It is recommended that Jones' stability criterion u lies between -1 and -3 -1 is less stable than -3 In commercially available bikes, u tends to fall within a much narrower range than this. In Bicycling Science 3rd Edition, the authors claim that they published the incorrect formula in the 2nd edition. Using the formula from the third edition, values tend to be positive numbers not numbers lying between -1 and The third edition downplays the significance of the Jones' stability criterion.
Bicycles and Tricycles. Street, Roger. Christ- church, U. Von Salvisberg, P. Der Radfahrsport in Bild und Wort. Munich, ; reprint, Hildesheim, Germany: Olms Presse, Wilson, David Gordon.
James C. Emmaus, Penn. Wolf, W. Cycling History, vols. Volumes 1—3 are out of print and available only in some libraries. As a power producer, the human body has similarities and dissimilarities to the engine of an automobile. Energy is taken in through fuel food and drink, in the case of humans. The peak effi- ciencies of the two systems in cars, the energy transmitted to the crank- shaft divided by the energy in the fuel; in humans, the extra food used in working are remarkably close to one another, in the region of 20 to 30 percent.
But automobile engines seldom work at peak efficiency, and in any case, peak efficiency in a car engine is attained only close to full power, whereas the rider of a multispeed bicycle can operate much closer to peak efficiency at all times. Also, human output, un- like 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. Hu- mans 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 intention of the author and contributor in this chapter is to pro- vide a basic understanding of how energy gets to the muscles of the rider of a bicycle and of how muscles produce power at the pedals on the bicycle he is riding.
Readers should then be qualified to absorb the main conclusions of research papers in this area. We shall also comment on some bicycle configurations and mechanisms as they relate to the generation of human power. We take the philosophical position that athletes do sophisticated things to maximize performance, many of which are not yet understood. Loading weight.
Indicator Adjustable lamps constant-speed drive.
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Figure 2. Load and speed are set; rider tries to keep center lamp lit. Run stops when rearmost lamp lights up. Exercise bicycles and ergometers of the pattern depicted in figure 2. For accu- rate work the wheel speed and the average braking torque must be mea- sured precisely. One effective preelectronic technique involves a band brake whose drag is set by a weight. Rider power at a given belt speed figure 2.
Much of the information referred to in this chapter has been obtained through careful experiments, typically with ergometers. There has also been a bias toward testing athletes already self-selected for physical capability and college students, predominantly male, in Western countries, and this population is not representative of humanity everywhere.
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 to working an ergometer before tests are performed and measurements are taken. The proper test would be to track two equivalent groups as they followed different specified regimens. Also, an ergometer is usually fixed to the ground, whereas a bicycle can freely be tilted and moved relative to the pedaler, so that body motions and forces are affected.
Crouching is unnecessary on an ergometer but should possibly be enforced in research studies if accurate comparison to road racing is desired. There are exercisers on the market in which most of the power is dissipated in fans, thus simulating the square-law effect of wind resistance, but the air flow on such exercisers is not usually directed at the pedaler and in any case could not approach the cooling provided by the relative wind in bicycling.
Therefore, power output on ergometers especially in the long term is likely to be lower than could be achieved by the same subjects pedaling or rowing their own familiar machines through cooling air in a race that they want to win.
Such measurements may be more realistic than ergometer data. Modern on-bicycle power-measuring systems such as Schoberer Rad Messtechnik SRM and PowerTap see chapter 4 are free from the fore- going objections, and we anticipate a very substantial rise in reported performances as more riders are sampled, using these systems, on their own bicycles, and especially in the heat of competition.
Courtesy Nijmegen University. Most ergometers have frames, saddles, handlebars, and cranks similar to those of ordinary bicycles. The crank drives some form of resistance or brake, and the whole device is fastened to a stand, which remains sta- tionary during use. Other ergometers can measure the output from hand cranking in addition to that from pedaling. Some permit various types of foot motion and body reaction, including rowing sliding-seat actions. 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 instanta- neous power pedal force in the direction of pedal motion, multiplied by pedal speed would show peak values of perhaps — W, with an average of perhaps W. Therefore, some form of averaging is usually employed.
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There are additional problems associated with the determination of very-short-duration extreme power levels from 1 kW to 2 kW or even greater. The best-accepted high-power ergometer test is known as the Wingate anaerobic test, in which a high resistance is sud- denly applied, and the pedaler immediately strives to pedal at maximum speed for thirty seconds, initially accelerating the flywheel dramatically even above rpm if the pedaler is powerful , 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. They can be adapted for accurate power measurement, if the problem of controlling and measuring torque can be solved. Load devices based on the dissipation of a small, tire- driven roller heat up the tire, which reduces the rolling resistance substan- tially. Magnetic eddy-current load units also heat up their conductive elements, increasing the electrical resistance and more than halving the initial magnetic torque.
Air-blowing units require calibration and are mod- erately affected by the proximity of objects that alter airflow. Frictional brake drag also tends to be affected by temperature rise, so the unit must be designed using negative feedback to impose a torque that is essentially independent of the friction coefficient.
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The usual way to describe pedaling performance quantitatively is to fix a power level usually by asking the subject to maintain a fixed pedaling speed at a known braking torque and to determine the time to exhaustion. The results are plotted as a power-duration curve. The advantage of testing pedaling performance indoors, on an ergo- meter, is that the resistance is likely to be steady. Because each individual has different muscle mass, muscle makeup, inherited abilities, and state of conditioning, he or she will have a unique power-duration curve.
Bicycling Science by David Gordon Wilson
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 bicycling performance, of course, is that different body types may have more or less aerodynamic drag—important in level riding—and more or less weight—important when riding uphill. These data will be 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 fixed power level: the curves do not reflect human power drop-off with time. 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 fol- lowing section on critical-power curve fitting to power-duration data.
Bicycling Science, 3rd Edition
Such efforts are interesting because they encapsulate data efficiently and permit mathematical approaches to pedaling optimiza- tion and because they may reveal aspects of the physiological mechanisms governing endurance. Washington 1, record, Maximum sustainable power, W.
NASA curve for "healthy men"— 1 day. Curves connect the termina- tions through exhaustion of constant-power tests. Anaerobic work capacity refers to an amount of stored energy that can be released very quickly. A variety of papers using methods applying this equation exhibit nice curve fits over ranges between two and twelve minutes, at power levels typically in the range from W to W obviously not championship power levels, which would be two-and-a-half or even three times as great.
In principle, two data points suffice to construct the line, but of course further trials will demonstrate the variability and quality of fit. Each of these power levels can be equated to a given vertical velocity pedaling up a steep hill or running up flights of stairs. Some criticisms of this simple correlation are outlined in Gaesser et al. In fact, some anaerobic work capacity will be held back; and the shortest-term maximum power will fall well below predictions. In he demonstrated the equiva- lence of ramp and constant-power determinations of critical power Mor- ton et al.
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 ef- fort similar to a hill climb, or perhaps following a change in diet. And per- formance research should focus on changes to the entire power-duration curve, not just the duration at one single power level. As an example of this, Jenkins and Quigley subjected twelve untrained male college students to eight weeks of ergometer endurance training three sessions per week, forty minutes per session.
On average, critical power CP increased from W to W over the course of the training, with no significant effect on anaerobic work capacity AWC.