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

From the Bureau of Transportation Statistics, National Transportation Statistics 2003

Sum forces on the vehicle

grla RRRmaF

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

Power required to overcome Ra

• Power– work/time – force*distance/time

– Ra*V

3

2VACP fDRa

sec5501

lbfthp

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

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 %)

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

Braking Force

• Ratio

• Efficiency

rear

front

fhl

fhlBFR

rlf

rlrrf

max

maxgb

We develop this to calculate braking distance – necessary for roadway design

Braking Distance

• Theoretical

• Practical

Gga

g

VVd

2

22

21

grlb

b

fg

VVS

sin2

22

21

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

Stationing – Linear Reference System

Horizontal Alignment

Vertical Alignment

0+00 1+00 2+00 3+00

100 feet

>100 feet

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

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

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

Crest Vertical Curves

221

2

200 HH

SAL

A

HHSL

2

212002

For S < L For S > L

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)

Underpass Sight Distance

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

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

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

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