2 Human Power Generation

Introduction

As a power producer, the human body has similarities and dissimilarities to an automobile engine. Energy is taken in through fuel (food and drink, in the case of humans). “Useful” energy is put out in the form of torque on a rotating crankshaft (in the case of cars) or in a variety of muscular movements (in the case of humans), and “waste” energy is dissipated as heat, which may be beneficial (for both) in cold weather. The two systems have peak efficiencies, the energy of movement divided by the energy in the fuel (for cars) or in the extra food used in working (for humans) remarkably close to one another, in the region of 20–30 percent. But automobile engines seldom work at peak efficiency, and in any case, they attain peak efficiency only close to full power, whereas the rider of a multispeed bicycle can operate much closer to peak efficiency at all times. And whereas the automobile is powered by a “heat engine,” the human body is similar to a fuel cell, a device that converts chemical energy in fuel directly to work. Also, human output, unlike that of the automobile engine, changes over time because of fatigue, possibly hunger, and eventually the need for sleep. A human can draw on body reserves (i.e., stores of several different fuels); the piston engine can work steadily until the fuel runs out and then delivers nothing. Humans also vary greatly from one to another, and from one day to another, and from one life stage to another, in terms of the power output they can produce.

The authors’ intention in this chapter is to provide a basic understanding of how energy gets to the muscles of a bicycle’s rider and subsequently produces mechanical power at the pedals. The chapter also comments on some bicycle configurations and mechanisms as they relate to the generation of human power. It takes the philosophical position that athletes do sophisticated things to maximize performance, many of which are not yet understood. Timing and direction of foot force, choice of crank length and gear ratio, when to stand up or “bounce” the upper body—all seem to diverge from simple logic. One is reminded of the agreement of the thermodynamicist and the practical engineer in stating that “science has learned more from the steam engine than the steam engine has learned from science.” (The second law of thermodynamics was formulated long after the first successful steam engines had been developed.)

Measuring Human Power Output

Exercise bicycles and ergometers of the pattern depicted in panel (a) of figure 2.1, in numerous variations, have been employed long and successfully. In these machines, the flywheel’s inertia minimizes crank-speed variations somewhat during brief variations in pedaling torque. For accurate work the wheel speed and the average braking torque must be measured precisely. One effective preelectronic measurement technique involves a band brake whose drag is set by a weight, theoretically giving unchanging, accurate data. However, generations of researchers have used simplistic calculations for the Monark-style brake band configuration shown in panel (b) of the figure; these calculations appear to overestimate force by 10–15 percent. Usually the force F = F_T − F_S (the difference between the tight and slack parts) is simply assumed to be the same as the weight of the mass B, but the real relationship for a wrapped rope is F = (1 − e⁻Θ^μ) F_T, with Θ being the wrap angle and μ the coefficient of friction, which varies typically between 0.15 and 0.30. Other ergometer models using magnetic braking and electronic force sensing do not have this problem but need to be calibrated for accurate testing (see Zommers 2000, Gordon et al. 2004, Franklin et al. 2007, and especially Vandewalle and Driss 2015, which describes different friction ergometers with equations).

A different type of ergometer uses a bicycle mounted on a treadmill. Rider power at a given belt speed (figure 2.2) is controlled by the slope (or any rearward pull force, if used). The measured power includes rolling resistance and bicycle drive train efficiency and is thus slightly higher than the cyclist’s power. It is shown here for historic reasons.

Much of the information presented in this chapter has been obtained through careful experiments, typically with ergometers. Most ergometers are pedaled in the same way as bicycles; other types are rowed, cranked, stepped, or walked. They are capable of precise energy measurements under the limitations mentioned. However, the following reservations about ergometer-based human-performance research must be kept in mind:

• People vary widely in performance, and unless very many are tested (seldom the case), the data cannot be generalized to the whole of humanity. There has also been a bias toward testing athletes (already self-selected for physical capability) and college students, predominantly male, in Western countries.
• Pedaling or rowing an ergometer usually feels different than riding a bicycle. It may take more than a month of regular use before someone becomes “proficient” on an ergometer. Muscle adaptation to full oxygen-using capability can take years of extensive training. Subjects are seldom given the opportunity to adapt for more than a few minutes (occasionally hours, but almost never more than that) to working an ergometer before tests are performed and measurements are taken.
• Quite apart from imperfect adaptation to an ergometer, the extant research in this area rarely follows a person’s response to years of exercise from start to finish. Comparing a group of exercisers to a group of nonexercisers may suggest that exercise confers physical vigor, but the logic is weak: already-vigorous people may simply be the ones who tend to exercise. The proper test would be to track two equivalent groups as they followed different specified regimens.
• One reason pedaling an ergometer may feel strange is that the resistance to acceleration felt at the pedals (provided by a flywheel or other moving parts) is often much less than (as little as one-tenth of) the inertial resistance of the rider and bicycle, leading to a bothersome variation in pedal speed at substantial power levels. That is, it is often more like constant-torque pedaling as on a very steep hill climb, rather than constant-speed pedaling, as when cycling fast. Tom Compton of the website Analytic Cycling (analyticcycling.com) has developed a “pedal-force simulator,” an electronically controlled brake that he says in this respect gives a bicycle on a roller-trainer almost the same feel as real cycling. Developers of electronic bicycles with pedal generators are faced with the same problem, which amounts to introducing virtual inertia into a system lacking sufficient real inertia.
• An ergometer bicycle is often fixed, whereas an actual bicycle can freely be tilted and moved relative to the pedaler, affecting body motions and forces.
• There are differences in posture between an ergometer and a bicycle: except on a recumbent, a competitive bicyclist must crouch to minimize aerodynamic drag, possibly restricting breathing. Crouching is unnecessary on an ergometer but should possibly be enforced in research studies if accurate comparison to road riding is desired.
• Subjects pedaling ergometers may not be given adequate cooling, and heat stress, as revealed by copious sweating, can limit their long-term output. There are exercisers on the market that dissipate most of the power via fans, thus simulating the square-law effect of wind resistance, but the airflow on such exercisers is not directed at the pedaler and in any case could not approach the cooling provided by the relative wind in real cycling.
• The motivation of competition (for maintaining a painful effort) can far exceed the stimulation of a laboratory setting.

Therefore, subjects are likely to achieve lower power output on ergometers (especially in the long term) than they could by pedaling or rowing their own familiar machines in a race that they want to win and cooled by their own apparent wind.

Most ergometers have frames, saddles, handlebars, and cranks similar to those of ordinary bicycles. The crank drives some form of resistance or brake in parallel with a flywheel, and the whole device is fastened to a stand, which remains stationary during use. Some ergometers can measure the output from hand cranking in addition to that from pedaling. Others permit various types of foot motion and body reaction, including rowing actions. The methods employed for power measurement range from the crude to the sophisticated. One problem of ergometry is that human leg-power output varies cyclically (as does that of a piston engine) rather than being smooth (as with a turbine). Even in steady pedaling, a device indicating instantaneous power (pedal force in the direction of pedal motion, multiplied by pedal speed) would show peak values of perhaps 375–625 W, with an average of perhaps 250 W. Therefore, some form of electronic or mechanical averaging or both is usually employed, the simplest being the use of a flywheel. In some cases the subject is supposed to keep pedaling at a constant rate over 1–2 min to obtain accurate results; in other systems the power can be integrated and averaged electronically over any desired number of crank revolutions (Von Döbeln 1954; Lanooy and Bonjer 1956).

There are additional problems associated with the determination of very-short-duration extreme power levels (1–2 kW or even greater). It is very hard to hold power constant, and for the very shortest times, it is important to measure the work done over completed crank rotations only. The best-accepted high-power ergometer test is known as the Wingate anaerobic test (discussed later in the chapter), in which a high resistance is suddenly applied to a Monark-style ergometer and the pedaler immediately strives to pedal at maximum speed for 30 s, initially accelerating the flywheel dramatically, then allowing its speed to drop as fatigue sets in. Timing equipment determines the interval of each successive flywheel rotation, allowing average power during that rotation to be determined. Actually, it is better to average over crank rotations rather than wheel rotations, to smooth out the cyclic power variations occurring in each crank revolution. For the shortest times, simply using fast, accurate ergometer electronics that sense speed will also detect heretofore unexpectedly high peak power. For example, the ergometer record of nearly 2,400 W for 5 s (see Nüscheler 2009) is almost double the peak power indicated in the second edition of this book and well over the 1,500–1,700 W measured for football players doing staircase tests for durations of 2 s (Hetzler et al. 2010).

Sturdy old exercise bicycles with heavy, braked flywheels are very similar in function to laboratory-grade ergometers. They can be adapted for accurate power measurement, if the problem of controlling and measuring torque can be solved. Unfortunately, energy-dissipating devices based on the losses of a small, tire-driven roller heat up the tire, changing the rolling resistance substantially. Magnetic (eddy-current) load units also heat up their conductive elements, increasing the electrical resistance and more than halving the initial magnetic torque. Temperature rise also tends to affect frictional brake drag, and even air fan devices can vary in resistance. Zommers (2000) describes how an ergometer using a small roller, inefficient generator, and resistance as load can nevertheless be calibrated to furnish accurate results. Whatever method is used for measuring, the unit must be designed to impose a torque that is essentially independent of friction coefficients and other temperature-dependent properties.

Some of the available test data on human power output are increasingly taken from subjects cycling on pavement, with various ingenious means used to measure work output (or oxygen consumption, which in steady state can be roughly related to work output, if calibrated in the lab, or both) (see figure 2.3). Measurements resulting from such setups may be more realistic than ergometer data and can give additional information, such as the onset of fat metabolization (Bergamin 2017). In such measurement schemes, however, someone wearing various sensors, in particular a breathing mask, is likely to find that the measurement apparatus creates a noticeable resistance to movement, breathing, or both and this will reduce performance somewhat (Davies 1962). Alternatively, cyclists’ power output in closely monitored rides like popular cycle races can to some extent be determined indirectly and is sometimes displayed in television coverage.

Modern on-bicycle power-measuring systems such as Schoberer Rad Messtechnik (SRM) and PowerTap (see chapter 4) are free from the foregoing objections, and this has led to a very substantial rise in reported performances as more riders have used these systems, on their own bicycles, and especially in the heat of competition. This competition can be on the road, but increasingly cyclists “compete” on the internet, uploading their individual performances onto specific websites. This begs the question when we will start to see “virtual cyclist” data that are made up rather than measured.

Describing Pedaling Performance Quantitatively

Pedaling performance is usually described quantitatively by fixing a power level (usually by asking the subject to maintain a fixed pedaling speed at a given resistance) and determining the time to exhaustion. Different power levels can be sustained for durations anywhere between a few seconds and many hours. The results are often plotted as a power-duration curve, which seems to provide the best overall picture of a person’s power-producing strengths and weaknesses.

Testing pedaling performance indoors, on an ergometer, has the advantage that the resistance is likely to be steady. Outdoors, even “level-road” riding may involve periods of large variations, because of slight grades in the road, wind gusts, or accelerations.

Because individuals have different muscle mass, muscle makeup, inherited abilities, and state of conditioning, each will have a unique power-duration curve. When it comes to good athletic performance, some people are relatively stronger over particular durations and thus are better suited for events of those durations. This is partly why sprinters are not also climbers. (Another aspect of cycling performance, of course, is that different body types may have more or less aerodynamic drag, which is important in level riding, and more or less weight, which is important when riding uphill.)

Figure 2.4 shows power-duration data for “first-class athletes” and “healthy men” (designations in the original graph on which the figure is based) and for good cyclists. These data are referred to repeatedly throughout the book. They are derived from ergometer tests, from tests of bicyclists on bicycles, and from estimates based on the results of time-trial races. Each data point given is the maximum duration of pedaling at a certain power level: the curves do not reflect human power drop-off with time. The chain-dotted line estimates the best athletes’ maximum performance with an optimum mechanism. Unfortunately the subjects’ weights are seldom known, so specific power data cannot be given. Data for women are scarce and not comparable, because women are generally lighter, as the single data point given for a female athlete shows.

The top performances at different power levels are typically achieved by different types of individuals. The outer envelope reflects outstanding performances by rather large, strong men, with sprinters producing the short-time data and distance racers the longer-time results. However, the performance of any particular individual, in a given state of training and feeding, can be described by a curve of roughly similar form (see the next section). On-road on-bicycle power-measuring systems have become more sophisticated and numerous in recent years. They generally store complete logs of power versus time, and the underlying software can use the results of an ongoing ride to update the rider’s personal power-duration envelope.

Critical Power: Fitting Curves to Power-Duration Pedaling Data

Individuals’ power-duration curves have been subjected to a variety of curve-fitting efforts aimed at identifying the greatest power level that short-term tests suggest could be sustained “forever,” which is commonly known as critical power (CP). Such efforts are interesting because they encapsulate data efficiently and permit mathematical approaches to performance optimization and also because they may reveal aspects of the physiological mechanisms governing endurance. A similar term is functional threshold power (FTP, defined as the power level that can be sustained for 1 h).

The simple regression used originally for such curve fitting of individual power-duration data appeared as a linear relationship between total work performed (that is, the selected power level times duration) and duration, in the form

total work = anaerobic work capacity + (critical power × duration).

(Anaerobic work capacity, or AWC, refers to an amount of stored energy that can be released very quickly.) This equation embodies the simplified idea that any power beyond the pedaler’s steady-state capacity is drawn from a nonreplenished finite energy reserve. Alternatively, this equation can be expressed as a linear relation between sustained power and duration: power = (AWC/duration) + CP.

A variety of research using such equations exhibits nice curve fits over ranges between 2 and 12 min, at power levels typically in the range from 200 to 400 W (obviously not championship power levels for those durations, which could be two to three times as great). In principle, two data points suffice to construct a straight-line relationship, but of course further trials are useful to demonstrate the variability and quality of fit. An initial guess at short-duration power settings, based on rider mass, might be 2 and 4 W/kg for an unfit person, 4 and 6 W/kg for a fit recreational cyclist, and 6 and 10 W/kg for a cycling champion. (Each of these power levels can be equated to a given vertical velocity from pedaling up a steep hill or running up flights of stairs.)

Gaesser et al. (1995) outline some criticisms of these simple correlations; for example, the erroneous implication that an individual’s entire anaerobic work capacity can be depleted in a relatively short time span. In reality, some anaerobic work capacity will be held back, and the shortest-term maximum power will fall well below predictions. Other researchers (see, e.g., Jenkins and Quigley 1990) have determined that a series of relatively short tests determines critical power well above the lactate threshold (described later) and that very few riders can sustain that intensity for even 30 min. Morton and Hodgson (1996, 500) review various proposed equations comprehensively and conclude that the model presented in the foregoing paragraphs “has a simple appeal, its parameters are well understood, and it has always been found to be a good fit to data over the 2- to 15-minute range. Extensions ... incorporate a more realistic representation of the human bioenergetic system, and fit data over a wider range of power and duration, from 5 s to 2 h.”

In principle, specialized power-duration curves could be developed for any particular conditions of interest, for example, with two different cadences or body positions, or before and after a preliminary fatiguing effort similar to a hill climb, or perhaps following a change in diet.

Actual power-duration data (or directly derived performance parameters such as critical power and anaerobic work capacity) seem more directly relevant for characterizing human performance improvements than physiological measurements such as lactate threshold, maximal oxygen uptake, or fuel efficiency. And such performance parameters are more easily measurable, requiring only a known-resistance exercise bicycle or an on-bicycle power-monitoring system.

Many cyclists have fitted their bicycles with power meters and exchange the resulting data online, often power-duration pairs, such as FTP. Johnstone (2018) posts FTP values that users of his web service say that they reach. For males, these values plot a nice Gaussian bell curve centered at about 3.5 W/kg, with the minimum at 1.5 W/kg and the maximum at 5.5 W/kg. For females, they result in an asymmetrical hill-shaped curve, also centered at about 3.5 W/kg, and with sharper cutoffs: minimum at 1.2 W/kg and maximum at 4.6 W/kg. Johnstone compares these curves with actual data mostly measured at shorter durations than 1 h. Because a full-hour test is very arduous and often impossible, training cyclists like to extrapolate from shorter tests, as explained earlier in the chapter, with a 20 min test having become a standard. How to do this is explained by Hunter Allen (2013), author of a standard training book with exercise physiologist Andrew Coggan. They use a 5 percent drop-off in power between 20 and 60 min durations. Though many seem to have accepted this figure, the website Fast Fitness.Tips (2019) says it applies to athletes only and that 8 percent is more representative, with the figure even rising to 15 or 20 percent for untrained persons. This assertion seems plausible when one observes the rather short stamina of untrained people when cycling or hiking and corresponds to the drop-offs shown in the National Aeronautics and Space Administration (NASA) curves in figure 2.4: almost no drop-off for “first-class athletes” and about 50 W for “healthy men.” Coggan (2016) himself provides data for two hundred seasoned athletes that indicate a drop-off of 10 pp, or 14 percent, from 20 to 60 min, as well as a dozen or so personal measurements over a relatively large range. An online calculator from a company selling a fitness analysis system (Baron Biosystems 2018) allows the curves of figure 2.4 to be vaguely reproduced using just one to three data pairs.

Anaerobic Power: The Wingate Test and Alternatives

Anaerobic power is revealed in a person’s ability to leap or to sprint up a few flights of stairs. As described subsequently, it is governed by immediate and anaerobic energy stores in the specific muscles being used. The so-called immediate fuels are adenosine triphosphate (ATP) and creatine phosphate (or phosphocreatine), liberated through rapid partial metabolism of glycogen without oxygen. Because of the special problems presented by short-term, high-power ergometry, anaerobic power is not often assessed.

The most popular anaerobic power measurement is the Wingate anaerobic test, introduced by Ayalon, Bar-Or, and Inbar (1974) and further described by Inbar, Bar-Or, and Skinner (1996), which commonly uses a simple flywheel-style ergometer, braked by a weight-loaded friction band. In a typical protocol for the test, the rider stays seated, pedaling at 60 rpm with no resistance. For a gear ratio and wheel diameter with 5.9 m “development” (i.e., slippage past the brake in one pedal revolution), a sizable resistance equal to 8.5 percent of body weight is suddenly applied to the friction band, and the rider strives to produce maximum power (while remaining seated) for 30 s. Flywheel speed is measured every 5 s (or better yet, the time of every completed crank revolution is logged). A powerful sprinter may bring the pedal revolutions per minute (rpm) up to 160 within the first few seconds of a test, only to have it drop to about 60 rpm by the end.

Apart from energy used to accelerate the flywheel and to cover transmission losses (which should be a small amount), a bicycle’s pedaling power output is the wheel’s peripheral speed times braking force. Three numbers need to be determined in order to calculate this output: the average speed (based on the total number of flywheel revolutions for the entire test) and the highest and lowest speeds (i.e., the highest and lowest average speeds over 5 s, respectively). From these and the resistance (known) are calculated 30 s average, peak, and minimum power (AP, PP, and MP, respectively). Finally, the fatigability index (FI), defined as the percentage drop from PP to MP, is also calculated. (Roughly speaking, PP corresponds to immediate fuel sources, whereas MP tends to approximate the maximum glycolytic power; see discussion later in the chapter.)

The Wingate test has typically been applied to noncyclist subjects to evaluate effects of diet or exercise. Naturally it is also used in evaluating elite competitors. However, ascertaining the true 5 s peak power directed to the flywheel, as would be revealed by on-bicycle power instrumentation such as PowerTap or SRM, is unlikely, in part because of the flywheel’s inertia: during the violent initial acceleration, actual power may briefly reach twice the brake power or even more, and PP will be underestimated. (Initial acceleration does not affect MP and AP as much as it does PP.) In one example from Reiser, Broker, and Peterson (2000), inertial power correction yields PP values that are 20 percent higher. Such a correction, however, requires knowledge of the flywheel moment of inertia.

Another hindrance to true peak-power determinations is the relatively low resisting force felt at the pedals, usually less than half the body weight. To address this issue, Hermina (1999) tests fifteen elite road cyclists at brake resistances from 7.5 to 14.5 percent of body weight. At the lowest resistance the mean PP is 951 W, whereas at the greatest it is 1,450 W.

Franklin et al. (2007) examine a further criticism of the Wingate test performed on popular Monark-style ergometers. The basic Wingate test procedure uses a weight that applies tension to a brake band wrapped around the flywheel and assumes the resistance is equal to this weight. With models using a differential pulley as shown in figure 2.1, this is only approximately the case with friction coefficients between the flywheel and the band or rope greater than about 0.3, but measurements reveal lower friction coefficients and overestimation of power by up to 12–15 percent. This means that much of the data up to the present day is inaccurate unless the exact method of measurement is documented.

Martin, Wagner, and Coyle (1997) devise an alternative to the Wingate test in which a Monark-style ergometer is modified to use flywheel acceleration alone (no brake) to determine the power. Thirteen subjects (average weight 80.6 kg) pedaled for 3–4 s (6.5 crank revolutions) starting from rest, with the instantaneous speed accurately measured, enabling the average and peak values for torque and power to be worked out without any direct torque or force measurements. Averaging over the best pedal-crank revolution yielded values of about 1.3 kW, or 16 W/kg. Figure 2.5 shows how instantaneous power (curve with peaks), as a function of instantaneous speed, varies strongly around the pedaling circle and between successive pedal revolutions (actually the revolution of one leg, or half-revolutions), attaining the maximum during the third pedal revolution just before reaching 130 rpm.

Measuring the average power (P) between two times t₁ and t₂ is straightforward, as it is just the difference in kinetic energy (KE) at the two times divided by the period between the two times. The relationship to the moment of inertia I and the speedup of the flywheel is given by

P = ΔKE / Δt = 0.5I (ω₂² – ω₁²) / (t₂ – t₁).

All that is needed is a one-time calculation or measurement of the flywheel’s I (~0.4 kg m² for the Monark model used) and a high-resolution recording of the instantaneous flywheel speed ω (in rad/s). The ratio of the pedal gear to the flywheel gear is chosen to get the desired range of pedaling speed (in this case ~7.4).

Another way to determine, for example, maximal 5 s power is on a fixed-speed (isokinetic), motor-driven ergometer. Averaging the measured torque of such an ergometer requires electronic instrumentation, and multiple tests are needed to obtain results for different cadences. Beelen and Sargeant (1992) use such an ergometer to show that peak power is commonly produced at 120–130 rpm, as Martin, Wagner, and Coyle also show; however, in 1995, the spinning champion Manfred Nüscheler produced his peak power, above 2,200 W, at 150 rpm (see Nüscheler 2009).

To sum up, the Wingate test, its variants, and other methods give somewhat different results, and the ergometers used in the testing are themselves subject to further variations and even errors, so computations of maximal anaerobic power are very approximate unless further documented with exactly what was measured.

Physiology of Pedaling: A Primer

The physiology of exercise, a complex subject, has evolved substantially from decade to decade as research has progressed. Neither of the book’s authors nor its contributor was or is a researcher in this general field, so the book’s attempt (in the following) to reconcile and summarize material published mostly during the 1980s risks criticism by experts in the field. Nevertheless the material seems worth presenting, because the subject is complicated and the field remains awash in mythology from still-earlier decades. The presentation in this section is intended to prepare readers to gain insight from current and future exercise research.

For the big picture, the discussion here relies heavily on comprehensive texts by Åstrand and Rodahl (1977), Brooks, Fahey, and White (1996), and McArdle, Katch, and Katch (1996), all of which merit repeated study and some of which are available in new editions. McMahon (1984) engagingly presents many specialized details about muscle-fiber behavior. More recently, online discussion groups have offered a tremendous informal resource for the subjects of on-road power measurement technology, physiological determinants of performance, and related training recommendations.

Overview of How Muscles Work

Human muscle cells convert chemical potential energy into mechanical work, using a variety of fuels, originally derived from foodstuffs, that are stored in the body. Every muscle is composed of a large number of fibers (or cells) of three more or less distinct types. A platoon of such fibers, known as a motor unit, is assigned to each of the many nerves (motor neurons, or motoneurons) controlling a given muscle. These fibers may be visualized as extending from one muscle endpoint to the other, but this is not always accurate. A tilted fiber arrangement called pennation involves multiple fibers of shorter length, effectively creating a short, wide muscle. In pennation, fibers are angled to the direction of muscle contraction, rather than along this direction. This arrangement permits the connection of two long, overlapping tendons (tension elements that connect muscles to bones) with many short fibers, which increases the force a pennated muscle can exert compared to one with a smaller number of long fibers, but reduces its range of motion; it can’t shorten to the same degree as the latter.

Muscles exert tension only (this physiological condition is termed contraction), and therefore can perform mechanical work only, as they shorten, drawing together their attachment points on two different bones. A limb or hand “pushes” only because the body has a system of levers (composed of bones), pivots (joints), tensioning cords (tendons), and antagonistic muscles, so that the pull of one set of muscles produces a movement of a limb or extremity in one direction and that of the other set in the other direction. Figure 2.6 shows a schematic representation of the main leg muscles.

If a muscle actually lengthens while pulling (as occurs when one is lowering a barbell, for example, or slowly squatting), it is absorbing and dissipating work, rather than producing it. Such behavior is known as eccentric contraction or negative work and must be minimized if power or endurance is to be maximized. It is a matter of faith that humans, no less than animals, instinctively adjust their behavior to prevent energy from being lost in negative work.

Nerve stimuli, in the presence of a fuel, cause muscle contraction. Muscles use no fewer than six types of fuel (see the next section) individually or in combination, and the choice is not under conscious control. Instead, the power level the muscle user elects effectively “calls upon” the appropriate fuel choice or choices, at least until depletion. In cycling specifically, at the very highest power levels for a given individual (generally above 1,500 W, or ~2 hp, for strong men), exhaustion occurs in just a few seconds. At a considerably lower power level, say 500 W, a strong rider may last a few minutes; at 350 W, an hour or longer; at 250 W, it may be possible to pedal all day. All these durations have analogs in cycling events: short match sprints (about 10 s), track time trials (a few minutes), hour and road time trials, and long road races, which can last even for days (e.g., the Race Across America).

After contracting briefly, a muscle fiber again relaxes. However, if a muscle is required to exert force for a longer time—for example, while supporting a weight—the nerve stimulating the motor unit involved will “fire” repeatedly, and if the firing period is shorter than the fiber relaxation time, the motor unit will exert a steady, maximal tension. During such “isometric” contraction, the muscle does not shorten. The fact that isometric contraction has a maximum tolerable duration is believed to arise from the blood vessels’ being squeezed, thus restricting the muscle’s blood supply. Even though the weight, in this example, is not being lifted during this time, and so in the thermodynamic sense no external work is being done, the muscle still requires energy either from its stores or from the bloodstream. To maximize external work and to minimize fatigue, isometric contractions should therefore be avoided as much as possible when bicycling.

Beyond the elementary picture of the muscle presented here lies the entire complex subject of exercise physiology, which must be explored to understand human bicycling performance.

The Six Muscle Fuels

As noted previously, muscles make use of six different types of fuels, some short acting and others usable for long durations. Figure 2.7 charts the movement and transformation of these six muscle fuels. All of the fuels involved are interconverted, transported, stored, and used differently. In addition, there are short-lived chemical intermediaries not discussed here that play crucial roles in human power production. A person’s fuel stores and the ability to transport fuel, oxygen, and waste products depend on genetics, training, and state of hunger or fatigue.

Two Fast-Acting Fuels

As noted previously, the so-called immediate fuels are adenosine triphosphate (ATP) and creatine phosphate (also phosphocreatine, or PCr). These are created within the muscle fibers from other fuels and do not release any harmful waste products requiring processing or removal other than heat. ATP is the only fuel used directly by a cell’s contractile proteins; all other fuels are useful only insofar as they can regenerate ATP within the muscle fiber. ATP can be used as fuel without delay (no oxygen required) and replenished just as rapidly through conversion of one of many other fuels.

Each muscle fiber stores enough ATP for about 2 to 5 s of all-out effort and enough PCr (which can be metabolized very rapidly without oxygen to form ATP) for about a further 10 s of ATP effort.

Because it can be utilized without any need for oxygen, a muscle fiber’s stored reserve of ATP is an anaerobic energy source. It is the key resource used in leaping, or in accelerating from rest in a 100 m dash, or in lifting a maximal weight. At much lower power levels lasting minutes or longer, ATP is still the only fuel powering a muscle’s contractile proteins; however, at such power levels it is generated at a steady rate (for example, by oxidation of other fuels), and the muscle fibers’ net reserve is not depleted.

In a shortening contracted muscle, the transformation of ATP releases approximately equal amounts of heat and contractile work. That is, this final stage of the work-producing process has up to 50 percent efficiency.

Three Longer-Duration Carbohydrate Fuels

In respect to intense efforts lasting 20 s through 2 h, three carbohydrates are of surpassing interest. These carbohydrates are the simple sugar glucose (essentially six carbon atoms combined with six water molecules); its stored form, the long-chain polysaccharide (starch) compound, glycogen; and its partially metabolized form, lactate. Glucose and glycogen can be used either aerobically (with oxygen, and slowly) or anaerobically (without oxygen, and far more quickly, but extremely incompletely). Anaerobic carbohydrate metabolism leaves behind high-energy lactate, either to be used immediately elsewhere or later (when oxygen is available) or to be reconstituted to glucose or glycogen. When used aerobically, the body’s glucose and glycogen can provide power for a couple of hours. Alternatively, the glycogen in a muscle can be depleted anaerobically through conversion to lactate in just a few minutes.

Glucose reaches a muscle from the bloodstream, which it might enter from the digestive system or be released into from the liver, where it either is stored as glycogen or has been resynthesized from lactate. Glucose can be delivered to muscles only fast enough to supply up to one-third of the energy needs of intense steady-state exercise, so incoming glucose alone is not sufficient to produce high power levels. However, an adequate blood-glucose level is essential, because glucose is also the primary fuel for the brain. If exercise depletes the body’s supply of glucose, allowing levels in the blood to drop, a bicycle rider will feel weak and dizzy (hypoglycemic). Periodic intake of carbohydrates (for example, in a sugar drink) is effective in preventing this condition and is also somewhat beneficial for longer-duration exercise performance.

Once glucose enters a muscle cell (fiber), it can release energy in one or two steps. The first (anaerobic) step is to split in half to form two lactate molecules, with each half also giving up hydrogen to form pyruvate. It might be appropriate to term pyruvate a carbohydrate fuel also, but since it apparently is not stored or transported, it is presented here as a mere temporary intermediate compound. This decomposition, called glycolysis (a term also commonly misapplied to the splitting of muscle glycogen, which is more properly called glycogenolysis), releases only about 7 percent of the energy available in the glucose, but it can occur rapidly without using oxygen.

The second step proceeds in either of two ways. If the pyruvate is taken into the muscle cell’s oxidative structure (mitochondria) and enough oxygen is also taken in, the other 93 percent of the energy is released aerobically in its conversion to water and carbon dioxide. This aerobic process of generating ATP produces roughly equal amounts of heat and available energy from the synthesized ATP, so that the steady-state formation of ATP is about 50 percent efficient. (The 50 percent efficiency of forming ATP aerobically and the 50 percent efficiency of using ATP to power the muscle, noted earlier in the chapter, lead to an overall aerobic “fuel efficiency of working” of about 25 percent.)

On the other hand, if the pyruvate is not oxidized in this way because there are too few mitochondria in the muscle cell to process the amount of pyruvate being produced, it simply regains its hydrogen to become lactate. The body must quickly clear lactate created in anaerobic glycolysis (more usually, glycogenolysis, since glucose cannot be delivered very quickly, and glycogen stored in the muscle is readily available) from the muscle fiber if it is to continue functioning. The accumulation of too much lactate in the blood will also put an end to exercise through the increasing pain that results as it accumulates.

In exercise at very high power levels, lactate concentrations in the blood may become unendurable within 30 s. However, at somewhat lower power levels, it may take quite a few minutes to reach that condition, both because less lactate is being produced and because the body’s lactate-removal system is able to handle most of it.

The essential point to remember is that glucose can be used either slowly and completely, achieving a high yield and medium power level, or rapidly but incompletely, achieving a low yield and high power for a short time only. Although an excessive accumulation of lactate prevents further work, lactate is far from a worthless poison: it is a highly significant fuel, since most of the energy of the precursor carbohydrate remains within it to be used. Apparently, lactate is reconverted to pyruvate, either in the liver, where it is further reconstituted to glucose, or in a muscle fiber, where it can be oxidized to perform work, or it can even be restored to glycogen. (The specific outcome apparently depends on a person’s state of fatigue and level of hunger and whether exercise continues.) This highly mobile energy form’s transport around the body for local use has been termed the lactate shuttle (Brooks, Fahey, and White 1996). However, the literature is not very definite on many issues collectively referred to as the fate of lactate.

As is discussed later in the chapter, some lactate is produced even at low and medium aerobic power levels. In exercise at a constant rate, the concentration of lactate in the blood will climb to a fixed level, usually less than 5 millimoles (mmol)/L, related to exercise intensity and removal rate. If lactate is produced at a rate greater than it can be cleared (stored, oxidized, or reconverted), then its concentration in the blood begins an upward trend that will eventually terminate working through the mechanisms just discussed. The critical exercise intensity that produces lactate at this rate is termed the onset of blood-lactate accumulation (OBLA) (McArdle, Katch, and Katch 1996).

In recent years it has been generally accepted that elevated lactate concentration defines the highest tolerable steady-state (i.e., over the range of 20 to 120 min) exercise intensity. However, a welter of terms and proposed definitions have somewhat muddied matters. Such concepts as the lactate threshold and anaerobic threshold (now considered a misnomer, because lactate elevation is not usually due to an inadequate oxygen supply) have also been defined, either when lactate reaches a specific concentration (4 mmol/L) or at the point at which the slope of the plotted relation between steady-state concentration and exercise intensity increases. (The ventilatory threshold, or onset of panting, was originally believed to mirror the lactate threshold; however, Brooks, Fahey, and White [1996] have clarified that the near-simultaneous onset of panting as the lactate threshold is reached is mere coincidence.) Elite riders in a 10 to 15 min race may reach blood-lactate concentrations of 15 mmol/L, whereas in a 1 h race the lactate level is below 8 mmol/L because of the lower intensity of the power output.

Glucose is first in this section for reasons of simplicity, not of importance. Far more important to athletic muscle power than glucose itself is its starch, muscle glycogen, a long-chain polymer of glucose. Fuel for 1.5 or even 3 h of high aerobic power can be stored within working muscles in the form of glycogen, which unfortunately is incapable of moving from well-stocked fibers to others from which it has been depleted; its energy can be transported to other fibers only in the form of lactate. Muscle glycogen is typically 2 percent of a rider’s muscle mass, if the rider is on a normal diet. It is one-quarter of this, or 0.5 percent, if the rider is on a low-carbohydrate diet, and it can be up to 4 percent after the depletion and overfeeding scheme known as carbohydrate loading or glycogen supercompensation. Glycogen is stored in muscles with three times its mass of water, so a person with 20 kg muscle mass engaging in carbohydrate loading may store up to 4 percent × 4 × 20 kg = 3.2 kg of glycogen with its accompanying water.

Muscle-stored glycogen can be degraded to pyruvate extremely rapidly compared to glucose, as glycogen does not have to travel through the bloodstream as glucose does. The pyruvate created through glycogen degradation can be used aerobically just as fast as the muscle mitochondria can process it (unless the oxygen supply is artificially restricted; see Coyle et al. 1983), and thus the combination of incoming glucose and muscle-stored glycogen produces higher aerobic power than incoming glucose alone.

To achieve power levels higher than a muscle’s mitochondria and the body’s oxygen-delivery systems can support, anaerobic glycogenolysis (pyruvate generation) can be increased to far higher levels than in aerobic work. In producing two or three times the maximum power level available through aerobic glycogenolysis, while releasing only 7 percent of the fuel’s energy, anaerobic glycogenolysis evidently degrades glycogen thirty to forty times as fast as in complete oxidation. Thus the anaerobic version of the process, in just a few minutes of intense effort, can deplete a store of glycogen sufficient for a 2 h aerobic effort, although rapid lactate accumulation may prevent this depletion from occurring all at once. The immediate aftermath is a painfully high blood concentration of lactate. (The time required to achieve a given lactate level depends, as noted earlier in the chapter, on how much the production rate exceeds the clearance rate.)

Fat: The Fuel for Very-Long-Duration Effort

Fat is the final fuel in our list. Fats belong to a larger group called lipids. There are many different fatty compounds, composed principally of numerous carbon atoms with up to twice as many hydrogen atoms, plus relatively few atoms of oxygen. Because both its carbon and hydrogen are available to combine with oxygen, fat releases about twice as much energy per gram as carbohydrates. Furthermore, unlike glycogen, it is not stored with additional water. Body fat, our major energy store, is principally triglyceride, a glycerol molecule joining three fatty-acid molecules. For fat, which is not soluble in the blood, to travel in the bloodstream, the fatty acids are joined to proteins to form lipoproteins, which are.

Fat is used only aerobically and for most of us is solely a low-intensity fuel. It supplies most of the body’s energy needs at rest and during exercise up to medium intensity. However, it takes considerable time to reach the muscles and is taken up by the muscle cells relatively slowly. At its greatest delivery rate, it supplies oxidative energy more slowly than muscle glycogen. However, the body holds enough stores for many days: fat stores can fuel weeks of effort. The typical human body stores 200 to 800 megajoules (MJ, ~50,000–200,000 kcal) as fat, because completely oxidized fat yields 37 kJ/g (9 kcal/g), enough energy for 100–200 h of hard work (or more realistically, 200–400 h of moderate work interspersed with rest). Stored glucose and glycogen can furnish only 1–2 percent of that amount of energy.

There are two opposite reasons to maximize fat utilization or lipolysis instead of using up carbohydrates: on one hand, to allow extremely long-duration efforts without “refueling,” and on the other, to lose weight. Although intense exercise will result in quick weight loss, it will mainly be in the form of carbohydrates and water. It is possible to metabolize an entire kilogram of glycogen in a hard ride, which also means losing its associated 3 kg of water. As prolonged high-intensity effort is reckoned to inhibit fat utilization, exercise at that level may hardly touch the body’s fat stores. In any case it is not possible to cycle at high power for long periods without replenishing glycogen with food, drink, or both. In exercise at low intensity, mainly fat is oxidized, but of course very little. This is good if it is necessary to carry on for days or weeks without food, but inefficient if the object is to get rid of body fat. In exercise at medium intensity, roughly half the energy used comes from fat, but in absolute terms its usage may be at a maximum of, say, 0.25 g/min (see Croci et al. 2014), so it would take about a whole week of daytime effort to lose 1 kg of fat.

Daley (2018), using research by Venables, Achten, and Jeukendrup (2005), has developed an online calculator for the ratio of fat to carbohydrate usage as a function of heart rate, for example, about 1:1 at 65 percent of maximum heart rate. (A rule of thumb for the maximum heart rate in beats per minute is 220 minus age in years.)

However, the foregoing statements must be further refined with respect to time: Güntner et al. (2017) show that it takes a while for the body’s fat metabolism to begin and then it can stay high or increase even when resting, in especially pronounced cases, up to 3 hr after exercise if nothing is eaten, with strong variation from person to person. About one-third of the subjects Güntner and colleagues tested showed a significant increase after 1–1.5 hr, another third showed a slower linear increase from the beginning, and the final third little correlation. A compact breath sensor developed at ETH Zürich allows individuals easily to determine the onset of their lipolysis, as described by Bergamin (2017), thus removing the uncertainty. The sensor measures acetone, which correlates with lipolysis onset.

“Fat burning” is a widely and somewhat controversially discussed subject. Proponents say that repeated bouts of short, high-intensity (interval) training causes the body to rapidly shift into “fat-burning mode.” This assertion appears contradictory to the previous statements in favor of low-intensity steady-state training, but the contradiction can apparently be resolved through the use of both strategies. It might be worth pointing out, in the context of this book, that cycling for transportation and touring can usually provide both: hills and traffic lights (which involve accelerating after stops) automatically motivate periods of high-intensity work, and level sections of terrain permit any desired rate of low-intensity work.

Muscle Fibers

A muscle is typically controlled by 50–500 nerves. Each nerve controls a bundle, or motor unit, of several hundreds or even thousands of muscle fibers, of which there are three types (discussed later in the section). Each fiber is a single hairlike cell (between 0.01 and 0.1 mm thick and sometimes as long as the muscle) containing a great many force-producing protein filaments known as myofibrils. The fibers in any one motor unit are all of the same fiber type, and those of each motor unit are intertwined with fibers from nearby motor units within the muscle. The proportion of each type of fiber, in a given muscle of a given person, is found to be mostly unalterable. Furthermore, the total number of fibers in a muscle is considered fixed early in life: muscle dimensional changes are due primarily to hypertrophy (increase in size) of the constituent fibers.

Three fairly distinct types of muscle fiber can be distinguished by chemically staining a muscle cross section: slow oxidative, fast glycolytic, and fast oxidative glycolytic. Each type differs in how it uses fuel and produces force and work, although the differences among them in these areas may not always be marked, as cells adapt through training: their behaviors are actually placed along a continuum. Any one muscle is composed of a mixture of the three types, all more or less adapted through training to either endurance (aerobic) or force or power (immediate and glycogenolytic) activities.

At one end of the spectrum, slow oxidative (SO) fibers (also known as Type 1 fibers) are richly supplied with oxygen-using mitochondria. They are reddish because of the oxygen-storing myoglobin they contain, as in the dark meat of a chicken. Endurance training can increase both the mitochondrial density of and the number of capillaries supplying oxygen to these fibers substantially. SO fibers are ideal for steady-state (endurance) activities, taking up oxygen at the highest rate to metabolize glucose, glycogen, or fat aerobically. They never grow very thick and exert relatively little force. They respond slowly to nervous stimulation and so are referred to as “slow-twitch” fibers. They have little ability to support rapid, oxygen-free liberation of carbohydrate energy (anaerobic glycolysis or glycogenolysis). On the other hand, they are able to contract repeatedly without fatigue. Since this type of fiber actually produces steady muscle force through repeated contractions of individual fibers, postural muscles tend to be composed of SO fibers.

At the other extreme, fast glycolytic (FG) fibers (also known as Type 2b fibers) respond faster and more forcefully to nervous impulses. They largely lack both mitochondria and myoglobin and hence are pale, like the white meat of a chicken. They have a metabolic predilection for rapid anaerobic conversion of glucose or glycogen into lactate, producing high force and power with little delay (“fast twitch”). They are frequently described as “fatigable,” presumably through glycogen depletion or lactate accumulation. Through overload training, FG fibers can be enlarged in cross section, therefore increasing short-term muscle strength fueled either by carbohydrate or immediate sources (ATP and PCr). It has been suggested that glycogen stores can be higher in FG than in other types of fibers and that they are much better at using PCr.

A third type of fiber is the fastoxidative glycolytic (FOG, also known as Type 2a). It is believed that some FOG fibers may be converted from FG fibers as a result of endurance training. If so, they give up some glycolytic capacity for a substantial boost in aerobic ability. Textbooks describe FOG fibers as combining characteristics of SO and FG fibers.

As suggested earlier in the chapter, each power level muscles are commanded to exert invokes some combination of fuel transport and conversion mechanisms. Exhaustion of one resource or saturation with one waste that is not being removed fast enough will determine duration at any given power level. A lesser rate of using fuel or producing waste will therefore permit longer duration. Differences in the physiological mechanisms operating at different power levels would also be expected to alter the duration until exhaustion.

Fiber Recruitment

The proper selection of muscle fibers to perform a given task is important. For example, short-term gains in weight-lifting ability can be attributed to improved fiber recruitment, rather than actual muscle-strength gains. If glycolytic motor units were recruited first for endurance (low-force) activities, they would quickly become depleted of glycogen without making use of much of the available oxygen. Although motor-unit recruitment is not directly under conscious control, it does seem to be a function of the central nervous system.

High-Power Aerobic Metabolism: Lactate Threshold and Glycogen Depletion

Not all of the physiological mechanisms defining an individual’s power-duration curve have been studied to the same degree. Two that have received considerable attention, highest steady-state power (aerobic) and highest power sustainable for 1–2 min (anaerobic), relate to important types of cycling efforts.

High-power aerobic metabolism operates as follows: the highest power levels sustainable for about 30 min or longer are essentially steady state, neither using up any rapidly depleted resources nor increasingly accumulating painful lactate. From minute to minute, virtually all the power produced through such metabolism involves inhaled oxygen.

Carbohydrate stores—depletion of muscle glycogen or even blood glucose—often set the maximum duration of such high-intensity steady-state efforts. Sometimes other factors such as dehydration or cramping also play a role. Experiments described in textbooks comparing initial muscle glycogen to maximum possible duration of effort have amply confirmed that in well-trained endurance athletes, at least, muscle glycogen is the limiting resource that terminates hard steady-state effort (i.e., determines endurance). In addition, measurements of glycogen levels in both legs when only one leg is allowed to pedal (Åstrand and Rodahl 1977, chap. 14) show that glycogen is not mobile: the working leg depletes its stores and is exhausted, whereas the resting leg remains fully charged.

Increasing the energy delivered by the body’s fat system or the pedaling rotations per minute (the reduction in pedal force reduces fast-twitch-fiber recruitment, with its associated anaerobic glycogenolysis) can reduce consumption of muscle glycogen in cycling. Furthermore, muscle glycogen stores can be supercharged through carbohydrate loading: depleting glycogen stores substantially over 2–4 days, then eating a superabundance of carbohydrates. This process has proved to double the levels of endurance achieved by normal well-fed but “unloaded” persons. Since muscle glycogen is also useful in shorter, more powerful efforts, carbohydrate loading would seem to be a useful practice for all but the shortest events. Since glycogen regeneration after consumption and depletion is supposed to take more than a day, an important question concerns the size of the glycogen stores that athletes can maintain in multiple-day events.

In the past, it was widely believed that the maximum rate at which fuel could be oxidized was set by the rate at which the lungs and the body’s circulation could deliver oxygen to the working muscles and that this rate could be determined in a test of VO₂max (maximal oxygen consumption), as described by Daley (2018) and later in the chapter. However, at least for athletic endurance cyclists, this is no longer believed to be generally true. Instead, the rate of fuel oxidation seems to be limited by the somewhat lesser rate at which working muscles can oxidize fuels without excessive lactate production, which depends on the total mass of muscles being used, their fiber type, and their degree of adaptation (via mitochondria and capillaries) to oxidizing fats. The most effective fibers for taking up oxygen are the relatively weaker and slower-acting slow oxidative fibers. Appropriate training can double the capacity of these fibers to use oxygen. (Their weakness is not a problem for the cyclist, since the typical foot force produced in long cycling events is only about 10 percent of the maximum achievable pedaling force.)

As there is no obvious connection between the maximum steady rate at which muscles can take up oxygen and VO₂max, the latter ought to be power limiting in at least part of the population. (Coyle et al. [1983], discussing heart-disease patients, offer an extreme example of this.) However, even if this is true, individuals with limits set by VO₂max should be expected to be few among successful competitors (Brooks, Fahey, and White 1996). It is now believed that the blood-lactate level arising from the balance between lactate production of the working muscles and various mechanisms for clearing lactate determines the maximum work intensity most individuals can tolerate. A small amount of lactate is produced whenever pyruvate is available, that is, whenever carbohydrates are used as fuel. Much more is produced when SO fibers are required to produce more than a certain amount of energy from carbohydrates, or when FG fibers are recruited, or when a fiber has a poor oxygen supply. The rate of lactate production can then overwhelm the body’s lactate-clearing capacity, which typically seems to occur quite independent of how much oxygen the circulation can deliver. Training reduces the amount of lactate produced at any given workload and increases the rate at which it can be used (cleared), therefore reducing the level of lactate in the blood. In addition, training can increase the body’s ability to tolerate elevated lactate levels.

Up until 1990, no consensus had been reached about precisely how to define the body’s lactate threshold—for example, as a concentration level, as a slope change, or as an increase in concentration above the baseline. A seemingly rational definition is OBLA, the exercise intensity at which blood-lactate concentration can no longer remain steady: production exceeds clearance, and the blood-lactate concentration climbs inexorably until exercise ends.

There is good reason to expect that pedaling styles or devices that allow the use of a greater mass of muscles will increase a rider’s maximum steady-state (i.e., aerobic) power level. Indeed, it is widely accepted that top Nordic skiers, who use their arms as well as their legs, tend to take up more oxygen than top cyclists and so produce greater steady-state power.

Riders are known to exhibit reduced aerobic power as they age. Figure 2.8 plots average speeds in 50 mi time trials versus age and estimates breathing capacity from the speeds.

Evaluations of pilots for the Massachusetts Institute of Technology (MIT) Daedalus flight in the 1980s yielded some interesting physiological data from a maximum-power long-term effort. These evaluations required the pilots to pedal for an estimated 4 h. As shown in figure 2.9 (Bussolari 1986–1987), two subjects were required to pedal at 70 percent of their maximum aerobic power and were monitored through measurements of their inhalation and exhalation and through blood samples taken periodically throughout the 4 h. They were allowed to drink as much as they wished. The solid lines in the various panels of the figure show the data for a female pilot who, according to Steven Bussolari, who conducted the study, had engaged in carbohydrate loading before the test and drank periodically throughout. She finished the 4 h in a condition good enough to have allowed her to continue for another 30–60 min. The dashed lines show the data for a male pilot who did not attempt carbohydrate loading, drank less than half the quantity of liquid that the female pilot consumed, and had to quit after 3.5 h because of leg soreness and cramping. As the figure shows, these discomforts were not brought on by a high lactate level.

High-Power Anaerobic Metabolism: Lactate Accumulation and Fast-Twitch-Fiber Population

In significant anaerobic efforts such as a sprint or climbing a short, steep hill, the muscles involved output far more power than the maximum aerobic power, by a factor of three to six, initially produced using the immediate fuels ATP and PCr. As those compounds are depleted, the power exerted by the muscles drops to a lower level, supplied primarily through the anaerobic glycogenolysis of muscle glycogen. As mentioned earlier, this results in a massive release of lactate.

When high-power work is performed for a very short time only, the glycogenolytic system is hardly engaged; the anaerobic fuel systems do not build up any lactate. This is one principle behind so-called interval training: great effort can be expended repeatedly, if the duration of such effort is kept short.

High-power anaerobic (both immediate and glycolytic) metabolism is predominant in the 5–20 s range of exercise duration. For lesser efforts, causing exhaustion in under 2 min, oxygen-derived power still represents less than 50 percent of the total energy expended (and some oxygen is already stored in muscle myoglobin), so an outstanding oxygen-using system is presumably of little value in such efforts.

Although lactate buildup ends high-power glycogenolysis, repeated intense efforts will actually deplete FG fibers of their glycogen. Therefore, to be able to perform a large number of sprints, for example, a superabundance of glycogen, which can be developed through carbohydrate loading, would be desirable.

A muscle’s anaerobic work capacity, determined in critical-power curve fitting, suggests a rapidly deliverable “reserve quantity” of work. Presumably anaerobic work capacity can be approximated by measuring the stores of immediate fuels and adding an amount of muscle glycogen sufficient to raise blood lactate to intolerable levels when consumed. Some riders can tolerate higher lactate levels than others, however, and some riders can clear lactate faster than others. In addition, drinking a solution of bicarbonate of soda can help buffer blood lactate, thus permitting somewhat longer effort at very high power. (This is not considered to be doping, but it does have side effects in the intestinal tract.)

The fibers best adapted for brief, high-power activities are the FG and maybe the FOG fibers. Part of the adaptation of these fibers to these activities is a growth in volume (cross-sectional area) that provides for more work-producing protein and greater force, which shows up as a larger muscle. In addition, there are enzymes that catalyze the conversion of glycogen to lactate, and their levels must be adequate for this conversion to take place.

A high population of enlarged fast fibers is probably necessary to produce the maximum level of glycogenolytic power possible. However, the literature repeatedly stresses that this is not the whole story, inasmuch as some very strong people, including bicycle sprinters, do not have particularly large muscles. It seems that the ability to recruit the proper fibers at precisely the right time is also important. Whether this facility is innate, as opposed to trainable, is little discussed in the literature.

Food and Efficiency

As explained earlier in the chapter, muscles have an overall aerobic fuel efficiency of about 25 percent. Tests performed by Pugh (1974) on bicyclists riding on an ergometer and on a track confirmed that the work produced accounted for about 25 percent of the extra fuel used. Bussolari (1986–1987) and Bussolari and Nadel (1989) quote 24 percent and give detailed measurements partly summarized in figure 2.10 (p. 86). In addition to the five rather similar pilots whose results are shown in the figure, Bussolari and Nadel tested twenty others and reported mechanical efficiencies between 18 and 34 percent at aerobically sustainable power levels, per body mass, of 3–5 W/kg. If the roughly 1 W/kg that is additionally required for basal metabolism (see discussion later in the chapter) is counted, the total efficiency is less, especially at low power levels. Zommers (2000) comprehensively summarizes food efficiency, and for pedaling about 60 rpm at low power right up to the anaerobic threshold, finds 22–24 percent for net efficiency or working efficiency. These terms use the total power metabolic input measured during exercise but then subtract that measured when sitting on the ergometer without exercise. See also the next section.

There are several ways of defining food’s usable energy content (see FAO 2003). The values published in tables or on food packets generally use 37 kJ/g (9 kcal/g) for fat, 17 kJ/g (4 kcal/g) for carbohydrates and protein, and 8 kJ/g (2 kcal/g) for dietary fiber. Not all of this energy content is available to the body’s muscles, however, as there are several losses. The largest is from digestion itself, which produces heat (thermogenesis or thermic effect of food), which reduces the previously quoted numbers somewhat depending on the actual food and individual—by up to 25 percent for proteins. Also, humans cannot digest practically any of the cellulose or lignin content in food (e.g., the insoluble parts of dietary fiber), so the energy contained in these is not counted in human nutrition.

Eating a 50 g snack bar with an energy content of 1 MJ (= 1 MWs ≈ 0.278 kWh) per hour theoretically provides continuous 278 W metabolic power or 69 W mechanical power for one hour, assuming 25 percent efficiency and not counting basal metabolism. That is enough for ordinary cycling.

At low power levels there is no immediate correlation between power and food eaten, as it is masked by considerable body stores and basal metabolism, so counting calories is not suitable for measuring performance except over long periods. However, food must be oxidized for the body to use it, and as the body stores only a few breaths’ worth of oxygen, measuring oxygen usage during breathing is a far faster method for conducting such measurements.

Oxygen Uptake and Metabolism

Measuring oxygen (O₂) usage or carbon dioxide (CO₂) production is potentially a very powerful tool for revealing how much “fuel” is being metabolized to supply a person’s total energy needs, and both O₂ usage and CO₂ production can be calculated through a process called indirect calorimetry. Knowing the metabolic power P_M (the rate of food-energy consumption) is useful on the one hand for planning food requirements and on the other hand for deriving the actual mechanical power provided by the muscles. The latter can be calculated as the difference between P_M measurements while working and at rest times aerobic muscular efficiency. The following observations are general but in part apply to standard air pressure near sea level and about room temperature. High-altitude effects are discussed in chapter 3.

For greatest precision the actual amounts of consumed O₂ and exhaled CO₂ are measured, that is, the volume per minute breathed times the diminution in O₂ concentration and the CO₂ increase in the exhaled air. The analysis can be performed either continuously with stationary or wearable equipment or after the exhaled air has been collected in a Douglas bag.

The same calculations can also reveal which fuel is being consumed. When carbohydrates are oxidized, every O₂ molecule is converted to a CO₂ molecule. Thus a 1:1 ratio of CO₂ to O₂ (the so-called respiratory quotient, or RQ) indicates a state of pure carbohydrate usage. On the other hand, when fats are oxidized, only about 70 percent of the O₂ forms CO₂; the rest creates water. Thus a CO₂:O₂ ratio of 0.7:1 indicates a state of pure lipid usage. For ratios between 0.7:1 and 1:1, the proportions of carbohydrate and fat usage (assuming no oxidation of protein; see discussion later in this section) can be calculated. Fat oxidation yields 4.70 kcal/L (~19.7 kJ/L) O₂, whereas carbohydrates deliver 5.05 kcal/L (~21.1 kJ/L). Thus 1 L/min of O₂ consumed (which means breathing 20–25 L/min of air; see discussion later in this section) represents 352 W metabolic power for carbohydrates or 328 W for fat. If we subtract 80 W basal metabolic power (see discussion later in this chapter) and assume 25 percent efficiency, this represents 68 W mechanical power.

For intermediate metabolic values Weir (1949) devised a formula still in use today. A derivation for metabolic power P_M in watts is

P_M = MV %CO₂ (2.72 / RQ + 0.766),

in which MV is the minute volume (volume breathed per minute) in liters per minute, %CO₂ the CO₂ in the expired air in percent, and RQ the respiratory quotient given in the preceding paragraph. (For P_M in kcal/d, multiply by 20.65.) If RQ is known or can be estimated or assumed, only one of the gases need be measured. The CO₂ rather than the O₂ concentration is specified in the equation because it is easier to measure. If an average value of RQ = 0.85 is used, a particularly simple approximation emerges: P_M ≈ 4 MV %CO₂.

Weir’s exact formula includes a term for protein consumption, which could be determined by measuring urinary nitrogen. Proteins contain about 16 percent nitrogen, and 1 g in urine corresponds to almost 6 L of O₂ breathed. Consumed proteins deliver about as much energy as carbohydrates but have a lower RQ of 0.82. One needn’t bother with the exact formula normally, as the food most people consume contains 11–14 percent protein (Weir 1949). The simplified Weir formula in the last paragraph is adjusted for 12.5 percent protein, and even if other amounts of protein are consumed, the resulting error is small. (Given a free choice, most people will tend to eat in such a way that protein supplies about 14 percent of their metabolic power. If one eats primarily protein-poor foods containing almost only carbohydrates and fat, one has to eat too much in order to achieve the 14 percent and will gain weight. Highly sugary drinks and energy bars may be good fuels for heavy cycling but are otherwise too protein deficient. Protein bars are also available, but nuts and dried fruit are likely to be healthier.)

Another caveat is in order: over the short term, not all energy is produced via oxidation. Brief, intense efforts rely on immediate fuels and anaerobic glycogenolysis, and their oxygen cost is deferred. (And after exercise ends, changes in, for example, body temperature alter the basal metabolism, thus obscuring total fuel usage, because it is taken as being constant.) Oxygen measurements at unsustainable exercise intensities do not reflect steady state and must be interpreted cautiously.

Humans normally tend to exhale with a relatively constant CO₂ concentration of 4–5 percent (the coauthor 4.5–4.6 percent at rest). This is because the urge to breathe is already apparent at 5 percent and becomes very strong at 6 percent. At the other end of this range, CO₂ concentrations below 4 percent require deep or fast breaths even at rest, and “hyperventilating” at 3 percent is laborious.

If 5 percent is taken for the carbon dioxide concentration, the formula becomes P_M ≈ 20 MV, or if 4 percent is selected, P_M ≈ 16 MV, both for RQ = 0.85. Knipping and Moncrieff (1932) give P_M = 14.63 MV, which implies %CO₂ slightly above 4 percent, RQ slightly under 1, or both, as well as that 24 times the volume of O₂ absorbed must be breathed as air. For 5 percent CO₂ and RQ = 1, the figure is 20.

Measuring MV requires special equipment, so the foregoing rules of thumb are not very useful directly. However, measuring the breathing rate (BR, the respiratory frequency, or breaths per minute) is easy, and MV is BR times the tidal volume (TV, volume of a breath in liters). The latter is often taken to be 0.5 L for adults (or 7 mL/kg body mass) at rest. For TV = 0.5 L at 5 percent CO₂ and RQ = 0.85, metabolic power in watts is found to be P_M ≈ 10 BR. At 4 percent CO₂ and RQ = 1, it would be about 7.3 BR.

These rough estimates can be refined somewhat, as TV itself increases with BR. To estimate power from BR alone requires a known relationship between MV and TV. While there is a considerable amount of data at resting metabolism (e.g., from hospital patients), there is little to be found at higher power levels. Mathur (2014) plots BR and TV versus mechanical power, compiling various sources. If a single function is fitted to these plots, an approximate curve fit gives P (not P_M!) ≈ 200 ln(BR) − 515, with the units used previously. For what type of person and which conditions this equation is meant to apply and how accurate it could be are not shown, but it works quite well for the 78 kg coauthor for medium power levels, assuming that the resting metabolic rate (see discussion later in the chapter) is considered. Nicolò, Massaroni, and Passfield (2017) use a different approach and find a linear relationship from “fairly light” work at 65 percent of the subjects’ maximum breathing rate to the maximum “very very hard” work at the maximum breathing rate. To sum up, then, preceding paragraphs have given formulas for P_M, and this one, for (net) working P. Some of these formulas are given for use in the form of spreadsheets in Schmidt 2019.

Alternatively, once calibrated, a given individual’s heart rate (HR) can also provide an approximation of oxygen usage and power. For example, see Perez, Wisniewski, and Kendall 2016–2017, in which P = 2.5 HR − 200 approximates the measurements of two men using exercise bicycles, with P in watts and HR is in beats per minute.

If the oxygen usage rate is plotted for an increasing sequence of intensities of a particular exercise (allowing appropriate time for somewhat steady conditions to develop), the curve often shows a relatively sharp “knee” and levels out at an apparent maximum in oxygen uptake for that exercise. Even short, intense efforts can elicit the maximum uptake. This maximum rate of oxygen delivery, VO₂max, was long believed to represent a systemic (heart and lung) limitation on oxygen delivery. Although such a limitation surely does exist, it is more likely that a bicyclist’s VO₂max actually represents the working muscles’ ability to take in oxygen. Different exercises, for example, have been found to lead to somewhat different values of VO₂max for the same person.

VO₂max may relate primarily to heart-stroke volume, which can be increased 10–15 percent with training, and blood hematocrit (red-cell concentration), which can be elevated through artificial means such as altitude training, blood doping, or use of the hormone erythropoietin (EPO). Even intense training cannot increase VO₂max much, however, in those who are already pretty fit. Tables of normative values available from various sources suggest that the VO₂max values of the very unfit are about half that of the very fit (at the same age), and that about the same factor applies to the old compared to the young (at the same fitness level), but that very fit old people are a bit better off than very unfit young people.

A focus on VO₂max dominated exercise studies for a long time. Nowadays some version of the lactate threshold (e.g., OBLA) is seen as the trainable limit. VO₂max is frequently well above this limit (and in any event is not very trainable). This new perspective on performance determinants encourages a cautious optimism that employing more large muscles could permit bicycle riders to put out greater long-term power, perhaps even approaching their systemic limit to oxygen delivery. Bicycles with both hand and foot cranking are continually being reinvented to this end. The lack of notable racing-performance success with such bicycles hints at an array of difficult requirements, including a smooth energy-conserving pedaling motion and the ability to pedal and crank hard without disturbing the steering. (This is one arena in which ergometer-based success should clearly precede construction of an on-road prototype!). Although VO₂max does not obviously define maximum steady-state pedaling power, it cannot yet be ignored altogether as a determinant of athletic performance. Certainly ease of breathing has an effect on performance. This is also dependent on the pedaling position and is discussed further later in the chapter.

Energetics in Pedaling

In ideal circumstances, the (extra) energy cost of pedaling could be attributed directly to the work done on the pedals. However, in practice, some muscles (not necessarily in the leg) are used during pedaling in isometric or even in eccentric contraction. Furthermore, using or replenishing the various fuels that feed the muscles in use has various immediate and delayed metabolic costs. We do not know the relative contributions to fuel inefficiency of each such factor.

It is obvious that other, nonpedaling muscles are increasingly engaged at high-force or high-cadence pedaling. When force is high, a bicycle’s rider must use these muscles to prevent being lifted from the saddle or slid along the seat. The same is true at high cadence, when the momentum of the descending thigh mass tends to straighten the leg fully and lift the rider from the saddle. But it doesn’t seem that muscle use can be the only factor determining muscular fatigue. One of the main conundrums in studies of pedaling is why a lowered seat should so greatly harm performance, since the same work is being asked of the same muscles.

Quite a few muscles actuate the joints of the leg (see figure 2.6). Confusion about the functions of these muscles can be reduced by first concentrating on the one-joint muscles, namely, those that cross just one joint. It can be seen that each joint has at least one muscle situated to extend it and an opposing muscle situated to flex it. These opposed pairs would not normally cocontract (i.e., exert opposing tensions simultaneously) when the goal is power production, because one would then be performing negative work, which irreversibly absorbs useful energy. (Cocontraction is instead a strategy used to enhance structural stiffness or to resist injury.)

What remains are two-joint muscles such as the rectus femoris and the long head of the biceps femoris, which exert torque about two joints without touching the intervening bone. The “logic” of these muscles can deviate from the simple logic of one-joint muscles. For example, both muscles just mentioned simultaneously shorten leg extensions such as those in jumping or pedaling. Therefore, in such motions, when these muscles are cocontracted, both perform positive work. (The initially surprising observation of these working muscles seeming to oppose each other is referred to as Lombard’s paradox.)

Basal Metabolism

The human engine has an additional characteristic not generally found in machines: it can’t be switched off, and some fuel must be consumed to keep it going even when it is at rest. (In this sense it is somewhat similar to a traditional steam plant, in which fuel must be burned continuously to keep steam pressure up even when no power is being delivered.) Human energy requirements are conventionally split into basal or resting metabolism and work metabolism.

Basal metabolism is usually expressed as the basal metabolic rate (BMR), but what is mostly meant is actually the slightly higher resting metabolic rate (RMR) (also called resting energy expenditure or REE). BMR involves a more complicated measurement representing really minimal bodily functions without digestion, and RMR represents the energy rate per day for normal living, but without physical activity. Both are usually given in kilocalories per day, or sometimes in kilojoules per hour, or in International System of Units (SI) units as power expressed in watts (1 J/s = 1 W). (Units common in the field require frequent conversions, as all usual time units from seconds to years are in use!) For example, 1,000 kcal/d (~41.7 kcal/h ~175 kJ/h) is ~48.5 W, and 100 W is ~2,065 kcal/d. The first example would correspond to an old and small person, the latter to a young and large person. Besides those in age and size there are differences due to gender and ambient and body temperatures as well as clothing. Several predictive equations exist and are available in countless online BMR calculators. The best known are the older Harris-Benedict (Harris and Benedict 1918) and newer, similar Mifflin-St. Jeor equations, both of which take gender, age, and body height and weight as inputs, presumably with “normal” temperatures and clothing. The Mifflin-St. Jeor equation gives BMR in kilocalories per day as (10 × weight in kilograms) + (0.0625 × height in meters) − (5 × age in years) + 5 (for men) or – 161 (for women). Lee and Kim (2012) list and compare these and a few other equations, but none seem to relate to the very important relationships between different temperatures and clothing, which can work in opposite directions: it is obvious that a cooler ambient temperature, lighter clothing, or both will increase metabolism, because more heat is lost from the skin. But a decrease in body core temperature of 1°C can cause a decrease in basal metabolism of 10–13 percent (see Landsberg et al. 2009). Lacking the results of unpleasant experiments, the question can be discussed (see, e.g., Selkov 2015) or the condition of a thermoneutral environment, in which a minimal BMR is defined to maintain core body temperature at 37°C, can be assumed.

The Weir formula given earlier in the chapter can also be used if breathing measurements are available. This gives the RMR if the subject is actually resting.

The main relationship is often expressed in terms of body (skin) surface area, for example, 936 (kcal / d)/m² (~45.4 W/m²) for young adult males, 888 (43.0) for middle-aged males, and 864 (41.9) for adult women (McArdle, Katch, and Katch 1996). Body surface area has been related to height and mass by a number of correlations, for example, the formula from NASA 1969 (given only for men):

Body area = 0.007184 M^0.425 (100 H)^0.725,

in which body area is measured in square meters, height H in meters, and mass M in kilograms. (Typical body areas for average men are 1.5–2 m².) This leads to the estimate of 1,750 kcal/d (~85 W) basal metabolism for a male of height 1.75 m and mass 75 kg, right between the Harris-Benedict and Mifflin-St. Jeor predictions.

Working Metabolism

The main part of the total metabolic rate P_M (described earlier) that is of interest here is that having to do with the mechanical work available for cycling. It can be derived by subtracting from P_M the metabolic rates not involved in productive work—that is, the BMR and thermic effect of food described earlier, and the thermic effect having to do with nonproductive movement that is not related to the cycling activity. What is left over after subtracting these can be called work metabolism or thermic effect of activity.

Work metabolism can be directly estimated as actual kilojoules or kilocalories of mechanical work divided by an efficiency factor, typically between 0.2 and 0.3. Each 100 W of mechanical power production thus requires a 333–500 W (280–430 kcal/h) rate of energy supply in food intake above that needed to maintain life and living. Thus where a normal meal of 500–1,000 kcal (or about 2–4 MJ) might be considered to supply 8 h of sedentary energy needs, an additional such meal is needed for each 1–2 h of cycling effort.

We acknowledge that our focus is mostly on the limits and potentialities of top athletic performances, generally involving people who may have embraced sport because they are naturally constituted for it. Of course, most pedaled distances are actually traveled by average persons at a far easier pace than that pursued in athletic competition and are less strenuous and more efficient.

Energy Cost of Cycling

From chapter 4 onward, this book examines in detail the various resistances affecting cycling and hence the energy cost for traveling a given distance or the power required for a given bicycle and speed. For the moment, taking typical values, two quite different examples are examined, with various different system boundaries each:

1. First, a person with a daily commuting distance of, say, 5 km (3 mi) at a speed of 15 km/h (9 mph), thus taking 20 min/d for this. Chapter 4 shows that the propulsive power required is approximately the same as the BMR described earlier, and if an efficiency of 25 percent from food to muscle power is assumed, four times this. Compared to the BMR of a whole day, however, the commute’s energy cost is less than 6 percent of this, and because even an office job involves more metabolic power than just the BMR (say, 20–40 percent extra), the food energy required for the commute is more likely to be 4 to 5 percent of the total amount. Affluent people, who have difficulty keeping their body weight anyway, will consider this small amount of energy “free.” Viewed just by itself, however, the trip costs roughly 400 kJ in food or 80 kJ/km or J/m, or if the BMR just during the trip time is included, roughly 100 J/m. It is low figures like this that give rise to claims of cycling being the most efficient form of transportation.
If the system boundary is widened further, the gray energy needed to produce the bicycle and the energy cost of the time required to earn money to pay for the bicycle could be included. If it is an expensive bicycle and the cyclist has a typical job that itself involves heavy energy use, the total energy cost of cycling is seen to be far from zero, but rather substantial, even if orders of magnitude less than that of owning or using a car.
2. Second, a hard-working professional cyclist, for example, a courier or racer, with, say, 8 h/d at several times the BMR. There is no question of this energy being “free.” If it is assumed that 150 km are covered during working hours at 150 kJ/km, about 23 MJ or 5,400 kcal food energy is required in addition to the food for living. As the latter is roughly three times less, it makes no great difference whether it is included in the energy for work or not. However, it does make a great difference whether the “whole cyclist” is considered part of the work purpose or not. If the former, the cyclist’s whole life, or at least his or her working life, must be included in the energy calculation, which then becomes extremely less efficient. In free societies, such costs are considered external, but somebody still has to pay for them.
Widening the system boundary further, the gray energy of even an expensive bicycle is less important than that of the food consumed. The latter can vary widely depending on what is eaten and how it is produced. Home-grown food can be nearly “free,” but a working cyclist won’t have the time or “energy” for this and will often buy highly processed foods that use up many times their food value to produce and transport. Viewed this way, employing a bicycle courier may not be more energy efficient than employing a courier using a motor vehicle, unless the cyclist both takes it easy and shops carefully for food.

This discussion shows that mainly the choice of system boundary determines whether cycling for a purpose (other than recreation or sport) can be considered energy efficient. It also gives a clue that “relaxed” cycling may be the most efficient overall, or perhaps “hybrid” cycling, as described in later chapters.

Experiments in the Amount of Breathing Oxygen Required

Detailed calculations relating to power as a function of oxygen breathed were presented earlier in the section “Oxygen Uptake and Metabolism.” The lungs of a young, average-weight male, at rest and not using any voluntary muscles, absorb roughly 5 mL/s (0.3 L/min) of oxygen, which corresponds to about 100 W thermal power. This quantity is in addition to any other absorption required by exercise. At the upper limits of steady-state aerobic athletic performance, more than 80 mL/s may be absorbed.

In ordinary air, 1 L of oxygen is found in about 4.8 L of air. However, about 24 L of air must be passed through the lungs for each liter of oxygen absorbed (see earlier calculation and Knipping and Moncrieff 1932). Thus, the human engine requires about 400 percent “excess” air. Most other engines, such as internal-combustion and steam engines, require only 5–10 percent excess air to ensure complete combustion of the fuel they consume. Gas turbines more nearly approach human lungs, taking in about 200 percent excess air. It should be stressed at this point that human metabolism does not operate like the described machines, which are heat engines and work by physically heating a material, which produces a force and an expansion. For the heat to flow through the machine, one part must be cooled to a lower temperature. Thermodynamics teaches us that the work capacity is tied to the available elevated temperature relative to that of the heat sink, often the environment, at a lower temperature. The fraction of the supplied energy transformed to work is limited by the second law of thermodynamics to (T_{2 −} T₁)/T₂ when temperature (T) is measured on the absolute scale. Therefore if the human body were a heat engine with T₂ = 37°C ≈ 310 K and T₁ = 20°C ≈ 293 K, its maximal efficiency would be 5.5 percent. Because the body’s maximal efficiency is actually about 25 percent, which as a heat engine would require an upper temperature as high as boiling water, it is clear that it produces work in a different way, such as in a fuel cell, in which chemical energy can be converted directly at a near-ambient temperature level. However, in both heat engines and fuel cells, energy not converted to power must appear as heat and be removed. (All animals, including humans, also excrete wastes that have some calorific heating value that should be included in a complete calculation.)

Figure 2.10 shows the relationship between oxygen absorbed and mechanical power delivered to the pedals for five volunteers piloting the human-powered aircraft Daedalus. Both the oxygen uptake and the power are given per kilogram of body mass, because of the importance of the power-to-mass ratio. For this series of tests a woman (other data for whom are given in figure 2.9) produced the best power-to-weight ratio, with “power” defined as 70 percent of the person’s maximal aerobic power, an output most endurance athletes can sustain for hours (some can achieve 80 percent). The final choices for volunteers were made among bicycling champions, who were taught piloting, which turned out to be easier than picking pilots and trying to make them into outstanding endurance athletes. The variation in oxygen uptake among the five individuals in good condition was not large.

Although not a strict determinant of physical work capacity, maximal oxygen uptake is commonly used as a rough indicator of potential and a useful normalizing quantity. Most people should be able to work easily at one-third of maximal uptake, but exceeding two-thirds of maximal uptake for a long duration may require considerable training. For a nonathletic, not-young person, the maximum oxygen-absorption rate (i.e., VO₂max) is assumed to be about 50 mL/s or 3 L/min (approximately 60 percent that of an elite competitor; see, e.g., Daley 2018). When such a person, riding a bicycle, is using a third of this oxygen-breathing capacity, the power output is about 75 W (~0.1 hp). An average fit man or woman could work under these conditions for several hours without suffering fatigue to an extent that precludes reasonably rapid recovery. A power output of this kind propels a rider at approximately 5.5 m/s (20 km/h, 12.3 mph) on a lightweight touring bicycle on level ground. Figure 2.11 collects miscellaneous data on caloric expenditure of bicyclists given by Adams (1967), Harrison (1970), and others.

Breathing ability decreases with age. An athlete’s peak breathing capacity comes at about age twenty, and as a rule of thumb, breathing capacity is halved by age eighty. Results of the 1971 UK 50 mi amateur time trials, in which the ages of the best “all-rounders” and of the “veterans” were given, are consistent with a breathing-based theory of performance. Panel (a) of figure 2.8 plots the average speed for each rider against the rider’s age. As the figure shows, there is no recognizable falloff in performance up to age forty, after which there is a steady drop to that for the oldest competitor, aged seventy-seven. In panel (b) of the figure, these performances have been converted to breathing capacity, estimated using Whitt’s (1971) method. When the curve is extrapolated to eighty years, the estimated breathing capacity is indeed very close to half the peak value. However, such reductions in performance with age could have a different explanation altogether: in today’s society, even an athlete may be sedentary 85 percent of the time. Maybe the falloff shown in figure 2.8 occurs particularly when a person takes a sedentary job.

Up to a breathing rate of about 0.67 L/s (40 L/min), people tend to breathe through the nose if they have healthy nasal passages. Nasal passages usually open during exercise, even when someone has a heavy cold. Above this rate, the resistance to flow offered by even a healthy nose becomes penalizing, and mouth breathing is substituted. A normally healthy individual riding on the level in still air on a lightweight bicycle reaches this limiting rate for nasal breathing at about 14 mph (6.3 m/s).

Pedaling Forces

Up to this point the chapter has been concerned with the production of mechanical human power, but it has not yet described how this power is actually transmitted to a wheel (propeller, etc.). Even if the mechanical transmissions are lossless, measurements show that more muscular power is involved than is actually available for propulsion, because the limbs’ movements cannot at all times transmit their forces in an optimal manner. The following sections describe efforts to match optimally the kinetics of the human body to those of a bicycle or vehicle.

Average Thrust

A steadily riding racing bicyclist tends to use very consistent but moderate pedal thrusts, amounting to mean applied tangential forces of only about one-third to one-sixth of the rider’s weight. The rider’s peak vertical thrusts are greater (approximately 1.5 times the mean) but still relatively small. No doubt this type of movement enables the rider to maintain a steady seat position and steer steadily.

It is easy to calculate from a bicycle crank length and a given pedaling speed the average value of pedal thrust required to achieve a given power output on that bicycle. The peripheral pedal speed around the pedaling circle can be used in the equation Average pedal propulsive force (N) = power (W)/foot speed (m/s), which presumes that only one foot is pushing at a time. Foot speed is determined as revolutions per second times the circumference of the pedal circle (typically 1.07 m). (To convert from newtons to pounds force, divide by 4.45.)

Detailed Pedal-Force Data

Hull and his colleagues (Newmiller, Hull, and Zajac 1988; Rowe, Hull, and Wang 1998) have taken precise pedal-force measurements to a high art. To permit such measurements, specially designed pedals are instrumented with strain gauges and calibrated to measure force components in up to three directions and possibly also twisting moments tending to bend the pedal spindle. Angle sensors are used to determine the orientation of each pedal relative to the crank and of the crank relative to the bicycle. A computer logs all data, typically hundreds of times per second. Coyle et al. (1991) offer some pedal-force diagrams, and figure 2.12 shows one provided by Radlabor-Smartfit. Panel (a) shows total force vectors and demonstrates that much of the force does not contribute to propulsion, mainly the radial components on the bottom half of the pedaling circle, shown in panel (b) graphed as a function of the crank angle. This isn’t as bad as it looks, as legs are accustomed to providing large nonproductive forces at low energy cost, as when standing and walking. The tangential force provides power, represented by the shaded area in panel (b), in this case 340 W at a cadence of 96 rpm, for a rider using drop handlebars. This figure includes the small amount of negative power between crank angles of about 190° and 350°. If the latter is subtracted instead of added, the effective power reduces to about 275 W.

Because of such pedal- and crank-orientation issues, pedal force is not the simplest way to measure pedaling power; sprocket torque or chain tension is easier, or dedicated devices. Pedal-force diagrams are mainly used for analysis, custom bike fitting, and rehabilitation. Measuring pedals like the Smartfit Pedalforce are meant for laboratory ergometers and are particularly fast, allowing athletes or patients to view their pedaling patterns as they pedal and improve them with a kind of biofeedback. Fonda (2015) gives an account how such methods can improve pedaling. Predictive or simulation software such as the online pedaling model of AnalyticCycling.com can also generate pedal-force diagrams; the latter model, however, does not include the inertial effects of the moving limbs.

Some care is required for proper interpretation of such results. In principle, if someone not exerting any muscle forces (apart from keeping the ankles from flopping) is strapped onto a bicycle, for each stationary orientation of the cranks, the feet will apply some force to the pedals, primarily because of the weight of the thighs and the elasticity of the uncontracted muscles. The effect of muscle elasticity can be demonstrated by sitting relaxed on a bicycle with no chain. Trunk inclination affects the at-rest crank orientation. The direction of the net force is roughly along the line from knee to pedal. If a motor then drives the cranks (while the passive person is properly strapped to the saddle), additional pedal forces will be observed, mostly relating to the acceleration and deceleration of the thighs, acting in roughly the same directions. These dynamic foot forces can become very great as pedaling cadence is increased.

If these purely mechanical, non-power-producing forces are subtracted from the actual measured forces of a pedaling person, what remains are the muscular forces, which alone create propulsive power. The mechanical forces almost totally obscure the muscular forces at the top and bottom dead centers of the pedaling motion and also on the upstroke. (In steady-state power production, a person’s slight tendency to lift while pedaling doesn’t usually overcome the weight of the leg.)

Once the partially obscured nature of the pedaling forces is appreciated, one might ask about optimal magnitudes and directions for pushing around the pedaling cycle. With the many different muscles in the leg, each with its own size, fiber makeup, and state of fatigue, such optimalities may never be specified in general. However, there is a very important observation to be made: it is widely supposed that muscular force in pedaling should ideally be oriented along the pedal path (i.e., perpendicular to the crank); otherwise some amount of force will be “wasted.” (In fact, the most common suggestion is that the total measured force should be kept tangent to the pedal path.) This supposition is generally invalid: the example of a piston engine shows that there is nothing inefficient about exerting a force along the connecting rod. As a general rule, better performance (power, efficiency, endurance) can be expected if the muscular force applied to the pedal is permitted to deviate somewhat in direction from tangency to the pedal path. In fact, Papadopoulos (1987), assuming only certain sets of muscles to be active, shows that constraining the force direction leads to the performance of negative work by some muscles and the irreversible absorption of mechanical energy. Zommers (2000) researches ankling, that is, moving the ankle joint in addition to the knee and hip, and finds the efficiency to be lower than with “normal” pedaling.

Constrained motions (e.g., a fixed-length crank forcing the pedal to move in a circle) allow existing muscles to furnish their maximum power. Unconstrained motions (e.g., a crank that freely telescopes), however, require the pedaler to exert a total foot force exactly perpendicular to the crank (i.e., constrained force) and should severely reduce the rider’s power, although as a training aid, they may encourage certain underused muscles to develop greater strength. An upright-seated pedaler can turn the pedal cranks via any of a variety of distinct pedaling styles. Some styles involve strong tangential forces when the pedals are at their upper and lower extremes, or in contrast a “thrusting” style with brief high forces during the downstroke, or perhaps an unusual degree of lifting force (or leg-weight reduction) on the upstroke. Others involve additional phased pedal thrusts to counterbalance high-cadence bouncing at the saddle or control of foot-force direction to avoid slippage when there is nothing holding the foot to the pedal. Side force at the saddle, the handlebars, or both or a rotational couple of forces at the handlebars may result from high pedaling torque. Upper-body bobbing or fore-aft sliding are not unusual at high effort levels. Many other techniques or styles may be recognized, only some of which are for extreme (high-torque or high-cadence) situations.

As an example, consider stand-up pedaling. If all the cyclist’s body weight during stand-up pedaling is applied to each pedal in turn, then crank torque is a simple rectified (i.e., positive-only) sinusoidal function with a fixed amplitude. Even if the rider’s arms share in the work by tipping the bicycle (a good example of a nonmechanism way to add arm work), power is strictly related to the body weight times the speed of the descending pedal. How can one change the stand-up pedaling torque so as to adjust pedaling speed? To increase pedaling speed, one could obviously also pull up on the rising pedal and increase crank torque to any level. But pedaling more slowly is normally not possible without changing gears, pausing at each dead center, or applying negative work with the rising leg.

Effects of Body Position, Pedaling Motion, and Rate

Up to this point, the chapter has been concerned with the overall physiology of muscles and exercise and some general background on pedaling. It now takes up a variety of questions related to the specifics of pedaling. There is almost no theory to guide the discussion in this area, so the main thrust is to report on efforts to devise improved pedaling mechanisms. The mechanisms themselves are mainly described in chapter 9, but a start is made here with those that are thought to have specific physiological rather than only technical advantages (or disadvantages).

Pedaling and Rowing Motions

Harrison (1970) developed his curve for short-duration pedaling or cycling (curve 1 in figure 2.13) based on measurements taken from a group of active men, not record athletes. The significance of his results lies, therefore, in measurements of the relative power produced by the same individuals using different motions and mechanisms. Harrison’s findings seem to be particularly significant because his subjects produced, in some cases, more power through motions to which they were unaccustomed than through bicycle pedaling, with which they were all familiar. The curves for linear (“rowing”) foot and hand motion (curves 2 and 4) lie considerably below the cycling curve for short time durations but rise above it after 1 min.

Measurements taken on a rowing ergometer have an additional reason for showing a diminished power output: if the subject’s feet are fixed with respect to the ground, as they are normally fixed with respect to the boat when one is rowing, there are large energy variations from the rower’s accelerating and decelerating his body from rest positions at the ends of the stroke, something that occurs to only a minor extent in actual rowing (in which the light boat, rather than the heavy rower, does the accelerating and decelerating). It is actually possible for the rower to convert backward-moving kinetic energy to propulsive work, as long as the arms rather than the leg or trunk muscles are used to come to rest. However, to decelerate a boat’s forward motion probably requires some negative work (in addition to elastic energy storage) in the leg and trunk muscles, particularly at high stroke rates. It is an interesting open question when such additional (but uncounted) power production, by a different set of muscles, is likely to reduce the desired power output. The simplest expectation is for fixed-power rowing endurance to be less when the feet are fixed to the stationary frame (curve 2) than when the seat is fixed and the feet are allowed to move (curve 4), as Harrison found.

Of great interest are Harrison’s results for what he called “forced” rowing. He set up a mechanism that defined—that is, constrained—the ends of the rower’s stroke and conserved the moving masses’ kinetic energy, either with the feet fixed (curve 3) or the seat fixed (curve 5). A car engine’s piston-crank-flywheel mechanism is of this type. With forced rowing and the seat fixed, considerably longer durations of power than with normal pedaling are obtained at all power levels. This apparently significant finding has not, to the authors’ knowledge, been used to break any human-powered-vehicle record. Indeed the known records carried out with a rowing bike (see rowingbike.com/en/records/) have used an unconstrained rowing mechanism.

Pedaling and Hand Cranking

The question frequently arises as to whether one can add hand cranking to pedaling and obtain a total power output equal to the sum of what one would produce using each mode independently, or at least somewhat more than by pedaling alone. Kyle, Caizzo, and Palombo (1978) show that for periods of up to 1 min, hand and foot cranking can generate 11–18 percent more power than foot cranking alone. The power produced is greater when the arms and legs are cranking out of phase than when each arm moves together with the leg on the same side. In later work, Powell and Robinson (1987), in tests of seventeen males and fifteen females, find that power production in a ramp test can be increased by more than 30 percent over pedaling alone when arm cranking is combined with pedaling. VO₂ max is higher for the combined arm-and-leg power than for leg power alone, supporting the statements made previously about the use of this measure. The chapter stated earlier that about half the advantage of combined arm-and-leg power over leg power alone is due to aerobic metabolism and half to anaerobic metabolism. Powell (1994) finds that in cranking at 50 W and 60 rpm, shorter cranks (100–125 mm) are less efficient than longer ones (125–165 mm). He also finds no significant difference between in-phase (parallel) cranking and out-of-phase cranking (like foot pedals), although they differ with respect to stability (torque in roll) and body restraints.

With hand cranking alone, power levels as shown in figure 2.14, in which general male athletes achieve 550–850 W with about four crank revolutions per second, male canoeists 1,000 W, and female canoeists 550 W, cranking slightly slower, are achievable. Neville, Pain and Folland (2009) conducted arm-cranking measurements on elite sailors, who must “grind” sail winches as quickly as possible. They found peaks of 1,400 W for 7 s at 120 rpm and 330 W for 3 min at 80 rpm, while the sailors were standing with the crank axis at about half the stature height. The crank length used was 0.25 m and the distance between the handles 0.44 m.

Upright and Recumbent Pedaling

Riders of recumbent bicycles sometimes claim advantages over standard positioning not only because of lower aerodynamic drag, but also because of freer breathing, as the bend in the recumbent position is less than that of the crouch imposed by a standard upright racing position. (This might not apply to semirecumbent positions corresponding to crouched positions but rotated 90°.) Specialist triathlon bicycles move the rider’s body forward slightly in relation to the pedals, which reduces this bend.

Early measurements showed an apparent small reduction in power when a bicyclist switches from a conventional pedaling position to a recumbent one or no difference. Antonson (1987) studies the oxygen efficiency of recumbent and conventional bicycling positions at less than maximum workloads in thirty men: ten recumbent cyclists, ten cyclists used to conventional machines, and ten physically active noncyclists. Each is asked to pedal for 6 min at 52 W, followed by 6 min at 155 W, for each of the two positions, while being measured for oxygen consumption, ventilation, and heart rate. Antonson finds no significant differences in oxygen consumption or ventilation among the three groups, though the noncyclists are found to have a higher heart rate than those in the other two groups. She finds no indication that either group of bicyclists benefits from being accustomed to one position or the other. Bussolari and Nadel (1989) test twenty-four male and two female athletes in the two positions and find no significant difference in oxygen efficiency (figure 2.10). Egaña, Columb, and O’Donnell (2013) compare upright, various semirecumbent, and supine positions at high intensities and find little difference between the first two but less endurance in the supine position.

There are two pitfalls in particular to be avoided in such a comparison. One is in the definitions. The word recumbent is sometimes taken to mean supine, “flat on one’s back,” but more often to mean sitting as one does driving a car, a style more accurately referred to as semirecumbent. One would expect to produce a lower amount of power when on one’s back. The upright posture can be taken as that used on an all-terrain bicycle or “sit-up” bike. One might expect a reduction in maximum aerobic power for the crouched racing position because of the restriction in breathing the position imposes, as has been speculated elsewhere. The other pitfall involves the question of accustomization, which is always difficult when a “new” position is being tested. It might take months of practice before one’s muscles are adapted to a new position, yet in tests one is usually allowed only minutes to accustom oneself to a shift in position.

Backward Pedaling

The concept of pedaling backward instead of forward seems unnatural. However, Spinnetti (1987) experiments with low-power backward pedaling, then carries out careful measurements that show he can produce higher levels of short-duration maximum power pedaling backward (215 W) than forward (179 W) (figure 2.15). One should not draw conclusions on the basis of one series of tests on one person, but the power differential Spinnetti finds is intriguing. In the case of recumbents with a high bottom bracket (requiring “uphill” pedaling), the authors have found backward pedaling to be more pleasant, as the “power stroke” is angled downward more.

The next topic is a similarly unusual pedaling system that seems to allow increased power to be produced through involvement of more muscle groups.

PowerCranks and Active Involvement of the Lifting Muscles

One clever approach to involving additional major muscles in pedaling is that given by Frank Day’s PowerCranks, which are built with one-way clutches so that each leg has to lift itself (helped neither by the counterbalancing weight nor by the down push of the other leg). Used only in training, they force some large muscles to develop that most people are content to leave uninvolved. PowerCrank.com claims an increase in power and hence cycling speed after some weeks of training; users and quite a few easily found studies support this assertion. Luttrell and Potteiger (2003) find in comparative tests that a PowerCranks group has significantly higher gross-efficiency values than a normal-cranks group (e.g., 23.6 ± 1.3 percent versus 21.3 ± 1.7 percent), as well as significantly lower heart rates and VO₂ values. However, Burns (2008) finds no significant improvements for a PowerCranks group and less efficiency and economy compared to cycling with normal cranks.

It seems logical that training new muscles increases power and not surprising that efficiency in actual use doesn’t increase or even decreases. In contrast to the human arms, the human legs are “engineered” mainly for pushing and less for pulling.

Effect of Saddle Height

Using a single subject (a thirty-nine-year-old man, obviously not very athletic), Müller (1937) obtains the results shown in figure 2.16. For durations less than 0.5 h, he finds that the subject achieves at least one and a half times greater endurance at each power level when the saddle is raised 40–50 mm above the “normal” height, that for which the heel can just reach the pedal with the leg stretched and the posture upright. Equivalently, he can tolerate about 7 percent more power for each session. No less important, perhaps, is the dramatic 15–30 percent reduction in power, or 80 percent reduction in endurance, when the saddle is set 100 mm lower than normal.

Similar research with more subjects by Hamley and Thomas (1967) shows maximal anaerobic power with the saddle height to the pedal spindle set, at its lowest position, at 109 percent, and AnalyticCycling.com’s online model (using specified thigh, shin, and crank lengths and a fixed foot) shows a similar tendency, as well as that the maximum is a peaky one, with a sharp drop if the saddle height is increased further.

Peveler (2008) carries out measurements with groups of cyclists and noncyclists, comparing the 109 percent inseam recommendation with later ones specifying minimal knee angles between 25° and 35° (measured from a straight leg). He finds a poor correlation between these recommendations because of variations in limb proportions and a slight but significant efficiency maximum at the 25° knee angle, especially at aerobic power levels, as well as a mean personal preference of about 27° within the cyclist group.

With recumbent bicycles, seat height of course has different implications, and the main parameter to adjust is the more or less horizontal distance between the seat rest and the bottom bracket. Too and Landwer (2008) investigate this and other parameters.

Effect of Crank Length

The length of the cranks in conventional bicycles is fixed within narrow limits. With the saddle at the normal height above the pedals, as defined by Müller (1937), and with the pedals at a distance above the ground such that in moderate turns (when the bicycle will be inclined toward the center of the turn), the pedals do not contact the ground, and the saddle is then at a height at which the rider can just put the ball of one foot on the ground when stopped while still sitting on the saddle. The crank length is then chosen so that almost all riders will feel comfortable. This length is normally, for adult riders, taken as 165 mm (6.5 in) or 170 mm (6.7 in). Thus, the height above the ground of the bottom-bracket axle is fixed. An attempt to fit longer cranks will lead to a reduction in pedal clearance when cornering. (In a similar vein, it should be noted that the rider’s need to fit the maximum wheel radius between his or her legs, in order to travel more distance with each pedal stroke, also drove the crank length for high-wheel bicycles downward.)

Few riders, then, have an opportunity to try long cranks, because each crank length strictly requires a frame specially designed for that length. In this respect, bicycles with higher bottom brackets (those designed for off-road use, and even more so, recumbent bicycles), have an advantage. Most data on the effects of crank length are based on tests that have been taken on ergometers. But ergometer data can be regarded with suspicion, as has been implied, and this has certainly been true with regard to data on long cranks. So few people have been able to experiment with significantly longer cranks on actual bicycles that their impressions must also be treated with reserve.

The older literature describes several tests of different crank lengths and generally finds no advantage of particular lengths at normal pedaling speeds, a disadvantage of long cranks at high pedaling speeds, and an advantage of these in low-speed, high-torque pedaling. This is hardly surprising, but it is difficult to separate the effect of the crank length per se and the automatic effective “change of gear.” It is also not surprising that longer cranks are recommended especially for larger people. Nettally.com/palmk/crankset.html recommends cranks to be 0.216 times the inseam length and discusses this recommendation at length.

Müller and Grosse-Lordemann (1936) test the effect of crank lengths on an ergometer, employing only one subject. Their approach is to use three crank lengths—140, 180, and 220 mm—set the power output the subject must produce, and measure the maximum duration for which this output can be sustained. For all power levels, the subject is able to produce the most total work (that is, work for the longest periods) when using the longest cranks. At the highest power levels, the subject’s body efficiency (work output divided by energy input in food) is also highest when the longest cranks are used.

Harrison (1970) gives his five subjects, none of whom is particularly tall, an initial choice of crank length and finds that they prefer the longer cranks (177 and 203 mm; 7 and 8 in). Harrison intended to perform all of his tests at two different crank lengths; however, he finds from initial tests that “crank length played a relatively unimportant role in determining maximum power output” and uses just one (unspecified) length for most of his tests.

More recent data mostly confirm these earlier findings. Too (1998–1999) measures the anaerobic power outputs of six male subjects, aged twenty-four to thirty-five, employing the Wingate protocol (see the section earlier in the chapter on this), in conventional and recumbent positions, using cranks from 110 to 265 mm in length. Too obtains the highest average power readings for 180 mm cranks for both positions. This crank length also yields the highest peak power for the conventional position, whereas the shortest cranks, 110 mm, allow the recumbent bicyclist to produce the highest peak power. For all crank lengths, peak and average power are higher in the recumbent position. This result seems at variance with earlier data quoted previously. Figure 2.17 summarizes the recumbent data (Too and Williams 2000). A newer study (Too and Williams 2017–2018) with upright cyclists produces a formula that suggests optimal crank lengths at peak power are shorter than normal.

In summary, as well as being impractical to increase on a conventional bicycle (no manufacturer currently seems to be making cranks whose lengths can be varied during use), crank length is apparently not of major importance in the quest for producing maximum power, although shorter-than-normal cranks appear indicated for high cadences and longer-than-normal ones for low cadences. However, for racers, even factors of seemingly minor importance can produce a win. To choose the optimum among all the factors involved is too detailed a topic for this book; a study of the references quoted and of others, existing and, undoubtedly, coming, is recommended.

Nonround Chainwheels

Elliptical chainwheels can be fitted to normal cranks, in which case the pedal motion remains circular, but of varying speed or gearing ratio. The usual purpose of elliptical chainwheels is to reduce the supposedly useless time during which the pedals are near the top and bottom dead centers. This orientation with the smallest size occurring at the dead centers is referred to as the “normal” one in this section. As a topic, they have some similarity to long cranks, in that there are fierce proponents and antagonists and little reliable data. Four of Harrison’s (1970) five subjects produce virtually identical output curves (power versus duration) using circular and elliptical chainwheels. One, apparently Harrison himself, produces about 12.5 percent more power with the elliptical chainwheel. All prefer the elliptical chainwheel for low-speed, high-torque pedaling. Harrison does not specify the degree of ovality of the chainwheel used but does state that the foot accelerations required are high. One of Harrison’s illustrations shows a chainwheel with a very high degree of ovality (about 1.45).

An elliptical chainwheel’s degree of ovality can be specified using the ratio of the major to the minor diameter of the underlying ellipse. In the 1890s, racing riders using elliptical chainwheels with ovalities of about 1.3 became disillusioned with their performances, and these chainwheels fell out of favor. In the 1930s the Thétic chainwheel, with an ovality ratio of 1.1, became quite popular. No deterioration of performance compared with that on a round chainwheel was recorded, and a small proportion of riders improved their performances by a few percent. According to a personal correspondence between Frank Whitt and the senior author in 1973, experiments with chainwheels having ovalities up to 1.6 have confirmed that high ovality (perhaps 1.2 or greater) decreases performance.

In the 1980s Shimano introduced a chainwheel, Biopace, that though nonround was not elliptical. The scientific background is given by Okajima (1983), who enables his group to determine the leg-joint torques for normal circular-chainwheel pedaling. Okajima points out that the knee has a period of strongly negative torque:

We saw two specific restrictions to be solved:

1. the difficulty of spinning, both in the motion and in the direction the force must be applied, restricts the speed of muscle contraction during pedaling to a rather slow rate, and requires the force to be on the high side, and

2. the knee joint is overused, while the hip joint is underused (the ankle is rather passive).

We decided that an appropriately uneven angular velocity pattern would reduce the loss of kinetic energy, and also make it easier for the rider to switch between the firing of different muscle groups at appropriate times (to be specific, at the reversal of knee torque).

Figure 2.18 shows the shapes of three chainwheels resulting from the Shimano study (used together in a triple chainwheel). As the figure shows, the eccentricity is not very pronounced and is turned in other direction from that of the elliptical chainwheels described earlier.

Various internet authors suggest a definitive advantage using Biopace chainwheels; others suspect marketing hype. Hansen et al. (2009) carry out comparative physiological tests on Biopace and circular chainwheels and record slightly lower lactate values with the Biopace. Van de Kraats (2018), in an extensive section on oval chainwheels, calls the Biopace “the maximal wrong choice” and lists recent arguments for the superiority of asymmetrical chainwheels with normal orientations and ovalities of about 1.1 and 1.2, including wins and records with the Osymetric chainwheel (1.2) (see figure 2.19) and the elliptical Q-ring (1.1). Van de Kraats describes (and links to) many further studies and models twelve chainwheels in an online simulator. A theoretical study by Rankin and Neptune (2008) suggests a 3 percent increase in power against circular from using normal elliptical chainwheels with eccentricities of 1.35, 1.3, and 1.25 at cadences of 60, 90 and 120 rpm, and at average powers of about 850–1,050 W.

A more versatile mechanism giving the same effect as a nonround sprocket was the Brown SelectoCam, also sold as the Stronglight Power-Cam (later Houdaille). In this mechanism, a bell-crank riding around a fixed central cam advanced and retarded the round chainring relative to the crank, twice each revolution, without the manufacturing om and chain-shifting disadvantages of a variable sprocket radius (see US Patent 4,281,845 [1981]).

Lever or Linear Drives

Many people have invented and reinvented forms of the linear drive, in which each foot pushes on (for instance) a swinging lever, with a strap or cable attached to the lever at a point along it that can be varied to give different gearing ratios. The cable is in turn attached, perhaps through a length of chain, to a freewheel on the back wheel and to a return spring (figure 2.20). The American Star high-wheeler (figure 1.16) had this type of drive, although its gear was not variable. Pryor Dodge has been gracious enough to allow us to reproduce the jacket photograph of his 1996 book The Bicycle (figure 2.21) showing a superb example of a swinging-lever drive. The drive’s manufacturer, Terrot, claimed at the time (the early 1900s) that the alternating levers avoided the dead point common with cranks and thus allowed for easier hill climbing. The coauthor’s experience with the Thuner Trampelwurm road train (see chapter 10) confirms this. This road train has various types of pedal drives, including unconstrained swinging “rowing” levers that are especially useful when strenuously climbing or accelerating from rest, because they can always be operated at a chosen phase and amplitude where maximum force is available. However, although there are no dead centers, there are jerky reversals of direction, and these drives thus are not very pleasant or efficient for normal (level) riding.

The overwhelming disadvantage of such swinging-lever drives is that the muscles must typically accelerate and decelerate the legs or arms in the same way as in shadowboxing (Wilson 1973). Harrison (1970) finds rather low outputs for motions of this type (figure 2.13). However, some believe that this disadvantage holds only for the most primitive embodiments: careful design should make it possible to oscillate the feet at high cadence with little loss. With geometrical slowing (a reducing sprocket radius or a drive linkage approaching its condition of zero mechanical advantage), kinetic energy is recaptured at the stroke end. (See figure 9.20 for the mechanism of the Thijs Rowcycle.)

With coupling between the left and right pedals, as in figure 2.21, one foot may lift the other in the same way as with a rotating crank. This still creates jerky reversals of no propulsion. Another disadvantage in swinging-lever drives is the impossibility of wheeling so-equipped bicycles backward.

Constrained swinging-lever or linear drives do not have these disadvantages but do have dead centers that can prevent movement from rest. Once they are moving, the action is more or less sinusoidal and can achieve the highest effectiveness, according to figure 2.13 (“forced rowing”). However, as they are not connected via a freewheel, such drives take some skill to use, as the rider must synchronize to the phase given. This can be difficult, as people not used to treadle-driven sewing machines or railway draisines find out when starting to use such equipment. If a freewheel is used, one problem is exchanged for another. Although the rider can stop at any time, it is again possible to get stuck in a dead-center position, and not just at rest. The Thuner Trampelwurm road train also has some constrained swinging-lever pedals, and they are a nearly useless abomination compared to the other drives. A better design might change this.

Drives for Human-Powered Boats and Aircraft

Examining the physiological differences between the many ways of propelling traditional human-powered boats (HPBs) with oars and paddles is outside the scope of this book, but observations can be made on propeller drives for HPBs and human-powered aircraft (HPAs).

Unlike pedals for road vehicles, which at least when the rider is pedaling forward are in effect coupled rigidly to the road and therefore to the entire inertia of vehicle and rider, propeller drives slip with respect to the fluid they act on. Pedaling propellers with much slip is more at constant torque rather than constant speed, like pedaling a stationary exerciser without a flywheel. It is more difficult, or at least requires practice, to achieve high levels of torque effectiveness and pedal smoothness. The former is defined as the percentage of power delivered by the foot in the forward direction. A value of 100 percent implies pulling up on the upstroke. The latter is defined as the ratio of average power to peak power during a pedal revolution. A value of 100 percent implies no variation. See Johnstone 2014. In the case of propellers it is best to pedal at the peak of their efficiency curve, which implies little variation in speed and torque in the case of high-efficiency propellers of sufficient size. When underway, such propellers slip only a few percent relative to their fluid and thus force pedaling at a certain speed relative to the vehicle speed, determined by the gear ratio, as with a bicycle. Cyclic variations in speed result immediately in large variations in torque and thrust and are thus coupled to the inertia of vehicle and rider. Pedaling then feels similar to pedaling on land, if the gearing is chosen well, and presumably much that has been said about land pedaling applies here also. However, as such propellers’ efficiency curve has a pronounced peak, it is best to pedal smoothly enough to stay near this maximum during the entire pedal revolution.

Noncircular Cranking

Harrison (1970) shows that a constrained straight-line motion, with kinetic-energy conservation at the ends of the stroke, enables riders to produce greater short-term power than circular pedaling can generate. There has been limited but constant interest over more than a century in the question of whether a foot motion between circular and straight would be better than either of the two individually. Figure 2.22 shows the most common form of mechanism for producing such elliptical foot motions.

We have seen no results of ergometer tests of human power produced using such mechanisms. However, Miles Kingsbury in the United Kingdom has manufactured a modern form of such mechanisms, under the name K-drive, that has been used to win several races (Larrington 1999). Perhaps the K-drive’s primary advantage lies in reducing the area swept out by the moving foot, so that a smaller, streamlined fairing may be used. In its present embodiment it adds weight and friction (because of several additional moving links), so the winning performances achieved with it must be regarded as significant.

Some Other Forms of Power Input

Mechanisms such as rotating hand cranks or rocking handlebars have been developed to allow riders to employ muscles other than the legs for propulsion. But perhaps surprisingly, conventional upright bicycles already offer this capability to some degree:

• When a cyclist is standing, tilting the bicycle away from the descending pedal enables the rider to perform substantial arm work easily. The diminution of pedal displacement at the given crank torque permits estimation of the amount of arm power exerted. For example, in tipping the bicycle from 15° right to 15° left, the arms are doing about 20 percent of the work, according to estimates made for this book. Presumably the legs can then push harder or move faster, for an overall increase in power output. A possible mechanical aid to arm work is a laterally movable saddle. When unlocked, such a saddle can bear the rider’s weight but still permit the bicycle to be tipped forcefully by the arms.
• Pulling the torso forward (i.e., sliding along the saddle toward the handlebars) during each downstroke also enables a cyclist to use the arms powerfully at very low cadences and high torques.
• Especially when standing, a cyclist can leap upward with the assistance of the torso’s uncoiling and push or pull somewhat vertically with the arms. (Not only can this technique add work produced by other muscles, but it makes it possible to convert low leg extension speeds to high, after which the rider descends on a straight, nonworking leg.)

Recumbents may be disadvantaged in this regard because they do not permit the rider to use additional muscles in this way. A spring-preloaded, rearward-slidable seat on a recumbent might provide a useful analog to the energy transformations of stand-up pedaling on an upright bicycle.

There are many ways of propelling skates, skateboards, and scooters, but we know of no data on measured efficiencies compared to pedaling, not even for the basic one-legged kicking thrust. Anybody who uses kick-cycles or modern Draisines, however, easily feels that these require more effort at the same speed, compared to pedaled vehicles. Reasons that come to mind are that the foot must be accelerated (backward) to at least road speed, and the other leg must be partially bent. With skating movements this is also partly the case, but less so, as the thrust is more sideways, with higher force and less speed.

Thermal Effects (How Cyclists Keep Cool)

Bicycling can be hard work. For each unit of work put into the pedals, a bicyclist must get rid of about three units of heat in addition to the normal body heat from basal metabolism. It is as important that the body not become overheated when producing power as that it not lose more heat than can be replenished in cold conditions. As pointed out earlier in the book, the measurement of bicyclists’ power output using ergometers is open to criticism because the conditions for heat dissipation on ergometers are critically different from those on bicycles. The performances of bicyclists riding in time trials and other long-distance races are, however, very amenable to analysis. Such time trials are of far longer duration than the few hours usually assumed (see, e.g., Wilkie 1960) as the maximum period over which data on human power output are available. Time trials (unpaced) are regularly held for 24 h periods; distances of 775 km (480 mi) are typical.

Bicycling generates a relative airflow of such magnitude that it bears little resemblance to the drafts produced by the small electric fans often used for cooling people pedaling ergometers, and these in turn can be much better than nothing. As a consequence, under most conditions of level cycling, the bicyclist works under cooler conditions than does an ergometer pedaler. At high speeds, most of the rider’s power is expended in overcoming air resistance. Looking at this in a positive way, the power isn’t all “wasted” but represents very effective cooling. Even if large cooling fans of the same power were used for ergometer experiments, the cooling effect would be less than that for the moving bicyclist.

Basic Cooling Mechanisms

The human body is cooled through four basic mechanisms: radiation, convection, conduction, and perspiration. The HyperPhysics website gives basic information about these mechanisms, with examples for an unclothed body at rest (see Nave 2018). Although its focus is space applications and not moving air as in cycling, NASA 1969 offers a detailed and comprehensive compilation on body thermal effects, including all the formulas and factors in this section and the next one, unless they are otherwise referenced.

Without wind and at or below room temperature, the primary cooling mechanism is heat radiation, and at elevated temperatures it is perspiration. The first three mechanisms noted in the previous paragraph can also absorb energy, that is, they can heat rather than cool the body. A further consideration is respiration or breathing, which can also cool the body through evaporation, like perspiration, and by a lesser amount, through convection.

Although each part of the skin cools differently, depending on orientation, exposure, and clothes, for approximations it is useful to know its total surface area. According to the formula given earlier, in the section “Basal Metabolism,” a man 1.8 m tall and weighing 80 kg has a skin area of 2 m², and one 1.5 m tall and weighing 50 kg, 1.43 m².

Heat-Transfer Data and Deductions

Skin of any color is an almost perfect (99 percent) “black body” radiator in the infrared. Heat radiation to the environment is very sensitive to actual temperatures, as they are raised to their fourth powers in the Stefan-Boltzmann equation typically used for calculating it. A skin area of 2 m² at a temperature of 34°C would radiate about 365 W into a 0°C environment, 133 W into 23°C, and 13 W into 33°C; at more than 34°C, energy would be absorbed, not lost. (In addition, if 10 percent of this area is exposed squarely to bright sunlight [~1 kW/m²], about 130–160 W [average white to average black skin] are absorbed.) Real figures are less, as some of the surfaces radiate toward each other (giving 65–75 percent of the total from crouched to semierect positions), and some like those of the fingers are rapidly cooled, thus decreasing radiation. Another caveat: the balance of infrared radiation occurs between the skin and a facing surface, which can be a wall, a canopy of leaves or material, a layer of humid air or a cloud, but not dry air, which is transparent to such radiation. An environment at thermal equilibrium might be more or less at air temperature, also with high humidity or a low cloud, but with a clear sky much of the heat of a surface facing upward is radiated into higher layers of the atmosphere with a much lower temperature: an infrared thermometer pointed at the clear sky can show below-freezing temperatures even on a hot day. At night this is easily felt, and because of his or her orientation, a recumbent rider will radiate more heat than an upright cyclist. For clothed parts of the body, it is the outer surface temperature of the clothing that counts. Most fabrics are less perfect radiators (giving 70–80 percent of skin values), whereas reflective sheets (such as “rescue blankets”) radiate almost nothing themselves and reflect infrared radiation back to the skin.

If air temperature is higher than skin temperature, perspiration, the evaporation of sweat from the skin, and additionally, exhaled moisture are normally the only available means of cooling. Indeed the other mechanisms then all transport heat into the body. If 1 kg/h of water is evaporated without dripping or getting wiped away, this represents almost 675 W cooling power. Although this quantity is independent of the ambient air, the amount of evaporation possible is strongly dependent on the humidity. If humidity is very high, much of the sweat the body produces cannot evaporate and may instead drip away, removing far less heat. Wind strongly increases evaporation. According to Clifford, McKerslake, and Weddell (1959), evaporative cooling is proportional to V^0.63 (airspeed, measured from 0.6 m/s to 4 m/s) and also to the saturated vapor pressure at skin temperature (about 5 kPa) minus the ambient vapor pressure.

Convective cooling is proportional to surface area, the temperature difference between skin and air, and a heat transfer coefficient h_c, which is sensitive to airspeed and Reynolds number (see chapter 5), various other fluid-dynamic coefficients, and second-order conditions such as posture and airflow patterns. The third edition of this book showed that there can be greater than 100 percent variation in the local h_c in cross flow around a cylinder (such as an arm). In completely still air, there is no convection, and the (insulating) layer of air next to the skin nearly assumes its temperature. In this case, heat mainly flows by conduction through successive layers of still air. However, the slightest current, whether induced by the warm skin itself (buoyancy of locally heated air), movements of limbs, wind or fans, or the apparent wind of cycling itself, starts to remove this insulating air and raises the heat-transfer coefficient. Because of the many variables involved, an exact calculation is not possible, but various approximations have been proposed for an overall coefficient as a function of airspeed. On the basis of their experiments in Antarctica, Siple and Passel (1945) propose an empirical formula: , in units of kilocalories per hour per square meter per degree Celsius, with airspeed V ranging from 2 to 20 m/s. The result can be multiplied by 1.1622 ... to yield the equivalent in SI units, that is, 23–35 W/(m² K) for the range specified. (This is explored further in the “Windchill” section later in the chapter). Colin and Houdas (1967) imply h_c = 2.3 + 7.5 V ^0.67, which generates 14–58 W/(m² K) for the range specified. Although both formulas yield h_c ≈ 30 W/(m² K) at V = 7 m/s, a typical cycling speed, this is coincidental, as the two groups took their measurements using different methods in different environments. Data from other researchers suggest functions more similar to those of Colin and Houdas. What all of this means is that 2 m² skin moving at 7 m/s at room temperature (i.e., 10 K cooler) is convectively cooled by about 600 W.

Heat transfer of course also depends on clothing. NASA 1969 expresses garments’ thermal resistance garments in “Clo” units: 1 Clo = 0.155 K m²/W (for a 1.8 m² man) and represents comfortable indoor or light street clothing. Clo values vary from zero (nude) through 0.25 (underwear) and 2 (light winter clothing) to 7 (fox fur). 1 Clo will allow the average surface temperature of a person at rest to cool by about 5 K. The challenge for cycling clothing, however, is not high thermal resistance (apart from gloves and shoes in very cold conditions), but allowing perspiration without getting soaking wet.

The effect of adequate cooling may be inferred from Wilkie’s (1960) finding, from experiments involving ergometer pedalers, that if it is necessary to exceed about 0.5 h of pedaling, subjects must keep their power output down to about 150 W (0.2 hp). However, peak performances in 24 h time trials can be analyzed using wind- and rolling-resistance data from chapters 5 and 6 to show that about 225 W (0.3 hp) are being expended over that period. The pedaler’s exposure to moving air is principally responsible for the improvement in cooling. An ergometer pedaler who attempts a power output of 0.5 hp (373 W)—the same power output required to propel a racing cyclist doing a 40 km (25 mi) distance trial of nearly 1 hr—in normal laboratory ambient temperatures can expect to give up after perhaps 10 min and will be perspiring profusely. Again the effect of moving air upon a pedaler’s performance is very apparent.

In the design of heating and ventilating plants, the maximum heat load produced by a worker doing hard physical labor (the recommended room temperature for which is 55°F or 12.8°C) has long been accepted as 2,000 Btu/h (586 W) (Faber and Kell 1943). Most of the heat is lost through evaporation of sweat. If this includes 100 W basal metabolism and an efficiency of 25 percent is assumed, such a worker would produce about 122 W mechanical power. This would also seem to be an acceptable limit for pedaling ergometers or cycling very steeply uphill for long periods.

Figure 2.4 shows that athlete cyclists can exert greater than 400 W (0.54 hp) for periods of up to 1 h. A common range of endurance when pedaling ergometers at 0.5 hp (373 W) is 5–15 min (Whitt 1973), which again demonstrates vividly the value of flowing air in prolonging the tolerable period of hard work.

Even at lower speeds, the apparent wind can give enough cooling for relatively high-power cycling. For example, in a hill climb of the Grossglockner, Bill Bradley rode at about 5.4 m/s (12 mph) at a power output of 450 W, in high-temperature but low-humidity (40 percent) conditions.

Bicycling in Cold and Hot Conditions

A problem faced by advocates of bicycling as a means for daily commuting to and from work is that even temperate regions have days, and sometimes weeks, of extreme weather conditions during which bicycling may be unpleasant for many and impossible for some. There is no one set of temperature boundaries below and above which bicycling becomes impossible. Many fair-weather cyclists put their machines away for the winter when the morning temperatures drop to 10°C (50°F) and will not ride in business clothes at temperatures above 25°C (77°F). However, many hardier folk find bicycling still enjoyable at –15°C (5°F) to 35°C (95°F), or an even wider range of temperatures, also depending on wind and humidity. The main problem at temperatures below the lower end of this range seems to be the feet. The size of insulated footwear is limited to that which can fit on bicycle pedals, and it is a fairly common experience that, at –18°C (0°F), even when the trunk of the body is becoming overheated through exertion, the feet can become numb with cold.

Windchill

Wind intensifies the effects of cold air. Weather forecasters often express these effects in terms of windchill: the air temperature that would have to exist, without wind (but at walking speed), to provide the same cooling to a human body as a particular combination of actual temperature and actual relative wind. The windchill temperatures tabulated by the US National Weather Service use an empirical formula giving the perceived temperature as a function of the actual temperature (assumed to be below 10°C or 50°F) and the wind speed (assumed above 1.3 m/s), for which there are many online calculators (see, e.g., Brice and Hall 2019 b). The following formula yields two results: first the windchill index in units of watts per square meter, after the original formula of Siple and Passel (1945) mentioned earlier:

Windchill Index = (11.622 V^1/2 − 1.1622 V + 12.145) (33 − T),

in which V is the wind speed in meters per second and T the actual temperature in degrees Celsius. This is the formula for the heat-transfer coefficient given earlier, with kilocalories per hour converted to watts, multiplied by the difference between the ambient temperature and that of the skin (33°C). In 2001 the National Weather Service replaced this formula with the following one, which provides the windchill temperature in degrees Fahrenheit:

Windchill Temperature = 35.74 + 0.6215 T − 35.75 V^0.16 + 0.4275 T V^0.16,

in which V is the wind speed in miles per hour and T the actual temperature in degrees Fahrenheit. The calculator and information from Brice and Hall 2019b also give other units.

The Wikipedia article on windchill explains well the history and rationale of the method. Using calculators or published charts, one can find the effect on a rider’s perceived temperature of bicycling into a relative wind. For instance, if the air temperature is –18°C (0°F) and one is bicycling into a relative wind of 5 m/s (11 mph), one is subjected to the same amount of cooling as if one were walking at a temperature of –27°C (–17°F). The calculated windchill index is about 1,650 W/m². Even if this is applicable only to skin exposed fully to the wind, it roughly shows what would happen to an unclothed human, and with what heat flux the body has to supply exposed skin (e.g., perhaps 40 W here for an exposed face). If the local blood supply cannot furnish this, the skin temperature drops and frostbite ensues. This can also happen to the fingers if the gloves worn are too thin.

A cyclist’s feet are particularly at risk because they are periodically traveling at a higher relative velocity (as they come over top dead center) and then at a lower velocity relative to the wind. Because the cooling relationship to relative wind is nonlinear, the average cooling effect is more severe. In particular, winter users of fast e-bicycles may suffer cold fingers, feet, and faces. As electric power is readily at hand, electrically heated gloves and shoes are a possibility.

The body core temperature of an adequately clothed cyclist is normally never at risk, as going faster normally produces more heat than is lost. An exception is going downhill, during which it is easy to lose a great deal of heat on long winter descents.

Heat and Humidity

At higher temperatures, humidity becomes very important. The bicycle is highly prized for personal transportation and for local commerce throughout Africa and Asia. In northern Nigeria, for example (where the senior author lived for two years), the air is so dry throughout most of the year that the availability of water limits one’s range on a bicycle more so than the temperature. The long-distance bicyclist Ian Hibell was able to ride through the Sahara (principally at night), limited again by his water supplies. He could not carry sufficient water for the longer stages between oases and relied on gifts of water from passing motor travelers. Even the United States occasionally experiences heat waves with a month or so of temperatures around 40°C, often coupled with high humidity. Yet some bicyclists continue to ride to work, even though bicyclists experience even higher ambient temperatures on roads.

The US National Weather Service has produced a heat index analogous to the windchill index just described, and in Canada, a similar humidex formula is in use. Both are well-described in Wikipedia articles; Brice and Hall 2019a (see also Weather Prediction Center 2014) provides a calculator and the underlying formula, too long to include here. The calculators and their associated formulas are used similarly to those for the apparent windchill temperature, except that relative humidity is entered instead of wind speed. For example, if the temperature is 40°C (104°F), the heat index formula returns those values for the perceived temperature if it is rather dry at, say, 22 percent relative humidity, or even a bit less if it is drier. But at 50 percent humidity, the felt temperature is about 55°C, with a severe risk of heat stroke. Higher humidity values yield extreme results, but it is not quite clear for which ranges the heat index formula has been validated.

While cycling in temperature extremes is generally not much of a problem in level riding, this is not so for gradients. Cycling steeply uphill promotes heavy sweating. In warm conditions this is merely inconvenient or unpleasant, but in cold conditions the skin and clothes are moist just when their being so is most dangerous, for example, when cycling downward again, during which the evaporative cooling will be excessive unless additional clothing is donned. It is no wonder that the recent surge in popularity of e-bicycles has mainly been in hilly locales. The additional power permits uphill cycling with far better cooling, as well as cycling in business clothes without their becoming unduly moist.

There are caveats when using fast e-bicycles in hot or cold conditions, however. In the latter, any exposed or only thinly shielded skin is highly cooled, and the otherwise warm body may experience strong pain in those areas. In hot weather the cooling is so good that the body is motivated to cycle at especially high power levels. Sweat is produced but evaporates immediately and isn’t noticed. The moment the rider stops and for a while afterward, sweat is still being produced, but evaporation decreases, and it starts dripping off. To avoid this, speed must be reduced well before stopping.

There are three lessons to be learned from the experience of the hardier riders who brace themselves for cycling against what seem to be extreme conditions. First, the promotion of good circulation through exertion helps the body cope with high temperatures and high humidity as well as with cold weather. Second, the relative airflow that bicycling produces is a major factor in making riding in hot weather tolerable and usually enjoyable. Third, the fact that so many riders choose to bicycle in extreme conditions (rather than being forced to do so by economic necessity) shows that many other healthy but more timid cyclists could push their limits with regard to conditions conducive to or comfortable for cycling without fear of harm.

Streamlined Vehicles

Normal unfaired bicycles and HPVs give optimal cooling in warm to hot conditions. Even better are those with sunroofs, like the coauthor’s 1985 solar-assisted tricycle, used with comfort in all sorts of conditions. With fairings, especially those of velomobiles or racing HPVs, which fully enclose the rider, most of this cooling is lost. Exposing at least the head or opening the canopy or the sides for ventilation helps considerably, but at the penalty of more air resistance, not acceptable for racing or record attempts and not ideal for velomobiles when it rains. Wichers Schreur (2004) provides an analysis and recommendations, showing that good interior ventilation is possible and if optimal ducts for the air intake are used, the power loss is under 1 W. Unfortunately at low speeds, for example, uphill, the airflow will be insufficient to prevent discomfort and heavy sweating.

Velomobiles can be fitted with small electric fans directed at the rider’s head and shoulders. Even a few watts increase comfort enormously.

Racers of these vehicles are in greater danger of actually overheating, especially when large canopies also act as partial solar collectors. The rules for HPV racing or records prohibit cooling with stored energy, such as with the fans mentioned, ice, or precooled vests. They, do, however allow water sprays.

In cold conditions the fairings are thermally more advantageous, but ventilation is still required, especially to prevent the misting up of windshields.

Artificial Cooling

In addition to simple fans, wet cloths, or water sprays, it is in principle possible to wear clothes with built-in cooling elements. Vests are available that incorporate pads of phase-change materials. Water ice, the most common phase-change material, can absorb 334 kJ/kg when melting at 0°C, much more than the 10 kcal/kg (41.8 kJ/kg) absorbed by (nonevaporating) cooling water at 20°C that is heated by the skin to 30°C. Many other substances are available that melt at almost any desired temperature and mostly absorb between 160 and 230 kJ/kg. Evaporating water can, however, remove 2,260 kJ/kg, so a rider would have to use about 10 kg of phase-change materials to have the same effect as with optimal evaporative cooling with 1 kg of sweat or sprayed water.

The book’s authors have never heard of its being done, for obvious practical reasons, but in principle clothes cooled by circulating water (or heat pipes), connected to a radiator, could offer almost any desired degree of cooling for any length of time, without using up anything other than a small amount of power for a circulating pump. NASA 1969 goes into great detail on how this is accomplished in space suits. However, in hot conditions, a dry radiator wouldn’t work, and a form of heat pump would be needed. This isn’t quite as absurd as it sounds, as the theoretical coefficient of cooling power (COP_cooling = Tc /[T_h − T_c], with cold and hot temperatures in Kelvin) could be greater than 30, so an efficient human-powered heat pump could cool with much more power than that needed to operate it, even though at least four times the operating power would appear additionally as heat.

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