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JCE4600Fundamentals of Traffic Engineering

Introduction to Geometric Design

Agenda Kinematics

Human Factors

Stopping Sight Distance

Cornering

Intersection Design

Cross Sections

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AASHTO Green Book

Kinematics

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Equations of Motion

v = vo+at x = vot + 0.5at2

x = (v2-vo2)/(2a)

x = distance traveled v = final velocity vo = initial velocity a = acceleration t = time

Brake Distance v = 0

x = (vo2)/(2a)

How do we determine acceleration?

Major Sources of Resistance

Grade

Rolling

Aerodynamic

Ra – Aerodynamic Rrlf – Rolling, front Rrlr – Rolling, rear Ff – Friction, front Fr – Friction, rear W – Weight g – Grade angle m – Vehicle mass a – Acceleration

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Balance of Forces Force balance

Friction force = Acceleration force + resistance

ma = ± FFriction ± FGrade – Force Resistance

Rolling and Aerodynamic forces are typically discounted

FFriction = fWN = fWcosg

FGrade = sing

f=friction coefficient

Breaking Distance

Db = Breaking Distance (ft)

v = final velocity (ft/sec)

vo = initial velocity (ft/sec)

g = gravity force (32.2 ft/sec2)

f = friction coefficient

G = Percent Grade/100

Db = Breaking Distance (ft)

v = final velocity (mph)

vo = initial velocity (mph)

f = friction coefficient

G = Percent Grade/100

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Friction Coefficient

Friction between sliding objects is lower than when the same objects are still

This is why it is harder to push something from standstill than keeping it moving

Tires that are not slipping have a zero velocity at the point they touch the ground; thus - maximum friction

Friction Chart

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Road Adhesion

Pavement Maximum Friction

Slide Friction

Good, dry 1.0 0.8

Good, wet 0.9 0.6

Poor, dry 0.8 0.55

Poor, wet 0.6 0.3

Ice 0.25 0.1

Antilock Braking Systems

Serve three purposes Allow steering while braking

Keep wheels from locking to maintain the coefficient of road adhesion from dropping to the sliding values

Achieve a braking efficiency near 1.0 by appropriately managing the braking force ratio between the front and the rear

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Braking Distance Example

A student drove his 1983 Dodge into a dorm adjacent to the student parking lot. Police found 30’ long skid marks leading to the point of impact. The damage assessment found that the speed at the time of impact was 10 mph. The parking lot was level, and the pavement was wet (f = 0.6). The speed limit in the parking lot is 15 mph. How fast was the student traveling at the time that he began to skid?

Was he speeding?

What would have the impact speed have been had the parking lot been on a 6% uphill grade ? How about a 3% downhill grade?

What would the impact speed have been given level, icy pavement (f = 0.1)

Would there have been a different result, coefficient of friction and vehicle braking capabilities being equal, if he would have been driving a fully loaded newspaper truck?

Human Factors

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g-g Diagram

Human Factors - Driving Activities

Control Steering and speed control

Guidance Vehicle path

Navigation Trip and route planning, wayfinding

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Guidance/Control Process Diagram

Perception Reaction Time

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Stopping Sight Distance

Stopping Sight Distance

SSD = Stopping Sight Distance (ft)

tpr = perception/reaction time (2.5 sec)

v = final velocity (mph)

vo = initial velocity (mph)

f = friction coefficient G = % Grade/100

Two components: Braking distance

Wet pavement and tires

Emergency braking: 3.4 m/sec2 (11.2 ft/sec2)

2.5-second perception/reaction distance

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SSD Example

You are driving 30 mph on a down grade of 4% and see a pedestrian at a distance of 275 feet. Your perception/reaction time is 2.5 seconds and f = 0.3. Do you hit the pedestrian? If so, what is the impact speed?

Would you have hit the pedestrian if you were intoxicated, and your perception - reaction time were 4 seconds?

Cornering

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Vehicle Cornering

When a vehicle traverses a horizontal curve it has a tendency to continue on the straight line

The driver forces the vehicle to traverse the curve The side friction between the road and the tires keeps

the vehicle from slipping out of the curve

Vehicle Cornering

Rv – radius of curve a – angle of incline e – superelevation W – weight Wn – weight normal Wp – weight parallel to road Ff – side friction Fc – centripetal force Fcn – centripetal force normal Fcp – centripetal force

parallel to road

cos

sin

2

ccp

ccn

vc

FF

FF

gR

WVF

sin

cos

WW

WW

p

n

tan100e

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Equations of Motion

Rmin = min. radius (ft)

V = design speed (mph)

e = superelevation (ft/ft)

f = side friction factor

Rmin = min. radius (ft)

V = design speed (fps)

e = superelevation (ft/ft)

g = gravity force (32.2 ft/sec2)f = side friction factor

• Side friction factor, f fmax = 0.165 to 0.30 for low-speed urban streets f max= 0.08 to 0.17 for rural and high-speed urban roadways

• Superelevation, e Maximum e = 0.12 or 0.08 if snow and icy conditions prevail

(0.06 used in some northern states)

Slide Slip Friction Chart

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Cornering Example

Consider the design for a curve with a 60 mph design speed, maximum side friction = 0.15, and and superelevation = 0.08. What is the minimum radius of the curve?

Can a larger radius be used? Why?

How does the answer change if a 5% superelevation is used?

Overturning

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Overturning

fOT = T/2H

f required < fmax and f required < fOT = Success!

f max or fOT < required = Failure

f max < required and f max < fOT = Sliding

fOT < required and fOT < fmax = Overturning

Overturning Example

Consider a 8’ wide truck with a center of gravity 6’ from the pavement. Given a speed of 70 mph and e = 0.08, fmax = 0.8, and R = 250 feet. What happens?

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Intersection Design

Sight Distance Considerations

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Intersection Sight Distance Case A; No Control

Assume both vehicles can stop or adjust speed before intersection

2 second perception/reaction time and 1 second maneuver time

Case B; Stop Control Assume stopped vehicle can cross intersection or enter traffic stream safely from stop.

3 Cases: Left-turn, Right-turn, Cross

Assume non-yielding vehicle travels at prevailing speed

Case C; Yield Control Assume yielding vehicles can stop or adjust speed before intersection AND stopped

vehicle can cross intersection or enter traffic stream safely from stop.

3 Cases: Left-turn, Right-turn, Cross

Assume non-yielding vehicle travels at prevailing speed

Case D; Signals Depending on protected/non-protected movements

Case E; All way stop Drivers need to be able to see each other

Case F; Left-turn from Major Road Similar to yield case

Case A; No Control

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Case B; Stop Control

Case B; Stop Control

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Case C; Yield Control

Other Design Considerations

Alignment and Profile Roadways should meet at right angles (>70o)

Flat grades are desired (<3%)

Cross Section Left-turn lanes should reflect speed, volume, and vehicle mix.

3.6 meter (12 foot) lanes are desirable for auxiliary lanes.

Turning Radius Dependent upon angle of turn, turning speed, and type of design vehicle.

Intersecting arterials should accommodate WB-65 design vehicles

Collectors and local streets should accommodate single-unit (SU) trucks

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Cross Sections

Major Elements

Travel Lanes

Road margins Shoulders, curbs, swales, medians

Traffic separation devices Barriers, medians, crash cushions

Sidewalks and bikeways

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4 Lane Divided Rural Section

Travel lanes 12 ft standard, 9 ft minimum, 14 ft shared bike use lane

Shoulder 6 ft typical, range from 2-12 ft

Median 6 to 100 ft

Rural Divided with Frontage Roads

Frontage roads used to limit access to highway, provide access to adjacent property

Frontage roads are typically 2-lane, standard design details Frontage roads create unique issues at intersections

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R/W Example

What would the R/W width be for a 6 lane divided rural roadway? 6 travel lanes * 12’ = 72 feet

Full width median = 60 feet

4 shoulders * 8 feet = 32 feet

Totals 164 feet plus 2 clear zones/drainage swales

Typical 6 lane rural R/W 200 feet +

Shoulders

Emergency use for parking or errant vehicles

Lateral clearance

Structural support to roadway

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Homework (±1.5 hours); Due: Next Class1. A driver loses control of their vehicle and skids 70 feet on a level asphalt

surface (f = 0.7) and then 50 feet on the adjacent level gravel shoulder (f = 0.5). What was the speed of the at the beginning of the skid?

Assuming your answer from above, how far would they have slid on the gravel (f = 0.5) if the asphalt would have been ice covered (f = 0.1)?

2. Given a curve with a superelevation of 6%, 700 foot radius, and icy pavement (f = 0.1): What is the maximum speed you can travel before you start to slip?

What is the minimum speed you can travel before you start to slip?

3. A driver traveling at 55 mph sees a deer at 200 feet and leaves 60 foot skid marks before impact. (f = 0.7; 0% grade) What is the perception reaction time?

What is the speed at impact?

4. Consider a 8’ wide truck with a center of gravity 6.5’ from the pavement. Given a speed of 65 mph and e = 0.04, fmax = 0.8, and R = 300 feet. What happens?