Bicycle performance

How much power humans can generate and for how long varies with physical form. The specific power may be expressed in watts per kilogram of body mass. Active humans can produce 1.5 W/kg (untrained), 3.0 W/kg (fit), and 6.6 W/kg (top-class male athletes). 5 W/kg is about the level reachable by the highest tier of male amateurs for longer periods.[8] Maximum sustained power levels during one hour range from about 200 W (NASA experimental group of "healthy men") to 500 W (men's world hour record).[9]

The energy input to the human body is in the form of food energy, usually quantified in kilocalories [kcal] or kilojoules [kJ, which is equivalent to kWs or kilowatt-seconds]. This can be related to a certain distance travelled and to body weight, giving units such as kJ/km⋅kg. The rate of food consumption, i.e. the amount consumed during a certain period of time, is the input power. This can be measured in kcal/day or in J/s = W (1000 kcal/d ≈ 48.5 W).

This input power can be determined by measuring oxygen uptake, or in the long term food consumption, assuming no change of weight. This includes the power needed just for living, called the basal metabolic rate BMR or roughly the resting metabolic rate.

The required food can also be calculated by dividing the output power by the muscle efficiency. This is 18–26%. From the example above, if a 70 kg person is cycling at 15 km/h by expending 60 W and a muscular efficiency of 20% is assumed, roughly 1 kJ/km⋅kg extra food is required. For calculating the total food required during the trip, the BMR must first be added to the input power. If the 70 kg person is an old, short woman, her BMR could be 60 W, in all other cases a bit higher.[10] Viewed this way the efficiency in this example is effectively halved and roughly 2 kJ/km⋅kg total food is required.

Although this shows a large relative increase in food required for low power cycling, in practice it is hardly noticed, as the extra energy cost of an hour's cycling can be covered with 50 g nuts or chocolate. With long and fast or uphill cycling, the extra food requirement however becomes evident.

To complete the efficiency calculation, the type of food consumed determines the overall efficiency. For this the energy needed to produce, distribute and cook the food must be considered.

The highest speed officially recorded for any human-powered vehicle (HPV) on level ground and with calm winds and without external aids (such as motor pacing and wind-blocks, but including a defined amount of gravity assist) is 144.18 km/h (89.59 mph) set in 2016 by Todd Reichert in the Eta Speedbike, a streamlined recumbent bicycle.[12] In the 1989 Race Across America, a group of HPVs crossed the United States in just 5 days.[13][14][15][16] The highest speed officially recorded for a bicycle ridden in a conventional upright position under fully faired conditions was 82 km/h (51 mph) over 200 m.[17] That record was set in 1986 by Jim Glover on a Moulton AM7 at the Human Powered Speed Championships during Expo86 World Fair in Vancouver. The fastest bicycle speed in slipstream is 296 km/h (183.9 mph), set by Denise Mueller-Korenek in 2018 on the Bonneville Salt Flats. This involved slipstreaming behind a dragster.

Dangerous steering wobble may occur at high speeds, riding with no hands on the handle bars at lower speeds, and when the front forks are weighted with panniers.

For cycling on the level at a constant speed, a large weight reduction saves only a negligible amount of power and it is on the contrary beneficial to add mass in the form of aerodynamic improvements. But for climbing steeply, any weight reduction can be felt directly. E.g., a reduction of 10% of the total system weight (bicycle, rider, and luggage combined) will save nearly 10% power.

A reduced mass is also directly felt when accelerating. For example, the Analytic Cycling calculator Archived 2022-01-15 at the Wayback Machine gives a time/distance advantage of 0.16 s/188 cm for a sprinter with 500 g lighter wheels. In a criterium race, if a rider has to brake entering each corner, then this is wasted as heat. For a flat criterium at 40 km/h, 1 km circuit, 4 corners per lap, 10 km/h speed loss at each corner, one hour duration, there would be 160 corner "jumps". For 90 kg rider and bike, this adds roughly one third effort compared to the same ride at a steady speed, and a mass reduction of 10% of the total system weight (bicycle, rider, and luggage combined) could thus give about a 3% advantage.

The mass of tires and rims must be accelerated linearly and rotationally. It can be shown that the effect of rim and tire mass of typical spoked wheels is effectively doubled. Reducing their mass is thus especially noticeable in the case of sprints and corner "jumps" in a criterium.[19]

The power ${\displaystyle P_{D}}$ needed to overcome air drag or resistance is:

${\displaystyle P_{D}\,={\tfrac {1}{2}}\,\rho \,v_{r}^{3}\,C_{D}\,A}$ in still air, or

${\displaystyle P_{D}\,={\tfrac {1}{2}}\,\rho \,v_{a}^{2}\,v_{r}\,C_{D}\,A}$ in a headwind,

where

${\displaystyle \rho }$ is the air density, which is about 1.225 kg/m³ at sea level and 15 deg. C.[20]

${\displaystyle v_{r}}$ is the speed relative to the road,

${\displaystyle v_{a}}$ is the apparent headwind, and

${\displaystyle C_{D}\,A}$ is a characteristic area times its associated drag coefficient.

The concept of apparent wind is only directly applicable here if it comes from a true headwind or tailwind. Then ${\displaystyle v_{a}}$ is the scalar sum of ${\displaystyle v_{r}}$ and the headwind or the difference between ${\displaystyle v_{r}}$ and the tailwind. If this difference is negative, ${\displaystyle P_{D}}$ must be regarded as assistance rather than resistance. If however the wind has a sideways component, the apparent wind must be calculated with a vector sum and, especially if the bicycle is streamlined, the calculation of lateral and drag forces becomes more complex; a proper treatment involves considering the forces on the surfaces like the forces on sails.

The drag coefficient depends on the shape of the object and on the Reynolds number, which itself depends on ${\displaystyle v_{a}}$. However, if ${\displaystyle A}$ is the cross sectional area, ${\displaystyle C_{D}}$ can be roughly approximated as 1 for usual cycling speeds of a rider on an upright bicycle.

The power ${\displaystyle P_{R}}$ for overcoming the tires' rolling resistances is given by:

${\displaystyle P_{R}=v_{r}\,mg\cos(\arctan s)C_{rr}\approx v_{r}mgC_{rr}}$

where g is gravity, nominally 9.8 m/s^2, and m is mass (kg). The approximation can be used with all normal coefficients of rolling resistance ${\displaystyle C_{rr}}$. Usually this is assumed to be independent of ${\displaystyle v_{r}}$ (speed of the bicycle on the road) although it is recognized that it increases with speed. Measurements on a roller-mechanism give low-speed coefficients of 0.003 to 0.006 for a variety of tires inflated to their maximum recommended pressures, increasing about 50% at 10 m/s.[21]

The vertical climbing power ${\displaystyle P_{S}}$ on slope ${\displaystyle s}$ is given by

${\displaystyle P_{S}=v_{r}mg\sin(\arctan s)\approx v_{r}mgs}$.[22]

This approximation approaches the real solution for small, i.e. normal grades. For extremely steep slopes such as 0.35 the approximation gives an overestimation of about 6%.

As this power is used to increase the potential energy of bike and rider, it is returned as motive power when going downhill and not lost unless the rider brakes or travels faster than desired.

The power ${\displaystyle P_{A}}$ for accelerating the bike and rider having total mass m with acceleration a and rotationally also the wheels having mass ${\displaystyle m_{w}}$ is:

${\displaystyle P_{A}\approx v_{r}(m+m_{w})a}$

The approximation is valid if ${\displaystyle m_{w}}$ is assumed to be concentrated at the rims and tires and these are not slipping. The mass of such wheels can thus be counted twice for this calculation, independent of the wheels' sizes.

As this power is used to increase the kinetic energy of bike and rider, it is returned when decelerating and not lost unless the rider brakes or travels faster than desired.

The total power can be summed as:

${\displaystyle P\,=(P_{D}\,+P_{R}\,+P_{S}\,+P_{A}\,)/\eta \,}$

where ${\displaystyle \eta \,}$ is the mechanical efficiency of the drive train described at the beginning of this article.

Given this simplified equation, one can calculate some values of interest. For example, assuming no wind, one gets the following results for power delivered to the pedals (watts):

• 175 W for a 90 kg bike + rider to go 9 m/s (32 km/h or 20 mph) on the flat (76% of effort to overcome aerodynamic drag), or 2.6 m/s (9.4 km/h or 5.8 mph) on a 7% grade (2.1% of effort to overcome aerodynamic drag).
• 300 W for a 90 kg bike + rider at 11 m/s (40 km/h or 25 mph) on the flat (83% of effort to overcome aerodynamic drag) or 4.3 m/s (15 km/h or 9.5 mph) on a 7% grade (4.2% of effort to overcome aerodynamic drag).
• 165 W for a 65 kg bike + rider to go 9 m/s (32 km/h or 20 mph) on the flat (82% of effort to overcome aerodynamic drag), or 3.3 m/s (12 km/h or 7.4 mph) on a 7% grade (3.7% of effort to overcome aerodynamic drag).
• 285 W for a 65 kg bike + rider at 11 m/s (40 km/h or 25 mph) on the flat (87% of effort to overcome aerodynamic drag) or 5.3 m/s (19 km/h or 12 mph) on a 7% grade (6.1% of effort to overcome aerodynamic drag).

Reducing the weight of the bike + rider by 1 kg would increase speed by 0.01 m/s at 9 m/s on the flat (5 seconds in a 32 km/h (20 mph), 40-kilometre (25 mile) time trial). The same reduction on a 7% grade would be worth 0.04 m/s (90 kg bike + rider) to 0.07 m/s (65 kg bike + rider). If one climbed for 1 hour, saving 453 grams (1 lb) would gain between 69 and 107 metres (225 and 350 ft) – less effect for the heavier bike + rider combination (e.g., 0.06 km/h (0.04 mph) ⋅ 1 h ⋅ 1,600 m (5,200 ft)/mi = 69 m (226 ft)). For reference, the big climbs in the Tour de France and the Giro d'Italia have the following average grades:

Giro d'Italia gradients[23]

• Stelvio Pass: 7.45% over 24.3 km
• Colle delle Finestre: 9.1% over 18.6 km
• Colle dell'Agnello: 6.5% over 22 km
• Passolanciano-Maielletta, also known as Blockhaus: 9.4% over 22 km
• Plan de Corones: 10% over 5.2 km
• Mortirolo: 10.4% over 12.5 km
• Monte Zoncolan: 12% over 10.1 km

Tour de France gradients

• Tourmalet: 7%
• Galibier: 7.5%
• Alpe D'Huez: 8.6%[24]
• Mont Ventoux: 7.1%