CEE 3604: Introduction to Transportation Engineering
Fall 2012
Assignment 2: Basic Transportation Data Analysis
Date Due: September 14, 2011
Instructor: Trani
Problem 1
One of the basic problems in transportation engineering is determining travel time and distance for vehicles traveling between
points in a network. Data loggers using Global Positioning System (GPS) in cars and buses provide a good tool to understand
the efficiency of highway networks. Data collected in Blacksburg using an instrumented vehicle is provided in the file called
cardDataLog.m and shown in Figure 1.
Figure 1. Sample Car Data Information Collected in Blacksburg.
a)
Import the data using Matlab’s “load” command as demonstrated in class.
b)
Create a new Matlab script to do the following:
b.1) Create three new vector variables label them: time, speed and acceleration. These three vectors contain the
column data in each file.
b.2) Plot time traveled (in x-axis) vs speed (y-axis). Label axes as needed (include units) and change default font sizes
to size 20 for both x and y labels. Change the color of the line to solid blue. Comment on the shape of the profile
observed.
b.3) Plot time traveled (in x-axis) vs acceleration (y-axis). Label axes and change default font sizes to size 20 for both x
and y labels. Change the color of the line to red. Comment on the shape of the profile observed.
c)
Estimate the average speed for the complete profile. In Matlab we can easily calculate averages using the mean
command. For example:
mean(x) calculates the mean of a vector variable x. Does the average speed seems reasonable?
d)
Estimate the total distance traveled by this car. Use a numerical approximation similar to the procedure demonstrated
in the lectures notes Performance of Ground Vehicles (http://128.173.204.63/courses/cee3604/cee3604_pub/
transportation_technology.pdf) pages 21 and 31-31d.
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Problem 2
This past summer Virginia Tech collected traffic data on Highway 460 near Blacksburg. A file called Hwy460_Data.txt contains
samples of vehicle speed and highway density data collected. Traffic density and speed are two key variables of interest to
transportation engineers to study the level of service offered by highway. The file contains information similar to that shown below
Figure 2. Sample Traffic Data Collected on Highway 460.
Create a Matlab script to:
a) Load the highway data as demonstrated in class.
b) Create two variables named speed and density to study perform the next steps in the problem.
c) Use Matlab to plot the values of traffic density (x-axis) vs speed (y-axis). Comment of the trend observed. Label the axes
in the plot and use a green marker “^” to indicate each data point in your plot.
d) Using the “Basic Fitting” capabilities in Matlab (look at the “Tools” pull down menu in your plot), fit a first degree
polynomial to the data. Indicate the equation of the polynomial and comment on how well the polynomial fits the data.
e) If highway “volume” is measured as the product of density and speed, improve your script to estimate the volume of traffic
for every data point of speed-density recorded.
f) Plot the traffic volume (y-axis) vs. speed (in x-axis). Do you notice any trend? Comment.
Problem 3
An empirical formula to estimate the fuel used by a Boeing 747-400 (see Figure 3) flying international routes is given by:
Fuel = 3181 + 18.4D flown
where:
Fuel is the fuel used in kilograms.
D flown is the distance flown in nautical miles (one nautical mile is 1.15 statute miles)
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Figure 3. Boeing 747-400 at Punta Cana International Airport (A. Trani).
a) Use Matlab or Excel to estimate the fuel used for a given distance ( D flown )
b) Plot the fuel used (in pounds) various distance segments ranging from 1,000 to 5,500 nautical miles (at steps of 100 nm).
Plot the solutions obtained in part (a) and label accordingly.
c) Find the fuel use for a trip from Punta Cana (airport code PUJ) to Moscow (airport code UUDD) (route distance is 5,030
nautical miles). You can distances between airports at: http://www.gcmap.com.
d) Repeat (c) for a Honolulu-San Francisco flight (2,745 nm).
e) A hybrid car like a Toyota Prius has a fuel economy of 46 miles per gallon under normal highway driving conditions. Find
the number of miles a Prius could travel using the fuel consumed by the Boeing 747-400 in that single flight. A gallon of
jet fuel is equivalent to 3.045 kilograms.
Problem 4
A new HIgh-Speed Rail System under evaluation for the California Corridor has the following technical characteristics:
S = 20 sq. meters, froll = 0.02, rho=1.225 kg/cu.m., Cd = 0.40 (dim), Cl = 0.1 (dim) and mass = 450,000 kg. The train has the
tractive effort characteristics shown in Table 1.
Table 1. High-Speed Rail Tractive Effort Characteristics.
Speed (m/s)
Tractive Force (N)
0
360,000
30
285,000
60
220,000
90
180,000
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a) Derive a 2nd order polynomial (use either Matlab basic curve fitting function or Excel trend line analysis) that relates the
tractive effort and speed. The equation should be of the form:
where TE is the tractive force (N), a, b and c are regression coefficients obtained by regression analysis, and V is the speed (m/
s) of the high-speed rail system.
b) Using the equation obtained in part (a) derive the fundamental equation of motion for the vehicle similar to that shown on
page 16 of the course notes Performance of Ground Vehicles (http://128.173.204.63/courses/cee3604/cee3604_pub/
transportation_technology.pdf).
c) For the High-Speed rail repeat the analysis presented in the lecture notes (see pages 21-31d) to estimate components of
travel time between two stations located 100 km away from each other. Assume a deceleration rate of -1 m/s2. State the
acceleration, cruise and deceleration travel time in a simple table. For the 100 km trip, the operator would like to reach
175 mph in the cruise profile. To determine acceleration time use a step size of 1 second. You can do this analysis either
in Excel or Matlab (your choice).
CEE 3604 A2
Trani
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