CEE320 Midterm Exam
• 10 True/false (20% of points)
• 4 Short answer (20% of points)
• 3 Calculations (60% of points)
– Homework
– In class examples
Course material covered
•
•
•
•
Introduction
Vehicle dynamics (chapter 2)
Geometric design (chapter 3)
Pavement design (chapter 4 except 4.3,
4.5, including 4th power thumbrule)
Suggestions for Preparation
• Review each lecture and identify the main points
and formulas. Write these on summary notes.
• For each lecture, write an question. Do this in a
group, and share questions.
• Solve these questions from scratch, do not just
review solutions.
• Review homework and in class examples. Do
the problem yourself.
• Make a list of the tables in the text, their title,
and the page number. Include a note of what it
is used for.
Transportation Engineering
• The science of safe and efficient movement
of people and goods
Road Use Growth
Increase Multiple (Based on 1960 Values)
4.00
3.50
Vehicle Miles Traveled
3.00
2.50
Registered Vehicles
Statute Miles of Roadway
2.00
1.50
1.00
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Year
From the Bureau of Transportation Statistics, National Transportation Statistics 2003
Sum forces on the vehicle
F  ma  Ra  Rrl  Rg
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%)
Ra 
from National Research Council Canada

2
CD Af V 2
Power required to overcome Ra
• Power
– work/time
– force*distance/time
– Ra*V

3
PR  C D A f V
2
a
ft  lb
1 hp  550
sec
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:
Rrl  f rlW
V 

f rl  0.011 

 147 
Grade Resistance Rg
Composed of
– Gravitational force acting on the vehicle
– The component parallel to the roadway
Rg  W sin  g
θg
For small angles, sin  g  tan  g
Rg  W tan  g
tan  g  G
Rg  WG
Rg
θg
W
G=grade, vertical rise per horizontal distance (generally specified as %)
Engine-Generated Tractive
Effort
M e 0 d
Fe 
r
Fe = Engine generated tractive
effort reaching wheels (lb)
Me = Engine torque (ft-lb)
ε0 = Gear reduction ratio
ηd = Driveline efficiency
r = Wheel radius (ft)
Fmax 
W
lr  f rl h 
L
h
1
L
Front Wheel Drive
Braking Force
• Ratio
BFR f
• Efficiency
r max
b 
lr  h  f rl  front


l f  h  f rl  rear
g max

We develop this to calculate braking distance – necessary for roadway design
Braking Distance
• Theoretical
• Practical
 b V12  V22 
S
2 g b   f rl  sin  g 
V12  V22
d
a

2 g   G 
g

Stopping Sight Distance (SSD)
• Worst-case conditions
– Poor driver skills
– Low braking efficiency
– Wet pavement
• Perception-reaction time = 2.5 seconds
• Equation
2
V1
SSD 
 V1t r
a

2 g   G 
g

Stationing – Linear Reference
System
Horizontal Alignment
0+00
2+00
1+00
Vertical Alignment
100 feet
>100 feet
3+00
Vertical Curve Fundamentals
G1
PVC
PVI
δ
G2
PVT
L/2
L=curve length on horizontal
x
y  ax  bx  c
2
Choose Either:
• G1, G2 in decimal form, L in feet
• G1, G2 in percent, L in stations
Relationships
At the PVC : x  0 and Y  c
dY
 b  G1
dx
At the PVC : x  0 and
d 2Y
G2  G1
G2  G1
Anywhere :
 2a 
a
2
dx
L
2L
G1
PVC
PVI
δ
G2
PVT
L/2
L
x
Other Properties
• K-Value (defines vertical curvature)
– The number of horizontal feet needed for a
1% change in slope
L
K
A
• A as a percentage
• L in feet
Crest Vertical Curves
For S < L
AS 
For S > L
2
L

200 H1  H 2

2

200 H1  H 2
L  2S  
A

2
Sag Vertical Curves
Light Beam Distance (S)
G1
headlight beam (diverging from LOS by β degrees)
PVT
PVC
h1=H
G2
PVI
h2=0
L
For S < L
AS 
L
200H  S tan  
2
For S > L
200H  SSD  tan  
L  2S  
A
Underpass Sight Distance
Underpass Sight Distance
• On sag curves: obstacle obstructs view
• Curve must be long enough to provide
adequate sight distance (S=SSD)
S<L
S>L
AS 
Lm 
H1  H 2 

800 H c 

2


2
H1  H 2 

800 H c 

2


Lm  2S 
A
Horizontal Curve Fundamentals
 1

E  R
 1
 cos  2 
T  R tan
PI
E

2
18,000
D
 R

100
L
R 
180
D


M  R1  cos 
2

Δ
T
M
PC
L
Δ/2
R
PT
R
Δ/2 Δ/2
Stopping Sight Distance

100 s
SSD 
Rv  s 
180
D
SSD (not L)
180SSD 
s 
Rv
Ms

 90 SSD 

M s  Rv 1  cos
 Rv 

Rv 
 Rv  M s 

SSD 
cos 
90 
 Rv 
1
Obstruction
Rv
Δs
Superelevation
• Minimum radius that
provides for safe
vehicle operation
• Given vehicle
speed, coefficient of
side friction, gravity,
and superelevation
• Rv because it is to
the vehicle’s path
(as opposed to edge
of roadway)
Rv 
V2
e 

g fs 

100 
