5. CEE
320
Winter
2006
Aerodynamic Resistance Ra
Composed of:
1. Turbulent air flow around vehicle body (85%)
2. Friction of air over vehicle body (12%)
3. Vehicle component resistance, from radiators
and air vents (3%)
2
2
V
A
C
R f
D
a
3
2
V
A
C
P f
D
Ra
sec
550
1
lb
ft
hp
from National Research Council Canada
6. CEE
320
Winter
2006
Rolling Resistance Rrl
Composed primarily of
1. Resistance from tire deformation (90%)
2. Tire penetration and surface compression ( 4%)
3. Tire slippage and air circulation around wheel ( 6%)
4. Wide range of factors affect total rolling resistance
5. Simplifying approximation:
W
f
R rl
rl
147
1
01
.
0
V
frl
WV
f
P rl
rl
R
sec
550
1
lb
ft
hp
7. CEE
320
Winter
2006
Grade Resistance Rg
Composed of
– Gravitational force acting on the vehicle
g
g W
R
sin
g
g
tan
sin
g
g W
R
tan
G
g
tan
WG
Rg
For small angles,
θg W
θg
Rg
8. CEE
320
Winter
2006
Available Tractive Effort
The minimum of:
1. Force generated by the engine, Fe
2. Maximum value that is a function of the
vehicle’s weight distribution and road-tire
interaction, Fmax
max
,
min
effort
tractive
Available F
Fe
10. CEE
320
Winter
2006
Engine-Generated Tractive Effort
• Force
• Power
r
M
F d
e
e
0
2
min
sec
60
rpm
engine
550
lb
ft
torque
sec
lb
ft
550
hp
Fe = Engine generated tractive effort
reaching wheels (lb)
Me = Engine torque (ft-lb)
ε0 = Gear reduction ratio
ηd = Driveline efficiency
r = Wheel radius (ft)
11. CEE
320
Winter
2006
Vehicle Speed vs. Engine Speed
0
1
2
i
rn
V e
V = velocity (ft/s)
r = wheel radius (ft)
ne = crankshaft rps
i = driveline slippage
ε0 = gear reduction ratio
13. CEE
320
Winter
2006
Maximum Tractive Effort
• Front Wheel Drive Vehicle
• Rear Wheel Drive Vehicle
• What about 4WD?
L
h
L
h
f
l
W
F
rl
f
1
max
L
h
L
h
f
l
W
F
rl
r
1
max
16. CEE
320
Winter
2006
Example
A 1989 Ford 5.0L Mustang Convertible starts on a flat grade from a dead
stop as fast as possible. What’s the maximum acceleration it can achieve
before spinning its wheels? μ = 0.40 (wet, bad pavement)
1989 Ford 5.0L Mustang Convertible
Torque 300 @ 3200 rpm
Curb Weight 3640
Weight Distribution Front 57% Rear 43%
Wheelbase 100.5 in
Tire Size P225/60R15
Gear Reduction Ratio 3.8
Driveline efficiency 90%
Center of Gravity 20 inches high
19. CEE
320
Winter
2006
Braking Distance
• Theoretical
– ignoring air resistance
• Practical
• Perception
• Total
g
rl
b
b
f
g
V
V
S
sin
2
2
2
2
1
G
g
a
g
V
V
d
2
2
2
2
1
p
p t
V
d 1
p
s d
d
d
a
V
V
d
2
2
2
2
1
For grade = 0
20. CEE
320
Winter
2006
Stopping Sight Distance (SSD)
• Worst-case conditions
– Poor driver skills
– Low braking efficiency
– Wet pavement
• Perception-reaction time = 2.5 seconds
• Equation
r
t
V
G
g
a
g
V
SSD 1
2
1
2
22. CEE
320
Winter
2006
SSD – Quick and Dirty
a
V
V
V
V
G
g
a
g
V
V
d
2
2
2
2
2
1
2
2
2
1
075
.
1
2
.
11
075
.
1
2
.
11
1
2
47
.
1
0
2
.
32
2
.
11
2
.
32
2
0
47
.
1
2
1. Acceleration due to gravity, g = 32.2 ft/sec2
2. There are 1.47 ft/sec per mph
3. Assume G = 0 (flat grade)
p
p
p Vt
t
V
d 47
.
1
47
.
1 1
V = V1 in mph
a = deceleration, 11.2 ft/s2 in US customary units
tp = Conservative perception / reaction time = 2.5 seconds
p
s Vt
a
V
d 47
.
1
075
.
1
2
24. CEE
320
Winter
2006
Primary References
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005).
Principles of Highway Engineering and Traffic Analysis, Third
Edition). Chapter 2
• American Association of State Highway and Transportation
Officals (AASHTO). (2001). A Policy on Geometric Design of
Highways and Streets, Fourth Edition. Washington, D.C.
