Measuring maximum neuromuscular power is useful in determining the effects of exercise training programs (6) or ergogenic treatments(2) and in explaining physiological factors responsible for individual differences in performance (5). Several activities have been used for the measurement of highintensity short-term power output in humans, including running(21,22), vertical jumping(8,11,13-15,24), and cycle ergometry(1,3,18,19,23,25,26). Of these activities, only cycle ergometry allows precise measurement of power independent of body weight as the imposed load. Five cycle ergometer methods have been used to measure maximal power: 1) the Wingate Anaerobic Test, which uses a single resistive load on a friction braked ergometer(1), 2) the force-velocity test which requires measurements with application of several separate resistive loads on a friction braked ergometer (26), 3) the method of unbraked flywheel which, like the inertial-load method of this investigation, uses only the resistance of flywheel inertia (18), 4) the method that measures power owing to both frictional resistance and flywheel inertia (3,19,25), and 5) the isokinetic method which controls pedaling rate and measures torque applied to the cranks (23). Results of these methods indicate that the torque-velocity relationship for cycling is roughly linear, and the power-velocity relationship is roughly parabolic in shape with maximum power occurring at a pedaling rate of between 98 and 130 rpm. This parabolic shape suggests that maximum power can be identified only by making measurements over a range of pedaling rates to determine the apex (i.e., true maximum power) of the power-velocity relationship (23,26).
Each of the cycle ergometer methods represents a compromise between the complexity of the equipment, the complexity of test administration, the stress placed on the subject, the validity of the results, and whether instantaneous or averaged measures of power are required. At one end of that spectrum, the Wingate Anaerobic Test is simple to administer and requires that the subject perform only one bout on a standard cycle ergometer. However, that technique may not elicit maximum power (10) and does not provide instantaneous measures. The force-velocity test (26) also requires only standard equipment, but may underestimate maximum power by not accounting for flywheel acceleration (19), it requires that the subject perform multiple bouts (26), and it does not provide instantaneous measurements. The isokinetic method produces valid measures of instantaneous and averaged maximal power but requires that subjects perform multiple bouts at various pedaling rates, and it is performed on highly modified equipment that is not available commercially. The methods that measure a combination of friction and inertial torque (3,19,25) or inertia alone(18) have been shown to elicit maximum power in a single bout. Both methods require modifications to a cycle ergometer, as well as a computer interface and data processing software, and neither has been shown to provide measures for instantaneous power. Additionally, the validity of the measured power obtained by the method of unbraked flywheel has not been established by mechanical calibration. Thus, none of the cycle ergometer methods currently available has been shown to elicit maximum power in a single bout and to produce valid measures for both averaged and instantaneous power.
Therefore, the purpose of this investigation was to develop and validate a cycle ergometer test that accurately identifies maximum power and describes averaged and instantaneous values for the torque-velocity and power-velocity relationships over a range of pedaling rates during one short exercise bout. To that end, this investigation had three aims: 1) to establish the validity of the inertial-load method for measuring torque, 2) to determine whether the inertial-load method provides a reliable measure of mechanically applied torque and maximum power of subjects, and 3) to determine maximum power and describe the torque-velocity and power-velocity characteristics of a group of healthy, active male subjects.
Materials. A Monark (Varberg, Sweden) ergometer (Model 818) was modified to measure cycling torque and power during 3-4 s of maximal exercise using inertial loading, where resistance was provided solely by the moment of inertia of the accelerating flywheel (Fig. 1). Modifications included structural reinforcement, intermediate gearing, an optical sensor, and a computer interface that records velocity of a target disk on the flywheel. The ergometer frame was reinforced to withstand the rigorous use of repeated accelerations, bolted to the floor, and fitted with high quality cycling components: handlebars (SR steel track), 165 mm cranks(Mavic Model 631, Georgetown, MA), bottom bracket (Mavic Model 616-0002), and pedals (Shimano PD-7401, Shimano American Corp., Irvine, CA). The 165-mm length cranks were selected because they are the standard length for track cycling where the emphasis is on maximum power rather than the 170-175 mm length cranks that are typical for road cycling where the emphasis is on endurance performance. Pedals were adjusted to maximum release tension, and cleated cycling shoes were provided to all subjects. The seat was located in a forward position (approximating a bicycle seat tube angle of 75°) similar to that used by sprint cyclists.
An intermediate gear drive (Shimano Dura-Ace free hub, Model FH 7403) was installed between the crank and the flywheel (Fig. 1) to provide a large overall gear ratio (i.e., 7.43 to 1). This gear ratio allowed subjects to complete the 6.5 crank revolutions in approximately 3-4 s and to reach 120 rpm (approximately the velocity of maximum power) in approximately 2 s. The flywheel was balanced using automotive wheel weights to prevent vibration.
Measurement of the ergometer flywheel angular velocity was performed with an optical sensor assembly mounted on the ergometer frame, measuring the movement of a slotted target disk mounted on the flywheel(Fig. 1). The sensor assembly contained an infrared light emitting diode (source) and a photo-transistor (receiver). The target disk rotated between the source and receiver to either pass or interrupt the infrared light. The time required for the flywheel to rotate the width of one slot was measured and recorded with a microcontroller (Intel 80C52 8bit 12Mhz) based computer interface card installed in a bus slot of an Intel 486 based personal computer. This interface card has been previously described(16). The optical sensor was programmed to produce a square wave output at each interruption of the infrared light beam. This data collection technique is equivalent to using a sampling frequency of 1 MHz, but data are recorded only at discrete angular displacements of the flywheel. The target disk was machined with 15 slots: 14 slots separated by 22.5° (i.e.,π/8 rad) and one “index” slot of 45° (i.e., π/4 rad). This index slot allowed identification and measurement of the angle between each individual slot to correct for machining tolerances in the slots. The overall gear ratio (7.43:1) resulted in data acquisition occurring every 3° of pedal crank rotation (6° at the index), independent of pedaling rate.
Calculations. Angular velocity (ω) of the flywheel was determined from the time differences between consecutive edges of the slots on the target disk (ω = Δθ/Δt whereΔθ = angle between target disk slots in rad andΔt = time between target disk slots in seconds). Our initial efforts to measure flywheel acceleration (α =Δω/Δt) produced oscillations in torque (unrelated to the normal biomechanical oscillations) similar to those reported by others(25). These oscillations were eliminated by 1) using an independent microprocessor dedicated to data collection, 2) accounting for machining errors in the target disk slots by measuring each Δθ precisely and identifying each individual Δθ by the use of an index slot, 3) using a timing accuracy of ± 1 μs, and 4) using a digital low-pass filter. Techniques 1-3 yielded values for velocity that appeared continuous even before filtering. However, some of the changes in delta time between consecutive target disk slots were less than 1 μs and, therefore, the clock accuracy (± 1 μs) became a source of random noise which produced discontinuous values for acceleration when calculated by numerical differentiation. Low-pass filtering of the data using a quintic generalized cross validation spline (28) with a cut-off frequency of 8 Hz removed these discontinuities. The filtered angular velocity and acceleration data were used for all subsequent calculations.
Instantaneous torque (TI) applied to the cranks was calculated every 3° of crank rotation as TI = αIG, where I is the moment of inertia of the flywheel and G is the gear ratio. Instantaneous power(PI) was calculated every 3° of crank rotation as PI =αωI.
Torque, averaged over each complete crank revolution (TREV), was calculated as the rate of change of angular momentum (TREV = I[ωi+1 - ωi]/[ti+1 - ti]), whereωi+1 and ti+1 are the angular velocity and time at the end of the crank revolution (i.e., cranks in a vertical position), andωi and ti are the angular velocity and time at the beginning of the crank revolution. Each trial began with the cranks aligned at an angle of 50° to the vertical, and therefore the first one-half crank revolution is not included in these averaged values. Crank position throughout each trial was determined from the recorded flywheel position and the known gear ratio (i.e., θcrank = θflywheel/G). Torque during each crank revolution was averaged from right to left leg and left to right leg; therefore, data collected from 6.5 crank revolutions produced 11 averaged torque-velocity points (i.e., revolution 0 to 1 not included, 1st point is 0.5 to 1.5, 2nd point is 1.0 to 2.0, 3rd point is 1.5 to 2.5, 11th point is 5.5 to 6.5 where whole and half revolutions refer to vertical crank orientation). Similarly, power averaged over each complete crank revolution(PREV) was calculated as the rate of change in kinetic energy(PREV = ΔKE/Δt = 0.5 I [ωi+12- ωi2]/[ti+1-ti]). The time to reach PREVmax and the time to complete 6.5 revolutions of the pedal cranks were identified. Also, the final pedaling velocity reached at the end of the 6.5 revolutions of the pedal cranks was identified.
Flywheel inertia. The moment of inertia of the flywheel about the axle was calculated as the sum of nine component parts. The flywheel itself was decomposed into four parts: the outer guide rings, the main outer mass, the web, and the central hub. The remaining parts were the steel bearing race, the target disk hub, the target disk, the free-wheel, and the balance weights. All of these, except the balance weights, are cylindrical shapes and have a moment of inertia (I) of I = m(ri2 + r02)/2 where m is the mass of the cylinder and ri and ro are the inner and outer radii of the cylinder. The mass of the steel bearing race, target disk hub, target disk, and free-wheel were measured directly. The mass of the flywheel's individual shape components were estimated by multiplying the flywheel's density (calculated as the flywheel mass divided by total flywheel volume) by the volume of each cylindrical shape. The balance weights were treated as a point mass with I = mr2 where m is the mass and r is radius from the center of the flywheel axle to the weights. This technique yielded a calculated flywheel moment of inertia of 0.39621 kgm2.
Calculation of inertial load. Work done by the subject to reach any given pedaling rate during an inertial-load test is related to the kinetic energy stored in the flywheel. Similarly, for any given pedaling rate, the kinetic energy stored in the flywheel is related to both the moment of inertia of the flywheel and the gear ratio (i.e., KE = ½Iω2 =½I[pedaling rate × gear ratio]2). Therefore, we have defined the inertial load as one-half the product of the flywheel moment of inertia and the overall gear ratio squared (inertial load = IG2/2). In this investigation the combination of gear ratio (7.43:1) and flywheel moment of inertia (0.3962 kgm2) produced an inertial load of 10.93 kgm2.
Validity. Mechanical validation of the system was performed by comparing the mechanical torque (TM) measured by the inertial-load method with torque applied (TA) by the standard Monark resistive strap and pendulum (19). The ergometer was pedaled up to above 110 rpm and then the flywheel was allowed to decelerate against resistive loads of 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 kg (resistive torque of 1.27 to 10.15 Nm). Ten trials were performed at each resistive torque. When TM is plotted against TA, the results should be a linear function of the form TM = TA + Tf, where Tf is the friction torque of the flywheel bearings and free-wheel mechanism. Also, if TA is plotted against flywheel angular deceleration (-α), the slope of the line (-ΔTA/Δα) should be equal to the flywheel's moment of inertia.
Although additional inertia is associated with the pedals, cranks, gears, and drive chain, we have not included those in our calculation. Therefore, values presented include only the torque and power transmitted to the flywheel.
Reliability. Reliability of the inertial-load method was assessed both mechanically and biologically by the repeated application of a mechanical torque to the flywheel via the Monark resistive strap and by examining the repeated values for maximum power, torque, and pedaling rate of subjects over the four bouts.
Subjects. Thirteen active males (age 27.4 ± 5.5 (SD) yr, mass 80.6 ± 9.2 kg, estimated lean thigh volume 5.5 ± 0.9 L), were recruited to participate in this study. Their age and mass were recorded, and lean thigh volume was estimated (see Anthropometry below). This study was approved by the Institutional Review Board at the University of Texas at Austin, and the subjects provided written informed consent.
Anthropometry. Leg circumferences and lengths were measured at gluteal furrow, mid-thigh, and proximal patella using a fiberglass measuring tape and a GPM anthropometer (20). Skinfolds were measured at anterior and posterior mid-thigh using a Harbenden skinfold caliper (20). Body mass was measured on a platform scale(Acme FW 150 KAI) with an accuracy of ± 0.02 kg. Limb diameters at gluteal furrow, mid-thigh and proximal patella were estimated from the circumference (diameter = circumference/π). Anterior and posterior skinfold thickness (SFT) was used to estimate the tissue layer thickness using the equations of R. M. Jones (R. M. Malina, personal communication, 1992, used with permission): Equation Lean limb diameters (LD) were estimated by subtracting the anterior and posterior tissue layer from the total diameter, and it was assumed that the tissue layer thickness was constant at all three sites. Lean mid-thigh cross-sectional area was estimated as πLD2/4. Lean thigh volume was estimated as the sum of two truncated cones (17).
Human torque and power trials. Subjects reported to the laboratory and performed a 5-min warm-up by cycling at 100-120 rpm with a power of 100-120 W. They then rested for 2 min and performed four bouts of maximal acceleration with 2 min resting recovery between bouts. Subjects started from rest and accelerated maximally for approximately 3-4 s on a verbal command with standardized encouragement. Data was recorded for 6.5 crank revolutions. Seat height was self selected by each subject, and the same height was used for all trials. Subjects were instructed to remain seated throughout the bout.
From each of the four trials for a given subject, the following calculations were performed. Instantaneous torque (TI,Fig. 2) and power (PI, Fig. 3) were calculated continuously (every 3° of crank rotation). From that, the instantaneous peak values of torque (TIP,Fig. 2) and power (PIP, Fig. 3) within each one-half crank revolution were identified. These represent the highest values during contraction of alternating legs. Also, torque(TREVFig. 2) and power (PREV,Fig. 3) were averaged for each full crank revolution. The highest values of PREV and PI achieved during each bout were defined as maximum crank revolution power (PREV max,Fig. 3) and maximum instantaneous power (PI max,Fig. 3), respectively. For each trial, the torque-velocity relationship was determined for both TREV and TIP. Linear extrapolation of both torque-velocity relationships(TREV and TIP) was performed to obtain values for maximum velocity (VREV max and VIP max, Fig. 2) and maximum torque (TREV max and TIP max, Fig. 2).
Statistics. Validity was assessed by comparing the mechanical torque (TM) measured during calibration trials with the torque applied(TA) using a paired Student's t-test. Reliability was assessed using coefficient of variation for both the human subject trials and for the calibration trials and using intraclass correlation coefficient. For each subject trial, torque (TREV and TIP) was correlated with pedaling rate. PREV max and PI max were correlated with body mass and with estimated lean thigh volume.
Validity. Torque applied (TA) by the resistive strap and pendulum was highly correlated with torque measured (TM) by the inertial-load method (r2 = 0.999). There was no difference between measured and applied torque after accounting for bearing and free-wheel friction torque (0.0378 Nm). The moment of inertia of the flywheel, calculated from its mass and geometry, was 0.39621 kgm2. This was essentially equal to the calibration value obtained from the slope of the applied torque versus flywheel deceleration relationship (-ΔTA/Δα = 0.39624 kgm2). The calibration value (0.39624 kgm2) was used for all subsequent calculations.
Reliability. Coefficient of variation for repeated application of the calibration torque was 1.1 ± 0.5%. The mean coefficient of variation over the four trials performed by the subjects was 3.3 ± 0.6% for PREV max, 2.7 ± 0.9% for VREV max, and 4.4 ± 1.0% for TREV max. The coefficient of variation for the instantaneous values was 4.2 ± 0.6% for PI max, 3.6 ± 0.9% for VIP max, and 5.7 ± 0.9% for TIP max. The intraclass correlation coefficient was 0.99 for repeated application of torque by the resistive strap. The intraclass correlation coefficient was also 0.99 for the subjects' PREV max over the repeated bouts.
Characteristics of torque-velocity and power-velocity relationship. Table 1 presents the maximal values averaged over each crank revolution. Table 2 presents the maximal instantaneous values. Values for each subject represent the average of the four bouts. The mean torque-velocity and power-velocity relationships for all subjects are shown in Figures 4 and 5, respectively.
Both TREV and TIP were significantly (P < 0.001) correlated with pedaling rate for each bout (r = 0.98 ± 0.01 and r = 0.94 ± 0.01, respectively). Linear extrapolation of TREV versus pedaling rate yielded values for VREV max, 237 ± 5 rpm, and TREV max, 203 ± 9 Nm (2.53 ± 0.10 Nm·kg-1). Similarly, linear extrapolation of TIP versus pedaling rate yielded values for VIP max, 234 ± 6 rpm, and TIP max, 320± 12 Nm (3.99 ± 0.16 Nm·kg-1).
PREV max was 1317 ± 66 W (16.4 ± 0.8 W·kg-1, 239 ± 6 W/L LTV) and was achieved at a pedaling rate of 122 ± 2 rpm (Fig. 5, Table 1). PI max averaged 2137 ± 101 W (26.6 ± 1.2 W·kg-1, 390 ± 12 W/L LTV) and occurred at a pedaling rate of 131 ± 2 rpm (Fig. 5, Table 2). Correlation of maximum power with body mass was low (r = 0.43 for PREV max and r = 0.34 for PI max), but was higher with estimated lean thigh volume (r = 0.86 for PREV max and r = 0.80 for PI max,Fig. 6).
PREV max was reached in 1.8 ± 0.1 s and occurred on the third crank revolution (3.0 ± 0.2 revolutions). The time to complete 6.5 revolutions of the pedal cranks was 3.4 ± 0.1 s, and the velocity at the completion of the 6.5 revolutions was 175 ± 3 rpm. This velocity yields a value for kinetic energy stored in the flywheel of 3.7 ± 0.1 kJ.
This investigation has demonstrated that the inertialload method provides valid measurement of torque and reliably determines averaged and instantaneous cycling torque-velocity and power-velocity relationships across a range of pedaling rates from a single exercise bout. These findings set this method apart from other established cycle ergometer methods that: 1) may not describe the power-velocity relationship and identify maximum power(1), 2) require repeated bouts to determine maximum power(23,26), 3) fail to account for flywheel acceleration (26), (4) that have not been validated by reported mechanical calibration (18), or 5) do not provide instantaneous measures for torque and power(3,25).
Both the validity and reliability of our method were excellent. Calibration trials were highly accurate, indicating a high degree of validity in the measurement of mechanical torque. The low variability in the calibration trials (CV = 1.1%), demonstrated the high reliability of our method. Furthermore, the coefficient of variation for the subject trials for PREV max was 3.3 ± 0.6%, which is lower than the reliability values for previously reported power tests of 5.3% reported by Coggan and Costill (4) and 6% by Sargeant et al.(23).
Inertial loading or resistance is an application of Newton's 2nd law of motion. In a rotational system with a fixed axis of rotation, the net torque about the fixed axis is the product of moment of inertia and angular acceleration (i.e., ΣT = Iα). Therefore, as a person applies maximal torque to accelerate the flywheel, the highest power the individual is capable of generating is registered at the increasing velocities of contraction. In the present investigation, the inertial load was set at 10.93 kgm2 by the combination of a 7.43:1 (i.e., 52:7) gear ratio and a flywheel moment of inertia of 0.39624 kgm2. Pilot testing conducted before this investigation indicated that maximum power was stable across a range of inertial loads from 5.6 to 12.6 kgm2. The inertial load used in this investigation of 10.93 kgm2 was within that stable range, allowed these subjects to reach maximum power at about the midpoint of the test (3.0 ± 0.2 crank revolutions), and provided averaged power calculations across a wide range of pedaling rates (80-171 rpm).
The combination of moment of inertia of the flywheel (0.39624 kgm2, the pedaling rates reached at the end of 6.5 crank revolutions (175 ± 3 rpm) and the large gear ratio (7.43:1) resulted in high velocities at the flywheel (136 ± 2 rad·s-1) and a high value for kinetic energy stored in the flywheel (3.7 ± 0.1 kJ). Given the mass of our subjects (80.6 ± 9.2 kg) and assuming that a bicycle has a mass of 10 kg, the kinetic energy stored in the flywheel is equivalent to the energy stored at a cycling velocity of 9.0 ± 0.1 m·s-1 (32.6± 0.5 kph or 20.2 ± 0.3 mph). Furthermore, the pedaling rates reached during the test (175 ± 3 rpm) would be reached at that cycling velocity using a bicycle gear ratio of 1.47:1, or a combination of a 39 tooth front chain ring and a 27 tooth rear cog. Thus, the inertial-load test is somewhat analogous to a maximum power acceleration from rest in first gear on a road bicycle.
Both measures of torque (TIP and TREV) were highly correlated with pedaling rate for each bout (r = 0.98 ± 0.01 for TREV and r= 0.94 ± 0.01 for TIP). The mean torque-velocity relationship for all subjects is shown in Figure 4. These mean values are even more highly correlated with pedaling rate than the individual bouts(r >0.99 for TREV both TIP). Estimation of V max was similar using extrapolation of VREV (i.e., 237 ± 5 rpm) and VIP max (i.e., 234 ± 6 rpm). V max is the velocity at which torque is predicted to be zero. The observation that predicted zero torque and V max were similar using TIP and IREV would be expected and provides additional evidence of the validity of the inertial-load method.
Previous investigations of cycling power have reported maximum cycling power values that range from 12.4 W·kg-1 for active subjects to 17.1 W·kg-1 for elite power athletes(9,27). Our mean value for PREV (16.4± 0.8 W·kg-1) was within the range, but toward the high end of previously reported data. Our present values ranged from a low of 12.3 W·kg-1 produced by a swimmer to a high of 20.2 W·kg-1 produced by a track cyclist. Our range of values for both VREV max (209-260 rpm) and VI max (207-267 rpm) are similar to previously reported values of 220-262 rpm (9,27). Also, our range of values for TREV max (2.01-3.03 Nm·kg-1) is similar to those previous values 2.0-2.6 Nm·kg-1-1 (9, 27 (calculated from the reported data). Our values for TIP max (3.05-4.97 Nm·kg-1) were higher than values previously reported. The mean value for TIP max (320 ± 12 Nm, 3.99 ± 0.16 Nm·kg-1) represents a force of 1939 N (for our subjects, 2.5 times body weight) directed normal to the crank arm.
Our values for PI max ranged from 21.4 to 33.2 W·kg-1(26.6 ± 1.2 W·kg-1). Other methods for measuring maximal instantaneous power such as vertical jumping(11,14) and weight lifting(12) have determined maximum instantaneous power to be about twice as high as our values (i.e., 53-72 W·kg-1 for male athletes and 43 W·kg-1 for sedentary young adults). This is expected, however, because previous investigations(7,23) have shown that almost all power generated while cycling comes during leg extension. Therefore, it is reasonable that the PI max for cycling should be approximately one-half of the maximal power achieved during bilateral activities because at any given time only one leg is extending or pushing down on the pedal.
Maximum instantaneous power values presented in the present investigation and in the work of Sargeant et al. (23) were about 62 and 65% higher, respectively, than average power for one complete crank revolution during maximal effort. However, Coyle et al.(7) have shown that when cycling at approximately 90% of˙VO2max, peak instantaneous power was 110% higher than average power (calculated from the reported data). These findings might imply that the technique employed during prolonged cycling (7) represents an optimal combination of muscle activation patterns, whereas the technique observed in the present investigation and by Sargeant et al.(23) represents maximum neuromuscular recruitment of all muscle groups that produce cycling power.
A previous investigation has shown high correlation between upper leg volume and cycling power (r = 0.72, 9). In the present investigation, estimated lean thigh volume was also highly correlated with PREV max (r= 0.86). Additionally, correlation of the maximum value for PREV max(recorded during any of the four bouts) with estimated lean thigh volume was even higher (r = 0.90). However, we did not determine what factors are responsible for the remaining 20-25% of variation. Since we have already accounted for muscle size, two areas not yet investigated are the skill level of the subject and the muscle fiber type. In the present investigation, the lowest value of power per thigh volume (197 W/L) was by a swimmer, while the highest value (277 W/L) was by a former U.S. national sprint cycling champion. This information is anecdotal; yet it agrees with the observation that power can be influenced by neuromuscular adaptations that are specific to the mode and velocity of training (6). In the present investigation, no measures of muscle fiber type were made.
In summary, the inertial-load method provides a valid, reliable, and accurate determination of cycling power. Moreover, this method allows averaged or instantaneous measurement of torque and power over a wide range of pedaling rates in one short exercise bout. The results for PREV max, TREV max, and V max were similar to those reported for the force-velocity and isokinetic methods, but were performed in a single 3- to 4-s bout. These findings suggest that the inertial-load method provides a unique set of attributes that make it valuable for investigations of maximal neuromuscular function.
The authors would like to thank the subjects for their enthusiastic participation. Also, we thank Dimitrios Kalakanis of The University of Texas at Austin and Dr. Ton van den Bogert of The University of Calgary for their technical assistance with data filtering. Finally, we thank Mr. Art Wester of Mavic USA for donating the bicycle cranks used in this investigation.
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