CE 4640: Transportation Design

1. CE 4640: Transportation Design Prof. Tapan Datta, Ph.D., P.E. Fall 2002

2. Speed Measures • Time Mean Speed • Space Mean Speed • 85th Percentile Speed

3. Sample Calculation of TMS and SMS A B d = 2 miles Run #1: t1 = 2 min, d/t1 = 60 miles/hour Run #2: t2 = 2.5 min, d/t2 = 48 miles/hour Run #3: t3 = 3 min, d/t3 = 40 miles/hour (d/ti) = 60+48+40 = 148 miles/hour TMS = (d/ti)/n = 148/3 = 49.33 miles/hour

4. Calculation of TMS and SMS (ti) = t1+t2+t3 = 2+2.5+3 = 7.5 min (ti/n) = 7.5/3 = 2.5 min SMS = = 48 miles/hour 2 miles x 60 min/hour 2.5 min

5. Spot Speed Studies • Where to take the studies: • Trend locations • Problem locations for specific purposes • Representative locations for basic data surveys • Locations where before-and-after studies are being conducted • The specific location for the speed study should be selected to reduce the influence of the observer and the measuring equipment as much as possible

6. Factors Affecting Spot Speeds • Driver • Vehicle • Roadway • Traffic • Environment

7. Time and Length of Study • Peak Hour • Morning Peak • Afternoon Peak • Off Peak Hour

8. Speed Study: Ways to Measure Speed Two ways: • Using a stop watch and measuring the time it takes to travel over a specified distance time2 time1 Speed = d/(time1 -time2)

9. Speed Study: Ways to Measure Speed • Using a Radar Gun

10. Radar Gun Operates on Doppler Principle that the speed of a moving target is proportional to the change in frequency between the radio beam transmitted to the target and the reflected radio beam.

11. Time Mean Speed (TMS) Average speed of all vehicles passing a point on a highway over a specified time period TMS = (ft/sec or miles/hour) where d = distance traversed (ft or mile) ti = travel time of ith vehicle (sec or hour) n = number of travel times observed (d/ti) n

12. Space Mean Speed (SMS) Speed corresponding to the average travel time over a given distance SMS = (ft/sec or miles/hour) where d = distance traversed (ft or mile) ti = travel time of ith vehicle (sec or hour) n = number of travel times observed d (ti)/n

13. Relationship between TMS and SMS Assume: There are “n” number of streams with flow rates q1,…..,qn and velocities u1, ……,un Then, the total flow = Average time interval between vehicles = 1/qi Distance traveled in time (1/qi) = ui/qi = 1/ki Density, K = ki n qi  i=1 n i=1

14. Note:  = n  i=1 Relationship between TMS and SMS u = q/k, ku = q Time Mean Speed (TMS), Ut =  =  = Space Mean Speed (SMS), Us =  =  = Q/K,Q = K Us Ut = = = where fi = ki/K qiui qiui qi kiui ki Q qi kiui ki ki Kfiui2 qiui kiui2 Q Q Q

15. Relationship between TMS and SMS SinceQ = K Us Ut = Kfiui2 KUs fiui2 =fi[Us+(ui-Us)]2 = Us Us fi[Us2+(ui-Us)2+2Us(ui-Us)] = Us [fiUs2+fi (ui-Us)2+2fiUs(ui-Us)] = Us

16. Relationship between TMS and SMS Since, fi (ui-Us)  0, Ut = + where = Therefore, Ut = Us + s2 Us2  Us Us [ki(ui-Us)2] f(u - X)2 s2 s = n - 1 K s2 Us

17. Speed Data Measured Using Radar Gun

18. n x =  Percentile Speed Calculations    =  =

19. Statistical Calculations f(u - X)2 s = Standard Deviation, = 22442/299 = 8.66 mph n - 1 s2 = 8.662 = 75.06 mph Variance,

20. Statistical Calculations Median = L + (n/2 – fL)C/fm where L = Lower bound of the group in which the median lies n = Number of observations fL = Cumulative number of observations upto the lower bound of the group where the median lies fm = Number of observations in the group in which the median lies C = Speed interval

21. Statistical Calculations • For the example, the median lies between 36-40 mph. • Median = 36 + (300/2 – 103) 5 / 63 = 39.73 mph Mode is the area which occurs most frequently. In the example, mode is 42.5 mph in 41-45 mph range. Pace is the max. number of vehicles within a 10mph speed range.

22. 85th Percentile Speed The speed below which 85% of all traffic units travel, and above which 15% travel. Speed limits are determined based on 85th percentile speeds.

23. Graph Showing Percentile Speeds % Cum. Frequency 47.5 mph Speed

24. Design Vehicles • Standard dimensions of design vehicles given in AASHTO Green Book • Minimum turning radius • For passenger cars (designated as P): 24 ft • For large semi-trailer or full-trailer combination (designated as WB-50 & WB-60): 45 ft • Acceleration and Deceleration of vehicles vary depending on their size • For cars 6 – 9 ft/sec2 • For trucks 3 – 5 ft/sec2

25. Turning Path for WB-50 Design Vehicle

26. The Hill Area Study,Grosse Pointe Farms

27. Example: Grosse Pointe Farms Alley Entrance Turning Template for a Semi-Trailer Truck (AASHTO WB-12 design vehicle) at the Alley Entrance

28. Example: Grosse Pointe Farms Alley Entrance Turning Template for a Semi-Trailer Truck (AASHTO WB-15 design vehicle) at the Alley Entrance

29. Turning Radius Templates (Source: A Policy on Geometric Design of Highways and Streets 1994, American Association of American State Highway Transportation Officials)

30. Example: Grosse Pointe Farms Alley Exit Turning Template for a Semi-Trailer Truck (AASHTO WB-12 design vehicle) at the Alley Exit

31. Example: Grosse Pointe Farms Alley Exit Turning Template for a Semi-Trailer Truck (AASHTO WB-15 design vehicle) at the Alley Exit

32. Intersection Design Should do the following: • Reduce number ofconflict points • Control relative speeds of intersecting roads • Coordinate design with traffic control • Consider alternative geometry • Separate conflict points • Spatially • Temporally • Reduce area of conflict