Environmental Engineering Reference
In-Depth Information
In what follows some simple equations will be employed to illustrate the
propulsion power demand on a mid-size sedan type vehicle. The exemplar vehicle
is assumed to have the properties listed in Table 4.1, and these can be verified by
going to any automotive manufacturer's website.
Table 4.1 Attributes of a mid-size automobile
Vehicle
mass
Frontal
area
Coefficient of
drag
Coefficient of
rolling resistance
Vehicle speed
(60 mph)
0-60 mph
Accel time
A
f
(m
2
)
M
v
(kg)
C
d
(#)
C
rr
(kg/kg)
V
(m/s)
t
z
60
(s)
1,500
2.2
0.28
0.009
26.8
9
In addition to the vehicle attributes listed in Table 4.1, the solution of aero-
dynamic power requires air density, which will be taken as the standard tempera-
ture and pressure value at sea level, of
r
= 1.2 kg/m
3
. So, equipped with the vehicle
attributes and air density, the propulsion power during acceleration (neglecting
aerodynamic and rolling) is
P
accel
¼
F
accel
V
¼
MaV
¼
M VV
ð
4
:
1
Þ
Example 1:
Using (4.1) and data from Table 4.1, calculate the peak acceleration
power of a mid-sized vehicle over its 0-60 mph time.
Solution:
Direct substitution of values into (4.1) yields
26
:
82
¼
120 kW
26
:
82
9
P
accel
¼
1
;
500
Given the caveats in (4.1), the acceleration power demanded of the engine is
120 kW minimum to meet the acceptable acceleration performance.
During cruise in still air and level ground, the dominant contributors to pro-
pulsion power are aerodynamic drag and tyre rolling resistance (i.e. sidewall
compression losses). So, during constant speed cruise at 60 mph, the vehicle engine
need only sustain a relatively small power,
P
cruise
, defined as
P
cruise
¼
F
roll
V
þ
F
aero
V
P
cruise
¼ð
C
rr
Mg
Þ
V
þð
1
=
2
r
air
C
d
A
f
V
2
ð
4
:
2
Þ
Þ
V
This was a quick trip through the physics of vehicle aerodynamic drag and
rolling resistance, all incorporating only Newton's laws. The factor
g
is earth's
gravity of 9.8 m/s
2
. Note that the power needed to sustain vehicle cruise on level
