October 23, 2010

Operating at peak efficiency, the human body's efficiency at converting energy from food to work through pedaling is quite similar to that of an automobile: Wilson [1] puts human efficiency at between 20 and 30 percent, while Pietro [2] finds it varies between 22 and 26 percent. The remainder is released as heat or is contained in bodily waste. The exact efficiency achieved depends on the athleticism and training of the cyclist, the resistance supplied, and pedaling speed. Automobile engines, on the other hand, tend to average about 20% efficiency; while the combustion engine has higher peak efficiency, the human body is able to operate at close to maximum efficiency in a variety of situations. For the purposes of this paper it will be assumed that the human body has 25% mechanical efficiency while cycling.

Once energy is delivered to the pedals of the bicycle, there are a number of mechanical factors which can dissipate it before and after it is stored in the mechanical and gravitational potential energy of the bike and rider. Rolling friction is a term referring to the frictional forces present in the interfaces between gear sprockets and chains, wheel mounts and axles, tires and the road surface; when the bike is moving, all of these interactions dissipate energy as heat. As it turns out, well-maintained bicycles lose an insignificant amount of energy in the gears and drive chains that transmit work from the pedals to the rear wheel: a new and lubricated chain can have an efficiency of upwards of 98.5 percent. [1] Most of the rolling friction therefore stems from the friction between the tire and the ground, which experiment shows to be proportional to the weight of the bike and rider. The ratio of rolling friction to weight is known as the rolling coefficient. On concrete or asphalt roads, the type of tire and pressure used on a bicycle can cause the rolling coefficient to vary from .017-.0021 yielding rolling resistances of 14.2 to 1.8 N for a bicycle and rider weighing a combined 85 kg. [2]

The dominant dissipative effect on the kinetic energy
of a quickly-traveling bicycle on level ground is wind resistance. [1]
The actual friction between the bike and rider and the air is small; the
majority of the dissipated energy is lost as the travelling bicycle
pushes air out of the way, creating a turbulent wake [1]. As this
resistive force is proportional to the square of the velocity of the
bicycle, it is described by the dimensionless drag coefficient of the
bicycle and rider C = 2 F/(&rho v^{2} A), where F is the
frictional force, ρ the density of air, v the velocity, and A the
cross-sectional area. It is measured experimentally that for a 70 kg
rider 175 cm in height, a "traditional" bike with the cyclist in a
sitting posture has C = 1.1 and A = 0.51 m^{2}, while for top
racing bikes with riders in a "dropped" posture C = 0.65 and A = 0.40
m^{2}. [2]

Taking the worst case scenario for both the rolling
friction and wind resistance for a 70 kg rider with 15 kg bicycle
travelling at 10 m/s, we calculate (using ρ = 1.2
kg/m^{3})

The air resistance term would begin to dominate completely if we took higher velocities, but this seems like a reasonable estimate for a casual commuter cyclist.

Combining this with the results from the first section, we see that a bicyclist weighing 70 kg with a 15 kg bike traveling at 10 m/s uses up (in the worst case) approximately

If we had instead used the best case numbers from above, we would have calculated a power usage of approximately 696 W = 0.17 kcal/s, a factor of 3 improvement in efficiency.

© Ben Stetler. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] D. Wilson, *Bicycle Science* (MIT
Press,2004).

[2] P. Pietro, "Cycling on Earth, in Space, on the
Moon," European Journal of Applied Physiology **82**, 345 (2000).