Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 6, Problem 13P
To determine
The density of maximum volume, value of the maximum volume, plot of speed versus density and volume versus speed. And also, comment on the differences between the two set of curves.
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1.) From the traffic studies performed along a street shows the distances each vehicle traveled every 3 seconds on a portion of the highway.
Vehicle Distance, m 1 82.6 2 89.9 3 84.6 4 82
a.compute the space mean speed of the traffic, in kph.b.compute the flow of traffic.c.compute the density of traffic.
The data shown below were obtained by time-lapse photography on a highway. Use regression analysis to fit these data to the Greenshields model and determine the following.
Speed (mi/h)
Density (veh/mi)
16.7
84
25.7
69
35.2
54
43.1
40
54.4
19
56.1
14
(a)
the mean free speed (in mi/h)
mi/h
(b)
the jam density (in veh/mi)
veh/mi
(c)
the capacity (in veh/h)
veh/h
(d)
the speed at maximum flow (in mi/h)
mi/h
A car is stopped at an entrance ramp to a freeway; its driver is preparing to merge.
At a certain moment while stopped, this driver observes a platoon of vehicles a distance x0 upstream and initiates the merge maneuver. The platoon approaches the entrance ramp at a constant speed v. The stopped car can accelerate from speed 0 to v at uniform acceleration rate a.
Find the latest time at which the stopped car can safely start the merge maneuver; i.e., derive an expression for the “latest safe start time” in terms of the variables x0, v and a. Assume this latest time enables the platoon to maintain its constant speed and "just touch" the merging car's trajectory. Ignore the physical dimensions of the car.
Chapter 6 Solutions
Traffic and Highway Engineering
Ch. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10P
Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - The arrival times of vehicles at the ticket gate...Ch. 6 - Prob. 27P
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- A vehicle moving at a speed of 50 mph is slowing traffic on a two-lane highway. What passing sightdistance is necessary, in order for a passing maneuver to be carried out safely? Calculate the passingsight distance. In your calculations, assume that the following variables have the values given: Passing vehicle driver's perception/reaction time = 2.5 sec Passing vehicle's acceleration rate = 1.47 mph/sec Initial speed of passing vehicle = 50 mph Passing speed of passing vehicle = 60 mph Speed of slow vehicle = 50 mph Speed of opposing vehicle = 60 mph Length of passing vehicle = 22 ft Length of slow vehicle = 22 ft Clearance distance between passing and slow vehicles at lane change = 20 ft Clearance distance between passing and slow vehicles at lane re-entry = 20 ft Clearance distance between passing and opposing vehicles at lane re-entry = 250 ftarrow_forwardThe table below shows data on speed and corresponding densities on a section of a collector road. It can be assumed that the traffic flow characteristics can be described by the greenberge model, develop an appropriate relationship between flow and density. Also deyerdete the capacity of this section of the road Speed kph density veh/km 60 20 46 32 40.8 38 39.3 40 35.7 45 32.6 50 30.8 53 28.4 57 24.7 65 18.5 80arrow_forwardBy employing linear regression on the field data for speed and density in the table below, find the macroscopic flow equation assuming the traffic flow follows to greenshield model. Calculate the free mean speed, jam density, and maximum flow. Speed (km/h) Density (veh/km) 53.2 20 48.1 27 44.8 35 40.1 44 37.3 52 35.2 58 34.1 60 27.2 64 20.4 70 17.5 75 14.6 82 13.1 90 11.2 100 8.0 115arrow_forward
- The primary elements of traffic flow are flow, density, and speed. Discuss with illustration the relationships between the three elements of a traffic flow.arrow_forwardThe data shown below were obtained by time-lapse photography on a highway. Use regression analysis to fit these data to the Greenshields model and determine The mean free speed The jam density The capacity The speed at maximum flow Speed(mi/h) Density (veh/mi) 14.2 85 24.1 70 30.3 55 40.1 41 50.6 20 55 15arrow_forwardIn a stream of vehicles, 20% of the vehicles travel at a constant 50 km/hr, 30% at a constant speed of 80 km/hr and the remaining vehicles travel at a constant speed of 100 km/hr. An observer travelling at a constant speed of 60 km/hr over a length of 6 km with the stream is passed by 10 more vehicles than he passes. When the observer travels against the stream at the same speed and over the same length of highway, the number of vehicles met is 390. What is the mean speed and flow of traffic stream being observed? How many vehicles travelling at 100 km/hr are met by the observer while he travels against the stream?arrow_forward
- An automobile starting from rest speeds up to 40 meters per seconds with a constant acceleration of 4 meter per seconds square, runs at this speed for a time, and finally comes to rest with a deceleration of 5 meters per second square. If the total distance traveled is 1000 meters, find the (a) distance traveled covered during the acceleration, (b) distance traveled at constand speed, and (c) the total time of travel.arrow_forwardThe observed speed and density of vehicles on a highway are shown below. Plot the graph. Determine the parameters of the traffic stream model and hence estimate the capacity of the highway. Density (Veh/km) Speed (km/h) 10 75 14 67 20 65 21 61 32 55 56 37 62 28 72 20 84 14 88 8 93 6 96 4arrow_forwardConsidering linear relationship between density and speed; you are required to estimate the corresponding flow and speed values to densities of 10, 20, 30, 40, 50, 60 and 70 vehicle/km if the free flow speed is 90 km/hr and at critical situation, it is founded that there are 110 vehicles on a section of road with length 2.0 km. using the estimated values, draw a sketch showing the speed flow - density relationships?arrow_forward
- A data collection study found a linear speed - density relationship for a highway as follows u/65 +k/120 =1 1-Write down the speed - density ( given ) , flow - density and flow - speed models , and plot their relationships 2-raffic study has shown that the time headways between successive vehicles on this highway are exponentially distributed and that 30% of the headways between vehicles are 4 seconds or greater. Apply the traffic models derived in the question a), compute speeds and densities corresponding to this flow.arrow_forwardA one way, two-lane road is shared by buses and cars. Buses travel at speed 40 mph and carry 20 people. Cars travel at speed 60 mph and carry 2 people. The fraction of vehicles that are buses passing a stationary observer is 0.2. Answer the following questions: (a) From the perspective of a stationary observer, what is the average number of passengers per vehicle? (b) What fraction of the vehicles on an aerial photograph would be buses? (c) If we take a photo of the road, what is the average number of passengers per vehicle based on this photo?arrow_forwardAssume you are observing traffic in a single lane of a highway at a specific location. You measure the average headway and average spacing of passing vehicles as 3.2 seconds and 20 m, respectively. Calculate the flow, average speed, and density of the traffic stream in this lane. can you explain how to solve thank youarrow_forward
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