3604: CEE Introduction to Transportation Engineering
Fall 2011
Assignment 1: Matlab and Basic Computations
Solution
Instructor: Trani
Problem 1
One of the basic problems in transportation engineering is determining the performance of vehicles traveling between two points.
The flight profiles of three domestic flights in the United States are provided as text files in this assignment. A sample file is
shown in Figure 1 for a flight between Dallas and New York.
a)
Import the data (all three flights) using Matlabs import wizard or sing the Matlab load command.
b)
Create a new Matlab script to do the following:
b.1) Create five vectors and label them: time, latitude, longitude, speed and altitude (all 5 columns of the file). These
five 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 16 for both x and y labels. Change the color of the line to solid blue. Comment on the shape of the profile
observed.
Figure 1. Time vs. Speed for ROA to CLT Flight.
b.5) Plot time traveled (in x-axis) vs altitude (y-axis). Label axes and change default font sizes to size 16 for both x and
y labels. Change the color of the line to red. Comment on the shape of the profile observed.
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Figure 2. Time vs. Altitude for ROA to CLT Flight.
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Problem 2
Two cars follow each other in a test highway that includes some stop signs. The lead car has a real driver, the following car has a
computer performing the duties of a driver. The experiment attempts to measure how good the control logic in the following car
follows the lead car without creating a collision. The speed and distance traveled profiles for the two cars participating this
experiment are shown in the data below. The data was collected using a standard GPS auto logger system. The cars are called
lead car and following car. Speeds are in m/s and distances measured in meters from a datum point. Note that at the start of
the experiment the lead car is 50 meters ahead of the following car (a negative distance for the following car means a distance
behind the lead car).
a) Import the data into Matlab using the import wizard or using the load command.
b) Create a Matlab script to plot the distance traveled by both cars as a function of time (plot time in the x-axis). Label your
axes and place a descriptive title for this plot.
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Figure. Matlab Script for Pat (b).
c) Plot the speeds of both cars in miles per hour (in y-axis) vs time (x- axis). Label the axes and add a title. Change the line
color to blue and line width 2.
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Figure. Speed vs. Time Plot for Two Cars.
d) Calculate the distance between the two cars at each point in time. Plot the distance as function a of time. Label
accordingly.
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Figure. Distance Between Two Cars vs. Time.
e) Find the average distance between the two cars during the experiment.
>> mean(distanceBCars)
Mean distance = 55.4 meters
f) Find the number of seconds the lead car spends at a red traffic light.
For 94 intervals of two seconds, the lead car is idle
intervalsIdle = find(leadSpeed==0);
% indices of intervals when lead vehicle is idle
noIntervals = length(intervalsIdle);
% no. of intervals when vehicle is idle
Problem 3
Data has been collected in the German Autobahn using new speed sensors. A file called autobahn.m contains samples of vehicle
speed and highway density data for this problem. 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
Create a Matlab script to:
a) Load the highway data.
b) 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.
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Figure. Matlab Script to Study and Plot the Autobahn data.
c) 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.
Figure. Linear Regression of Autobahn Data.
c) One busy day, traffic cameras record an average of 35 vehicles per kilometer. Estimate the range of speeds possible with
such density value.
By inspection of the plotted data, speed varies from 35 to 52 km/hr.
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d) 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.
Problem 4
An empirical formula to estimate the fuel used by a Boeing 757-200 flying in domestic routes in the United States is given by:
Fuel = 2450 + 6.75 D 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)
a) Create a Matlab function to estimate the fuel used for a given distance ( D flown )
Figure. Matlab Function to Estimate Fuel Used.
b) Create a new Matlab script to calculate parametrically the fuel used for various distance segments ranging from 500 to
3000 nm (at steps of 50 nm).
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Figure. Matlab Script Calling FuelBurn Function.
c) Plot the solutions obtained in part (a) and label accordingly.
Figure. Fuel Burn vs. Distance.
d) Find the fuel use for a trip from New York to Los Angeles (route distance is 2,450 nm).
18,988 kilograms of Jet fuel.
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