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 SMSB
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) = = 148 miles/hour
TMS = (d/ti)/n = 148/3 = miles/hour

4. Calculation of TMS and SMS
(ti) = t1+t2+t3 = = 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
time1
time2
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) where d = distance traversed (ft or mile)
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. Relationship between TMS and SMS
Note:  =
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 qi
qiui ki
kiui Q qi
kiui ki ki
qiui
kiui2
Kfiui2 Q Q Q

15. Relationship between TMS and SMS
Since Q = K Us
Kfiui2
Ut =
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. Percentile Speed Calculations
x =  n  
 =
 =

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

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
C = Speed interval

21. Statistical Calculations
For the example, the median lies between mph.
Median = 36 + (300/2 – 103) 5 / 63 = mph
Mode is the area which occurs most frequently.
In the example, mode is 42.5 mph in 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 of conflict points
Control relative speeds of intersecting roads
Coordinate design with traffic control
Consider alternative geometry
Separate conflict points
Spatially
Temporally
Reduce area of conflict