CE 578 Highway Traffic Operations

Lecture 2 and 3: Vertical Alignment and Sight Distance

Objectives

• Vertical curve design parameters

• Sight distance calculation

• Sight distance measurement

• Sight distance based design speed calculation

Vertical Curve Design Parameters

• G1 and G2 grade at tangents 1 and 2 (%)

• A change in grade (%)

• E external distance (ft)

• y vertical offset from tangent 1 to point P (ft)

• L vertical curve length (ft)

• x horizontal distance from VPC to point P (ft)

• P arbitrary pointy on curve

Vertical Curve Design Parameters (cont.)

2560

2565

2570

2575

2580

2585

2590

2595

2600

2605

2610

144

145

145

146

146

147

147

148

148

149

149

150

150

151

151

152

152

153

153

154

154

155

155

156

156

Station of P

Ele

vati

on

of

P

y E

VPI

VPC

VPT

G1

G2Px

L/2

L

Vertical Curve Equations

A G2 G1

EA L800

y 4 Ex

L

2

Pelevation VPCelevation

G1

100x y

Pstation VPCstationx

100

x 100

VPCelevation VPIelevation

G1

100

L

2

VPCstation VPIstation

L

2

100

VPTelevation VPIelevation

G2

100

L

2

VPTstation VPIstation

L

2

100

Sight Distance Calculation

• Crest vertical curve

– S <= L

– S >= L

• Solve for S• For passing conditions, usually sag curves not an issue

– Day-time conditions provide full sight of curve– Night time conditions can see head lights of on-coming vehicles

L 2 S200 h1 h2 2

A

LA S

2

100 2h1 2h2 2

Sight Distance Calculation (cont.)

• Horizontal curve (solve for S, use degrees)

– R radius from center of curvature to the middle of inside lane

– M middle ordinate or distance from sight obstruction to middle of inside lane

M R 1 cos28.65S

R

Horizontal Curve Sight Distance Measurement

Straight edge

Location of subject station

Centerlineintersect point

Sight obstruction(3.5 ft for passing)(2.75 ft for stopping)

S

Vertical Curve Sight Distance Measurement

Limit of passing sight distance

On-coming vehicle driver eye height (h2)

Driver eye height (h1) Tangent 1Tangent 2

S

Sight Distance Operational Effects

• Passing limitations– Driver ability to pass– Passing zone design

• Passing zone length

• Frequency

– Passing lane design• Driver anticipation of beginning

• Speed limitations

Assignment Problem 1

• USE PAGE 2 OF ASSIGNMENT 1• Calculate vertical curve design parameters

– Given• L• elevation of VPC• station of VPC• G1

• G2

– Find elevation and station of VPT and VPI• At VPC 236+00 curve• At VPC 251+00 curve

Assignment Problem 2

• USE PAGE 2 OF ASSIGNMENT 1• Calculate and measure the sight distance assuming

middle ordinate of 25 ft for:– PC 242+86.8 curve– PC 283+01.7 curve

• Calculate and measure the sight distance for:– VPC 236+00 curve