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