given by

that is,



For a bicycle (m = 90 kg, A= 0.75 m2), the transition from rolling-resist-
ance-dominated cycling to air-resistance-dominated cycling takes place at
a speed of about 12 km/h. At a steady speed of 20 km/h, cycling costs
about 2.2 kWh per 100 km. By adopting an aerodynamic posture, you can
reduce your drag area and cut the energy consumption down to about
1.6 kWh per 100 km.


For an eight-carriage train as depicted in figure 20.4 (m = 400 000 kg,
A = 11 m2), the speed above which air resistance is greater than rolling
resistance is

v = 33 m/s = 74 miles per hour.

For a single-carriage train (m = 50 000 kg, A = 11 m2) , the speed above
which air resistance is greater than rolling resistance is

v = 12 m/s = 26 miles per hour.

Dependence of power on speed

When I say that halving your driving speed should reduce fuel consumption
(in miles per gallon) to one quarter of current levels, some people feel
sceptical. They have a point: most cars’ engines have an optimum revolution
rate, and the choice of gears of the car determines a range of speeds at
which the optimum engine efficiency can be delivered. If my suggested ex-
periment of halving the car’s speed takes the car out of this designed range
of speeds, the consumption might not fall by as much as four-fold. My tacit
assumption that the engine’s efficiency is the same at all speeds and all
loads led to the conclusion that it’s always good (in terms of miles per gallon)
to travel slower; but if the engine’s efficiency drops off at low speeds,
then the most fuel-efficient speed might be at an intermediate speed that
makes a compromise between going slow and keeping the engine efficient.
For the BMW 318ti in figure A.12, for example, the optimum speed is about
60 km/h. But if society were to decide that car speeds should be reduced,
there is nothing to stop engines and gears being redesigned so that the
peak engine efficiency was found at the right speed. As further evidence

Figure A.12. Current cars’ fuel consumptions do not vary as speed squared. Prius data from B.Z. Wilson; BMW data from Phil C. Stuart. The smooth curve shows what a speed-squared curve would look like, assuming a drag-area of 0.6 m2.
Figure A.13. Powers of cars (kW) versus their top speeds (km/h). Both scales are logarithmic. The power increases as the third power of the speed. To go twice as fast requires eight times as much engine power. From Tennekes (1997).