CE5373 Homework 1
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School
Texas Tech University *
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Course
5373
Subject
Aerospace Engineering
Date
Jan 9, 2024
Type
docx
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2
Uploaded by SuperHumanRockWren8192
CE5373 Homework #1
Problem 1 – get you familiarized with using vehicle trajectory data to obtain q, k, v
The vehicle trajectories showing below were obtained from the US 101 data site. Find the average flow, density, and time-mean speed over the rectangular area based on the following information. a)
The Area is 0.1343*0.32=0.042976 km.min
b)
Vehicle ID and their time and location getting in and out of the area is given below (Units: x in meter; t in minute.)
Vehicl
e ID
t out
t in
x in
x out
1
6.09
6.05
225.4
234
2
6.14
6.05
210.9
234
3
6.17
6.05
203.7
234
4
6.2
6.05
189.7
234
5
6.24
6.05
167.7
234
6
6.29
6.05
140.6
234
7
6.34
6.05
118.1
234
8
6.38
6.05
106.8
234
9
6.38
6.09
99.2
209.1
10
6.38
6.11
99.2
195.6
11
6.387
6.14
99.2
183
12
6.38
6.17
99.2
174
13
6.38
6.2
99.2
165
14
6.38
6.23
99.2
155
15
6.38
6.25
99.2
147.8
16
6.38
6.3
99.2
130
17
6.38
6.31
99.2
122
18
6.38
6.35
99.2
108.2
Problem 2 – get you familiarized with using q, k, v relation to obtain the required traffic info. On a specific westbound section of highway, studies show that the speed-density relationship is:
v
=
v
f
[
1
−(
k
k
j
)
3 .5
]
. It is known that the capacity is 3800 veh/h and the jam density is 225 veh/mi. What is the space-mean speed of the traffic at capacity, and what is the free-flow speed.
Problem 3 – get you familiarized with traffic observation in the field 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 150 feet, respectively. Calculate the flow, average speed, and density of the traffic stream in this lane.
Problem 4 – get you familiarized with the fact that different observations means (over time vs. over space) are different
A one way road is shared by buses and cars. Buses travel at speed v’ and cars travel at speed v. The fraction of vehicles that are buses passing a stationary observer is p, what fraction of the vehicles on a photograph would be?
Problem 5 – get you familiarized with study of light traffic flow which is usually analyzed by probabilistic methods
At a specified point on a highway, vehicles are known to arrive according to a Poisson process. Vehicles are counted in 20-second intervals, and the vehicle counts are taken in 120 of these intervals. 1) Approximate the number of 120 intervals in which exactly 3 cars arrive. 2) Estimate the percentage of time headways that will be 10 seconds or greater and those that will be less than 6 seconds.
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