   Figure A.9. Simple theory of car fuel
consumption (energy per distance)
Assumptions: the car’s engine uses
energy with an efficiency of 0.25,
whatever the speed; cdAcar = 1 m2;
mcar = 1000 kg; and Crr = 0.01.
Figure A.10. Simple theory of bike
fuel consumption (energy per
distance). Vertical axis is energy
consumption in kWh per 100 km.
Assumptions: the bike’s engine (that’s
you!) uses energy with an efficiency
of 0.25,; the drag-area of the cyclist is
0.75 m2; the cyclist+bike’s mass is
90 kg; and Crr = 0.005.
Figure A.11. Simple theory of train
energy consumption, per passenger, for
an eight-carriage train carrying 584
passengers. Vertical axis is energy
consumption in kWh per 100 p-km.
Assumptions: the train’s engine uses
energy with an efficiency of 0.90;
cdAtrain = 11 m2; mtrain = 400 000 kg;
and Crr = 0.002.

the speed. The constant of proportionality is called the coefficient of rolling
resistance, Crr. Table A.8 gives some typical values.

The coefficient of rolling resistance for a car is about 0.01. The effect
of rolling resistance is just like perpetually driving up a hill with a slope
of one in a hundred. So rolling friction is about 100 newtons per ton,
independent of speed. You can confirm this by pushing a typical one-ton
car along a flat road. Once you’ve got it moving, you’ll find you can keep
it moving with one hand. (100 newtons is the weight of 100 apples.) So
at a speed of 31 m/s (70 mph), the power required to overcome rolling
resistance, for a one-ton vehicle, is

force × velocity = (100 newtons) × (31 m/s) = 3100 W;

which, allowing for an engine efficiency of 25%, requires 12 kW of power
to go into the engine; whereas the power required to overcome drag was
estimated on p256 to be 80 kW. So, at high speed, about 15% of the power
is required for rolling resistance.

Figure A.9 shows the theory of fuel consumption (energy per unit distance)
as a function of steady speed, when we add together the air resistance
and rolling resistance.

The speed at which a car’s rolling resistance is equal to air resistance is 