Environmental Engineering Reference
In-Depth Information
where
is a small dimensionless constant that accounts for the rotational inertia of the wheels and
drive train, and
dV
/
dt
is the acceleration of the vehicle. Of course, when the vehicle decelerates
(
dV
0) by using the brakes or closing the throttle, the negative power of equation (8.13) does
not put power back into the engine, so that
P
acc
is effectively zero during deceleration. In electric
drive vehicles, some of the deceleration energy can be recovered, stored in batteries, and used later
in the operating cycle, saving fuel.
The total power thus becomes
/
dT
<
P
=
P
acc
+
P
roll
+
P
hill
+
P
air
mV
V
3
2
dV
dt
+
)
ρ
=
(
1
+
)
C
R
g
+
g
sin
θ
+
(
C
D
A
(8.14)
The first three terms on the right-hand side of equation (8.14), the power required to accelerate the
vehicle, overcome the rolling resistance, and climb a hill, are each proportional to the vehicle mass
m
. In contrast, the last term, the power needed to overcome aerodynamic drag, is independent of
the vehicle mass, depending instead on the vehicle frontal area
A
, which is nearly the same for all
light duty passenger vehicles (see Table 8.2) but is noticeably larger for light-duty trucks. For a
given driving cycle, heavy cars will require more powerful engines and will consume more fuel,
more or less in proportion to vehicle mass (see Table 8.2), than will light vehicles. A very fuel
efficient vehicle is necessarily a light one.
For driving at a steady speed, only rolling and aerodynamic resistance must be overcome, the
power required being
V
3
2
)
ρ
P
steady
=
C
R
mgV
+
(
C
D
A
(8.15)
For the typical passenger vehicle, the rolling and aerodynamic resistance are equal at a speed of
about 60 km/h. For highway cruising at 120 km/h, the aerodynamic drag would be four times the
rolling resistance, the power required being less dependent upon vehicle mass than when driving
at low speed.
The parameters of vehicle design that lead to increased fuel economy include low values of
vehicle mass
m
, drag area product
C
D
A
, and rolling resistance coefficient
C
R
. In addition, recovery
of vehicle kinetic energy during deceleration for reuse during other portions of the driving cycle
will also improve vehicle fuel economy.
8.4.1
Connecting the Engine to the Wheels
Engine power is a maximum at the highest engine speed
N
m
, but less power is available at lower
engine speeds (see Figure 8.4). If we wish to maximize the power available at all vehicle speeds, it
is necessary to reduce the ratio of engine speed to wheel speed as the vehicle speed increases. This
is accomplished in the transmission, a device attached to the engine that provides stepped speeds
to the drive shaft that connects it to the wheels.
There are two forms of transmission: manual and automatic. In a vehicle with a normal trans-
mission, the vehicle operator disengages a clutch and manually shifts to a different gear before
engaging the clutch again. In an automatic transmission, a fluid coupling replaces the clutch and gear
shifting is accomplished by computer-controlled hydraulic actuators. The more operator-friendly
