Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Question
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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Students have asked these similar questions
Results of traffic flow studies on a highway indicate that the flow-density relationship
can be described by the expression:
6-10
q = u,k
k;
If speed and density observations give the data shown below, develop an appro-
priate expression for speed versus density for this highway, and determine the density
at which the maximum volume will occur as well as the value of the maximum
volume. Also plot speed versus density and volume versus speed for both the expres-
sion developed and the data shown. Comment on the differences between the two sets
of curves.
Speed (mi/h)
Density (veh/mi)
TT
50
18
45
25
40
41
34
58
22
71
13
88
12
99
Results of traffic flow studies on a highway indicate that the flow-density relationship can be described by
the expression.
Us
q=uck -
If speed and density observations give the data shown below, develop an appropriate expression for speed
versus density for this highway. (Use the following as necessary: k. Assume u is in mi/h and k is in veh/mi.
Do not include units in your answer.)
Speed (mi/h) Density (veh/mi)
11
ufk²
kj
57
53
45
39
28
21
18
density at maximum
volume
21
22
39
60
70
86
97
Determine the density (in veh/mi) at which the maximum volume will occur as well as the value of the
maximum volume (in veh/h).
80
X
Your response differs from the correct answer by more than 10%. Double check
your calculations. veh/mi
Results of traffic flow studies on a highway indicate that the flow-density relationship can be described by the expression.
ufk²
k;
q=u₁k-
If speed and density observations give the data shown below, develop an appropriate expression for speed versus density for this
highway. (Use the following as necessary: k. Assume u is in mi/h and k is in veh/mi. Do not include units in your answer.)
Speed (mi/h)
Density (veh/mi)
66.075
56
54
45
40
28
21
17
19
24
44
55
72
89
100
X
Determine the density (in veh/mi) at which the maximum volume will occur as well as the value of the maximum volume (in veh/h).
density at maximum
volume
maximum volume
132.15
X
Your response differs from the correct answer by more than 100%. veh/mi
48.403
X
Your response differs significantly from the correct answer. Rework your solution from the beginning and
check each step carefully. veh/h
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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- 4. The observations from a moving car method are given in the table below. The column (1) shows the number of vehicles overtaken by the test vehicle, (2) show the number overtaking the test vehicle, (3) shows the number of vehicles moving against traffic stream, (4) is the travel time with the traffic (s), and (4) is the travel time against the traffic (s). Assuming linear speed-density relation, what is the maximum flow, speed, and density the following following stretch can take. Show the details of the calculation. (1) (2) (3) | (4) (5) 5 119 618 422 268 26 12 389 213 188 24 9 401 226 396 2 55 410 274 255 26 9 374 226 396arrow_forwardAssuming that the expression: u = ue k, %3D can be used to describe the speed-density relationship of a highway, determine the capacity of the highway from the data below using regression analysis. k (veh/mi) u, (mi/h) 43 38.4 33.8 50 53.2 42.3 8 31 Under what flow conditions is the above model valid?arrow_forwardGiven a freeway flow study at a certain highway. The speed- density relationship is described in the givenequation or relationship: V s = 58- 0.40k Determine the following:a. Free-flow speed and jam densityb. Derive the equation describing flow and speed.c. Derive the equation describing flow and density.d. Determine the capacity of highwayarrow_forward
- On a segment of A1 motorway in Casablanca, Morocco, traffic flow data was collected. The measured maximum flow was 1750veh/h for one lane when the averge spacing was 26.3 m/veh. We are assuming that speed and density are linearly related. Obtain the critical density and speed values to show them on the speed-density, density-flow and speed-flow equations. Please also obtain the speed and density values when the flow is 850 veh/h during rush hourarrow_forward4. The relation of the density (d) along a roadway to vehicle speed (s: km/h) is given as d = 50- s/2 Determine the flow (q)-speed (s) and flow (q)-density (d) relationships and draw the variations of density-speed, flow-speed and flow-density on. Show the maximum and minimum points on these graphsarrow_forward1. Assume 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 seconds and 150ft, respectively. What is the average speed of the traffic stream? Note: you can use two methods to conduct the calculation. 2. Assume the speed and density at a freeway location follows a linear relationship. You observe traffic flow rate of 2250 vehicles/hour at 45 mph and 3000 vehicles/hour at 30 mph. What are the jam density, free flow speed (max speed), and capacity of this freeway location? How about the density and speed (i.e., the critical density and the critical speed) at the capacity?arrow_forward
- Given a freeway flow study at a certain highway. The speed- density relationship is described in thegiven equation or relationship:V s = 60- 0.48kDetermine the following:a. Free-flow speed and jam densityb. Derive the equation describing flow and speed.c. Derive the equation describing flow and density.d. Determine the capacity of highwayarrow_forwardThe data shown below were obtained on a highway. Use regression analysis to fit these data to the Greenshields & Greenberg model and determine the capacity AND R-SQUARE. Speed (km/h) Density (veh/km) 50 18 45 25 40 41 34 58 22 71 13 88 12 99 72arrow_forwardQ4 / The data from moving observer methods as shown in the table. Column 1 gives the sample number, column 2 gives the number of vehicles moving against the stream, column 3 gives the number of vehicles that had overtaken the test vehicle, and last column gives the number of vehicles overtaken by the test vehicle. Find the flowrate, density and mean speed. Also, plot the fundamental diagrams of traffic flow. 2 3 4 No. Sample 1 107 10 74 113 25 41 3 30 15 4 79 18 9.arrow_forward
- From data collected on a metropolitan arterial road, it has been found that speed (v in kph) and density (k in vpk) are related by the following expression: v=72 0.72k Plot the speed-density diagram. Write the equation of the plot on this diagram and show the values of free-flow speed, critical speed, critical density and jam density on this diagram. Plot the flow-density diagram. Write the equation of the plot on this diagram and show the values of free-flow speed, critical speed, critical density, jam density and capacity on this diagram. Plot the speed-flow diagram. Write the equation of the plot on this diagram and show the values of free-flow speed, critical speed and capacity on this diagram.arrow_forwardProblem 6 Traffic on a single-lane urban street observes the following flow-density relationship: q=30k(1-k/180), where q is the traffic flow in vehicles per hour (VPH), and k is the traffic density in vehicles per mile (VPM). Answer the following questions: a. | Calculate the free flow speed, capacity, and jam density of the traffic flow. b. What is the minimum spacing and the minimum (time) headway of the traffic flow? What is the traffic volume when the travel speed is 20 MPH? C.arrow_forwardThe traffic shows data on speeds and corresponding densities on a section of a rural collector road. If it can assumed that the traffic flow characteristics can be described by the Greenberg's model, develop an appropriate relationship between the speed and flow and their modelled plotted points to be shown in the Q-u diagram. How strong the correlation of the two are? Also determine the capacity of this section of the road. Traffic Data Speed (kph) 60 Density (Veh/km) 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_forward
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