Figure A.9. Simple theory of car fuel

consumption (energy per distance)

when driving at steady speed.

Assumptions: the car’s engine uses

energy with an efficiency of 0.25,

whatever the speed;*c*_{d}*A*_{car} = 1 m^{2};

*m*_{car} = 1000 kg; and *C*_{rr} = 0.01.

consumption (energy per distance)

when driving at steady speed.

Assumptions: the car’s engine uses

energy with an efficiency of 0.25,

whatever the speed;

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 m^{2}; the cyclist+bike’s mass is

90 kg; and*C*_{rr} = 0.005.

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 m

90 kg; and

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;

*c*_{d}*A*_{train} = 11 m^{2}; *m*_{train} = 400 000 kg;

and*C*_{rr} = 0.002.

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;

and

the speed. The constant of proportionality is called the coefficient of rolling

resistance, *C*_{rr}. 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