CEE 320
Spring 2008
Vehicle Dynamics
Example Problems
Problem 2.2
A vehicle manufacturer is considering an engine for a new sedan (CD
= 0.25, Af = 17 ft2). The car will be tested at 100 mph maximum speed
on a concrete paved surface at sea level (ρ = 0.002378 slugs/ft3).
CEE 320
Spring 2008
The car currently weights 2100 lb, but the designer selected an underpowered engine because he did not account for aerodynamic and
rolling resistances. If 2 lb of additional vehicle weight is added for
each unit of horsepower needed to overcome the neglected
resistance, what will be the final weight of the car if it is to achieve its
100 mph speed?
2.2 Answer
at Vm power = R a Vm + R rl Vm
additional power = W  550/ 2  275W
275W = 0.002378/ 2 0.30 21100 1.47 
3
CEE 320
Spring 2008
 100 1.47  
+ 0.011 +
2100 + W 100  1.47 
147


275W = 23794.4 + 6174 + 2.94 W
W = 110.2 lb
Total vehicle weight = 2210.2 lb
Problem 2.8
CEE 320
Spring 2008
A car is traveling on a paved road with CD = 0.35, Af = 21 ft2, W = 3000 lb,
ρ = 0.002378 slugs/ft3. Its engine is running at 3000 rpm and is
producing 250 ft-lb of torque. The car’s gear reduction ratio is 3.5 to 1,
driveline efficiency is 90%, driveline slippage is 3.5%, and the road-wheel
radius is 15 inches. What will the car’s maximum acceleration be under
these conditions on a level road? (assume the available tractive effort is
the engine-generated tractive effort)
Example 1
You are driving a 1989 Ford 5.0L Mustang Convertible up a snowcovered Crystal Mountain Blvd. on your way to go snowboarding with 3
friends (120 lbs each). Traffic on the road forces you temporarily stop on
a 6% uphill grade. Assuming the coefficient of road adhesion is 0.15 (no
chains), can you get moving again? If yes, How?
1989 Ford 5.0L Mustang Convertible
Horsepower 225 @ 4000 rpm
Torque 300 @ 3200 rpm
Curb Weight 3640
Weight Distribution Front 57%
CEE 320
Spring 2008
Wheelbase 100.5 in
Tire Size P225/60R15
Rear 43%
Example 2
Same situation but now you are in a 1993 Honda Civic EX sedan.
1993 Honda Civic EX sedan
Horsepower 125 @ 6300 rpm
Torque 106 @ 4800 rpm
Curb Weight 2520
Weight Distribution Front 59%
Wheelbase 103.2 in
CEE 320
Spring 2008
Tire Size P185/70R14
Rear 41%
Example 3
Same situation but now you are in a 2003 Honda Element EX 4WD.
Does the Element have to use its on-demand 4WD?
2003 Honda Element EX 4WD
Horsepower 160 @ 5500 rpm
Torque 161 @ 4500 rpm
Curb Weight 3595
Weight Distribution Front 56%
Wheelbase 101.4 in
CEE 320
Spring 2008
Tire Size P215/60R16
Rear 44%
Mass factor (γb)
1.04
Gravity (g)
32.2 ft/sec2
Coefficient of road adhesion (μ)
0.90 (good, dry)
Coefficient of rolling resistance (frl)
0.012
Grade (θ)
0 (flat)
Air density (ρ)
0.002378 slugs/ft3
Value
Palmer
(Caravan)
Turkiyyah
(X5)
Mahoney
(Explorer)
Mackenzie
(Focus)
Arduino
(Accord)
Weight
3764 lb
4519 lb
4078 lb
2677 lb
2855 lb
Drag coefficient (CD)
0.35
0.34
0.43
0.32
0.30
Braking efficiency (ηb)
0.95
0.95
0.95
0.95
0.95
Vehicle height
68.9”
67.2”
68.4”
56.8”
55.1”
Vehicle width
78.6”
73.7”
70.2”
66.7”
70.1”
Max torque
210 ft-lb
(4000 rpm)
315 ft-lb
(2600 rpm)
237 ft-lb
(3000 rpm)
133 ft-lb
(4500 rpm)
139 ft-lb
(4000 rpm)
Max power
180 hp
(5000 rpm)
324 hp
(5200 rpm)
203 hp
(5250 rpm)
136 hp
(6000 rpm)
130 hp
(5200 rpm)
18/24
13/17
16/21
26/35
23/31
Gas Mileage
Professor Braking Distance
• Braking from 60 mph to a stop
–
–
–
–
–
Rick Palmer (Dodge Caravan)
George Turkiyyah (VW Golf)
Joe Mahoney (Ford Explorer)
Pedro Arduino (Honda Accord)
Steve Muench (Honda Element)
Ka 
2
CD Af


K aV12
S
ln 1 

2 gK a  b W  f rlW  W sin  g 
 bW
CEE 320
Spring 2008

Professor Max Acceleration
• Same contenders
–
–
–
–
–
Scott Rutherford (Lexus RX 300)
George Turkiyyah (VW Golf III)
Laura Lowes (Toyota Forerunner Ltd.)
Joe Mahoney (Ford Explorer Sport)
Steve Muench (Honda Element)
CEE 320
Spring 2008
M e 0 d
Fe 
r
Fmax 

lr  f rl h 
W
L
h
1
L
Driveline efficiency (ηd)
85%
Gravity (g)
32.2 ft/sec2
Coefficient of road adhesion (μ)
0.90 (good, dry)
Value
Rutherford
(RX 300)
Turkiyyah
(Golf)
Lowes
(4Runner)
Mahoney
(Explorer)
Muench
(Element)
4WD?
YES
NO
YES
YES
YES
Weight
4065 lb
3174 lb
4055 lb
4078 lb
3578 lb
Wheel base (L)
103”
98.9”
109.8”
101.8”
101.4”
lr
58.8”
62.3”
56.8”
lf
44.2”
36.6”
44.6”
h
27”
20”
28”
30”
30”
3.938
3.78
2.804
2.48
2.864
16”
15”
16”
16”
16”
Maximum torque
242 ft-lb
(3600 rpm)
122 ft-lb
(2600 rpm)
282 ft-lb
(3800 rpm)
237 ft-lb
(3000 rpm)
161 ft-lb
(4500 rpm)
Maximum power
230 hp
(5600 rpm)
115 hp
(5200 rpm)
245 hp
(5200 rpm)
203 hp
(5250 rpm)
160 hp
(5500 rpm)
Gear reduction ratio
Tire radius