Taken from : Cycling Science - Summer 1996 - What Determines The Optimal Cadence?
As the sport of cycling has evolved, training methods have changed, equipment has been refined, and performances have been enhanced. However, one aspect of cycling performance has remained relatively unchanged, that is, the freely chosen cadences of cyclists during training and racing. Few coaches or exercise scientists would argue that cadences of 90 + 5 rpm are typical of those used during world-class performances in road racing or time-trialing, particularly over level terrain. Furthermore, there are no compelling reasons, either scientific or popular, that would lead a coach to recommend a significantly lower or higher cadence to an elite performer. Therefore, the working hypothesis of this article is that cadences in the range 85 to 95 rpm are optimal for performance. From a scientific point of view the obvious question of significance is then, "Why are cadences of 85 to 95 rpm, so typical of elite performers during competition, optimal?" The purpose of this article is to review and examine the multidisciplinary exercise science literature concerning optimal cadence, present one possible interdisciplinary explanation for the optimal cadence phenomenon, and address some common generalizations about cyclists and noncyclists that appear to be incorrect.
A popular explanation for the use of higher cadences is that they are more efficient, with efficiency being used in the general sense of accomplishing the task with a minimum of effort, expense, or waste. However, exercise efficiency has several precise definitions that are summarized in Gaesser and Brooks (1975). They defined and compared four types of efficiency measures with the goal of identifying the one that best represented human muscular efficiency.
These efficiency measures were 1 ) gross efficiency, the ratio of the work accomplished to energy expended, that is, the effectiveness of converting chemical energy into mechanical work; 2) net efficiency, the ratio of the work accomplished to the energy expended above that during rest, that is, the cost of resting metabolism is subtracted from the denominator in the computation; 3) work efficiency, the ratio of the work accomplished to the energy expended above that during cycling with no load, calculated by subtracting from the denominator the cost of moving the legs plus the resting metabolism, and 4) delta efficiency - the ratio of the change in the power output to the change in the energy expended at each power output. Gaesser and Brooks observed that at a constant power output, efficiency decreased as cadence increased, regardless of which definition of efficiency they used. Both earlier and subsequent studies have also shown that efficiency decreases as cadence increases at a constant power output (Benedict and Cathcart, 1913; Dickinson, 1929; Garry and Wishart, 1931; Seabury et al, 1977; Suzuki, 1979). The conclusion from these studies is, from an efficiency standpoint, higher cadences do not appear to be beneficial to the cyclist. Surprisingly, the cadences that produce the highest efficiencies are approximately 50 to 60 rpm.
Not all studies report a decline in cycling efficiency as cadence is increased. For example, Faria et al (1982) found that at a low power output ( 140 W), gross efficiency decreased from 18% to 14% as cadence increased from 68 to 132 rpm; but at approximately 290 W, gross efficiency remained constant at approximately 22%. Therefore, at higher power outputs, increases in cadence may not always decrease cycling efficiency. To explain the difference between their results and previous research, Faria et al. speculated that the skill level of the subjects may have played a role. Previous studies tended to test less-skilled riders who may have engaged noncycle-specific muscle groups, especially during the higher cadences and power outputs, resulting in increased oxygen consumption without any increase in useful work. Faria et al used experienced cyclists who were familiar with high cadences and power outputs and, therefore, perhaps their data more appropriately represented the cycling task. Clearly their data do provide evidence that cyclists are not disadvantaged via a reduction in efficiency during cycling at a high power output and high cadence.
The issue of cycling efficiency has recently been revisited by Sidossis et al (1992). They found that gross efficiency was similar at cadences of 60, 80, and 100 rpm during cycling at power outputs corresponding to 80% (280 W) and 90% (300 W) of an individual's maximal aerobic power (Figure 1). However, at 50% and 60% of 9&emdash;2 max' the efficiency of 100 rpm was significantly lower than either 60 or 80 rpm. These data are consistent with Faria et al (1982) and suggest that at high power outputs, higher cadences are not significantly less efficient compared to lower cadences. In contrast to Gaesser and Brooks (1975), Sidossis et al also found that delta efficiency increased from 21% to 24.5% as cadence increased from 60 to 100 rpm (Figure 2). Like Faria et al, they also suggested that differences between their data and previous work may have been due to the use of unskilled riders in previous studies who may have recruited muscles that were not cycling specific, raising oxygen consumption without increasing the amount of useful work done. According to these authors this possibility makes delta efficiency a more appropriate measure of muscular efficiency than gross efficiency. To explain the increase in delta efficiency as cadence increased, they suggested that the lower extremity muscles responsible for meeting the power output demands of the task may have been closer to the speed of shortening that maximized muscular efficiency (i.e., a speed of approximately 1/3 of the maximal speed of shortening in individual muscle fibers). It should also be noted that both Faria et al and Sidossis et al used power outputs that were considerably higher than used in previous studies, and that their efficiency data may therefore be more representative of a competition cycling environment.
Figure 1: The gross efficiency of cycling at 60, 80, and 100 rpm at various power outputs are expressed as a percentage of VO2max Note that gross efficiency at 100 rpm increases as power output increases so that at 70%, 80% and 90% VO2max the gross efficiencies at the three cadences are not significantly different. There is no disadvantage to pedaling at high cadences provided that power outputs are greater than 70% of an individual's maximal aerobic power.(Adapted from Sidossis et al Int I Sports Med,. 13(5), 407-41], 1992 .)
Figure 2: Delta efficiency during cycling at 60, 80, and 100 rpm. Delta efficiency, (i.e., the ratio o f the change in the work accomplished to the change in the energy expended), increases significantly for each increase in cadence so that it is highest at 100 rpm. These data suggest that muscular efficiency, as reflected by delta efficiency, may be enhanced at higher cadences. (Adapted from Sidossis et aL rnt J Sports Med, 13(5), 407-411,1992.)
An alternative to efficiency measures is to assess the economy of cycling at different cadences, and determine if it costs less in terms of oxygen consumption to ride at a given power output while spinning faster. The most economical cadence is the one that results in the lowest oxygen consumption. Indeed, one could argue that the externally measured efficiency values provide interesting theoretical data, but measures of economy have more relevance to performance. Studies using inexperienced or recreational cyclists, however, show that the most economical cadence falls between 50 to 60 rpm, and consistently demonstrate that pedaling at 90 to 100 rpm causes an increase in oxygen consumption in these subjects.
As alluded to by Faria et al (1982), a potential problem in understanding the influence of cadence on efficiency (and we might extend this to include economy) is that earlier laboratory studies did not focus on elite level cyclists pedaling at high power outputs. It has been suggested that experienced cyclists respond differently when compared to untrained or recreational cyclists, such that they are more economical or efficient at higher rpms. A key study addressing this lack of applicability of previous research was published by Hagberg et al (1981), who used experienced cyclists riding their own bicycles on a motordriven treadmill at 20 mph, up a slight grade. The subjects rode at their preferred cadence and at two cadences above and two below the preferred frequency. For the group the average preferred cadence was 91 rpm. The authors stated that oxygen consumption, blood lactate, and ventilation data were minimized at or near the preferred cadence and, therefore, minimizing these physiological variables was linked to preferred cadence selection. However, closer examination of their data (i.e., examining the quadratic equation that described the relationship between oxygen consumption and cadence), reveals that the lowest oxygen consumption occurred at approximately 70 rpm. Although this is slightly higher than the 50 to 60 rpm values commonly reported for inexperienced or recreational cyclists, it is still well below the preferred cadence for this group, and therefore does not support the position that minimizing oxygen consumption is critical in cadence selection. Therefore, even elite level cyclists, with many years of training and experience, do not appear to have adapted their physiology so that pedaling at their preferred cadences leads to a minimization in oxygen consumption.
A recent study conducted at Arizona State University provides additional support for this idea. This study measured the preferred cadences and most economical cadences of eight experienced cyclists cycling on their own bicycles on a cycling simulator (Velodyne trainer) at a power output of 200 W (Marsh and Martin, 1993). The preferred cadence for this group was 85 rpm, close to that reported by Hagberg et al (1981). The most economical cadence of 56 rpm fell in the middle of the range previously reported for inexperienced or recreational cyclists. This study clearly demonstrated that the preferred cadences of experienced cyclists were considerably higher than those at which oxygen consumption was minimized.
The issue of cycling experience is often raised as a potential explanation of observed differences in preferred cadence between cyclists and noncyclists (Coast and Welch, 1985; Faria et al, 1982; Hagberg et al, 1981). Data collected at Arizona State University suggest this may not be the case (Marsh and Martin, 1993). In the ASU study, experienced runners with no cycling experience, but of equal aerobic capacity to the cyclists, were asked to pedal at their freely selected cadence at a constant power output of 200 W. Surprisingly, their average preferred cadence was 92 rpm and their most economical cadence was approximately 63 rpm, essentially the same as the cadences recorded for the experienced cyclists (Figure 3). These data challenge the commonly held notion that many years of cycling experience are required to feel comfortable at high cadences. The data also suggest, some underlying similarities exist between the cyclists and runners perhaps due to their high fitness levels, or the aerobic training leading to the high fitness levels.
Figure 3: Steady-state oxygen consumption in cyclists and trained noncyclists during cycling at 50, 65 , 80, 95, and 110 rpm at a power output of 200 VV Note that the cadence at which VO2 is minimized is significantly lower than the preferred cadence in each group. Despite many years of cycling experience, the cyclists had not adapted so that they minimized oxygen consumption at their preferred cadence. Also the preferred cadences of the trained noncyclists were the same as the cyclists. Therefore many year s of cycling training are not necessarily required to feel comfortable at high cadences. (Adapted from Marsh and Martin, Med. Sci. Sports Exerc., 25(11), 1269-127A 1993.)
It could be argued that though running is a weight-bearing activity (as opposed to cycling, which is weight supported), it shares some commonalities with cycling; that is, it is cyclical, repetitive, and involves essentially the same muscles producing relatively small forces over extended periods of time. This could be another explanation for the similarities of these two groups. However, a study in our laboratory that extends the 1993 work by including untrained noncyclists to assess the influence of fitness indicates that fitness or training leading to aerobic fitness does play a role in cadence selection (Marsh and Martin, submitted for publication). We found that the untrained noncyclists preferred significantly lower cadences compared to cyclists and trained noncyclists. Also, untrained noncyclists decreased their preferred cadence as power output increased, while the preferred cadences of cyclists and trained noncyclists remained essentially unchanged as power output increased. This result, in part, corroborates the notion that noncyclists prefer lower cadences to cyclists, but it also suggests the influence of fitness or aerobic training in cadence selection. In summary, cycling experience, per se, is not a prerequisite to selecting a high preferred cadence, and there is reason to suspect that cadence selection is controlled by fundamental underlying mechanisms common to all people.
One factor that transcends the cycling experience issue is how we perceive the difficulty of a task. It has been suggested that an individual's perception of effort is an important factor when selecting a pedaling rate, and peripheral cues from the active muscles may therefore be given more consideration than economy or efficiency when selecting a preferred cadence. Ekblom and Goldbarg (1971) stated that "muscle strain" may provide feedback to the central nervous system, which strongly influences perceived exertion. In simple terms the hypothesis would be that the feelings we perceive in the legs during cycling lead us to select a pedaling rate so that we minimize the perceived effort of the task, even if we are using more oxygen. Typically a rating scale with values that range from very light effort up to maximal exertion is used to quantify an individual's perceived exertion (Borg, 1975). Using this technique, several studies have recorded perceived exertion at different cadences and constant power output, although it should be noted they were not interested specifically in how perceived exertion might influence cadence selection. Lollgen et al (1975) manipulated cadence from 40 to 100 rpm at power outputs of 50, 100, 150, and 200 W and found perceived exertion in trained and untrained subjects decreased with increases in cadence such that it was minimized at approximately 80 to 100 rpm.
While it is appealing to conclude perceived exertion is therefore an important factor in preferred cadence selection, other studies have shown that perceived exertion is not always minimized at these cadences. Stamford and Noble (1974) had high-fit subjects pedal at 40, 60, and 80 rpm at a power output of 160 W. They reported a parabolic relationship between perceived exertion and cadence, which was minimized at 60 rpm. Lollgen et al (1980) also reported a quadratic relationship between perceived exertion and cadence, which was minimized at 65 and 73 rpm during cycling at 70% and 100% of &emdash;2max (Figure 4).
Figure 4: Rating of perceived exernon (RPE) at 40, 60, 80, and 100 rpm during unloaded cycling, and at intensities corresponding to 70% and 100% of maximal aerobic power. Note that the absolute changes in the RPE scores are quite small at all three power outputs. However, there is a trend for perceived exertion to be minimized at higher cadences as power output increases, i.e., RPE minimized at 60 rpm at 70% VO2max and 80 rpm at 100% VO2max (Adapted from Loligen et aI Med Sci. Sports Exerc., 12(5), 345-351,1980.)
Recent unpublished data from a study conducted at Arizona State University suggest perceived exertion is minimized at cadences significantly lower than the preferred cadence at any given power output, but at cadences slightly higher than those that minimize oxygen consumption. These data are consistent with Coast et al (1986) who also found cadences that minimize perceived exertion tend to be slightly higher than those minimizing oxygen consumption. Cadences minimizing perceived exertion, however, are still significantly lower than the preferred cadences of cyclists. The data from the ASU study also showed that perceived exertion remained relatively unchanged between 65 and 95 rpm, but tended to increase at the extremes of the cadence range (50 and 110 rpm). Therefore, cadences in the middle of the range tested appeared to result in acceptable levels of effort for well-trained, experienced cyclists and well-trained noncyclists, whereas cadences at the extremes of the range would likely be avoided.
Now let us take a brief look at the biomechanics of pedaling and examine the forces applied to the pedals during cycling. Several studies have used force sensing devices mounted in the pedal to examine the pedal forces as cadence or power output is changed (Cavanagh and Sanderson, 1986; Davis and Hull, 1981; Hull and Jorge, 1985; LaFortune and Cavanagh, 1980; McLean and LaFortune, 1991; Patterson and Moreno, 1990). Several of these studies have shown that as cadence increases at constant power output, the peak force on the pedals decline. In a study of 11 recreational cyclists, Patterson and Moreno (1990) reported the resultant pedal force averaged across a complete crank cycle was minimized at 90 and 100 rpm at 100 and 200 W, respectively. Interestingly the preferred cadences of their subjects at 100 and 200 W were 94 and 98 rpm, respectively. It has been suggested that if the muscles produce smaller forces more often (as occurs when cadence is increased at constant speed), they are less likely to fatigue. The rationale for this will become apparent in the following paragraphs.
Optimal cadence has also been addressed from a biomechanical perspective. Hull and several co-workers have determined optimal cadences based on biomechanical variables (net joint moments and muscle stresses) rather than the more commonly used physiological variables such as efficiency or economy. These two biomechanical variables were selected with good reason. Under conditions where cocontraction of agonist and antagonist muscle groups is minimal (e.g., quadriceps and hamstrings), the net joint moment gives an indication of the muscle effort required for the task, and previous research suggests that minimizing muscle stress is important during submaximal locomotion (Crowninshield and Brand, 1981). Using experimental data and computer models of the lower extremity, Redfield and Hull (1986) found a cadence within the range of 95 to 105 rpm minimized the sum of the average absolute hip and knee moments during 200 W cycling. In follow-up work, Hull et al (1988) used a more sophisticated computer model to assess the influence of cadence on the muscle stresses of 12 lower extremity muscles. The optimal cadence, defined as that which minimized the sum of the 12 muscle stresses, was found to be 95 to 100 rpm (Figure 5). The importance of these studies was the observation that these two biomechanical variables showed close agreement with the cadences preferred by experienced cyclists. The conclusion from these studies is that minimizing net joint moments or muscle stresses, both of which are said to give insight into the level of muscle effort required for the task, may be important in preferred cadence selection. There are, however, some questions about the validity of the models used in these studies, and more generally, there are always concerns about the applicability of the model data to real-world conditions. Nevertheless, these studies show the best agreement between the preferred cadences of experienced cyclists and two variables that are minimized (i.e., optimized) during cycling.
Figure 5: Data from a computer modeling study that used a muscle stress-based objective function to determine the optimal cadence at 200 W. The sum of the muscle stresses of 12 lower extremity muscles was calculated as cadence was varied from 60 to 140 rpm. The model results clearly show that the optimal cadence (i.e., the cadence that minimized the objective function) was 95-100 rpm. This agrees very well with the preferred cadences of experienced cyclists and suggests the possibility that a mechanical variable may be important in preferred cadence selection. (Adapted from Hull et al Int I Sports Biomech., 4 , 7020, 1988. )
Another approach we can use to attempt to determine why experienced cyclists select high rpms is to combine the results of these biomechanical and physiological studies and include some information about the muscle fiber types used during cycling at different cadences. Briefly, our muscles consist of many thousands of muscle fibers, some of which are characterized as slowtwitch fibers, others characterized as fast-twitch fibers, and some that have characteristics that fall between these two extremes. The slow-twitch fibers possess an aerobic endurance quality, while the fast-twitch fibers are more powerful but fatigue faster. The intermediate fibers possess an ability to develop more power than the slowtwitch fibers, but do not fatigue as quickly as the fast-twitch fibers. A single nerve fiber running to one of the large muscles in the leg may control 500 to 1000 of these fibers, all of which will be either slow, fast, or intermediate. All of these fibers and the single nerve fiber controlling them are called a motor unit; the muscle fibers of the unit are activated by the same motor unit action potential and therefore contract in unison.
Fortunately, our bodies automatically select motor units to produce force based on the demands of the task. For tasks requiring low forces (e.g., standing, walking, recreational cycling at 5 to 10 mph on level ground), slow-twitch motor units are predominantly selected.
As the force requirements of the task increase (e.g., running, a 40-mph sprint finish at the end of a road race, powering up at steep hill on a mountain bike), fast-twitch units are selected in addition to the slow units already selected. Remember that laboratory studies have shown a decline in peak pedal forces as cadence increases at constant power output. According to the widely accepted motor unit recruitment principles outlined above, fewer fast-twitch fibers should be recruited at a high cadence compared to a low cadence. Is this what happens in cycling?
Previous studies have alluded to the influence of cadence on motor unit recruitment. Some authors have speculated that fast-twitch fibers are selectively recruited at higher cadences (e.g., Gaesser and Brooks, 1975). Often isolated muscle studies, which suggest that slow-twitch muscle fibers may not be able to contract and relax fast enough at high cadences to be responsible for any useful power output, are used to argue that selective recruitment of fast twitch fibers occurs at high cadences, despite the reduction in force per pedal cycle. The nearest direct measurement of fiber recruitment available to us are studies that assess glycogen depletion in muscle fibers by extracting a small sample of muscle tissue and assessing the glycogen content pre- and postexercise. With some limitations, this technique gives an indirect indication of whether slow or fast muscle fibers are selected during cycling at different cadences; those fibers that are not selected retain their glycogen stores. Early work by Gollnick et al (1974) concluded that variations in cadence had no effect on fiber recruitment patterns during cycling. However, these authors were primarily interested in the influence of power output and exercise duration, rather than cadence. Further, their methods of evaluating glycogen content were qualitative and later shown to be inadequate for quantifying small changes in glycogen content (Vollestad et al, 1984).
A recent study by Ahlquist et al (1992), which measured glycogen depletion using a quantitative technique, produced results consistent with the notion that muscle fibers are recruited based on the force demands of the task. They assessed glycogen depletion in slow- and fast-twitch muscle fibers of subjects cycling at 50 and 100 rpm at 85% of their maximal aerobic capacity. The results showed that at 50 and 100 rpm, a similar number of slow-twitch fibers were recruited. However, fewer fasttwitch fibers were recruited when the cadence was increased to 100 rpm. This was attributed to the increased muscle force required per pedal revolution at the lower cadence. This study provides evidence that the force demands of a task, rather than the velocity of contraction, determines the type of muscle fibers recruited, and the selection of a preferred cadence during cycling is perhaps linked to muscle fiber recruitment strategies. It does not appear to support the notion that cadences of 100 rpm are too high for slow-twitch muscle fibers to operate effectively and contribute to power output during cycling.
How then does the selection of fewer fast-twitch fibers effect the cyclist, and might this be the elusive answer as to why cyclists select high rpms during submaximal cycling? Slow-twitch fibers derive most of the energy necessary for muscular action via oxidative metabolism, in which glucose and fat are broken down and, in the presence of oxygen, large amounts of ATP are formed. ATP, or adenosine triphosphate, is the immediate source of energy for muscle action. In contrast, fast-twitch fibers break down more glucose than can be oxidized to carbon dioxide, which results in the production of lactic acid. While lactic acid can actually be reutilized as an energy source, in large quantities it has been linked to a decrease in muscle force production (see Metzger, 1992, for a thorough review of factors affecting muscle force production).
At any submaximal cycling speed, if we select a high cadence, the glycogen depletion study of Ahlquist et al (1992) suggests that we will minimize the recruitment of fast-twitch fibers. However, we can still supply ATP to the working muscles of the leg using predominantly slow-twitch or intermediate fibers. Since there is less reliance on fasttwitch fibers, there is less likelihood of a large increase in lactic acid in the working muscle. This theory fits nicely with the observation that fatigue seems to be delayed when using a high cadence, compared to a low cadence. In addition, individual differences in percentage of slow- and fast-twitch fibers may help to explain why some individuals prefer different cadences and why some of us excel at short sprints, while others perform better during long, sustained efforts. Recreational cyclists, who cycle slowly so that force demands are low, have no need to pedal at high cadences since they are already utilizing their slow-twitch fibers. They may even be pedaling at their most economical cadence, since they are in no hurry to get from A to B.
In summary, laboratory studies indicate that experienced cyclists do not use their most economical or efficient cadences. However, cadences of 90 to 100 rpm are probably beneficial in spite of decreases in economy and efficiency. The explanation proposed here suggests the use of high rpms results in a decrease in average pedal force per revolution and leads to the recruitment of fewer fast-twitch fibers, placing the reliance for muscle power development primarily on the slow-twitch and intermediate fibers. The advantage to the cyclist is there is less likelihood of a rapid accumulation of lactic acid, with the resulting decrease in muscle force production. More interdisciplinary studies in cycling, particularly those that combine biomechanical and physiological data, are needed to confirm or refute this theory.
It seems likely that physiological, psychological, and biomechanical factors all play a role in preferred cadence selection, albeit to a varying degree, depending on the goals of the task. For example, maximal sprinting tasks have not been considered in this article, and it is likely that the criteria for sprint cadence selection are different than for submaximal cycling tasks. As we have seen, one of the difficulties in attempting to provide a definitive answer to the question of what are the determinants of the preferred cadence is the inconsistent nature of some of the scientific literature. Also, this article works from the supposition that for a submaximal task, the human body will attempt to minimize those variables important to preferred cadence selection. The author is certainly not alone in this view, but acknowledges this logic may be flawed, and, in fact, the body may be trying to maximize some as yet undetermined variable, such as muscle power output (see Sargeant, 1994).
1) Ahlquist, L. E., Bassett, D. R, Sufit, R., Nagle, F. J., and Thomas, D. P. (1992). The effect of pedaling frequency on glycogen depletion rates in type I and type II quadriceps muscle fibers during submaximal cycling exercise. Eur. J. Appl. Physiol. 65: 360-364.
2) Benedict, F. G. and Cathcart, E. P. (1913). Muscular Work. Publication No. 187, Washington, DC: Carnegie Institute.
3) Borg, G. (1970). Perceived exertion as an indicator of somatic stress. Scand. J. Rehab. Med. 2: 92-98.
4) Cavanagh, P. R. and Sanderson, D. J. (1986). The biomechanics of cycling: studies of the pedaling mechanics of elite pursuit riders. Science of Cycling. Human Kinetics Publishers, Champaign IL.
5) Coast, J. R., Cox, R. H., and Welch, H. G. (1986). Optimal pedalling rate in prolonged bouts of cycle ergometry. Med. Sci. Sports Exerc. 18: 225-230.
6) Coast, J. R. and Welch, H. G. ( 1985). Linear increase in optimal pedal rate with increased power output in cycle ergometry. Eur. J. Appl. Physiol. 53: 339342.
7) Crowninshield, R. D. and Brand, R. A. (1981). A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14: 793-801.
8) Davis, R. R. and Hull, M. L. (1981). Measurement of pedal loading in bicyding-II. Analysis and results. J. Biomech. 14: 857-872.
9) Dickinson, S. (1929). The effciency of bicycle pedalling as affected by speed and load. J. Physiol. 67: 242-255.
10)Ekblom, B. and Goldbarg, A. N. (1971). The influence of physical training and other factors on the subjective rating of perceived exertion. Acta Physiol. Scand. 83: 399-406.
11) Faria, I., Sjojaard, G., and BondePetersen, F. (1982). Oxygen cost during different pedalling speeds for constant power output J. Sports Med.22: 295-299.
12) Gaesser, G. A. and Brooks, G. A. (1975). Muscular efficiency during steady-rate exercise: effects of speed and work. J. Appl. Physiol. 38: 1132- 1139.
13) Garry, R. C. and Wishart, G. M. (1931). On the existence of a most effficient speed in bicycle pedalling and the problem of determining human muscular effficiency. J. Physiol. 72: 425-437.
14) Gollnick, P. D., Piehl, K., and Saltin, B. (1974). Selective glycogen depletion pattern in human muscle fibers after exercise of varying intensity and at varying pedalling rates. J. Physiol.241: 45-57.
15) Hagberg, J. M., Mullin, J. P., Giese, M. D., and Spitznagel, E. (1981). Effect of pedaling rate on submaximal exercise responses of competitive cyclists. J. Appl. Physiol. 51: 447-451.
16) Hull, M. L. and Jorge, M. (1985). A method for biomechanical analysis of bicycle pedalling. J. Biomech.18: 307-316.
17) Hull, M. L., Gonzalez, H., and Redfield, R. (1988). Optimization of pedaling rate in cycling using a muscle stress-based objective function. Int. J. Sport Biomech. 4, 1-21.
18) LaFortune, M. A. and Cavanagh, P. R. (1980). Force effectiveness during cycling. Med. Sci. Sports Exerc. 12: 95.
19) Lollgen, H., Graham, T., and Sj0gaard, G. (1980). Musde metabolites, force and perceived exertion bicycling at varying rates. Med. Sci. Sports Exerc. 12: 345-351.
20) Lollgen, H., Ulmer, H. V., Gross, R., Wilbert, G., and Nieding, G. V. (1975). Methodological aspects of perceived exertion rating and its relation to pedaling rate and rotating mass. Eur. J. Appl. Physiol. 34: 205-215.
21) McLean, B. D. and LaFortune, M. A. (1991). Influence of cadence on mechanical parameters of pedalling. In Proceedings of the 13th International Congress of Biomechanics. University of Western Australia, Perth, Australia.
22) Marsh, A. P. and Martin, P. E. (1993). The association between cycling experience and preferred and most economical cycling cadences. Med. Sci. Sports Exerc. 25: 1269-1274.
23) Metzger, J. M. (1992). Mechanism of chemomechanical coupling in skeletal muscle during work. Perspectives in exercise science and sports medicine. Volume 5: Energy metabolism in exercise and sport (D. R. Lamb, Ed.) pp. 1-51, Wm. C. Brown.
24) Patterson, R. P. and Moreno, M. I. (1990). Bicyde pedalling forces as a function of pedalling rate and power output. Med. Sci. Sports Exerc. 22: 512516.
25) Redfield, R. and Hull, M. L. (1986). On the relation between joint moments and pedalling rates at constant power in bicycling. J. Biomech. 19: 317-329.
26) Sargeant, A. J. (1994). Human power output and muscle fatigue. Int. J. Sports Med. 15: 116-121.
27) Seabury, J. J., Adams, W. C., and Ramey, M. R. (1977). Influence of pedaling rate and power output on energy expenditure during bicycle ergometry. Ergonomics. 20:491-498.
28) Sidossis, L. S., Horowitz, J. F., and Coyle, E. F. (1992). Load and velocity of contraction influence gross and delta mechanical efficiency. Int. J. Sports Med. 13: 407-411.
29) Stamford, B. A. and Noble, B. J. (1974). Metabolic cost and perception of effort during bicycle ergometer work performance. Med. Sci. Sports.6: 226-231.
30) Suzuki, Y. (1979). Mechanical efficiency of fast- and slow-twitch muscle fibers in man during cycling. J. Appl. Physiol. 47: 263-267.
31)Vollestad, N. K., Vaage, O., and Hermansen, L. (1984). Musde glycogen depletion patterns in type I and type II fibers during prolonged severe exercise in man. Acta Physiol. Scand.122: 433-441.
Anthony P. Marsh, Ph.D.
Department of Health and Physical
California State University,
Sacramento, CA 95819-6073
Taken from : Cycling Science - Summer 1996 - What Determines The Optimal Cadence?
See also Cycling Science - Spring 1996 - Editors Mailbox.