Environmental Engineering Reference
In-Depth Information
illustration the simple ISA architecture with a crankshaft mounted M/G is assumed.
Gear ratios for both engine and M/G will therefore be identical. For the transmis-
sion in the
i
th gear the tractive effort becomes
T
e
z
i
z
FD
h
TM
r
w
T
M
=
G
z
i
z
M
=
G
h
EM
r
w
F
trac
¼
F
eng
þ
F
M
=
G
¼
þ
ð
1
:
11
Þ
In (1.11) the gear ratios are as defined previously. Transmission and M/G
efficiencies have been included to account for losses in those components.
The next term in (1.5) to develop is the tractive effort necessary to overcome
aerodynamic drag. Representative values for drag coefficient,
C
d
, and vehicle
cross section viewed head-on from the +
X
-axis, generally taken as its frontal area,
A
f
, or approximately 90% of vehicle width,
W
, times its height,
H
, are listed in
Table 1.10. The aerodynamic drag force is
2
F
aero
¼
0
:
5
r
air
C
d
A
f
ð
V
þ
V
air
Þ
ð
N
Þ
ð
1
:
12
Þ
According to (1.12) when the vehicle is moving in the +
X
direction at velocity,
V
,
and the air has a component of speed,
V
air
,inthe
X
direction the vehicle is
moving into a headwind so the aerodynamic drag is greater than if it were moving
in still air. Conversely, a tail wind (
V
air
,inthe+
X
direction) would diminish the
aerodynamic drag force.
The third and fourth components on the right-hand side of (1.5) are front and
rear rolling resistance values. Because the vehicle weight balance is rarely 50:50,
the rolling resistance effects on the front and rear axles will in general be different.
If a moment equation is written about the
Y
-axis in Figure 1.25, the expressions for
mass partitioning noted in (1.3) result. From the vehicle specification data in
Table 1.11 and for the generic vehicle parameters listed in Table 1.10, the equations
for front and rear axle rolling resistance can be computed. Note that some texts might
expand the front axle rolling resistance to include the effects of aerodynamic force
application being off the
X
-axis so as to cause a pitching moment about the
Y
-axis,
thus loading or unloading normal force on the front axle. In this derivation such off-
axis application of aerodynamic drag forces will be neglected. The reason to
neglect the location of the aerodynamic force centre is that the distribution of drag
force across the vehicle's cross section is not known without wind tunnel test data.
The assumption that the point of aerodynamic force application is along the
X
-axis
is appropriate. An additional subtlety is the tendency of the vehicle to squat during
acceleration and dive during deceleration. Such pitching about the
Y
-axis will con-
tribute an additional normal load on the front and rear tyres, causing some modula-
tion of the tyre's rolling resistance, especially in stop-go driving. Taking such
pitching moments into account is good practice, but with modern suspension designs
that are anti-squat and anti-dive the effect of any minor pitching is entirely negligible
and are therefore not included here.
Taking as the main contributors to rolling resistance the static normal forces
and stated coefficients of rolling resistance, we obtain:
