Environmental Engineering Reference
In-Depth Information
force magnitude,
F
tyre
, and angle,
q
, relative to the vehicle longitudinal axis,
x
,
when the vehicle is negotiating a horizontal curve on a level 2 lane rural road at the
posted speed of 45 mph with four occupants (at standard mass). Road construction
guidelines specify minimum road radius and for this case a radius,
R
= 600 m, is
used. Highway safety statistics show that for
R
<
400 m on rural roads with hor-
izontal (i.e. flat) corners, accident rates increase exponentially. For this example,
assume that the propulsion force at the wheel is due mainly to rolling resistance
with an aerodynamic component and consider the fact that this vehicle has two
driven wheels, then the propulsion force
F
p
= 120 N.
Solution:
Quantify this for a single tyre using a quarter-car model composed of
¼th vehicle mass and tyre to road coefficient of friction,
m
= 0.8. Use the 2010
Prius IV data in Table 1.4 for vehicle mass of 1,383 kg plus four occupants at
M
pass
=
75.5 kg. The quarter-car mass is therefore
M
1/4
= 1,685/4 = 421 kg. The centripetal
force exerted on the tyre is then
M
1
=
4
R
421
ð
20
2
Þ
600
¼
280
:
7
V
2
F
c
¼
¼
The limiting traction force for one tyre is
Ft
lim
=
m
F
N
=
m
M
1/4
g
= 0.8(421)9.8 =
4,125.8 N, which is well beyond the cornering force. Since the propulsion force,
F
p
=
120 N, the magnitude of the force on the tyre is
h
q
ð
F
p
þ
F
c
Þ
i
tan
1
F
c
F
p
F
tyre
¼
F
tyre
¼
305
:
3
ff
66
:
8
The tyre force is directed at a large angle relative to the
y
-axis for this example
because the tractive force is so low. Consider what this might be for a Formula 1
vehicle accelerating out of a corner.
1.6 Predicting fuel economy
Vehicle fuel economy is calculated based on its performance over a standard drive
cycle. In simulations, the vehicle is characterized as closely as possible using
models for engine and driveline loss, plus aerodynamic and rolling resistance.
Actual fuel economy would be validated by 'driving' the target production vehicle
on a chassis dynamometer following this same drive cycle. Real world fuel econ-
omy is customer usage specific, but in general can be predicted using drive cycles
that are representative of geographical locations.
Fuel economy is also dependant on the type of fuel used. Standard emissions
testing and fuel economy validation require use of a standard fuel formulation
having well-established heat rate values. Generally, the lower heat rate value is
used in the calculation. For example, gasoline has a heat value of 8,835 Wh/L but
