and the rate of generation of kinetic energy in swirling air is:
So the total rate of energy production by the car is:
|power going into brakes||+||power going into swirling air||(A.2)|
Both forms of energy dissipation scale as v3. So this cartoon predicts that
a driver who halves his speed v makes his power consumption 8 times
smaller. If he ends up driving the same total distance, his journey will
take twice as long, but the total energy consumed by his journey will be
four times smaller.
Which of the two forms of energy dissipation – brakes or air-swirling –
is the bigger? It depends on the ratio of
If this ratio is much bigger than 1, then more power is going into brakes; if
it is smaller, more power is going into swirling air. Rearranging this ratio,
it is bigger than 1 if
mc > ρAd.
Now, Ad is the volume of the tube of air swept out from one stop sign
to the next. And ρAd is the mass of that tube of air. So we have a very
simple situation: energy dissipation is dominated by kinetic-energy-being-
dumped-into-the-brakes if the mass of the car is bigger than the mass of
the tube of air from one stop sign to the next; and energy dissipation is
dominated by making-air-swirl if the mass of the car is smaller (figure A.4).
Let’s work out the special distance d* between stop signs, below which
the dissipation is braking-dominated and above which it is air-swirling
dominated (also known as drag-dominated). If the frontal area of the car
Acar = 2 m wide × 1.5 m high = 3 m2