10 Jul homework Transportation Engineering
Question Description
Chapter 4 Traffic Engineering Studies
1. Speed data collected on an urban roadway yielded a standard deviation in speeds of ±5.6 mi/h. (a) If an engineer wishes to estimate the average speed on the roadway at a 95% confidence level so that the estimate is within ±2 mi/h of the true average, how many spot speed observations should be collected? (b) If the estimate of the average must be within ±1 mi/h, what should the sample size be?
2. The accompanying data show spot speeds collected at a section of highway located in a residential area before and after an increase in speed enforcement activities. Using the student’s t test, determine whether there was a statistically significant difference in the average speeds at a significance level of α=0.05 (the 95% confidence level). Also report, for both the before and after cases, the mean speed, standard deviation, 85th percentile speed, and percentage of traffic exceeding the posted speed limit of 30 mi/h.
( The attached pic is the data schedule )
3. Data collected at a parking lot indicate that a total of 300 cars park between 8 a.m. and 5 p.m. 5% of these cars are parked for an average of 2 hr, 20% for an average of 3 hr, 10% for an average of 4 hr, and the remaining cars are parked for an average of 9 hr. Determine the space-hours of demand at the lot.
Chapter 5 Highway Safety
4. Determine the crash modification factor (using Table 5.14) that can be used to estimate the change in frequency of the crash type targeted by a proposed improvement that will widen a two-lane rural highway from 18 to 22 ft if the highway has an AADT of 1250 veh/day.
5. Determine the predicted average crash frequency on a 5.2-mile segment of a rural divided multilane highway with 11-ft lanes and 8-ft paved shoulders that carries an AADT of 11,200 vehicles per day.
6. Determine the crash modification factor for a horizontal curve on a two-lane rural highway if the curve has a radius of 1,432 ft, a length of 625 ft, and no spiral transitions.
Chapter 6 Fundamental Principles of Traffic Flow
7. Observers stationed at two sections XX and YY, 500 ft apart on a highway, record the arrival times of five vehicles as shown in the accompanying table. If the total time of observation at XX was 15 sec, determine (a) the time mean speed, (b) the space mean speed, and (c) the flow at section XX.
Vehicle Section XX Section YY
A To To + 7.6 sec
B To + 3.4 sec To + 9.9 sec
C To + 7.9 sec To + 14.6 sec
D To + 12.0 sec To + 20.4 sec
E To + 14.9 sec To + 21.7 sec
8. Data obtained from aerial photography showed six vehicles on a 700 ft-long section of road. Traffic data collected at the same time indicated an average time headway of 3.7 sec. Determine (a) the density on the highway, (b) the flow on the road, and (c) the space mean speed.
9. In a freeway traffic stream, the capacity flow was observed to be 2200 veh/h/ln, and the jam density at this location had been observed to be 125 veh/ln/mi. If the traffic stream is modeled using Greenberg’s model, determine the optimum speed and optimum density. If the traffic stream is modeled using Greenshields’ model, determine the free flow speed, optimum density, and optimum speed.
10. The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be Poisson with a mean of 30 veh/hr. It takes an average of 1.5 min for the necessary tickets to be bought for occupants of each car.
(a) What is the expected length of queue at the ticket gate, not including the vehicle being served?
(b) What is the probability that there are no more than 5 cars at the gate, including the vehicle being served?
(c) What will be the average waiting time of a vehicle?
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