JCE4600
Fundamentals of
Traffic Engineering
Introduction to Geometric Design
Agenda
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Kinematics
Human Factors
Stopping Sight Distance
Cornering
Intersection Design
Cross Sections
1
AASHTO
Green Book
Kinematics
2
Equations of Motion
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v = vo+at
x = vot + 0.5at2
x = (v2-vo2)/(2a)
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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
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Grade
Rolling
Aerodynamic
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Ra – Aerodynamic
Rrlf – Rolling, front
Rrlr – Rolling, rear
Ff – Friction, front
Fr – Friction, rear
W – Weight
g – Grade angle
m – Vehicle mass
a – Acceleration
3
Balance of Forces
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Force balance
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Friction force = Acceleration force + resistance
 ma = ± FFriction ± FGrade – Force Resistance
Rolling and Aerodynamic forces are typically discounted
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FFriction = fWN = fWcosg
FGrade = sing
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f=friction coefficient
Breaking Distance
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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
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Db = Breaking Distance (ft)
v = final velocity (mph)
vo = initial velocity (mph)
f = friction coefficient
G = Percent Grade/100
4
Friction Coefficient
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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
5
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
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Serve three purposes
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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
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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.
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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
7
g-g
Diagram
Human Factors - Driving Activities
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Control
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Guidance
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Steering and speed control
Vehicle path
Navigation
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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
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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:
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Braking distance
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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
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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.
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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
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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
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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
Fc 
WV 2
gRv
Fcn  Fc sin 
Fcp  Fc cos 
Wn  W cos 
W p  W sin 
e  100 tan 
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Equations of Motion
Rmin = min. radius (ft)
V = design speed (fps)
e = superelevation (ft/ft)
g = gravity force (32.2 ft/sec2)
Rmin = min. radius (ft)
V = design speed (mph)
e = superelevation (ft/ft)
f = side friction factor
f = side friction factor
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Side friction factor, f
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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
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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
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Consider the design for a curve with a 60 mph design
speed, maximum side friction = 0.15, and and
superelevation = 0.08.
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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
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= 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
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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
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Case A; No Control
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Case B; Stop Control
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Assume both vehicles can stop or adjust speed before intersection
2 second perception/reaction time and 1 second maneuver time
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
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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
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Case D; Signals
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Case E; All way stop
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Case F; Left-turn from Major Road
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Depending on protected/non-protected movements
Drivers need to be able to see each other
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
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Alignment and Profile
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Cross Section
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Roadways should meet at right angles (>70o)
Flat grades are desired (<3%)
Left-turn lanes should reflect speed, volume, and vehicle mix.
3.6 meter (12 foot) lanes are desirable for auxiliary lanes.
Turning Radius
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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
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Travel Lanes
Road margins
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Traffic separation devices
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Shoulders, curbs, swales, medians
Barriers, medians, crash cushions
Sidewalks and bikeways
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4 Lane Divided Rural Section
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Travel lanes
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12 ft standard, 9 ft minimum, 14 ft shared bike use lane
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Shoulder
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Median
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6 ft typical, range from 2-12 ft
6 to 100 ft
Rural Divided with Frontage Roads
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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
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What would the R/W width be for a 6 lane divided
rural roadway?
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6 travel lanes * 12’ = 72 feet
Full width median = 60 feet
4 shoulders * 8 feet = 32 feet
Totals 164 feet plus
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2 clear zones/drainage swales
Typical 6 lane rural R/W 200 feet +
Shoulders
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Emergency use for parking
or errant vehicles
Lateral clearance
Structural support to
roadway
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Homework (±1.5 hours); Due: Next Class
1.
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).
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2.
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)?
Given a curve with a superelevation of 6%, 700 foot radius, and icy
pavement (f = 0.1):
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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)
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4.
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?
What is the perception reaction time?
What is the speed at impact?
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?
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