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

2. Before & After Speed Studies
To test the significance of difference in mean speeds observed “before” and “after” any control measure has been implemented.

3. Example Problem
Speed reduction measures have been installed at a horizontal curve. Is the change in vehicle speed due to a chance, or does it reflect a significant change in driving habits due to the installed measures?

4. Statistical Analysis Before After Mean Xb Xa Std. Dev. sb sa
Sample size nb na

5. D = Statistical Analysis Sb2 Sa2 nb na +
Implicit assumption is that Xb and Xa are sample means from the same population.

6. Statistical Analysis At 95% level of confidence,
if (Xb – Xa)  1.96 D
then the difference in the mean speeds are significant.

7. Example Problem Xb = 41.22 mph, Xa = 38.76 mph
Sb = 8.6 mph, Sa = 7.9 mph
nb = 300, na = 330
 D =
8.62
300 +
7.92
330
= 0.66

8. Example Problem Actual difference in the means
= – = 2.5 mph
 (Xb – Xa) = 2.5  1.96 * 0.66
or 1.3 mph
Conclusion:
The difference in means is significant at 95% level of confidence.

9. Travel Time and Delay Studies
Travel time is inversely proportional to travel speed.
Travel time and Delay indicates the Level of Service (LOS) provided by the roadway facility.

10. Space Mean Speed
Speed corresponding to the average travel time over a given distance. d
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
(ti)/n

11. Various Methods Test-Car Technique ~ Floating Car Method
License Plate Method
Observations from Vantage Points

12. Test-Car Technique ~ Floating Car Method
Utilizes a test vehicle which is driven over the test section in a series of runs
At least 12 runs should be made to adequately measure average speed and delays for any one direction
Use stop watches to record times at various control points, and also to measure the stopped time delays
Time, location and cause of delays are recorded

13. License Plate Method
Observers are posted at the entrance, exit and other strategic points
Each observer records last 3 or 4 numbers of each license plate, and time at which the vehicle passes the point
Requires careful, long and tedious office work to reduce the data manually

14. Observations from Vantage Points
Observers are stationed at elevated vantage points
Randomly select typical vehicles and record pertinent data as they progress through the section of roadway
Not good for long-run observation
Suitable observation points must be available

15. Intersection Delay Depends on:
Physical factors, such as number of lanes, width, grade, access control, channelization, but stops
Traffic factors, such as approach volume, turning movements, vehicle classification, driver characteristics, approach speed, parking, pedestrian
Traffic controls, such as type and timing of signals, stop/yield sign, turning and parking controls

16. Intersection Delay Studies
Similar to studies on a section of roadway, intersection delay studies are performed to collect data for:
Travel Time Delay
Stopped Time Delay
Measures the travel time from a point in advance of the intersection to a point in or beyond the intersection
Test car is driven between the same two points
Times are recorded using a stop watch

17. Acceleration and Deceleration
Distance traveled by a vehicle during acceleration from a stopped position:
da = 0.733at2
where da = distance traveled during acceleration (ft)
a = acceleration rate (mph/sec)
t = time of acceleration (sec)
0.733 = units conversion factor
Using the acceleration performance standards, we find:
For large car, da = 0.733(10)(7.52) = 412 ft
For tractor-trailer, da = 0.733(2)(7.52) = 82.5 ft

18. Acceleration Performance*
*Expressed in mph/sec

19. Acceleration and Deceleration
Distance required to decelerate a vehicle from one speed to another
db =
where db = braking distance (ft)
v = initial speed of vehicle (mph)
u = final speed of vehicle (mph)
30 = units conversion factor
f = coefficient of forward rolling/skidding friction
g = grade (decimal)
v2 – u2
30(f+g)

20. Acceleration and Deceleration
For example, a vehicle traveling at 60mph on a highway having a coefficient of friction of If the grade is level, what are the braking distances to decelerate to 30mph and to stop?
db to 30 mph = = 225 ft
db to stop = = 300 ft
602 – 302
30(0.40+0)
602 – 02
30(0.40+0)

21. Applications of Deceleration and Reaction Distance Formulas
Total stopping distance for a vehicle is the sum of perception-reaction distance and braking distance, given by:
ds = dp + db = 1.468vt +
where ds = stopping distance
dp = distance traveled during perception-reaction time
db = braking distance
v = initial speed of vehicle (mph)
u = final speed of vehicle (mph)
v2 – u2
30(f+g)

22. Applications of Deceleration and Reaction Distance Formulas
Safe stopping distance
Example: For a highway with a design speed of 70 mph and coeff. of friction of 0.29 and driver perception-reaction time of 2.5, safe stopping distance is:
ds = 1.468(70)(2.5) = ft
702 – 02
30(0.29+0)

23. Applications of Deceleration and Reaction Distance Formulas
Sign placement
Example: For placing a “Toll Plaza Ahead – Prepare To Stop” sign, which can be seen from a distance of 300 ft, and where the queue of vehicles go upto 150 ft from the toll gates, approach speed is 60 mph, coeff. of friction is 0.35 and reaction time is 2.5 sec, the safe stopping distance will be
ds = 1.468(60)(2.5) = ft
602 – 02
30(0.35+0)
contd…

24. Applications of Deceleration and Reaction Distance Formulas
Since the vehicle queue may extend upto 150 ft from the toll gates, the driver should be able to see the sign a minimum of = ft from the gates.
However, the sign can be read from 300 ft.
Therefore, the solution is: the sign must be bigger in size or more than one sign must be placed.

25. Applications of Deceleration and Reaction Distance Formulas
Clearance Interval of Traffic Signal
C.I. = Yellow time + All Red time
Yellow time, Y = t +
All Red time, AR =
where t = driver perception-reaction time for stopping (sec)
v = approach speed (ft/sec)
a = deceleration rate for stopping (ft/sec/sec)
G = percent grade
g = gravitational acceleration (32.2 ft/sec/sec)
W = width of intersection – upstream stop bar to downstream edge of pavement (ft)
L = length of clearing vehicle (ft) v
2 (aGg)
W + L v

26. Applications of Deceleration and Reaction Distance Formulas
Example
t = 1 sec
v = 30 mph = 44 ft/sec
a = 10 ft/sec/sec
G = 0.00 (level)
g = 32.2 ft/sec/sec
W = 80 ft
L = 20 ft W

27. Applications of Deceleration and Reaction Distance Formulasv 44
Yellow time, Y = t = = 3.2 sec
All Red time, AR = = = 2.3 sec
Clearance Interval = = 5.5 sec
2 (aGg)
2 (100)
W + L v 44

28. Applications of Deceleration and Reaction Distance Formulas
Crash investigation
Example: A vehicle is known to have skidded on a level asphalt surface (fa=0.50), and then on the adjacent gravel shoulder (fg=0.60), where it finally came to a halt. The average length of the skid marks on the asphalt surface was 120 ft, and on the gravel shoulder 40 ft. What was the speed of the vehicle at the beginning of the skid?

29. Applications of Deceleration and Reaction Distance Formulas
Solution:
The speed at the beginning of the gravel portion of the skid (u) can be calculated as:
u2 = 30(fg+g)dg = 30(0.60+0)(40) = 720
u = 26.8 mph
Speed at the beginning of the asphalt portion of the skid (v) is given by:
v2 = 30(fa+g)da + u2= 30(0.50+0)(120) = 2520
v = 50.2 mph