mileage figures for cars quoted in Chapter 3. Moreover, the theory gives
insight into how the energy consumed by your car could be reduced. The
theory has a couple of flaws which we’ll explore in a moment.

Could we make a new car that consumes 100 times less energy and still
goes at 70mph? No. Not if the car has the same shape. On the motorway
at 70mph, the energy is going mainly into making air swirl. Changing the
materials the car is made from makes no difference to that. A miraculous
improvement to the fossil-fuel engine could perhaps boost its efficiency
from 25% to 50%, bringing the energy consumption of a fossil-fuelled car
down to roughly 40 kWh per 100 km.

Electric vehicles have some wins: while the weight of the energy store,
per useful kWh stored, is about 25 times bigger than that of petrol, the
weight of an electric engine can be about 8 times smaller. And the energy-
chain in an electric car is much more efficient: electric motors can be 90%
efficient.

We’ll come back to electric cars in more detail towards the end of this
chapter.

### Bicycles and the scaling trick

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,

divided by the speed, v; that is,

The “4” came from engine inefficiency; ρ 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 × 12ρAv2 for
the bicycle by 4 × 12ρAv2 for the car. All the fractions and ρs 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:

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
Citroën 2CV 0.51
Cyclist 0.9
Long-distance coach 0.425
PLANES
Cessna 0.027
Learjet 0.022
Boeing 747 0.031

DRAG-AREAS (m2)
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.