Eur J Appl Physiol (1995) 71:559-561 © Springer-Verlag 1995

S. Green • D. Bishop • D. Jenkins

Effect of end-point cadence on the maximal work-time relationship

Accepted: 13 September 1995

A b s t r a c t This study examined the effect of end-point cadence on the parameters of the work-time relation- ship determined for cycle ergometry. Eight male sub- jects completed four maximal tests on an electrically- braked cycle ergometer that regulated a constant power output independent of cadence. The power outputs im- posed ranged between an average of 259 W and 403 W, whereas the corresponding durations ranged between 139 s and 1691 s. During each test subjects were re- quired to maintain a cadence of 80-90 rpm. Accumu- lated time to end-point cadences of 70, 60 and 50 rpm were recorded. The four work-time determinations for each of three end-point cadences were used to deter- mine linear relationships between work and time, yield- ing both a y-intercept, which represents anaerobic work capacity, and a slope, which is termed critical power (CP), for each end-point cadence. There was a signifi- cant increase in the y-intercept as end-point cadence decreased from 70 to 60 rpm (F[1,7] = 36.7, p < 0.001) or 70 to 50 rpm (F[1,7] =80.1, p<0.001), but not from 60 rpm to 50 rpm (F[1,7]=3.28, p>0.05). In contrast, there was no effect of end-point cadence on CP (F[2,14]=1.89, p<0.05). These results demonstrate that the end-point cadence selected to terminate tests only affects the y-intercept of the work-time relation- ship. To control for this effect, the cadence at which each test is terminated should be standardised if deter- mination of anaerobic work capacity, as represented by the y-intercept, is required.

K e y w o r d s Critical power • Anaerobic work capacity •

Methodology • Electrically-braked ergometer

S. Green (1~) • D. Bishop • D. Jenkins School of Human Movement Studies, Queensland University of Technology, Kelvin Grove Campus, Brisbane, Queensland 4059, Australia

Introduction

The relationship between muscular power output and the time over which this power can be sustained is hy- perbolic (Monod & Scherrer, 1965). The product of power and time (i.e. maximum work = Wlim) expressed as a function of time (Tlim) yields a linear relation which can be written a s W l i m = a-t-b Tlim, where param- eter a (the y-intercept) is an equivalent of work and the slope b is an equivalent of power (Monod & Scherrer, t965). The y-intercept has been taken to represent anaerobic work capacity, whereas the slope b repre- sents an endurance capacity and has been termed crit- ical power (CP) (Monod & Scherrer, 1965).

Recent attention has focused on methodological as- pects which influence the reliability, accuracy and mag- nitude of both CP and the y-intercept; these include the number of work-time determinations (Housh et al., 1990), the range of values for time to fatigue (Poole, 1986), the regression models used to describe the data and the cadence imposed during each test (Hill et al., 1995). An additional methodological aspect which has not been examined is the end-point cadence used to terminate each test.

Most investigators who used friction-loaded ergom- eters selected an end-point cadence - 1 % less than the cadence required during the test. This is consistent with the suggestion that each constant-load test should be terminated when the subject reaches fatigue (Monod & Scherrer, 1965; Poole, 1986); that is, when the power output, which depends on pedal cadence, cannot be sustained. This, however, does not apply to maximal tests performed on an electrically-braked ergometer which can control the power output independent of cadence. It has been suggested that once a predeter- mined cadence at high power outputs cannot be main- tained, a "precipitous" decline in cadence occurs which quickly leads to the cessation of pedalling (Hill, 1993), although the period of this decline has not been re- ported. As shown elsewhere for friction-loaded cycling (Green et al., 1994), the period during which the cad-

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ence declines might vary be tween subjects and, in the absence of a s tandard end-poin t cadence, might be a source of var iance in the es t imat ion of the work- t ime parameters . W h e t h e r or no t this is the case for electri- ca l ly-braked cycle e rgomet ry has not been examined.

Therefore , the purpose of the present invest igat ion was to examine the effect of different end-poin t cad- ences on the work- t ime paramete r s during constant- load cycling on an electr ical ly-braked ergometer .

Methods

Eight physically active males (mean+SD: age=27.4_+3.7y; mass = 82.0 + 4.2 kg) of varied training status volunteered for the present study. Each subject was familiar with the experimental procedures prior to the study.

Subjects were required to cycle to exhaustion on four occa- sions, separated by at least 48 h, over a two-week period. The or- der of each test was randomised. Each test was performed on an electrically-braked cycle ergometer (Lode Excalibur Sport, Quin- ton, USA) which was capable of maintaining the power output independent of pedal cadence. Power outputs for the four tests were varied to elicit a range in times to exhaustion between ap- proximately two and 25 min. Prior to each of the four tests sub- jects warmed-up for five rain at 125 W. During each test, subjects maintained their cadence between 80 and 90 rpm and, when the pedal rate fell to 70 rpm, 60 rpm and 50 rpm, three accumulated times were recorded. When the cadence fell below 80 rpm, sub- jects were verbally encouraged to maintain the highest possible cadence until it declined to 50 rpm, at which point the test was terminated.

For each end-point cadence (i.e. 70, 60 and 50 rpm), four val- ues of time to exhaustion (Zlim) and work output (W~im) were re- corded. From these data a linear relation, W~m =a + b'T~im, for each of the three end-point cadences was calculated.

Statistical Analysis. Differences in work-time parameters were de- termined using separate single-factor repeated-measures ANOVA. Omnibus probability values were corrected for devia- tions from sphericity using the Geisser-Greenhouse three-stage procedure, and a significant overall treatment effect was followed by pairwise comparisons. A modified Bonferroni correction was employed to control the familywise error. Alpha was set at 0.05.

Results

D a t a on the power outputs , work outputs and corre- sponding durat ions for the three end-poin t cadences are shown in Table 1. The re were significant increases

Table 2 Mean estimates and standard error of the means for crit- ical power (CP) and the y-intercept for the three end-point cad- ences

End-point cadence CP y-intercept (rpm) (watts) (k J)

70 245.1 + 12.9 23.3 +2.87 60 244.7 + 12.9 25.2 -+ 2.92* 50 244.5 _+ 1 3 . 0 25.9-+2.87*

* different from 70 rpm at p<0.001

( p < 0 . 0 5 to p < 0 . 0 1 ) in bo th exercise durat ions and work outputs across all power outputs as the cadence decl ined f rom 70 rpm to 60 rpm and f rom 70 rpm to 50 rpm. Es t imates of CP and the y- intercept for the three end-poin t cadences are p resen ted in Table 2. There was no effect of end-poin t cadence on CP (F[2,14] =1.89, p > 0.05). In contrast , there was a significant increase in y- intercept as end-poin t cadence decreased f rom 70 to 60 rpm (F[1,7] =36.7, p < 0 . 0 0 1 ) and f rom 70 to 50 rpm (F[1,7] =80.1, p<0 .001) . N o significant difference was found be tween the y- intercept de te rmined under the 60 rpm and 50 rpm condi t ions (F[1,7] = 3.28, p > 0.05).

Discussion

The main finding of this s tudy is that the y- intercept of the work- t ime relat ion is significantly greater when each bou t is t e rmina ted at a cadence of 50 or 60 rpm in compar i son to 70 rpm. In contrast , CP is not affected by the end-poin t cadence (Table 2). There fore , even when the power ou tpu t is mainta ined, a fall in cadence of 10- 20 rpm f rom 70 rpm significantly affects the y- intercept of the work- t ime relation.

The per iod during which the cadence decl ined f rom 70 rpm to 50 rpm ranged be tween averages of 13 s and 137 s for the highest and lowest power outputs , respec- tively (Table 1). This illustrates that the decline in cad- ence, when power ou tpu t is mainta ined, is not "precipi- tous" on an electr ical ly-braked e rgomete r (Hill, 1993). Moreover , the range in per iods spent be tween 70 and 50 rpm at the highest (3-20 s) and lowest (58-200 s) power outputs reveals a considerable be tween-subjec t

Table 1 Mean estimates and standard error of the means of the power outputs, work outputs and corresponding exercise dura- tions (s) of four exhaustive cycle tests in eight male subjects. The

three treatments (i.e. end-point cadences) for each power output are shown in brackets

Power (watts) 259 + 35 294-+ 41 341 -+ 39 403 -+ 20

Time [70] 1554 +-_ 119 527 + 50 259 + 35 129 + 12 Work (kJ) 403:t: 40 158+19 89+14 52+ 5

Time [60] 1641 -+ 118" 583 + 45* 275 + 33* 137 + 12" Work (kJ) 426-+ 41 173-+18 95-+13 55+ 5

Time [50] 1691 +- 127"*, *** 605 -+ 43**, *** 289 + 35**, *** 142 -+ 12"*, *** Work (kJ) 440_+ 44 180+18 100-+14 57-+ 5

* different from 70 rpm (p<0.05); ** different from 70 rpm (p<0.01); *** different from 60 rpm (p<0.05)

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variation in the time it takes to decline to a fixed end- point cadence. Such variability might also contribute to the imprecision in estimating the y-intercept.

A recent study (Hill et al., 1995) revealed that the y-intercept of the work-time relation was higher for a selfselected cadence (mean = 83-89 rpm for four maxi- mal bouts) compared with a higher and fixed cadence (100 rpm), suggesting that the difference in test cadence p e r se mediated this effect. However, the end-point cadence used in the selfselected condition (i.e. 50 rpm) was lower in comparison with the other condition (i.e. 95 rpm). On the basis of the present findings the differ- ence in the y-intercept observed by Hill et al. (i.e. 1.2 k J) can be entirely explained by the difference in the end-point, rather than the test, cadence.

The y-intercept is purported to represent anaerobic work capacity (Monod & Scherrer, 1965; Poole, 1986). Assuming this is the case, that the y-intercept increased without a change in CP (Table 2) suggests that the in- creased time of work across each of the four bouts evoked a greater anaerobic, but not aerobic. ATP con- tribution to work. The additional work completed at the highest to lowest power outputs as the cadence de- clined from 70 to 50 rpm progressively increased from 5.1 kJ to 36.4 kJ, respectively (Table 1). Although the aerobic contribution to ATP supply and work output will predominate at all intensities when the cadence be- gins to decline from 70 rpm, the ability to continue work beyond this point might enable an additional anaerobic contribution to ATP supply while the power of aerobic metabolism remains unchanged.

The ability to continue exercising as the pedal cad- ence declines might be attributed to an increase in work efficiency. This could be related to a higher ther- modynamic efficiency of ATP hydrolysis as muscle shortening velocity decreases (e.g. Di Prampero et al., 1988); it might also be related to a progressive reduc- tion in the amount of internal work as the cadence falls, although the reduction in the amount of internal work

( - 6 2 J . r e v - l : Luhtanen et al., 1987) at the highest power output (i.e. 0.13 kJ) accounts for only 5% of the difference in the y-intercept between the 70 and 50 rpm conditions. It is unlikely that the overall efficiency of 'anaerobic work' differs significantly between the con- ditions, and thus explains the different y-intercepts, since - 90% of the exercise time was spent at or above 70 rpm for all conditions. We have also assumed that the ergometer accurately maintained power output at cadences between 50 and 70 rpm, although further test- ing with a dynamic calibration rig is required to confirm this.

In conclusion, the end-point cadence selected to ter- minate tests affects the y-intercept, but not the slope, of the work-time relationship on a electrically-braked cy- cle ergometer. Therefore, to control for this effect, the cadence at which each test is terminated should be standardised.

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