CVEN 456/766 - Highway Design
Assignment 2
Due date: February 22, 2017, beginning of class
Note: One assignment per person. Answer all questions. All questions are of equal value
(20 points).
Question 1
Two drivers each have a reaction time of 2.5 seconds. Driver 1 is obeying a 55 mph
speed limit, and the other (Driver 2) is traveling illegally at 70 mph.
A) How much distance will each of the drivers cover while perceiving/reacting to the
need to stop, and what will be the total stop distance for each driver if they are
traveling in a slope with G=-2.5%?
B) Assume now that the Driver 2 is much more alert than Driver 1, who is actually
very sleepy. The perception-reaction time for Driver 2 is reduced by 33%, while it
is increased by 100% for Driver 1. Which driver is more at risk?
Solution
A)
B)
For driver 1, the perception-reaction time is 2.5 x 2.0 = 5.0 sec. The distance
traveled during this time period equals 403.33 ft. The total distance is 403.33ft + 312.99ft
= 716.32 ft.
For driver 2, the perception-reaction time is 2.5 x 0.66 = 1.65 sec. Thus, the
distance traveled during this time period becomes 169.40 ft. The total distance is 169.40
+ 507.00ft = 676.40ft.
Driver 1 is now the driver more at risk.
Question 2
In an intersection collision, one of the vehicles driven by an older driver leaves 30 m of
skid marks. A skid mark analysis indicates that the vehicle was traveling at 75 km/h at
the onset of braking. Perception tests were performed on the older driver and they found
that his/her capacity to absorb information was 4 bits. Using the median value for
computing the perception-reaction time, estimate the distance from the point of impact to
the position of the vehicle when the driver originally reacted. State any assumptions.
Solution
Assume that the driver did not expect to hit somebody else, using Exhibit 2-26, the
perception reaction time equals 3.3 sec (note: if you assume an expected event, use 2.5
sec). Another assumption is that the intersection is leveled.
The time it takes during the perception reaction time is:
75 x 1000/3600 x 3.3 = 68.78 m
Breaking distance is 30 m. Thus, the total distance is 30 m + 68.78 m = 98.75 m.
For the people who are curious, the total braking distance should be 64.52 m. One could
use the following equation to find the speed at which the vehicle hits the other vehicle:
V22  V12  2ad where “a” and “d” represents the deceleration rate and deceleration
distance respectively.
Question 3
A certain highway project is planned with an initial investment cost of $1.5M. The user
benefits for this highway (in excess of maintenance costs) are estimated to be $105,000
per year over its useful life of 20 years. At the end of the 20-year period, the residual is
estimated to be $300,000. On the basis of present worth concepts, should the project be
built? Assume an interest rate of 5 percent. What is the benefit-cost ratio? Briefly
describe potential approaches you could use to minimize user costs.
Solution
Bring back to yearly benefits to current year:
 1  i n  1 
Ps  A 
n 
 i 1  i  
Bring back residuals:
 1  0.05 20  1 
Ps  105, 000 
 1,308,532
20 
 0.05 1  0.05  
P
F
1  i 
n
P
300, 000
1  0.05 
20
 133, 066
B/C:
B/C 
1, 421,599
 0.947
1,500, 000
To increase the B/C ratio, try to lower the initial construction while still trying to
maintain the same maintenance costs. You could also to try to reduce maintenance costs.
To minimize user costs, shorter routes, try minimizing speed changes between segments,
improve the design to increase capacity are some of the examples that could be
implemented. Finally, one should also try to reduce the number of crashes that are
expected to occur with the assumption that they were included in the analysis.
Question 4
Briefly describe in ½ a page, the three types or definitions of speeds discussed in the
AAHSTO Greenbook. Which one should be the highest?
Solution
See Section 2.3.6 in the Greenbook for a description of the ‘Operating Speed’, ‘Running
Speed’, and “Design Speed’.
Design speed should be higher (in theory), although a small proportion of drivers are
expected to travel above the design speed.