## Bicycles and the scaling trick

Power Efficiency Guide

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Here's a fun question: what's the energy consumption of a bicycle, in kWh per 100 km? Pushing yourself along on a bicycle requires energy for the same reason as a car: you're making air swirl around. Now, we could do all the calculations from scratch, replacing car-numbers by bike-numbers. But there's a simple trick we can use to get the answer for the bike from the answer for the car. The energy consumed by a car, per distance travelled, is the power-consumption associated with air-swirling,

Drag coefficients divided by the speed, v; that is, energy per distance

The "4" came from engine inefficiency; p is the density of air; the area A = cdAcar is the effective frontal area of a car; and v is its speed.

Now, we can compare a bicycle with a car by dividing 4 x \pAv2 for the bicycle by 4 x jpAv2 for the car. All the fractions and ps cancel, if the efficiency of the carbon-powered bicyclist's engine is similar to the efficiency of the carbon-powered car engine (which it is). The ratio is:

energy per distance of bike cJdlkeAbikev^

bike energy per distance of car cdarAcarvjar

The trick we are using is called "scaling." If we know how energy consumption scales with speed and area, then we can predict energy con

Drag coefficients

 Cars Honda Insight 0.25 Prius 0.26 Renault 25 0.28 Honda Civic (2006) 0.31 VW Polo GTi 0.32 Peugeot 206 0.33 Ford Sierra 0.34 Audi TT 0.35 Honda Civic (2001) 0.36 Citroen 2CV 0.51 Cyclist 0.9 Long-distance coach 0.425 Planes Cessna 0.027 Learjet 0.022 Boeing 747 Land Rover Discovery 1.6 Volvo 740 0.81 Typical car 0.8 Honda Civic 0.68 VW Polo GTi 0.65 Honda Insight 0.47 Table A.7. Drag coefficients and drag areas. sumption of objects with completely different speeds and areas. Specifically, let's assume that the area ratio is Abi bike (Four cyclists can sit shoulder to shoulder in the width of one car.) Let's assume the bike is not very well streamlined: And let's assume the speed of the bike is 21 km/h (13 miles per hour), so vbike _ 1 Then energy-per-distance of bike energy-per-distance of car d'ke ^bike \ ,car A 'd Ac ^car vbike