ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
Mini-project 1 – Evaluating the risk of head injury from a vehicle crash
Computer tools like MATLAB can greatly simplify the work of processing massive amounts of
data. Many experiments or design projects generate large data sets, and writing a computer
program to handle the data can greatly reduce the amount of repetitious and tedious
computations you would have to do by hand.
In this project, you will be given sets of driver head acceleration data available from the National
Highway Traffic Safety Administration (NHTSA) for various crash tests, which you will process
and use to compute the risk of head injury associated with these crashes. The analysis you will
perform is part of the agency’s safety assessment of new vehicles, the results of which are shared
with consumers to help them make an educated vehicle purchase. This analysis also has
applications in the study of sports-related head injuries and in the evaluation of helmets.
This document discusses the source of the data, what you will do with the data, and the
deliverables for the project, followed by specific details of the analysis you will perform.
1 — About the data
A responsibility of the NHTSA, an agency of the U.S. Department of Transportation, is to write
and enforce federal regulations concerning motor vehicle safety. Under the New Car
Assessment Program (NCAP), the safety of a new vehicle is evaluated by analyzing data
collected from a series of crash tests. The NHTSA itself does not conduct these tests; the tests
are contracted out to performing organizations that report the results back to the NHTSA.
One of the tests performed is the 35 mph frontal
impact test, whereby a vehicle is propelled such
that it crashes head-on at 35 mph into a rigid
barrier that spans the width of the vehicle (see
Figure 1). The test dummies (a driver and
typically at least one passenger), the vehicle,
and the impact barrier are highly instrumented
to measure, for example, experienced
acceleration and loads. It is not uncommon for
this test to generate more than 600 sets of data,
although some information is redundant.
Figure 1. A 2016 Ford F-250 undergoing frontal
impact testing (NHTSA test no. 9484).
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
The data you will be using for your project are the components of acceleration experienced by
the mass center of the driver’s head during a frontal impact test for three vehicles: a 2014 Toyota
No. 035 Pre-Test Driver Dummy Window View
Corolla, a 2016 Honda CR-V, and a 2015 Ford F-150. All three tests were conducted for the
NHTSA by the same performing organization based in Wisconsin. The raw data from these
tests, along with data from other crash tests performed by different organizations for various
vehicles, are freely available through the NHTSA’s website (http://www.nhtsa.gov).
2 — Summary of what you will do with the data
The head acceleration data for each vehicle tested consist
of three acceleration signals recorded over time: x-, y-, and
z-components of acceleration, where the orientation of the
right-handed x-y-z axes is illustrated in Figure 2. Using
these data, you will accomplish the following tasks:
1. Calculate the resultant head acceleration, in terms
of g’s, for each of the three vehicle crash tests,
and plot the accelerations over time, in units of
No. 036 Post-Test Driver Dummy Window View
Figure 2. Relationship between the x-y-z
ms, in a single subplot figure with appropriate
axes and theA-18
vehicle’s motion. (The y-axis
labeling for comparison.
is pointing into the paper.)
2. Determine the peak resultant head acceleration, in terms of g’s, for each vehicle crash
test and print these values to a text file.
3. For each vehicle crash test, evaluate a head injury
severity
overWindow
a series
No. 035
Pre-Testmeasure
Driver Dummy
Viewof time
windows spanning the duration of the impact, and plot the severity measures over the
time window number in a single subplot figure with appropriate labeling for comparison.
4. Determine the peak value of the severity measure, the head injury criterion (HIC), for
each vehicle crash test and print these values to the text file containing the peak resultant
head accelerations. Also, identify the HIC values on the subplot figure of the severity
measures over the time window number.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
3 — Deliverables for this project
Create a single Word document that contains the following:
1. The subplot figure of the resultant head acceleration, in terms of g’s, over time, in units
of ms, for each vehicle crash test.
2. The subplot figure of the head injury severity measure over the time window number for
each vehicle crash test, with the corresponding HIC value identified on each subplot.
3. Copy and paste the contents of the generated text file: the peak head acceleration, in
terms of g’s, and the HIC for each vehicle crash test.
4. Copy your MATLAB code and paste it at the end of the Word document. Be sure to use
good commenting throughout – that is, a good header section, definitions and units for all
variables, good section labeling, etc.
By 5 pm on Thursday, March 31, 2016, do the following:
1. Use your Word document to create a PDF (.pdf), and upload the PDF to Moodle.
2. Upload your team’s MATLAB m-file (.m) to Moodle.
Upload only ONE submission per group.
In the following pages, the details of the analysis you will perform for this project are described.
The descriptions are organized as milestones for each project day in class. You are free to work
faster than what is suggested, but to keep from falling too far behind, you should try to keep up
with this schedule.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
Day 1 – Plot and analyze head acceleration for a single crash test
You will begin by working with one set of head
acceleration data, measured during a 35 mph frontal
impact test of a 2014 Toyota Corolla (see Figure 3).
Once you are able to correctly analyze this one set of
data, you will then repeat your analysis using data
from two other impact tests involving a 2016 Honda
CR-V and a 2015 Ford F-150. Today you will focus
on extraction and basic analysis of the acceleration
data for the Toyota Corolla; on Monday (Day 2) you
will tackle the more challenging head injury risk
analysis.
Figure 3. Photograph of a 2014 Toyota Corolla
Post-Test Left View of Test Vehicle
after frontal impact testing (NHTSA test no.
8407).
1 — Obtain and examine the head acceleration data
Download the Excel file containing the head acceleration data for the Toyota Corolla crash test
(toyota_corolla_data.xls) from the course website by right-clicking on the file and saving
it to your Mini-project 1 folder. The contents of the data file are summarized as follows:
Pre-Test Right View of Test Vehicle
A-6
1. The file contains a matrix with 4 columns and 3,500 rows.
2. The first column contains the times, recorded in units of seconds, at which the head
acceleration data were collected. Notice that the initial value of time is negative, which
means data collection began before the vehicle crashed into the impact barrier; this is not
a concern for our later analysis.
3. The second, third, and fourth columns represent, respectively, the measured head
acceleration experienced in the x-, y-, and z-directions.
4. The head acceleration data are expressed in terms of g’s, i.e., in terms of multiples of
gravitational acceleration (e.g., 1g = 9.81 m/s2).
5. Acceleration data were collected at every 0.1 ms.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
2 — Calculate and plot the resultant head acceleration
To evaluate the driver’s risk of head injury, we will first need the resultant, or net, acceleration
experienced by the driver’s head over time:
1. In a new m-file, extract the head acceleration and time data from the Excel file.
2. Calculate the resultant head acceleration over time, 𝑎(𝑡):
𝑎!! 𝑡 + 𝑎!! 𝑡 + 𝑎!! 𝑡 ,
𝑎 𝑡 =
(1)
where 𝑎! (𝑡), 𝑎! (𝑡), and 𝑎! (𝑡) are, respectively, the x-, y-, and z-components of the
head’s acceleration.
3. Plot the resultant head acceleration, which is in terms of g’s, over time. Express time in
units of ms. Be sure to include axis labels with units and a descriptive title. Use the
axis command to display times between −50 ms and 300 ms, and to set the head
acceleration range from 0 to 60g. Type help axis for assistance. If you correctly
computed the resultant head acceleration, then your plot will be identical to the one
shown in Figure 4.
60
Resultant head acceleration for a frontal impact test of a Toyota Corolla
50
Acceleration (g)
40
30
20
10
0
-50
0
50
100
150
200
250
300
Time (ms)
Figure 4. Resultant head acceleration over the duration of a frontal impact test involving a 2014 Toyota Corolla.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
3 — Determine the peak resultant head acceleration
From the computed resultant head acceleration, extract the peak acceleration experienced by the
driver during the crash test and print the value to a text file using the following format:
The peak resultant head acceleration experienced in the Toyota
Corolla crash test is XX.XXg.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
Day 2 — Evaluate the risk of head injury for a single crash test
Last Friday (Day 1) you performed basic analysis of the head acceleration data for the driver of a
2014 Toyota Corolla undergoing a frontal impact test. Today you will extend your analysis by
computing a severity measure used by the NHTSA to assess the risk of head injury from a crash.
1 — About the analysis
The NHTSA uses what is known as the head injury criterion (HIC) as a means of evaluating the
risk of head injury to the driver and passengers of a vehicle involved in a collision. The HIC has
its roots in studies from the 1960s and 1970s concerned with developing empirical relationships
between experienced head acceleration and damage to the head (skull fracture, brain injury, etc.).
Calculating the HIC begins with computing what we will refer to as “severity”:
1
severity = ⋅
𝑡! − 𝑡!
!!
!!
!.!
𝑎 𝑡 d𝑡 𝑡! − 𝑡! ,
(2)
where, as illustrated in Figure 5, 𝑡! and 𝑡! > 𝑡! represent two time instances, in units of seconds,
during the resultant head acceleration signal, 𝑎(𝑡), which is expressed in terms of g’s. Severity
is always positive and has units associated with it, but the units are not reported by the NHTSA.
Resultant head acceleration for a Ford F-250 crash
Figure 5. Illustration of a particular time window being used to compute severity.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
Current NHTSA guidelines state that the time window, 𝑡! − 𝑡! , used to evaluate severity must be
15 ms. Note that severity is not a single value for the duration of a crash because there are many
time windows to which we may apply Eq. (2); in other words, there are many combinations of
the times 𝑡! and 𝑡! such that the difference 𝑡! − 𝑡! = 15 ms.
For the Toyota Corolla data you are analyzing, time starts at −0.05 s and ends at 0.2999 s, with
time recorded every 0.1 ms. This implies there are 3350 available time intervals of 15 ms, with
each consecutive window shifted by 0.1 ms in time, and thus you must calculate 3350 values for
severity. Based on Eq. (2), the chain of severity computations you must execute is as follows:
1
severity = ⋅
(−0.0349) − (−0.0499)
(!"#$%! !)
!.!
!!.!"#
1
severity = ⋅
(−0.035) − (−0.05)
(!"#$%! !)
𝑎 𝑡 d𝑡 (−0.035) − (−0.05) ,
!!.!"
!.!
!!.!"#$
𝑎 𝑡 d𝑡 (−0.0349) − (−0.0499) ,
!!.!"##
⋮ 1
severity = ⋅
(0.2999) − (0.2849)
(!"#$%! !!"#)
!.!
!.!"""
𝑎 𝑡 d𝑡 (0.2999) − (0.2849) .
!.!"#$
The HIC is the maximum severity value obtained from this series of calculations. The
NHTSA requires that the HIC be no larger than 700, which corresponds to a 31% probability of
skull fracture for a mid-sized adult male.
2 — Perform the analysis
Continuing with your m-file you created on Day 1, your task for today is to determine and
report the HIC associated with the Toyota Corolla crash test by doing the following:
1. Compute the severity for each of the 3350 available time windows according to the
process described earlier.
2. Plot the variation in severity against the time window number. Use the figure
command to generate a new figure window without wiping out your resultant head
acceleration plot created on Day 1. Type help figure to see how the command is used.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
As usual, include descriptive axis labels and an appropriate title. Set the axes such that
the time window number ranges from 1 to 3350, and severity ranges from 0 to 250. If
your severity computations are correct, then your plot will be identical to the one shown
in Figure 6.
250
Variation in severity for a frontal impact test of a Toyota Corolla
200
Severity
150
100
50
0
500
1000
1500
2000
2500
3000
Time window number
Figure 6. Variation in severity over the duration of a frontal impact test involving a 2014 Toyota Corolla.
3. From the results of your severity calculations, extract the HIC and print its value to the
text file from Day 1 using the following format:
The head injury criterion (HIC) value calculated for the Toyota
Corolla crash test is XXX.XX.
According to the NHTSA’s final report for this crash test, the HIC is 206; hopefully your
result, rounded to the nearest integer, is consistent with the NHTSA’s findings.
4. Lastly, identify the HIC on your severity figure by denoting it with a circle marker at the
appropriate location.
Hint: You may use the max command to return not only the maximum value max_val
in a vector v, but also the index number ind_max that corresponds to max_val by using
the syntax [max_val, ind_max] = max(v).
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
Days 3 and 4 — Perform a comparison study involving three crash tests
Having successfully processed and analyzed the 2014 Toyota Corolla crash test data in Days 1
and 2, you are now ready to apply the same techniques to additional test data. Specifically, you
will visually and quantitatively compare the experienced head acceleration, the variation in
No. 009 Pre-Test Left View of Test Vehicle
severity, and the corresponding HIC for the Toyota Corolla crash
test with the same results from
frontal impact tests involving a 2016 Honda CR-V and a 2015 Ford F-150 (see Figure 7).
Figure 7. Photographs
of a 2016 Honda CR-V (NHTSA test no. 9492) (left) and a 2015 Ford-F-150 (NHTSA test
Photo No. 011 - Post-Test Left View of Test Vehicle
no. 9111) (right) after frontal impact testing.
No. 010 Post-Test Left View of Test Vehicle
A-5
1 — Compare the resultant head acceleration for each crash test
First, go to the course website to download the Excel files containing the head acceleration data
from the crash tests for the Honda CR-V (honda_cr_v_data.xls) and the Ford F-150
(ford_f_150_data.xls). The structure of these data files is exactly the same as that for the
Toyota Corolla data file.
Photo No. 012 - Pre-Test Right View of Test Vehicle
Next, start a new m-file, but have your m-file from Day 2 handy because you will be able to
reuse a good portion of this code. The m-file you are starting today is the one you will be
submitting to Moodle. Visually and quantitatively compare the resultant head acceleration for
the three vehicle crash tests by doing the following:
A-6
1. Load each data file, extract its contents, and compute the resultant head acceleration over
time.
2. Using the subplot command, create a subplot figure that plots each resultant head
acceleration profile (in terms of g’s) over time (in units of ms) on its own set of axes.
Your subplot figure must have the structure shown in Figure 8. Type doc subplot to
receive detailed help with the subplot command. Be sure to include axis labels with
units for each subplot. Use the same axis label text for all subplots. To easily compare
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
the head acceleration profiles, make the axes scaling the same for all subplots by using
the axis command, as you did in Day 1. For each subplot, identify the vehicle make and
model in a legend. Lastly, include a single title for the overall subplot figure just above
the first subplot (see Figure 8).
Subplot figure title
Resultant head acceleration (in g’s) over
time (in ms) for the Toyota Corolla
Resultant head acceleration (in g’s) over
time (in ms) for the Honda CR-V
Resultant head acceleration (in g’s) over
time (in ms) for the Ford F-150
Figure 8. Required structure for your subplot figure of the resultant head acceleration for all three crash tests.
3. For each crash test, extract the peak resultant head acceleration experienced by the driver,
and print all three values to a (new) text file using the following format:
Comparison of the peak resultant head acceleration experienced:
Toyota Corolla:
XX.XXg
Honda CR-V:
XX.XXg
Ford F-150:
XX.XXg
2 — Compare the variation in severity and the HIC for each crash test
You will now compare, both graphically and quantitatively, the variation in severity and the
corresponding HIC for the three vehicle crash tests as follows:
1. For each crash test, compute the severity for each of the 3350 available time windows
according to the process described in Day 2.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
2. Generate a subplot figure that plots each variation in severity against the time window
number on its own set of axes. Your subplot figure must have the structure shown in
Figure 9. As usual, use the same axis label text and the same axes scaling for all
subplots. Also, use a legend to identify the vehicle make and model, and include a single
title for the overall subplot figure just above the first subplot.
Subplot figure title
Severity over time window
number for the Toyota Corolla
Severity over time window
number for the Honda CR-V
Severity over time window
number for the Ford F-150
Figure 9. Required structure for your subplot figure of the variation in severity for all three crash tests.
3. For each crash text, extract the HIC from the severity computations, and print all three
values to the text file containing the peak resultant head accelerations using the following
format:
Comparison of the calculated head injury criterion (HIC) values:
Toyota Corolla:
XXX.XX
Honda CR-V:
XXX.XX
Ford F-150:
XXX.XX
4. Finally, identify the HIC value for each crash test on its corresponding severity subplot
by denoting it with a circle marker at the appropriate location.
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 123
Comp Apps I
3 — Work on your memo (Word document)
Download the Mini-project 1 memo template (mini-project-1-memo-template.docx) from the
course website. Replace the placeholder text in the Word document with appropriate text, and
include the following items:
1. The subplot figure of the resultant head acceleration, in terms of g’s, over time, in units
of ms, for each vehicle crash test.
2. The subplot figure of severity over the time window number for each vehicle crash test,
with the corresponding HIC identified on each subplot.
3. Copy and paste the contents of the generated text file: the peak head acceleration, in
terms of g’s, and the HIC for each vehicle crash test.
4. Copy your MATLAB code (from Days 3 and 4 only) and paste it at the end of the Word
document. Be sure to use good commenting throughout – that is, a good header section,
definitions and units for all variables, good section labeling, etc.
Remember, by 5 pm on Thursday, March 31, 2016, you need to do the following:
1. Use your Word document to create a PDF (.pdf), and upload the PDF to Moodle.
2. Upload your team’s MATLAB m-file (.m) to Moodle.
Upload only ONE submission per group.