
Cycling is a complex sport in which competitors must contend with a variety of strategies employed by opponents as well as many environmental factors. Chief among the latter is the hilliness of the terrain. Performance on hills is a primary factor in determining success in the major international cycling competitions. In this article I present a review of current scientific knowledge related to cycling up and down hills and describe what athletes can do to improve their performance on hills.
Competitive events in cycling include road races, time trials, and criteriums. Each of these present different challenges to the athletes.
Road races are characterized by the mass start. All riders begin together as part of the peloton, although individuals are actually members of separate teams. The principal concerns affecting road race performance are team tactics and drafting. Because riders remain grouped in the peloton, only the few who are in the front at any one time face the full effects of wind resistance, while others can easily maintain the peloton's pace by drafting. Usually, breakaway riders can outdistance the peloton only when the complex dynamics of team support allow it. The major exception to this rule, as discussed later, occurs when the peloton encounters hills.
Time trials pose different problems. Individual riders face the wind and the clock on their own. Individual power and endurance ultimately determine performance. For this reason, the time trial has received the nickname "the race of truth." Professional stage races, such as the Tour de France, utilize time trial stages to separate contenders from support riders (i.e. domestiques) in the overall standings, as well as winners from contenders. Triathletes are essentially engaging in a time trial during the bicycle leg of their competition.
Criterium races are mass start events held on a small, looped course. Riders perform multiple circuits of the course, with highspeed sharp turns. Performance is based largely on bike handling skills and sprint speed.
Of the three basic forms of bicycle races, the road race is the one most noted for its use of hilly terrain. The ensuing discussion of factors influencing performance on the hills will generally assume that a road race is involved.
As indicated in the following equation, there are three primary forces to be overcome in bicycling: rolling resistance, air resistance and gravity:
where W is power, k_{r} is the rolling resistance coefficient, M is the combined mass of cyclist and bicycle, s is the bicycle speed on the road, k_{a} is the air resistance coefficient, A is the combined frontal area of cyclist and bicycle, v is the bicycle speed through the air (i.e. road speed plus head wind speed), g is the gravitational acceleration constant, and i is the road incline (grade; however, this is only an approximation, as the sine of the road angle to the horizontal should technically be used).
On modern bicycles with narrow, high pressure tires, rolling resistance is negligible. Since the power required to overcome air resistance is proportional to the bicycle speed cubed (if there is no wind, and s = v), an exponential increase in power is needed as the cyclist attempts to increase speed.
Going uphill adds gravity to the forces that must be overcome. Since the cyclist has a finite power supply, he or she must necessarily slow down in proportion to the steepness of the hill, if steadystate aerobic metabolism is to be maintained. While this effect of hills is obvious, more subtle effects of this shift in forces have a dramatic impact on the competition.
Consider the effects of gradually increasing the road incline above zero while holding power constant. Since the air resistance component is proportional to speed cubed, only a relatively small decrease in speed is needed to offset an increase in incline at first. As the incline continues to increase, relatively greater decreases in speed must occur, given the curvilinear nature of the speed cubed relationship. Thus, a steep hill is required to substantially slow a competitive cyclist. The precise percent grade which has a meaningful impact cannot be specified, however, as this depends on the sustainable power level of each individual cyclist.
Given that the appropriate steepness has been reached, a major change in race dynamics occurs. As gravity supersedes air resistance as the primary force that must be overcome, drafting becomes a relatively less useful tool in the competition. At very slow speeds (on the order of 16 km·hr^{1} or less) air resistance is negligible, and drafting becomes nearly meaningless.
This shift in forces causes the peloton of a road race to break up, as those cyclists who have the highest aerobic power can outdistance less aerobic competitors who are now deprived of drafting derived assistance. An interesting aspect of this shift is to note that smaller cyclists generally excel on hill climbs, while larger cyclists are generally better on solo efforts on level ground. As a consequence of scaling geometry, mass increases with the cube of height, while surface area only increases with the square of height. This means that, although larger cyclists have a greater total frontal area to push through the air than smaller cyclists, their advantage in mass (and power generating capacity) is even greater. As a consequence, large cyclists have a higher ratio of power to frontal area than smaller cyclists, giving large cyclists an advantage in overcoming air resistance, as observed in time trials. It is not surprising that Miguel Indurain, the preeminent time trialist of the 1990's, was larger than most of his rivals.
However, since air resistance is negligible at slow climbing speeds, all cyclists are at a similar energy cost, relative to their body weight. Small cyclists excel at hill climbing because they generally have greater relative aerobic power (VO2max in ml·min^{1}·kg^{1 }) than do large cyclists. This is also a consequence of scaling geometry: relative to body mass, smaller organisms have greater alveolar and capillary surface areas in the lungs, greater capillary surface areas in the muscles, and greater crosssectional area of arteries for the delivery of blood. Examinations of elite endurance athletes from a variety of sports, including cycling, have revealed that VO2max scales with the 2/3 power of mass; that is, if a 60kg elite athlete has a VO2max of 80 ml·min^{1}·kg^{1}, then a comparably trained elite athlete who weighs 100 kg would be expected to have a VO2max of only 68 ml·min^{1}·kg^{1}. Thus, at the elite level, one expects superior performance from smaller athletes in aerobic events where power requirements are approximately proportional to body masssuch as distance running and uphill cycling. (Technically, the power requirement scales more closely to mass, i.e. M^{0.760.79} than does the power supply, M^{0.67}). It is not surprising that the preeminent climber of the 1990s, Marco Pantani, is one of the smallest men in the peloton at only 55 kg. Anything that can be done to reduce the weight of a cyclist and bicycle, without compromising the cyclist's aerobic power, will improve hillclimbing performance.
While the power requirements of cycling uphill can be easily described, there are many factors which affect a cyclist's ability to economically apply that power. Having a high sustainable aerobic power will not translate into superior speed unless it is effectively converted into external motion.
One factor that influences cycling economy is pedal cadence. A number of studies have demonstrated that cadences of 80 to 90 rpm allow the most economical use of aerobic metabolism when performing at high power outputs in level cycling. Despite this, competitive cyclists are often observed to climb hills at substantially lower cadences.
The reasons that some cyclists appear to prefer lower cadences during hill climbing are not clear. However, a simple mechanical explanation is evident. The addition of the gravitational component to the forces opposing the cyclist necessitate a marked reduction in road speed. Unless the cyclist has correspondingly lower gear ratios available on his or her bicycle, pedal cadence will fall. Road racers often do not possess sufficiently low gear ratios on their bicycles, unlike competitors in the offroad sport of mountain biking.
Perhaps due to the low cadences during climbs, road racers are often observed to stand while pedaling. This strategy effectively shifts their body weight forward over the pedals, which might allow for greater force production for the low speed, high force revolutions.
While these potential benefits should be examined, a laboratory investigation of climbing demonstrated that a high cadence (80  90 rpm) elicited the lowest oxygen consumption, just as was previously shown for level cycling. From available scientific evidence, it would appear that the use of lower gear ratios on climbs might enhance performance.
During descents, the negative slope of the hill in the power equation reflects the addition of gravitational potential energy to the power generated by the cyclist. In a freewheel (passive) descent, the cyclist's speed will be determined by the balance of the air resistance force and the gravitational force. As the cyclist accelerates, sv^{2} increases. Once k_{a}Asv^{2} (plus the negligible power term associated with rolling resistance) increases to match giMs, the cyclist will reach terminal velocity. Any further increase in speed must be achieved by adding energy through pedaling. However, on steep hills, terminal velocities may reach 70 km·hr^{1}. At such high associated values of sv^{2}, even the application of VO2max would result in only a minimal increase in speed.
Terminal velocity can be solved for in the cycling equation above by setting power at 0. If one assumes the rolling resistance term is also 0, and that there is no wind blowing (v = s), then the equation becomes:
Thus, the terminal velocity is roughly proportional to the square root of the ratio of M/A. Scaling reveals that larger cyclists have a greater ratio of mass to frontal area. They therefore descend hills faster as a consequence of purely physical, not physiological, laws. Since the larger cyclist has a greater mass, gravity acts on him or her with a greater force than it does on a smaller cyclist. (Note: A common misconception is to note the equal acceleration of two different sized objects in free fall in a vacuum, and assume that the force of gravity on both is equal. The force on the more massive object is greater, being exactly proportional to mass, which is why the more massive object is accelerated at the same rate as the less massive one.) While the larger cyclist also has a greater absolute frontal area than the smaller cyclist, the difference is not as great as that for their masses. Thus, the larger cyclist will attain a greater s^{3} before a balance of forces results in terminal velocity.
With lighter cyclists climbing hills faster due to their greater relative VO2max, and heavier cyclists descending faster due to their greater M/A ratio, one might assume that equal performances would occur in races involving equal up and down segments. However, ascents take longer than descents, so a speed advantage to small cyclists on the acsents produces a greater time advantage than large cyclists obtain on the descents. For this reason, smaller cyclists are generally superior competitors on hilly road races.
On very steep descents, the cyclist needs to pedal only to assist gravity in obtaining terminal velocity; i.e. during the initial acceleration at the beginning of the descent and when coming out of turns. During most of the descent, the cyclist freewheels. It follows that the cyclist can expend exhaustive effort on the ascent, since he or she is able to rest on the descent.
On hills of a more modest grade, should the cyclist maintain an even effort uphill and downhill? On a level road surface, a constant power application results in the fastest time over a given distance. Varying power results in speed fluctuations that add time to an overall performance. On hills, the ascents and descents create variations in speed even when the cyclist maintains a constant effort. Since more time is added during the climb than can be taken back on the descent, it would be competitively advantageous to apply greater effort during the ascent, in order to minimize the time added. Of course, energy supplies are finite, and the cyclist must compensate by reducing effort on the descent, as a means of recovery. This variable power strategy would reduce the magnitude of the speed fluctuations in going up and down hill, bringing the cyclist slightly closer to the ideal state of maintaining a constant speed. A computer simulation has demonstrated that this strategy results in the fastest time when riding up and down hills of any grade; the higher the grade, the more effective the strategy becomes.
The power variation needed to completely eliminate speed fluctuations would be physiologically impossible. However, the computer simulation demonstrated that even a modest increase in power (such as 5% above that typically used in level cycling) during the uphill portion of a ride would significantly reduce total time on a course with equal uphill and downhill segments. The greater the variation in power that the cyclist can handle, the greater the advantage in performance time. On climbs that are followed by steep descents, the cyclist should apply the greatest power he or she can sustain for the duration of the climb. As noted at the beginning of this section, the freewheel descent allows almost complete rest. It should also be noted that the computer simulation demonstrated that the variable power strategy is also effective in countering the effects of varying wind conditions.
The primary forces a cyclist must overcome are air resistance and gravity. Air resistance increases exponentially with speed. In the transition from cycling on a flat road to climbing a hill, the decreased speed reduces air resistance to the point where drafting other riders provides little benefit. At this point, riders with superior aerobic power to weight ratios will be able to breakaway from the peloton. Due to scaling considerations, this favors smaller riders. Climbing ability can be enhanced by minimizing weight, and also by pedaling at a consistently high cadence. Large cyclists can achieve greater downhill speeds, but overall performance still favors smaller cyclists on hilly courses. Overall performance is enhanced by using a variable power strategy: increasing effort slightly on uphills and compensating with decreased effort on downhills. On extremely steep descents, it is necessary to pedal only at the start and when coming out of turns, in order to quickly achieve terminal velocity.
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