JCE4600 Fundamentals of Traffic Engineering

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1 JCE4600 Fundamentals of Traffic Engineering Introduction to Geometric Design Agenda Kinematics Human Factors Stopping Sight Distance Cornering Intersection Design Cross Sections 1

2 AASHTO Green Book Kinematics 2

3 Equations of Motion v = v o +at x = v o t + 0.5at 2 x = (v 2 -v o2 )/(2a) x = distance traveled v = final velocity v o = initial velocity a = acceleration t = time Brake Distance v = 0 x = (v o2 )/(2a) How do we determine acceleration? Major Sources of Resistance Grade Rolling Aerodynamic R a Aerodynamic R rlf Rolling, front R rlr Rolling, rear F f Friction, front F r Friction, rear W Weight g Grade angle m Vehicle mass a Acceleration 3

4 Balance of Forces Force balance Friction force = Acceleration force + resistance ma = ± F Friction ± F Grade Force Resistance Rolling and Aerodynamic forces are typically discounted F Friction = fw N = fwcos g F Grade = sin g f=friction coefficient Breaking Distance D b = Breaking Distance (ft) v = final velocity (ft/sec) v o = initial velocity (ft/sec) g = gravity force (32.2 ft/sec 2 ) f = friction coefficient G = Percent Grade/100 D b = Breaking Distance (ft) v = final velocity (mph) v o = initial velocity (mph) f = friction coefficient G = Percent Grade/100 4

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

5 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 5

6 Road Adhesion Pavement Maximum Slide Friction Friction Good, dry Good, wet Poor, dry Poor, wet Ice 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 6

7 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 7

8 g-g Diagram Human Factors - Driving Activities Control Steering and speed control Guidance Vehicle path Navigation Trip and route planning, wayfinding 8

9 Guidance/Control Process Diagram Perception Reaction Time 9

10 Stopping Sight Distance Stopping Sight Distance Two components: Braking distance Wet pavement and tires Emergency braking: 3.4 m/sec 2 (11.2 ft/sec 2 ) 2.5-second perception/reaction distance SSD = Stopping Sight Distance (ft) t pr = perception/reaction time (2.5 sec) v = final velocity (mph) v o = initial velocity (mph) f = friction coefficient G = % Grade/100 10

11 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 11

12 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 R v radius of curve a angle of incline e superelevation W weight W n weight normal W p weight parallel to road F f side friction F c centripetal force F cn centripetal force normal F cp centripetal force parallel to road WV Fc gr F F cn cp 2 F sin c F cos c v W W n p W cos W sin e 100 tan 12

13 Equations of Motion R min = min. radius (ft) V = design speed (fps) e = superelevation (ft/ft) g = gravity force (32.2 ft/sec 2 ) f = side friction factor R min = min. radius (ft) V = design speed (mph) e = superelevation (ft/ft) f = side friction factor Side friction factor, f f max = 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 13

14 Cornering Example Consider the design for a curve with a 60 mph design speed, maximum side friction = 0.15, and and superelevation = 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 14

15 Overturning f OT = T/2H f required < f max and f required < f OT f max or f OT < required = Failure = Success! f max < required and f max < f OT = Sliding f OT < required and f OT < f max = 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, f max = 0.8, and R = 250 feet. What happens? 15

16 Intersection Design Sight Distance Considerations 16

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

17 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 17

18 Case B; Stop Control Case B; Stop Control 18

19 Case C; Yield Control Other Design Considerations Alignment and Profile Roadways should meet at right angles (>70 o ) 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 19

20 Cross Sections Major Elements Travel Lanes Road margins Shoulders, curbs, swales, medians Traffic separation devices Barriers, medians, crash cushions Sidewalks and bikeways 20

21 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 21

22 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 22

23 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). 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? 23

CEE 320. Fall Horizontal Alignment

CEE 320. Fall Horizontal Alignment Horizontal Alignment Horizontal Alignment Objective: Geometry of directional transition to ensure: Safety Comfort Primary challenge Transition between two directions Fundamentals Circular curves Superelevation