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CEE320 Midterm Exam
• 10 True/false (20% of points)
• 4 Short answer (20% of points)
• 3 Calculations (60% of points)– Homework – In class examples
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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)
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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.
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Transportation Engineering
• The science of safe and efficient movement of people and goods
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Road Use Growth
From the Bureau of Transportation Statistics, National Transportation Statistics 2003
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Sum forces on the vehicle
grla RRRmaF
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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
2VACR fDa
from National Research Council Canada
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Power required to overcome Ra
• Power– work/time – force*distance/time
– Ra*V
3
2VACP fDRa
sec5501
lbfthp
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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:
WfR rlrl
147101.0
Vfrl
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Grade Resistance Rg
Composed of – Gravitational force acting on the vehicle– The component parallel to the roadway
gg WR sin
gg tansin
gg WR tanGg tan
WGRg
For small angles,
θg W
θg
Rg
G=grade, vertical rise per horizontal distance (generally specified as %)
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Engine-Generated Tractive Effort
r
MF dee
0
Fe = Engine generated tractive effort reaching wheels (lb)
Me = Engine torque (ft-lb)
ε0 = Gear reduction ratio
ηd = Driveline efficiency
r = Wheel radius (ft)
Front Wheel Drive
LhLhfl
WF
rlr
1
max
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Braking Force
• Ratio
• Efficiency
rear
front
fhl
fhlBFR
rlf
rlrrf
max
maxgb
We develop this to calculate braking distance – necessary for roadway design
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Braking Distance
• Theoretical
• Practical
Gga
g
VVd
2
22
21
grlb
b
fg
VVS
sin2
22
21
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Stopping Sight Distance (SSD)
• Worst-case conditions– Poor driver skills– Low braking efficiency– Wet pavement
• Perception-reaction time = 2.5 seconds
• Equation
rtV
Gga
g
VSSD 1
21
2
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Stationing – Linear Reference System
Horizontal Alignment
Vertical Alignment
0+00 1+00 2+00 3+00
100 feet
>100 feet
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Vertical Curve Fundamentals
G1
G2
PVI
PVT
PVC
L=curve length on horizontal
L/2
δ
cbxaxy 2
x
Choose Either:• G1, G2 in decimal form, L in feet• G1, G2 in percent, L in stations
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Relationships
G1
G2
PVI
PVT
PVC
L
L/2
δ
x
1 and 0 :PVC At the Gbdx
dYx
cYx and 0 :PVC At the
L
GGa
L
GGa
dx
Yd
22 :Anywhere 1212
2
2
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Other Properties
• K-Value (defines vertical curvature)– The number of horizontal feet needed for a
1% change in slope
A
LK
• A as a percentage• L in feet
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Crest Vertical Curves
221
2
200 HH
SAL
A
HHSL
2
212002
For S < L For S > L
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Sag Vertical Curves
G1 G2
PVI
PVTPVC
h2=0h1=H
L
Light Beam Distance (S)
tan200
2
SH
SAL
A
SSDHSL
tan2002
For S < L For S > L
headlight beam (diverging from LOS by β degrees)
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Underpass Sight Distance
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Underpass Sight Distance
• On sag curves: obstacle obstructs view
• Curve must be long enough to provide adequate sight distance (S=SSD)
2800 21
2
HHH
SAL
c
m
S<L
A
HHH
SLc
m
2800
2
21
S>L
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Horizontal Curve Fundamentals
RD
000,18
1
2cos
1RE
R
T
PC PT
PI
M
E
R
Δ
Δ/2Δ/2
Δ/2L
2tan
RT
DRL
100
180
2
cos1RM
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Stopping Sight Distance
Rv
Δs
Obstruction
Ms v
s R
SSD
180
SSD (not L)
vvs R
SSDRM
90
cos1
v
svv
R
MRRSSD 1cos
90
DRSSD s
sv
100
180
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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)
100
2
efg
VR
s
v