short, hypohydration of up to 4% does not alter APP and FI. However, the present findings indicated a significant reduction in anaerobic FR that resulted from 3 and 4% hypohydration. Hypohydration at these intensities might have produced a higher drive in maintaining the power output during the 30 seconds Wingate test. Though, it should be noted that the reductions in FR occur within very narrow parameters, and circumspection therefore needs to be exercised so as not to transgress the boundaries of these parameters, lest detrimental effects may occur as few studies have shown that anaerobic power performance was markedly reduced at hypohydration of 5% or more [8], [23], [31]. This study demonstrated the relationship between water deficit and athletes' capability to perform using anaerobic power.

It is known that intense physical activity during hypohydration is associated with various physiological changes in the human body in maintaining homeostasis. In this study, it is expected that the body will try to adapt to minimal changes in body weight during hypohydration. Adaptations were observed at 3 and 4% of hypohydrations, where the FR decreased (subject less fatigue). By calculating the FR, we are able to discriminate the differences observed between the groups; hence, we strongly suggest its use in future work involving hypohydration and anaerobic performance.


Practically, it is clear that the calculation of FR provides more defined results of the anaerobic performance under narrow limits of hypohydration as compared to FI. The decreased in FR under moderate level of hypohydrations showed that the lighter body mass resulted from dehydration, makes body weight related sports such as in sprinting peak performance sustainable. Thus, this may be considered as one of sport strategy by related athletes and coaches.


Subjects who participated in this study are gratefully acknowledged.

Author Contributions

Conceived and designed the experiments: MNN AY. Performed the experiments: MNN. Analyzed the data: MNN AY. Contributed reagents/materials/analysis tools: MNN AY. Wrote the paper: MNN AY.


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The Measurement of Maximal (Anaerobic) Power Output on a Cycle Ergometer: A Critical Review

Tarak Driss 1 ,* and Henry Vandewalle 2

1CeRSM, E.A. 2931, Equipe de Physiologie et de Biomécanique du Mouvement, UFR STAPS, Université Paris Ouest Nanterre—La Défense, 200 avenue de la République, 92000 Nanterre, France

2Laboratoire de Physiologie, UFR de Santé, Médecine et Biologie Humaine, Université Paris XIII, Rue Marcel Cachin, 93017 Bobigny Cedex, France

*Tarak Driss: rf.01sirap-u@ssird.karat

Academic Editor: José M. Vilar

Author information ►Article notes ►Copyright and License information ►

Received 2012 Nov 19; Accepted 2013 Jun 22.

Copyright © 2013 T. Driss and H. Vandewalle.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article has been cited by other articles in PMC.


The interests and limits of the different methods and protocols of maximal (anaerobic) power (Pmax) assessment are reviewed: single all-out tests versus force-velocity tests, isokinetic ergometers versus friction-loaded ergometers, measure of Pmax during the acceleration phase or at peak velocity. The effects of training, athletic practice, diet and pharmacological substances upon the production of maximal mechanical power are not discussed in this review mainly focused on the technical (ergometer, crank length, toe clips), methodological (protocols) and biological factors (muscle volume, muscle fiber type, age, gender, growth, temperature, chronobiology and fatigue) limiting Pmax in cycling. Although the validity of the Wingate test is questionable, a large part of the review is dedicated to this test which is currently the all-out cycling test the most often used. The biomechanical characteristics specific of maximal and high speed cycling, the bioenergetics of the all-out cycling exercises and the influence of biochemical factors (acidosis and alkalosis, phosphate ions…) are recalled at the beginning of the paper. The basic knowledge concerning the consequences of the force-velocity relationship upon power output, the biomechanics of sub-maximal cycling exercises and the study on the force-velocity relationship in cycling by Dickinson in 1928 are presented in Appendices.

1. Introduction

For a long time, the physical examination of athletes mainly consisted in the study of cardiovascular performances and endurance. Most researches were focused on the assessment of maximal oxygen uptake (VO2max⁡) and the power or velocity which corresponds to VO2max⁡ (maximal aerobic power or velocity). In the laboratory, these tests were performed on a treadmill or a cycle ergometer. Large scale studies were often carried out on friction-braked cycle ergometers such as Fleisch ergostat [1] and von Döbeln ergometer [2].

The pertinence of the assessment of these aerobic tests was highly debatable for the athletes who were specialised in power events (sprint, jumping, throwing, etc.) and performed short “supramaximal” exercises, that is, exercises whose power output was higher than the maximal aerobic power. Physical examination could not be restricted to aerobic testing but had to include the assessment of anaerobic performance. Moreover, it became obvious that the assessment of mechanical factors determining athletic performances (strength, speed, and maximal mechanical power) should be added to the usual tests mainly focused on bioenergetics. Maximal mechanical power was estimated from the results of vertical jump tests and staircase tests derived from the tests previously proposed [3–5]. The laboratories involved in physical examination generally possessed a friction-braked cycle ergometer and several tests of maximal anaerobic power on a cycle ergometer were proposed [6–11]. The differences between these protocols of all-out cycling exercise mainly concerned the value of the load (i.e. the braking force) or the duration of exercise.

However, the validity of the results of these jump, staircase, or cycling tests was questioned. Indeed, well known experimental studies on mechanical properties of isolated muscles that were performed between 1935 and 1940 [12–14] have found that (1) the force production depends on the speed of shortening; (2) the force-velocity relationship can be described with an exponential [12] or hyperbolic equation [13]; (3) the parameters of these relationships (maximal isometric force, maximal velocity, curvature of the relationship) largely depend on the types of muscle fibers; (4) maximal power (Pmax⁡) corresponds to optimal values of force (Fopt) and velocity (Vopt); (5)  Pmax⁡, Vopt, and Fopt largely depend on muscle fiber types. The results of these first experiments carried out in frog muscles at low temperatures were confirmed by more recent studies in mammalian muscles at physiological temperatures [15, 16], in human fibers [17], and in mammalian or human skinned muscle fibers [18, 19]. The main results of these studies are developed in Appendix A.

In vivo, a hyperbolic force-velocity relationship during maximal voluntary contractions against different load was first observed in amputees [20]. Thereafter, the same hyperbolic relationship was observed for maximal voluntary contractions during monoarticular exercises such as elbow flexion, provided that the inertia and acceleration of the forearm were taken into account in the computation of the actual force exerted by the muscles [21]. In rehabilitation, isokinetic ergometers were soon used in the study of the relationship between force (or torque) and angular velocity, especially for the knee extensor and flexors [22].

Because of the dependence of Pmax⁡, Vopt, and Fopt on muscle fiber types, it is difficult to know the optimal conditions (loads or velocities) which correspond to the production of Pmax⁡ before the completion of the above mentioned cycling tests. As a consequence, different protocols have been proposed for the measure of Pmax⁡ of the legs or the arms and for the determination of force-velocity relation in cycling on friction-braked ergometers [23] or isokinetic cycle ergometers [24]. Currently, there is no consensus on the optimal protocol for the estimation of Pmax⁡ from torque-velocity (or force-velocity) relationships or single all-out cycling exercises. Although the validity of the Wingate test is debated, it is likely that this anaerobic test is the all-out cycling test which is currently the most often used not only in athlete testing but also in studies on the biological adaptation to strenuous exercise. For example, more than 600 articles are listed when the data bank PubMed is questioned about the Wingate test.

The effects of training, athletic practice, diet, and pharmacological substances upon the production of maximal mechanical power will not be discussed in this paper mainly focused on the methodology and limiting factors of all-out tests and Pmax⁡ in cycling. The influence of biochemical factors (acidosis and alkalosis, phosphate ions, etc.) upon the results of the all-out tests probably depends on the protocol. Therefore, the bioenergetics of the all-out cycling exercises is recalled in the present review in addition to the biomechanical characteristics specific of maximal and high speed cycling. Thereafter, the different protocols are presented before the discussion of the technical and biological factors that determine the results to these tests.

2. Biomechanics of High Speed and High Power Cycling

The biomechanics of submaximal cycling is presented in Appendix B. The following lines present some particularities of high speed versus low speed cycling and maximal versus submaximal cycling exercises.

With the other things being equal (same pattern of angular movements at the ankle, knee, and hip), the variation in potential energy (ΔEpotential  leg expressed in joules) within a pedal revolution is independent of pedal rate. But, the rate of variation in potential energy (dEpotential  leg/dt expressed in watts) is proportional to pedal rate in this case (Figures 1(c) and 1(d)). Kinetic energy is function of the square of velocity, and its importance largely increases with pedal rate (Figures 1(c) and 1(d)). Consequently, a larger transformation of the kinetic energy of the legs into mechanical work at the crank level is a possible explanation of the shift of the peak torque and the higher torque at the end of downstroke at high pedal frequency. Peak torque during a revolution is observed around 90° at low and medium pedal rates [25]. But at the peak velocity (≥200 rpm) of an all-out test against the inertia of the flywheel, peak torque occurs at pedal angles between 140 and 150° (Figure 2), that is, before the end of the downward pedal motion [26, 27]. As previously suggested in studies on submaximal cycling at 90 rpm [28] or between 60 and 120 rpm [29], most of the decrease of the segmental energy benefits the power transfer to the pedal. The clear opposition of Pcrank and dELeg/dt observed during downstroke at high pedal rates (Figure 2(b)) is in agreement with this hypothesis of an energy transfer even at high pedal rate. Cycling is a movement with several degrees of freedom, and the higher torque at the end of the downwards pedal motion can also be partly explained by differences in leg segment positions at low and very high velocities (Figures 1(a) and 1(b)).

Figure 1

(a) and (b) modelling of cyclist legs with three rigid segments; H, K, A correspond to hip, knee, and ankle joints; black dots and empty circles correspond to the centers of mass of the thighs, lower legs, and feet; dotted circles correspond to pedal...

Figure 2

(a) Comparison of the torques exerted on the crank at 90 (green dashed line) and 180 rpm (blue line). (b) Data at 180 rpm: PCrank (blue line) power exerted on the right crank; dELeg/dt (black line) variations in mechanical energy of...

In maximal sprint cycling, the use of the inverse dynamic technique has shown that most of the power during downstroke is produced at the hip instead of the knee as in submaximal cycling and that hip extension power is twice as great as knee extension power [30, 31]. These results do not mean that most of the mechanical work is performed by the hip extensor muscles instead of the knee extensor muscles during maximal cycling. Indeed, the coactivation of monoarticular knee extensors (the quadriceps muscles) and biarticular hip extensor-knee flexor muscles (the hamstrings) enables the energy transfer between hip and knee joints (see Appendix B). The first electromyographic studies on maximal cycling have found an increase in the contribution of knee flexors during upstroke at high velocity cycling (>200 rpm) [32] or at the end of an all-out 45-second exercise [33]. While submaximal cycling exercises are mainly performed with a reliance on knee extension and small contributions from knee and hip flexions, there was an important positive contribution from the muscles acting during the upstroke phase (almost 14% of maximal power output on the entire cycle) in a study on maximal sprint on a cycle ergometer [34], which confirmed the results of a simulation study [35]. During submaximal cycling at low pedal rate, the subjects generally do not pull on the pedal and a negative torque is observed during upstroke [36]. In contrast, during maximal exercise with toe clips, the subjects pull on the crank and the measured torque is positive during the whole pedal revolution at low and medium velocities. The study of joint-specific powers by the inverse dynamic method indicates that the contribution of knee flexion power over a whole revolution is approximately equal to the contribution of knee extension power during a maximal exercise [30, 31]. Consequently, in all-out cycling, a forth functional group (the uniarticular hip and knee flexors or FLEX, see Appendix B) should be added to the 3 synergies proposed by Hug et al. [37] for submaximal cycling. However, a negative torque is observed even with toe clips during upstroke at very high velocity (Figure 2(a)) [26, 27], which indicates a pedal contribution to the increase of leg mechanical energy between 180 and 360°. The contribution of flexor muscle activity during upstroke can be computed by substracting dELeg/dt (computed from video data) from Pcrank [38, 39]. In spite of a negative crank torque during upstroke at very high pedal rate, the muscular contribution to leg flexion is not negligible (area 4 in Figure 2(b)). When compared with submaximal exercises, the contributions of knee and hip flexion to power output increase during all-out cycling with toe clips and straps, and it is likely that all the muscle groups of the leg contribute to power production. However, it is possible that the activation levels of the gluteus maximus, hamstrings, tibialis anterior, and tensor fasciae latae are submaximal (<80%) during all-out cycling as suggested by the comparison with EMG activities during maximal voluntary contraction in isometric and isokinetic modes [40]. Plantar flexors should be able to produce high force levels at high shortening velocities in order to contract concentrically during knee extension and produce power. Moreover, high values of ankle torque are necessary for the transfer of the leg mechanical energy in addition to the work produced by the hip and knee extensor muscles. Consequently, it is possible that, at very high pedal rate, the ankle torque necessary to the leg-crank energy transfer becomes equal or higher than the torque corresponding to the maximal isometric contraction of the plantar flexor muscles at the end of the pedal downstroke. In a study on four cyclists, the contraction was eccentric for the biarticular ankle plantar flexors (gastrocnemii) in three subjects [39].

According to Freund [41], the rate limiting factor for alternating movements could be the subtraction of counteractive forces generated by the two antagonistic muscle groups: the contraction of the antagonistic muscle is superimposed on the relaxation of the agonist muscle. In cycling, the subtraction of counteractive forces could correspond to the actions of the contracting muscles of one leg and relaxation of the homologous muscles of the other legs: the muscles activated during the beginning of the downstroke of the left leg are the antagonist of the muscles activated during the beginning of the upstroke [42]. It is possible that the active muscles at the beginning of the upstroke have to offset the active state and an insufficient relaxation of active muscles during the downstroke [29, 35, 43]. This effect is assumed to be important at high movement frequencies and could limit not only maximal pedal rate but also optimal pedal rates (Vopt) and maximal power output [44] in agreement with the result of an experimental study on mouse isolated muscle [45]. Moreover, the higher the pedal rate, the earlier the activations of the different muscles within a pedal revolution because of their electromechanical delays [40, 46].

In summary, the variations in leg mechanical energy within one revolution increase with pedal rate, which results in (1) a higher contribution of nonmuscle forces to the torque exerted on the crank; (2) a shift of peak torque production toward the end of the downstroke at high pedal rates. Therefore, it is the values of power or torque averaged over one revolution that must be used in the assessment of maximal power output by the leg muscles or in the determination of the relationships between force (or torque) and velocity (or pedal rate).

3. Bioenergetics of Short All-Out Exercises

Paradoxically, the first protocols of maximal power assessment were not proposed to determine the mechanical properties of the legs or the arms. Indeed, the prevailing models of athletic performances were mainly based on exercise bioenergetics not biomechanics. The purpose of the short all-out sprint protocols was the assessment of the maximal power of the anaerobic metabolism, that is, the maximal rate of anaerobic ATP synthesis. The maximal mechanical power was assumed to be the expression of the maximal rate of anaerobic ATP synthesis. The long-lasting all-out exercise protocols were designed for the assessment of the maximal anaerobic capacity, that is, the maximal amount of ATP which can be supplied by the anaerobic metabolism. The maximal amounts of work performed during these tests were assumed to be the expression of the maximal amount of ATP which can be supplied by the anaerobic metabolism.

It is likely that the ATP resynthesis during a single all-out exercise lasting less than 5 seconds is mainly provided by anaerobic alactacid metabolism [47–50], that is, the breakdown of creatine-phosphate in creatine + inorganic phosphates. The energy supply of maximal exercises shorter than five seconds was first considered to depend mainly on creatine-phosphate breakdown, and the performances in these tests were considered as the expression of maximal alactic power.

It is likely that, during an all-out exercise, creatine-phosphate breakdown is higher in fast muscle fibers compared to slow fibers. For example, in type IIA fibers, [PCr] decreased to 46.6% of resting values after a 10-second all-out cycling exercise at 120 rpm, whereas the change in [PCr] was 53.9% in type I fibers [51]. In the same time, [PCr] was reduced to about 39.0% of resting values in the fibers expressing both IIA and IIX myosin heavy chains.

Creatine-phosphate (pKa = 4.5) is more acid than creatine (pKa = 6.8), and its breakdown in creatine + inorganic phosphate corresponds to an uptake of n hydrogen ions [52], which depends on pH (n = 0.38 and 0.70 moles for muscle pH = 7 and 6.4, resp.). A transient muscle alkalinization has been observed at the beginning of electrically stimulated contraction of isolated muscles [53, 54]. In a simulation of an all-out running sprint, the first five seconds corresponded to a muscle alkalinization [55].

Inorganic phosphates correspond to monoprotonated and diprotonated phosphate ions whose proportions depend on pH:


A large proportion of the phosphate ions should correspond to monoprotonated phosphate at the very beginning of exercise because of muscle alkalinization. The muscle fatigue due to the accumulation of phosphate ions resulting from creatine-phosphate breakdown is mainly due to diprotonated ions [56, 57]. Therefore, it is possible that the fatigue due to the deleterious effect of phosphate accumulation upon force and shortening velocity is not important at the very beginning of an all-out exercise because of muscle alkalinization.

Muscle biopsies of the quadriceps muscle taken at the end of 10 all-out cycling exercises indicate that lactate production begins earlier than it was previously assumed [58]. This early lactate production is also suggested in the simulation of an all-out 100 m run: the rate of lactate production is high after 5-6 seconds [55]. This increasing production of lactic acid counterbalances the initial muscle alkalosis and pH return to a value close to its initial value around the 10th second in this model [55]. Beyond the 10th second of an all-out test, the glycolytic and aerobic metabolisms provide most of the ATP resynthesis because of the depletion of creatine-phosphate [59].

The lactate concentration at the 30th second of an all-out test was only twice the concentration observed at the 10th second [58]. This lactate concentration lower than expected at 30 seconds could be explained by (1) a decrease in ATP hydrolysis; (2) an inhibition of glycolytic enzymes by acidosis; (3) lactate efflux outside the muscle fibers; (4) an increasing contribution of the aerobic metabolism. The activities of glycogen phosphorylase and phosphofructokinase are inhibited by acidosis, and the glycolytic rate corresponding to pH at the end of a 30-second all-out test should be approximately 50% lower than at the beginning [47, 60]. There is a lactate efflux outside the muscle fibers during a 30-second all-out test. However, blood lactate at the end of this exercise is much lower than muscle lactate, and several minutes are necessary for equilibration between muscle and blood lactate [60–63]. This lactate efflux depends on capillary supply which is more developed around slow fibers [64] and is improved by training.

Aerobic metabolism has been estimated to provide 9–40% of the energy utilised during a 30-second all-out test in function of the age and training status of the subjects [62, 65, 66]. The aerobic contribution to power production increases with the duration of supramaximal exercises [67, 68], and maximal oxygen uptake is reached during all-out tests lasting from 60 to 90 seconds [69].

The duration of a 30-second all-out test is too short to solicit the maximal anaerobic capacity. Indeed, power output at the 30th second of an all-out test is higher than the power output corresponding to maximal oxygen uptake [70]. Therefore, the cumulated oxygen deficit during an all-out test should increase beyond 30 seconds. Similarly, a 30-second all-out test is too short for maximal accumulation of lactic acid [62, 67, 71]. In spite of the high concentration of muscle lactate (120 mmoles·kg dry weight-1), the value of pH (6.7) at the end of a 30 second all-out test measured by Bogdanis et al. [59] was less acidic than the values observed in some protocols of short exhausting exercises (pH from 6.26 to 6.57) according to Hultman and Sahlin [52]. In another study, the anaerobic ATP production (creatine-phosphate breakdown + anaerobic glycolysis) was 32% less for 30 s of exhausting exercise than for 2 min of exhausting exercise [68].

Several protocols designed for the assessment of Pmax⁡ consist in the repetitions of all-out exercises against different loads. The contribution of fast muscles fibers to power output is important during high-power exercises [51, 72–74]. In addition, the capillary network around fast fibers is less developed, which should limit lactate clearance [64, 73]. Therefore, the recovery of power production should be longer in fast fibers because of higher levels of ATP and phosphocreatine breakdown and lactate accumulation [51]. The occlusion of the circulation immediately after exercise impedes creatine-phosphate resynthesis and pH restoration [75, 76], which demonstrate the aerobic resynthesis of creatine phosphate and the importance of blood circulation. In the case of repeated sprints, the intervals between exercise bouts should be long enough for the recovery in the most powerful subjects who possessed higher percentages of fast muscle fibers but, generally, lower aerobic potential.

Muscle pH recovers slowly, and the inhibition of the glycogen phosphorylase and phosphofructokinase activity by acidosis slowly disappeared [47], and the proportion of diprotonated inorganic phosphate should stay high because of muscle acidosis. Therefore, it is not possible to repeat long-lasting all-out cycling exercises (30–45 s and more) in the same session. In contrast, creatine-phosphate returned to 65 and 85% its initial value at 90 seconds and 6 minutes of recovery after a 30-second all-out test.

The assessment of maximal power is often included in session when other physical tests are performed (direct or indirect assessment of maximal oxygen uptake…). The possibility to produce maximal power after a preliminary exercise depends on the intensity and duration of this previous exercise. The value of Pmax⁡ fully recovers one minute after the completion of a cycling exercise at submaximal rate (60–80% VO2max⁡) [77]. In contrast, maximal power output was only equal to 87% Pmax⁡, 8 minutes after an exercise at 120% VO2max⁡ [77].

In summary, creatine-phosphate breakdown supplies ATP during the first seconds of all-out exercises. At the very beginning of exercise (<5 s), the effect of diprotonated phosphate accumulation is probably limited by the muscle alkalinization due to phosphocreatine breakdown. ATP synthesis by the lactic metabolism increases from the first seconds of exercise, and its contribution to energy supply is important beyond 5 seconds. Therefore, muscle acidosis potentiates the deleterious effect of diprotonated phosphate accumulation. During long-lasting all-out sprint ATP hydrolysis progressively decreases and the contribution of the aerobic metabolism prevails. The duration of a 30–45-second all-out test is too short to solicit the maximal anaerobic capacity and maximal lactate accumulation. The recovery of creatine-phosphate stores is aerobic, and, in the case of repeated sprints, the intervals between exercise bouts should be long enough for the recovery in the most powerful subjects.

4. Expression of Optimal Braking Force and Power Output

Maximal power output (Appendix A) corresponds to optimal values of force (Fopt) and velocity (Vopt). The way in which Fopt is generally expressed in cycling exercises (for example 75 g·kg−1 body mass) is considered as incorrect [78]. Body mass (BM) of humans is reported in kilograms as mass is the amount of matter in a body, but grams do not correspond to a force. Braking force should be expressed in newtons and body weight (BW); that is, the force exerted by gravitational attraction on body mass should also be reported in newtons (BW = 9.81 BM). However, the ratios kg·kg−1 BM (or g·kg−1 BM) and N·N−1 BW are dimensionless. In the present paper, optimal force is expressed as a percentage of body weight (for example 7.5% BW) [78].

Optimal braking force in cycling should depend on the strength of the subject [79] and be proportional to the cross-sectional area, that is, BM0.66. Therefore, in theory, Fopt should be equal to X0.66% BW. Consequently, with other things being equal, Fopt should be higher in small subjects, which is not the case in children. When expressed as a percentage of body weight, Fopt should be excessive in overweight people. There was no significant difference between obese and nonobese adolescents when Fopt was related to lean body mass, whatever the use of standard or power function ratios [80].

Nonetheless, the force exerted on the flywheel has no biological meaning because it depends not only on the force exerted on the pedal but also on the design of the cycle ergometer. The work performed during one pedal revolution against a braking force F is equal to the product of F and the meters of development (D), that is, the distance travelled by a point of the rim for each pedal revolution. Nowadays, the values of D of the friction-braked ergometers are generally equal to 6.11 m, which facilitates the calculation of power (P  in watts = load in kilograms × pedal rate in rpm). In the past, Fopt was sometimes expressed as J·kg−1 BM because of differences in the value of D between the available cycle ergometers. For D = 6.11 m, the work corresponding to one revolution against the optimal force 7.5% BW is equal to 4.5 J·kg−1 BM (0.458 kgm·kg−1 BM), which corresponds to an optimal force equal to 4.58% BW for another ergometer with a value of D equal to 10 m.

Muscular power output is proportional to the muscle cross-sectional area and fiber length and, consequently, proportional to the muscle volume. Therefore, Pmax⁡ should be related to active muscle volume (Pmax⁡·L−1 active muscles) when the study is focused on the assessment of the contractile properties of the skeletal muscles. Indeed, in isolated muscle, Pmax⁡  muscle related to muscle volume largely depends on muscle fiber types [16, 18, 19]. Moreover, Pmax⁡·L−1 should be independent of the body dimensions, arm levers, and pennation [81]. With the other things being equal, it is implicitly assumed that the active muscle volume is proportional to the leg muscle volume for all-out cycling exercises (or arm muscle volume for all-out cranking exercises). Pmax⁡ can be related to muscle volume determined from the sum of incremental volumes (equal to the products of slice thickness and cross-sectional area) obtained with magnetic resonance imaging [82]. However, this method is time consuming and expansive. Therefore, Pmax⁡ is generally related to some indirect indices of muscle volume such as thigh muscle area estimated from tomodensitometric radiographs [83], leg volume (lean leg volume or lean thigh volume) estimated by means of anthropometric techniques [84, 85], or quadriceps volume [86], estimated by means of a regression equation derived from autopsy studies [87]. Maximal power output can also be related to lean body mass [80]. However, the measure of lean body mass is difficult with the usual methods (skinfold) in obese subjects and should be determined by dual-energy X-ray absorptiometry (DEXA) [80]. Finally, the values of the different power indices (Pmax⁡, peak power, or PPcorr) are generally also related to body mass (Pmax⁡·kg−1 BM) in nonobese subjects because it is the easiest way to take into account anthropometric differences between subjects. Moreover, it is generally the only variable which can be compared between studies that use different methods for the estimation of muscle volume. As Pmax⁡·L−1, the value of Pmax⁡·kg−1 BM is considered as an expression of the contractile properties of the active muscle mass in nonobese subjects (see chapter on Pmax⁡ and muscle fibers).

However, it has been suggested that the use of such ratios to construct standards could be fallacious and misleading, and it has been proposed to use regression standards that describe the relationship between variables [88]. However, the expression of Pmax⁡ must be adjusted to the aims of its determination. In some cases, the use of regression between variables is probably the best use of Pmax⁡ when the purpose is to construct standards, provided that the data are collected in large populations. For example, an allometric scaling of Wingate test performances for body mass and lean body mass was studied in college women [89] or in children and adolescent [90] or young basketball players [91] with inclusion of gender and age in the models.

But, in many other cases, the expression of Pmax⁡ must be adjusted to the biomechanical constraints of the physical activity. The value of Pmax⁡ should be expressed in absolute value (W) when power production without any restriction in the body mass of the subject is the main factor limiting performance. The assessment of Pmax⁡ during a cranking exercise in the grinders of the America's cup is a good example of such an expression of power output [92]; the absolute value of Pmax⁡ in grinders (1420 W in cranking) was the main information in this paper. The value of Pmax⁡ should be related to body mass of the subject (Pmax⁡·kg−1 BM) when short accelerations of the body mass are factors limiting performance as for example in sprint, track cycling, soccer, handball, volleyball, and so forth. In theory, Pmax⁡ should be related to body weight (instead of body mass), when short exercises against the gravitational force are factors limiting performance (soccer, handball, volleyball, etc.). However, the variations in gravitational force can be considered as negligible on earth and there is no need to relate Pmax⁡ to BW in addition to BM. Pmax⁡ should be related to body surface when aerodynamic resistance is a limiting factor, for example, maximal speed in track cycling.

5. The Wingate Anaerobic Test

The Wingate anaerobic test (generally called “Wingate test”) first presented by Ayalon et al. [93] was derived from the test previously proposed by Cumming [94]. Thereafter, Bar-Or [6, 7] published comprehensive studies of the Wingate test and its applications. The Wingate test consists in pedalling with maximal (all-out) effort for 30 seconds against a constant braking force (7.5% BW for a Monark ergometer). Mean pedal rate is measured for each 5-second interval. For the Monark ergometers, mean power outputs corresponding to these intervals are given by the product of braking force and mean pedal rate.

Three indices of anaerobic performance are computed: peak power output (PP), mean power output (MP) over the 30 seconds of the whole test, and the decrease in power (fatigue index). In the first description of the test, peak power output corresponded to the highest 5-second mean power and the fatigue index was calculated as the difference between peak power output and the lowest power output of the successive 5-second intervals. Nowadays it is easy to measure the pedal rate at a high sampling frequency, and peak power is generally measured more accurately over a shorter time than five seconds (for example each second or over one revolution). Before the test, the subjects pedal at low pedal rate with a low resistance for a few minutes. This warm-up exercise is generally interspersed with two or three all-out sprints lasting only two to three seconds. Then, the subjects rest on the ergometer before the start. With the cycle ergometers available between 1970 and 1980, it was difficult to set the braking force before the subjects began to pedal. Therefore, the Wingate test started from a rolling start, around 60 rpm, against a low resistance, and then the load was rapidly set.

Other durations of all-out cycling tests were proposed such as a 40-second all-out test against a constant load equal to 5.5 kg [8, 95]. Detrimental physical responses (dizziness, headaches, nausea, vomiting, etc.) and subsequent subject apprehension have been reported to occur after the Wingate test. The mean power output during the 30 seconds of a Wingate test was highly correlated with the mean power measured during the first 20 seconds of the same exercise [96], which was confirmed by a study comparing 20- and 30-second all-out tests performed during different sessions [97]. An exponential regression equation was proposed to predict the performance in a “normal” Wingate test from the data of a 20 second all-out test. Therefore, a 20-second all-out test could be proposed in the place of the 30 second Wingate test. Leg fatigue was the only detrimental side effect reported following a 20 second all-out test, which should improve the reliability of the protocol and the compliance to the test.

The fatigue index was the least reliable of the three Wingate test indices, and its validity was questioned as it largely depends on aerobic performance. Consequently, peak power and mean power output were the main topics of most studies. Nonetheless, the validity of mean power as an index of anaerobic capacity is as questionable as the validity of the fatigue index [67, 68, 71, 98–101]. The aerobic metabolism provides a higher contribution to this energy demand in endurance athlete than in sprint athletes [99]. Therefore, peak power during a Wingate test is probably the only index that merits to be measured, provided that the load is optimal. However, a 30-second all-out test is exhausting, and it is not possible to test the subject with another load after a long recovery. In two other studies, it has been proposed to repeat short sprints (5–7 seconds) against different loads on a Monark ergometer with 3–5-minute recovery intervals and to measure peak power, only [9, 10]. The highest value of peak power (product of peak pedal rate Vpeak and loads) was considered as the maximal anaerobic power if Vpeak rate corresponding to this trial was close to 110 rpm.

6. Force-Velocity Tests on Cycle Ergometers

A protocol of all-out cranking exercise was designed to estimate the strength and speed characteristics in addition to the only assessment of Pmax⁡ [102]. A curvilinear relationship was expected as observed in mammalian isolated muscles or in monoarticular exercises in humans (see Appendix A). Therefore, the computation of the curvature indices (a/F0) was planned to suppress the effect of body dimensions, arm levers, and muscle pennation angles on the values of V0 and F0 [103]. This test derived from the protocol proposed by Pirnay and Crielaard [10] consisted in measuring peak pedal rate (Vpeak) on a Monark cycle ergometer with handles in place of pedals, during short maximal all-out cranking exercises (about 6 s) against many different braking forces (F). Indeed, a large number of experimental force-velocity data is generally necessary to compute curvature indices.

The force-velocity relationship in cranking (Figure 3) was first studied for cranking exercise in elite subjects practicing canoeing, kayaking, hand-ball, and boxing (Figure 4). The test began with a load equal to 1 kg. After 5 min of recovery, the braking force was increased by 1 kg, and the same exercise was performed again until the subjects were unable to reach a peak velocity higher than 100 rpm. The relationship between peak velocity and braking force was computed according to the least square method. The first and second bouts (1 and 2 kg) were considered as warming-up and learning exercises and were performed again at the end of the test. Therefore, the subjects generally performed 8 to 10 short all-out sprints, but the only second trials with 1 and 2 kg were taken into account in the computation of the force-velocity relationship. The linear relationship between Vpeak and F computed according to the least square method was transformed:


with V0 and F0 equal to the intercepts with the velocity axis and force axis, respectively (V0 = a and F0 = a/b). Since a linear relationship between F and Vpeak was observed, Pmax⁡ corresponded to an optimal pedal rate and an optimal load equal to 0.5V0 and 0.5F0, respectively. Consequently, Pmax⁡ was calculated as equal to

Pmax⁡ = 0.5V00.5F0 = 0.25V0F0.


Figure 3

Black dot, relationship between peak pedal rate during all-out cranking exercises against different loads on a Monark cycle ergometer; empty circle power output at peak pedal rate. Data collected on a hand-ball player, adapted from Vandewalle et al. [...

Figure 4

Parameters V0 and F0 of the individual force-velocity relationships on a Monark cycle ergometer; yellow stars, male boxers; green circle, male recreational athletes; squares, male recreational tennis players; blue and red diamonds, male and female canoeists...

Therefore, the individual performances could be presented on a V0-F0 plot where all the subjects with the same Pmax⁡ are located on the same branch of hyperbola (V0 = 4Pmax⁡/F0; Figure 4).

Some years later, a new model of Monark ergometer was available (Monark 864 with basket). This Monark ergometer enabled the use of higher braking forces and their setting before cycling. Therefore, the force-velocity test could be applied to leg exercises with some changes in the protocols [104, 105]. Indeed, it was not necessary to use a large number of loads to determine the force-velocity relationship because the observed relationship for cycling exercises was linear as it was previously observed for cranking exercises. Therefore, the numbers of exercise bouts was lower: 5 to 7 repetitions (4-5 different loads, with repetition of the first and second loads which were considered as warming-up and learning exercises). In male adults, the first load was 2 kg, and the increment was 2 kg instead of 1 kg for the arm protocol. The recovery interval was 5 minutes as in cranking force-velocity test. As for cranking exercise, the values of V0 and F0 were determined from the linear relationship between F and Vpeak. Pmax⁡ was computed as equal to 0.25V0F0. The highest values in Pmax⁡ (>20 W·kg BM−1) and V0 (>260 rpm) were observed in elite athletes practicing sprint events in running or cycling, whereas Pmax⁡ was lower than 10 W·kg BM−1 in children and elite long distance runners [105]. Similar linear regressions were reported for the relationships between load and peak velocity [106] or between load and 5-second average velocity [107]. The force-velocity test was considered as a test of maximal alactic power until a significant contribution of anaerobic glycolysis was found even after the first load [108].

Interestingly, a linear relationship between pedal rate and braking force on a friction-braked cycle ergometer has previously been observed in 1928 [109]. However, Dickinson did not published this article to present a test of maximal power in human but to verify Hill's hypothesis that “the average external force exerted during a muscular movement, carried out with maximal effort, may be regarded as equal to a constant theoretical force diminished by an amount proportional to the speed of movement” (see Appendix C). The force-velocity relationship obtained with Martin's cycle ergometer was comparable with today's results (Appendix C). But, ten years later, Hill [13] proposed his famous hyperbolic (instead of linear) force-velocity relationship that was not based on internal frictional resistance in the muscles. The results of Dickinson [109] were forgotten by most of the muscle physiologists and, consequently, ignored by the people interested in physical testing.

7. Torque-Velocity Test on an Isokinetic Ergometer

In 1981, Sargeant et al. [24] proposed to determine the relationship between pedal rate and the torque exerted on the cranks of an isokinetic cycle ergometer, that is, an ergometer whose pedal rate was constant and maintained whatever the force exerted on the pedals. This device consisted in a bicycle ergometer modified by the addition of a 3 hp (around 2200 W) electric motor which drove the cranks through a variable-speed gear box. This bicycle ergometer enabled pedal rate to be set and maintained in the range 23–180 rpm. Torque was measured by means of strain gages bonded on the cranks (0.17 cm cranks). The relationship between crank angular velocity and torque averaged over one revolution was linear (r > 0.97) for the five subjects who participated in the study. When torques T were related to upper leg volume (N·m·L−1), the regression (average of the five subjects) between torque T and pedal rate V was


which corresponded to V0 = 23.0 rad·s−1, T0 = 45.9 N·m·L−1, that is, about 3 N·m·kg−1 BM. A linear torque-pedal rate relationship was also observed in a study that used the same concept of cycle ergometer with pedal rate between 60 and 160 rpm [110, 111]. Pedal rates from 13 to 166 rpm could be used with this ergometer. However, testing was restricted to pedal rates above 50 rpm in the powerful subjects to avoid measurement errors due to the deformation of the cranks below 40 rpm. Lower pedal rates were used in women (i.e. less powerful subjects), and an exponential torque pedal rate relationship was observed between 11 and 160 rpm, in this study.

The relation between isokinetic pedal velocity and torque has also been studied on a cycle ergometer that controls the velocity and measures the tension of the chain (Fitrocycle, Fitronics, Bratislava) [112]. A linear relation between pedal rate and chain tension (average values of 60 subjects) has been found for pedal rate ranging between 50 and 140 rpm with 10 rpm increments:

F = −0.0574X + 13.68 (r = 0.9962).


The values of V0, T0, Pmax⁡ and the regression between T and V can be estimated from the data presented in this study:


8. Corrected Peak Power [113]

The force exerted on the pedal is used not only for the rotation of the flywheel against the braking force F but also for the acceleration of the flywheel up to peak velocity. At peak velocity (Vpeak) flywheel acceleration is equal to zero, and the force exerted on the pedal is used for the rotation against the resistance F, only. Therefore, Lakomy [113, 114] and Bassett [115] proposed to calculate the force necessary for flywheel acceleration to transform this force in an equivalent load (Facc) and to add Facc and F (Fcorr = Facc + F). Power output Prev during each revolution is equal to the product of the velocity during this revolution (Vrev) and Fcorr (Prev = VrevFcorr). According to the relationship between force and velocity, Fcorr decreases while Vrev increases up to peak pedal rate. Corrected peak power (PPcorr) corresponds to the maximal value of Prev during the acceleration phase.

Lakomy calibrated his ergometer by determining the relationship between flywheel deceleration and load. The flywheel was set in motion at a speed equivalent to 150 rpm and the deceleration resulting from the load in the absence of pedalling. The deceleration curves were obtained from 105 to 0 rpm. Then a linear regression between deceleration and load was obtained, and this equation was transformed to compute Facc during the all-out sprint from the measure of acceleration:


If there was no fatigue during a short all-out sprint, PPcorr should be independent of the load F and should be equal to Pmax⁡:

  1. if the load is equal to Fopt, Vpeak is equal to Vopt and PPcorr = VoptFopt = Pmax⁡;

  2. if the load is lower than Fopt, peak velocity is higher than Vopt and PPcorr  corresponds to the highest value of Prev during the acceleration phase, which correspond to the revolution when Vrev and Fcorr are equal to Vopt and Fopt, respectively;

  3. if the load is higher than Fopt, Vpeak is lower than Vopt and PPcorr is lower than Pmax⁡.

However, PPcorr was not independent of F [113]: PPcorr decreases (about 10%) with the increase in F from 5.5 to 11.5% BW. This result could be explained by fatigue because the values of Vopt are obtained later with high values of F (see chapter on fatigue). In this study, PPcorr also depends on sampling time (0.5 or 1 s), and it would be better to measure velocity averaged on a revolution instead of averaged over a given time.

The values of Pcorr were compared with the values of Pmax⁡ computed from a force-velocity relationship determined with 4 loads in two studies [116, 117]. The correlations between PPcorr and Pmax⁡ were significant, but PPcorr was approximately 10% higher than Pmax⁡ in both studies. The lower value of Pmax⁡ compared to PPcorr could possibly be explained by an early fatigue effect because the force-velocity test corresponds to peak velocity instead of data collected during the acceleration phase.

On the other hand, the reliability of PPcorr was lower than that of Pmax⁡ [117]. The reliability of PPcorr could be improved by more accurate measure of acceleration and the repetition of the test in the same session. Moreover, it is now possible to determine power output during an all-out sprint by measuring directly the torques exerted on the cranks (or the forces exerted on the pedals) instead of computing Fcorr from Facc.

In summary, the value of PPcorr is approximately 10% higher than Pmax⁡ calculated from the data of a force-velocity test because Vopt is reached earlier during the acceleration phase instead of peak velocity. On the other hand, the reliability of PPcorr was lower than that of Pmax⁡.

9. Pmax⁡ and Torque-Velocity Relationship during a Single All-Out Sprint

The determination of a torque-velocity relationship during a single all-out sprint [116, 118] was directly derived from the study by Lakomy on the correction of peak power. First, the flywheel inertia was measured from the regression between flywheel deceleration and load (see the previous). The relationship between crank torque (T) and crank angular velocity (ω) was studied during the acceleration phase of short (<7 s) all-out sprints. The average crank angular velocity ω during each revolution was measured up to peak velocity. For each revolution, the average torque T exerted on the pedal was calculated as equal to the sum of Tacc (the average torque necessary for flywheel acceleration during each revolution) and TB (the torque necessary for flywheel rotation against the braking force F) as in the study by Lakomy [113]. The acceleration of the flywheel was computed every 50 ms from the flywheel velocity data given by a disc with 360 slots fixed on the flywheel, passing in front of a photoelectric cell (669 impulses for each pedal revolution).

These all-out sprints were performed against 4 different braking forces (Figure 5) which corresponded to braking torques (TB) equal to 19, 38, 57, and 76 N·m at the crank level, that is, F equal to 2, 4, 6, and 8 kg. For each value of F, the individual relationships between ω and T could be described by a linear regression (Figure 6) and the values of ω0 and T0 for each load were determined by extrapolation from these individual regressions. The relationship between Vpeak and F was also determined. The value of Pmax⁡ calculated from the usual F-Vpeak relationship (Pmax⁡ = 0.25V0 · F0) was compared with Pmax⁡ 2 equal to 0.25ω0T0 for each value of F. In addition, PPcorr was also calculated according to Lakomy (see the previous) for the different values of F [113, 114]. There was no significant difference between Pmax⁡ 2 and PPcorr that were 10% higher than Pmax⁡. The lower value of Pmax⁡ was interpreted as the effect of fatigue on Vpeak that was reached later.

Figure 5

(a) Time pedal rate curve during all-out exercises performed by the same subject on a Monark ergometer against different loads (corresponding braking torque TB in N·m in brackets), and crosses correspond to 85% peak velocity. (b) Time-power curves,...

Figure 6

Relationships between crank torque T and crank angular velocity ω during all-out exercises on a Monark cycle ergometer against two braking forces F. Empty circles and red dashed line, data corresponding to F = 8 kg (TB = 76 N·m);...

Similar linear T-ω relationships were obtained in another study [119]. This protocol has also been adjusted for the assessment of Pmax⁡ of the arms from a single all-out cranking exercise [120]. Thereafter, the computation of the torque-velocity relationship during a single all-out sprint according to this method was used to study the effect of fatigue induced by short exhausting or long-lasting exercises [121–124].

It is can be demonstrated that, in the case of a linear regression (Figure 6) between pedal rate V and the maximal crank torque T corresponding to V, the relationship between V and time t is (Figure 7)


where φ is a time constant equal to


where γ is the gear ratio (for a Monark ergometer, γ = 52/14), r the radius of the flywheel, I the moment of inertia of the flywheel, F0 expressed in kilograms, and v0 = V0/60. The kinetics of Fcorr and P during an all-out exercise (Figure 7) are



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