# A   Cars II

We estimated that a car driven 100 km uses about 80 kWh of energy.

Where does this energy go? How does it depend on properties of the
car? Could we make cars that are 100 times more efficient? Let’s make
a simple cartoon of car-driving, to describe where the energy goes. The
energy in a typical fossil-fuel car goes to four main destinations, all of
which we will explore:

1. speeding up then slowing down using the brakes;
2. air resistance;
3. rolling resistance;
4. heat – 75% of the energy is thrown away as heat, because the energy-
conversion chain is inefficient.

Initially our cartoon will ignore rolling resistance; we’ll add in this effect
later in the chapter.

Assume the driver accelerates rapidly up to a cruising speed v, and
maintains that speed for a distance d, which is the distance between traffic
lights, stop signs, or congestion events. At this point, he slams on the
brakes and turns all his kinetic energy into heat in the brakes. (This vehicle
doesn’t have fancy regenerative braking.) Once he’s able to move again,
he accelerates back up to his cruising speed, v. This acceleration gives the
car kinetic energy; braking throws that kinetic energy away.

Energy goes not only into the brakes: while the car is moving, it makes
air swirl around. A car leaves behind it a tube of swirling air, moving at
a speed similar to v. Which of these two forms of energy is the bigger:
kinetic energy of the swirling air, or heat in the brakes? Let’s work it out.

• The car speeds up and slows down once in each duration d/v. The
rate at which energy pours into the brakes is:
 kinetic energy = 1⁄2mcv2 = 1⁄2mcv3 , (A.1) time between braking events d/v d

where mc is the mass of the car.  Figure A.1.A Peugot 206 has a drag coefficient of 0.33. Photo by Christopher Batt.

The key formula for most of the calculations in this book is:

kinetic energy = 12mv2

For example, a car of mass m = 1000 kg moving at 100 km per hour or v = 28 m/s has an energy of

12mv2   390 000 J  0.1 kWh. Figure A.2.Our cartoon: a car moves at speed v between stops separated by a distance d.
Figure A.3.A car moving at speed v creates behind it a tube of swirling air; the cross-sectional area of the tube is similar to the frontal area of the car, and the speed at which air in the tube swirls is roughly v. 