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\texttt{%
\begin{tabular}{ll}
To:    & James W. Bales, Christina Silcox \\
From:  & Strobe 6:~Adam Seering, Aubrey Tatarowicz, Daniel Hernandez,\\
       &  John Hawkinson \\
Date:  & 10 December 2008 \\
Re:    & Breaking Glass Final Report
\end{tabular}}\\
{\small \verb| $Id: final.tex,v 1.60 2008/12/12 10:49:55 jhawk Exp $|}

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\section{Summary and Recommendations}

This final project examined measurement of breaking glass using
both high-speed video photography and sync-and-delay still
photography.  We experimented with a wide variety of ways to break the
glass, and were able to produce quantitative measurements in several
cases.

We began investigating glass breaking with thermal shock, moved to
mild impact (falling weight), and ended up with high impact (BB
rifle).  We found the BB rifle produced the most reproducible and
consistent results.

We examined both crack formation in the glass as well as deformation
of the shape of the glass due to impact.  We obtained useful data and
used it to analyze the way shock waves move through glass.  We found
that the speed of the wave propagation and the crack formation were on
the order of the speed of sound in glass.

We examined glass breaking using the Edgerton Center's Schlieren
apparatus, but we did not discern any interesting optical properties
with the Schlieren system.

We recommend that:

\vspace{-3ex}
\begin{itemize}
\item We look into purchasing a faster high-speed video camera, such
as the Phantom 12.1, that can take video at rates fast enough to
capture at least 10-15 frames of glass cracking.  The Phantom 12.1 can
record at 1,000,000 fps (the current Phantom 7 is limited to 150,000 fps).

\item We re-take video with this faster camera in order to get better
time resolution in our measurements.

\item We look into purchasing or creating software that can take
two-dimensional images and turn them into three-dimensional
representations, to better understand the deformation of the glass's
surface.

\item We repeat the tests involving glass deformation using this
software.

\end{itemize}


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\section{Background}
\setlength{\parskip}{\baselineskip}
\label{s:background}

Our Mark 1 project determined what kinds of things we can see and
measure with breaking glass.  Our curiosity was piqued by rumor that
car thieves break glass car windows by hitting them with a hot object.
The combination of the impact and the thermal shock is allegedly
sufficient to easily crack sturdy automotive glass.

In researching how we should go about breaking the glass and what we
can measure, Dr. Bales referred us to a 2004 Strobe Lab group's report
investigating some aspects of breaking glass \cite{impacts}.  This
group investigated glass breaking by impact with a metal rod and also
with a BB shot from a gun.  The group recommended further study of
thermal cracks. We wanted to do further work based on their research,
including additional study of cracks due to thermal stress.

We want to use this information to get
more useful data and also combine this with the thermal aspect of
glass breaking.  This group recommends a study on the thermal effects
on glass breaking which is one of the things we wish to pursue.

\subsection{Glass Breaking Process}
Glass breaks when a stress fracture forms by some sort of stimulus,
and this fracture travels though the glass until the glass breaks.
This fracture speed has been studied in the past and is expected to
be between 1000 m/s and 1500 m/s \cite{impacts}.

\begin{figure}[!ht]
\centering
\includegraphics[]{fracture_shapes}
\parbox{6in}{\caption{Concentric and radial fractures. The red lines
are radial fractures. The black lines form a concentric
fracture. \cite{Jones}}\label{f:frac}}
\end{figure}

Fractures formed by impact take two distinct forms:\ radial fractures
and concentric fractures.  Radial fractures are considered primary
fractures and form on initial impact.  Concentric fractures form
around the point of impact. Figure~\ref{f:frac} shows the two types of
fracture patterns. The glass bends before breaking which causes these
different shaped breaks \cite{impacts}.  We want to study how the glass
bends.


\subsection{Measuring Glass Fracture Speed}
We used the high-speed video camera to measure glass fracture speed, and
tested this technique in our Mark 1
project.  This technique uses the frames captured by a high-speed
video camera to take data, so that the movement of a fracture can be
analyzed with respect to time \cite{fracture}.  We can do this
analysis by hand by calibrating the image using an object of known
size, like the length of the glass slide.  With this data, we can
extract position information and make velocity calculations.  This is
the same method as used in Lab 3 \cite{lab3}.

\subsection{Seeing Glass Deformation --- The Projected Grid Method}
    Glass deforms when it is struck by an object.  One of our
objectives is to capture this deformation on camera.  One method
explained to us by Dr.\  Bales is the ``projected grid method.''  This
method uses the idea that images look deformed when seen reflected off
of an uneven surface. This is how funhouse mirrors work.

Using this idea, we can use light and a physical grid to project an
image of the grid onto a glass surface.  Then, we can position the
camera to see the reflection of this grid.  If or when the glass
deforms, we can see this phenomenon captured by the camera because the
projected grid will look deformed.

\subsection{Bending of Material}
The bending of materials is typically analyzed in terms of stress:

\begin{equation}
\rho = \frac{F}{A}
\end{equation}

where $\rho$ is the nominal-stress tensor, describing how stress is
distributed throughout the beam. $F$ is the force applied to the beam
and $A$ is the cross-sectional area of the beam.

Stress can be thought of as an internal
pressure.  Stress and pressure have the same units; ``stress'' is
frequently used to describe solid objects where ``pressure'' would be
used to describe fluids.

Objects such as panes of glass seldom break due to linear forces;
rather, they break due to the internal torques that cause them to
bend.  Rewriting the equation in terms of the torque $M$ on the rod
gives

\begin{equation}
\rho \cdot y = \frac{M}{A}
\end{equation}

where $F = \frac{M}{y}$; $y$ is the distance from the center plane of
the beam to the point at which deflection is measured.  If the stress
of an object varies with position, such as with an object that is being
bent, this equation can be rewritten as

\begin{equation}
\label{e:adam3}
M = \int_A \rho \cdot y dA
\end{equation}

In most simple rods, $\rho$ has been shown to be a simple constant.
This makes this equation quite simple to work with.


\subsection{High-Speed Video Camera --- Phantom}
The Phantom High-Speed Video camera is capable of recording
$800\times{}600$ pixel video at 4,700 frames per second.  It has a maximum
frame rate of approximately 150,000 frames per second at a resolution
of $32\times{}32$ pixels.  This resolution and very high frame
rate make it a versatile choice for capturing useful video of
sudden or rapid events.

The Phantom connects to a control computer via Ethernet.  The Phantom
640 software on the computer allows the user to modify the frame rate,
resolution, shutter speed, and trigger
settings for the camera.  Once the video is captured, it can be
reviewed, trimmed, and saved.

The Phantom captures data at a higher data rate than bulk recording
devices, such as hard drives, can handle.  As a result, it stores
video in an on-board memory buffer.  When triggered, it saves the state
of the buffer, and it canthen send its
contents off to a connected laptop.  Once on the laptop, the video can
be played back and converted to various data formats for analysis.

The Phantom can be triggered through the laptop's graphical user
interface, or optionally through a separate external electrical
trigger.

The Phantom responds to the trigger by continuing to capture a
configurable number of frames after the trigger, anywhere from
1 frame to the entire capture buffer. Depending on the circumstance,
the camera can thus capture video prior to the trigger, or following the
trigger, or somewhere in between.

\subsection{Goals}
Based on this information, our goals were:

\begin{itemize}
\item To evaluate breaking glass with thermal shock.
\item To evaluate breaking glass with mild impact.
\item To evaluate breaking glass with high impact.
\item To obtain useful quantitative data about the breaking and shattering process.
\item To evaluate the deformation of glass (prior to breaking), and collect quantitative
      and qualitative data about it.
\item To measure the speed of crack propagation.
\item To measure the speed of shock wave propagation.
\end{itemize}


\section{Procedure}

During this project we experimented with several different methodologies for 
breaking glass and measuring results.  We broke small microscope slides, larger
glass sheets, and mirrors in our six lab sessions.  Tools used to break the
glass included a heat gun, a screwdriver, and a BB gun.  A high-speed video
camera and a digital still camera captured the images, sometimes with the help 
of a beam-break trigger device.  The procedures for the experiments are
detailed in the following four sections.

\clearpage
\subsection{Thermal Shock} % procedures
For the tests of thermal shock, we used the materials listed in Table
\ref{t:MaterialsHeatShock}. The lab setup is as shown in
Figures~\ref{f:HeatTest1} and \ref{f:HeatTest2}.

\begin{table}[!ht]
\centering
\small
\caption{Materials for thermal shock experiment.}
\begin{center}
\begin{tabular}{l|l|l|l}
\hline
\emph{Item}
&	\emph{Manufacturer}
&	\emph{Model}
&	\emph{S/N} \\
HSV camera
&	Vision Research
&	Phantom v7.1
&	Phantom HSV \\
Laptop computer
&	Dell
&	Latitude D830
&	MIT-0422773 \\
HSV software
&	Vision Research
&	Phantom 640
&	DNR\\
Microscope slides
&	VWR International
&	$75\times{}25\times{}1$ mm
& 	---\\
Digital multimeter
&	Fluke
&	179
&	93810559 \\
Type K thermocouple & Fluke & --- & ---\\
Lens (for Phantom Camera)
&	Tamron
& 	90 mm macro
& 	TAMRON1 \\
Digital Still Camera
& 	Sony
&	DSC-P72
&	338694 \\
Heat Gun
& 	Accupro
&	1500 Watt 
&	--- \\
Tripod (for Phantom Camera)
& 	Manfrotto
& 	3021BPRO
& 	--- \\
Hex Plate for Tripod
& 	---
&	---
& 	--- \\
Lamp
& 	Lowel
&	Pro 250 W
& 	--- \\
Fiber Optic Illuminator
& 	Dolan-Jenner Industries
&	190
& 	--- \\
Safety Glasses
& 	DNR
&	DNR
& 	--- \\
Black Rolling Cart
& 	---
& 	---
& 	--- \\
Wooden Boxes (2)
& 	---
& 	---
& 	--- \\
Eyedropper
& 	---
& 	---
& 	--- \\
Titration device & DNR & DNR & ---\\
Metal Lab Stands (2)
& 	--- 
&	---
& 	--- \\
White Paper (for diffusion)
& 	---
& 	---
& 	--- \\
Water
& 	---
& 	tap water
& 	---\\
Soldering iron & Weller & DNR & DNR\\
\hline
\end{tabular}
\end{center}
\label{t:MaterialsHeatShock}
\end{table}

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{fig1}
\parbox{6in}{\caption[Setup photo of thermal shock tests (initial
tests)]{The first setup used to do the heat tests.  We found that the
apple boxes started to get singed by the applied heat from the heat
gun, so the setup in Figure~\ref{f:HeatTest2} is the setup we 
used.  The lower image in the figure is a closer look at the
setup of the microscope slide with the heat gun and thermocouple.  The
thermocouple is connected to the multimeter.  The camera is about
45\textdegree{} above the slide.  The 250 W light lights the far
edge of the slide.}\label{f:HeatTest1}}
\end{figure}

\begin{figure}[!ht]
\centering \includegraphics[width=6.5in]{fig2}
\parbox{6in}{\caption[Setup photo of thermal shock tests (most
tests)]{The setup we used for the thermal shock for most experiments.
The clamp on the ring stand holds the microscope slide by one end as
seen in the lower photo in this diagram.  The light is aimed
directly into the edge of the microscope slide opposite the camera.}
\label{f:HeatTest2}}
\end{figure}



In our first test, we tried applying a soldering iron (with a tip
temperature of around 150\textdegree{}C) to the microscope slide.  Upon
contact, the slide did not react.  Upon extended contact, the slide
continued to not react.  We then removed the soldering iron and, after
allowing the glass to cool, applied a second iron, with a higher tip
temperature of around 250\textdegree{}C.  
Once again, the glass did not react.
We measured all temperatures with the thermocouple.

In our second test, we tried heating the glass with a heat gun.  We
were able to heat the glass to about
375\textdegree{}C.  This is much hotter than the soldering iron.
However, the glass remained unaffected to the naked eye.

In our third test, we tried heating the glass with the heat gun, then
dropping cold water on the glass to cool it rapidly.  We tried a
number of application methods, with varying results as discussed in
the ``Results'' section.  Specifically, we tested an eyedropper, a
cup, and a titration device held at different heights relative to the
glass.


\clearpage
\subsubsection{Trigger Mechanisms}
For testing different trigger mechanisms, we kept the setup from the
heat-expansion experiments, and added a number of ring stands to
support an optical trigger and a beam break trigger.  The triggers
were arranged as shown in Figure~\ref{f:TriggerMechanisms1}.

The optical trigger consists of an infrared LED spaced roughly 1 cm
away from an infrared detector. The beam break trigger has a laser
emitter and a detector that can be separated by several meters.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{beam_break}
\parbox{6in}{\caption[Beam break setup photo for water dropping on
slide]{This is the basic beam break setup that we tried.  The beam
break components were secured in place with tape on lab stands and
apple boxes until the beam was set so that the receiver lined up with
the emitter and that the beam crossed over the glass slide and in the
path of the water drop.  The beam break trigger was connected to the
Time Machine input, and the output of the time machine was connected to
the Phantom HSV camera.  The camera was set to trigger at the
beginning of the recorded segment with the triggering from the beam
break.}\label{f:TriggerMechanisms1}}
\end{figure}

The goal was to have a drop of water pass through the beam of each
trigger while airborne, prior to impacting the glass.  We assumed that
the water would fall in a very repeatable way, once released from its
container.  We tested for a successful trigger using the attached Time
Machine device.

\clearpage
\subsubsection{Lighting Techniques}
\begin{table}[!ht]
\caption{Materials for Lighting Experiment}
\centering
\small
\begin{tabular}{l|l|l|l}
\hline
\emph{Item}
&	\emph{Manufacturer}
&	\emph{Model}
&	\emph{S/N} \\
HSV camera
&	Vision Research
&	Phantom v7.1
&	Phantom HSV \\
Laptop computer
&	Dell
&	Latitude D830
&	MIT-0422773 \\
HSV software
&	Vision Research
&	Phantom 640
&	DNR \\
Microscope slides
&	VWR International
&	$75\times{}25\times{}1$ mm
&	--- \\
Digital Multimeter
&	Fluke
&	179
&	93810559 \\
Type K thermocouple & Fluke & --- & ---\\
Lens (for Phantom Camera)
&	Nikon
&	28 mm
&	Nikon1 \\
Digital P\&S Camera
&	Sony
&	DSC-P72
&	338694 \\
Tripod (for Phantom Camera)
&	Manfrotto
&	3021BPRO
&	--- \\
Hex Plate for Tripod
&	---
&	---
&	--- \\
Lamps (2)
&	Lowel
&	Pro 250 Watt
&	--- \\
Lab stand (ring stand w/o ring)
&	---
&	---
&	---\\
\hline
\end{tabular}
\label{f:MaterialsLighting}
\end{table}

For the tests of lighting techniques, we used the same camera setup as
for testing thermal shock.  We shifted the light around to test direct
lighting, back-lighting, and side-lighting (where light is passed
straight through the long edge of the glass, so that cracks will
reflect the light and appear to glow).  The equipment used is listed
in Table~\ref{f:MaterialsLighting}.


These lighting setups were implemented as shown in
Figure~\ref{f:LightingTechniques1}.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{fig5}
\parbox{6in}{\caption[Lighting setup photo for thermal shock tests]{This
figure shows the different lighting techniques we used.  We used any
combination of these techniques to obtain the results that we wanted.
The paper diffuser was not used at all times and was helpful in some
situations but not helpful in others.}\label{f:LightingTechniques1}}
\end{figure}

Additionally, we tried pointing the camera at the underside of slides
rather than at the top.


We also looked into using digital still cameras to capture images of
the glass.  A camera could be used to take still images of the slide
at a useful frame rate.  However, because of the lack of a shutter
release cable (for the Nikon D200), still photos of shattering glass
were not attempted.


\clearpage
\subsection{Mild Impact}
For the tests of glass impact, we set up a piece of glass suspended
between two apple boxes, similar to the setup for testing thermal
shock.
The glass
was then hit with a pendulum and a screwdriver, each from varying
heights ranging from $1''$ to $12''$.

This procedure was followed with both 1 mm microscope glass and
$\nicefrac{3}{32}''$ window-pane class.  We cut the window-pane glass
into $2\times{}8''$ rectangular pieces.

The equipment used is listed in Table~\ref{f:MaterialsGlassImpact}.
The setup for this was as shown in Figure~\ref{f:GlassImpact1}.

\begin{table}[!ht]
\caption{Materials for glass impact experiment.}
\begin{center}
\small
\begin{tabular}{l|l|l|l}
\hline
\emph{Item}
&	\emph{Manufacturer}
&	\emph{Model}
&	\emph{S/N} \\
HSV camera
&	Vision Research
&	Phantom v7.1
&	Phantom HSV \\
Laptop computer
&	Dell
&	Latitude D830
&	MIT-0422773 \\
HSV software
&	Vision Research
& 	Phantom 640
&	DNR \\
Microscope slides
& 	VWR International
& 	$75\times{}25\times{}1$ mm
& 	--- \\
Lens (for Phantom camera)
& 	Nikon
&	28 mm
&	Nikon1 \\
Digital P\&S camera
& 	Sony
&	DSC-P72
&	338694 \\
Tripod (for Phantom camera)
& 	Manfrotto
&	3021BPRO
&	--- \\
Hex Plate for Tripod
&	---
&	---
&	--- \\
Screwdriver
&	Craftsman
&	Flat head 41578
&	--- \\
Glass	
&	RF Supply
&	$8''$ x $10''$ x $\nicefrac{3}{32}''$
&	--- \\
Lamps (2)
&	Lowel
&	Pro 250 Watt
&	--- \\
Safety Glasses
&	---
&	---	
&	--- \\
Wooden Boxes (2)
&	---
&	---
&	--- \\
Graph paper
&	DNR
&	---
&	--- \\
Gaff tape
&	DNR
&	DNR
&	---\\
\hline
\end{tabular}
\end{center}
\label{f:MaterialsGlassImpact}
\end{table}


\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{fig4-impact}
\parbox{6in}{\caption[Setup photo of screwdriver impact tests]{The
setup used to perform the impact tests with the screwdriver.  The
glass is the $\nicefrac{3}{32}''$ thick glass and the sheet is cut to
$2\times{}8''$ and is secured with tape.  The sheet of paper is
suspended in front of the back light to diffuse the light going into
the camera.  The lens used is the 28 mm lens.}\label{f:GlassImpact1}}
\end{figure}

The object being dropped onto the glass was dropped once per test run
listed in the ``Results'' section of this report, at a height above the
glass as noted in Table~\ref{t:ResultsGlassImpact}.  The glass either broke on impact, or
did not break on impact.



\clearpage
\subsection{BB Rifle Fired at Glass Slides and Sheets}
\begin{table}[!ht]
\centering
\small
\caption{List of equipment to conduct the following two sections in lab.}
\begin{tabular}{l|l|l|l}
\hline
\emph{Item} & \emph{Manufacturer} &	\emph{Model} &	\emph{S/N}\\
BB rifle        & Crossman Air Guns & 760-C  &188214595\\
Catalog         & Digi-Key         & ---              &---\\
Fiber optic illuminator
                & Dolan-Jenner     & 190              &---\\
Lowel Pro light & Lowel            & 250 W            &---\\
HSV camera        		& Vision Research   	& Phantom v7.1      & Phantom HSV\\
Laptop computer   		& Dell              	& Latitude D830     & MIT-0422773\\
HSV software      		& Vision Research   	& Phantom 640       & DNR\\
50 mm lens      & Nikon            & 50 mm            &Nikon2\\
Tripod          & Manfrotto        & 3058             &A0747258\\
Apple boxes     & ---              & ---              & ---\\
Microscope slides & VWR International & $75\times{}25\times{}1$ mm   &  ---\\
BBs (4.5 mm caliber)       & Quick Silver     & Match Grade No. 7541  &---\\
Black wooden box   & ---              & ---              &---\\
28 mm lens      & Nikon            & 28 mm            &Nikon1\\
Ring stand      & ---              & ---              &---\\
Grid paper      & ---              & ---              &---\\
Hex plate       & ---              & ---              &---\\
Glass sheets    & RF Supply        & $8\times{}10\times\nicefrac{3}{32}''$    &\\
\hline
\end{tabular}
\label{t:altA}
\end{table}

The following two experiments (\S\ref{s:vcfbb}, \S\ref{s:vcfbbhsv})
were conducted during the same lab session and were created by making
slight alterations in the setup, making the equipment list the same.
The first of these experiments is viewing crack formation on glass
from BB impact.  The second experiment was viewing glass deformation
from BB impact.

\subsubsection{Crack Formation}
\label{s:vcfbb}

Table~\ref{t:altA} outlines the equipment used to conduct this
experiment.  The purpose of this experiment was to see the crack
formation on the glass during the process of a BB impact.
Careful lighting was essential.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramA}
\parbox{6in}{\caption[Setup photo for crack speed measurement; BB
gun]{The view from the perspective of the gun holder of the
setup used to capture the glass cracking from impact of a BB.  This
diagram is intended to show how the subject is lit in order to
illuminate cracks.  Figure~\ref{f:altB} better illustrates all of
the relative distances of the objects.}\label{f:altA}}
\end{figure}

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramB}
\parbox{6in}{\caption[Setup diagram for crack speed on glass
slide]{The bird's eye view of the diagram setup used to capture crack
formation from BB impact on a glass slide.  We used the 50 mm lens for
this test, unlike the glass sheet trials.  The thick book was taped to
the box and was used to catch BBs.  The slide was attached using tape
as seen in Figure~\ref{f:altA}.}\label{f:altB}}
\end{figure}

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramC}
\parbox{6in}{\caption[Setup diagram for crack speed on glass
sheet]{The bird's eye view of the diagram setup used to capture crack
formation from BB impact on a glass sheet.  This is very similar to
Figure~\ref{f:altB}.  The main changes that we needed to do for this
setup was widen the apple box distance, change the lens to 28 mm, and
change the camera-to-subject distance.}\label{f:altC}}
\end{figure}

     For both the glass sheets and the glass slides, the procedure was
the same.  For the diagrams for the glass slide setup refer to
Figures~\ref{f:altA} and \ref{f:altB}.  For the diagrams for the glass
sheet setup, see to Figures~\ref{f:altA} and \ref{f:altC}.

     In order to setup for these experiments, the glass was taped to
the apple boxes on either end of the glass as shown in
Figure~\ref{f:altA}.  We positioned the book behind the glass and in
the line of fire of the BB in order to catch the BBs.  The Phantom was
positioned so that the angle of incidence was about 45\textdegree{}
with the glass.  We aimed the BB rifle so that the BB hits the glass
normal to the surface and in the center of the
glass.  A 250 W Lowel Pro lamp
was positioned directly above the glass and aimed down onto the glass
edge. This was the only lighting except for the room's ambient light.

     To set up the computer, we used the method described in the
section \ref{s:background}, connecting the output of the Phantom
camera to the Dell computer.  The Phantom 640 software was opened in
order to record the video from the Phantom camera and control the
camera settings.

     The most difficult task was this apparatus is getting the
sync-and-delay to work so that the high-speed video captures the
entire phenomenon.  Since we were only capturing about one second of
video with the frame rates we use for this test, careful timing
was important.  We found that using a beam break or sound trigger was
fairly difficult, and it was sufficient to trigger manually.  Using this
method, we captured the glass breaking each time.  We set up the
trigger so that the frames captured after the trigger were saved.

We
gave the BB gun the needed number of pumps, and then
loaded the BB into the gun.  Then, we made sure that the camera was
set up with the correct parameters.  From previous tests, we knew we
had to use a frame rate of around 75,000 fps, so that is what the
camera was configured to.  The aperture of the lens was adjusted
between f/1.8 and f/4 in order to ensure enough light.  The exact
apertures used are in the results section.

Once the camera was ready to record, the shooter would aim the gun and
turn the safety off.
We would count down, and then fire the gun and trigger the Phantom
simultaneously.
Since
the frames were saved after the trigger, we reliably captured
the glass breaking.

%\clearpage
\subsubsection{Deformation with HSV --- Our First Try}
\label{s:vcfbbhsv}

     In order to view the deformation of glass from the impact of the
BB, we added a projected grid to the previous setup.  In doing so, we
removed the light from above the glass sheet.  The materials for this
procedure can be found in Table~\ref{t:altA}.  Figure~\ref{f:altD}
illustrates the basic setup used at this time to record glass
deformation.  Figure~\ref{f:altE} shows how we projected the grid.  In order to
project the grid, we used a Lowell Pro 250 W lamp and placed grid paper
in front of it.  The light and grid setup were aimed at the glass.  In
order to see the deformation, we needed to focus on the grid projected
onto the glass rather than the glass.
We focused the camera so the reflected image of the grid was sharp.
In order
to capture the data, we used the same sync-and-delay method as in \S\ref{s:vcfbb}.
                                
\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramD}
\parbox{6in}{\caption[Setup diagram for glass deformation]{The bird's
eye view of the diagram setup used to capture glass deformation as a
result of the BB impact.  This is similar to Figures~\ref{f:altB} and
\ref{f:altC}, except the grid paper apparatus has been added.  The
grid paper apparatus can be seen in a close-up in
Figure~\ref{f:altE}.}\label{f:altD}}
\end{figure}

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramE}
\parbox{6in}{\caption[Setup photo for glass deformation; grid and
     diffuser]{A figure of the method used to project the grid
     onto the glass for this high-speed camera setup.  The grid paper
     is formed by printing a grid onto paper.  The paper is held by
     taping it to a ring stand.}\label{f:altE}}
\end{figure}

\clearpage
\subsubsection{Deformation with HSV --- Our Second Try}

\begin{table}[!ht]
\centering
\small
\caption{Materials for Mirror and Grid Experiment}
\label{t:D1}
\begin{tabular}{l|l|l|l}
\hline
\emph{Item} & \emph{Manufacturer} &	\emph{Model} &	\emph{S/N}\\
HSV camera        		& Vision Research   	& Phantom v7.1      & Phantom HSV\\
Laptop Computer   		& Dell              	& Latitude D830     & MIT-0422773\\
HSV Software      		& Vision Research   	& Phantom 640       & DNR\\
28 mm lens             		& Nikon             	& DNR             & Nikon1\\
50 mm lens             		& Nikon             	& DNR             & Nikon2\\
Digital Still Camera   		& Sony              	& DSC-P72           & 338694\\
Tripod            		& Manfrotto         	& 3021BPRO          & ---\\
Hex Plate for Tripod   		& ---               	& ---               & ---\\
Lamp              		& Lowel             	& Pro 250 Watt      & ---\\
BB rifle          		& Crossman Air Guns	& 760-C             & 188214595\\
BBs (4.5 mm caliber)  		& Daisy                 & Match Grade No. 7541    & ---\\
Catalog     	   		& Digi-Key          	& DNR      & ---\\
First Surface Mirrors  		& \scriptsize American Science \& Surplus   	& 
  4112P1 $77\times{}194\times{}3$ mm  & ---\\
Glass             		& RF Supply         	& 8 x 10 x $\nicefrac{3}{32}''$     & ---\\
Ground Glass      		& \scriptsize American Science \& Surplus  	&
  2728P6, $2\times{}2\times{}\nicefrac{1}{32}''$      & ---\\
Wire grid         		& DNR      	& DNR      & ---\\
Lab stand         		& ---               	& ---               & ---\\
Ruler             		& ---               	& ---               & ---\\
Gaff tape       		& DNR      	& DNR      & ---\\
Wooden Boxes (2)  		& ---               	& ---               & ---\\
Tall wooden box for gun		& ---               	& ---               & ---\\
Safety glasses    		& DNR               	& DNR               & ---\\
\hline
\end{tabular}
\end{table}

The experiment was set up as shown in Figure~\ref{f:D1} using the
materials listed in Table~\ref{t:D1}.  The mirror was secured to the
wooden boxes with tape.  A thick catalog was placed behind the
mirror to catch the discharged BBs.  A section of wire mesh was
clamped to a piece of ground glass and placed between the 250 W
lamp and the mirror.  The HSV camera was then angled to capture the
projected image of the grid on the mirror.  We started with the 28 mm
lens and switched to the 50 mm lens for the higher resolution (320 x
240 pixels) videos.

The HSV camera was connected to the Dell computer via an Ethernet
cable.  The Phantom software was set to post-trigger, and as the
shooter counted down, the person operating the computer would click
the trigger button immediately before the shooter fired the BB gun.
We ran several trials with the mirrors and the $\nicefrac{3}{32}$''
glass as well.  We pumped the gun fewer times (to reduce the impact)
for the glass trials since it was not as thick as the mirrors.  The
glass does not reflect as well as the mirrors, so we used a wider
aperture.  We also experimented with the expanded dynamic range (EDR)
values in the Phantom software.

\begin{figure}
\centering
\includegraphics[width=6.5in]{figure12}
\parbox{6in}{\caption[Setup photo for deformation; entire setup]
{Setup for BB/grid experiment. The wire grid and ground glass are
clamped and positioned between the 250 W lamp and the glass taped to
the wooden boxes.}\label{f:D1}}
\end{figure}


\clearpage
\subsubsection{Deformation with Still Images}

\begin{table}[!ht]
\centering
\small
\caption{Equipment used to conduct BB breaking glass with still
images.}
\begin{tabular}{l|l|l|l}
\hline
\emph{Item} & \emph{Manufacturer} &	\emph{Model} &	\emph{S/N}\\
BB rifle                & Crossman Air Guns     & 760-C 	       &    188214595\\
BBs (4.5 mm caliber)    & Quick Silver          & Match Grade No. 7541 &    ---\\
Catalog                 & Digi-Key              & DNR                  &    ---\\
Lowel Pro light (250W)  & Lowel                 & 250 W                &    ---\\
1 kW Halogen            & DNR                   & DNR                  &    ---\\
Tripod                  & Manfrotto             & 3021B Pro            &    ---\\
Apple boxes             & ---                   & ---                  &    ---\\
Wooden spacer boxes     & ---                   & ---                  &    ---\\
BB gun frame            & ---                   & ---                  &    ---\\
DSLR camera             & Nikon                 & D200                 &    ``D200''\\
Chicken wire            & ---                   & 1 cm squares         &    ---\\
Sheet of plexiglass     & ---                   & 13''x13''              &    ---\\
Tape                    & ---                   & ---                  &    ---\\
90 mm lens              & Tamron                & 90 mm macro lens     &    Tamron1\\
SPOT                    & Prism Science Works   & SPOT                 &    Edgerton1\\
Time Machine            & Mumford               & ``Time Machine''     &    Timer1\\
Trigger device		& Mumford		& beam break	       &    DNR\\
\hline
\end{tabular}
\label{t:altB}
\end{table}

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramF}
\parbox{6in}{\caption[Setup photo for glass deformation]{Setup for
capturing still images of glass deformation using a projected grid
method.  The grid is formed from left to right, a piece of chicken
wire, a sheet of plexiglass, and a sheet of paper taped together.
This creates a grid that also diffuses the light
source.}\label{f:altF}}
\end{figure}

     In order to capture the glass deformation on the still camera,
again the projected grid method was used with equipment listed in
Table~\ref{t:altB}.
We had to project the grid
with a strobe in order to capture the desired image.
Figure~\ref{f:altF} depicts the general setup we used in order to
capture the glass deformation.  In this figure, you can see that the
grid is held between the strobe and the subject.


     To set up this apparatus, we first moved the apple boxes and BB
rifle into place.  The grid was placed in the location seen in
Figure~\ref{f:altF}.  Next, we moved the 250 W Lowel Pro
behind the grid in order to have a constant light source.  We used the
Lowel Pro to do all of the positioning of the camera and focusing.
Before moving the camera into place, we tried to find the location of
the grid reflection on our piece of glass.  We made any necessary
adjustments to the Lowel Pro and the grid.

The Lowel Pro, at this
point, is in the location of SPOT in Figure~\ref{f:altF}.  Once we
positioned the camera, we focused on the grid projected by the piece
of glass.  This was important in capturing the glass deformation.
Once we were confident that the camera was focused correctly, we
replaced the Lowel Pro with SPOT, trying to place in SPOT in
the position held by the Lowel Pro.  Then, we turned all of the lights
off in the room and ran tests to make sure we were getting a good
exposure and that SPOT was positioned correctly.  The camera was set
to ``bulb,'' and we opened the shutter.  Then, we manually triggered
SPOT to strobe and closed the shutter.  We looked at the recorded image
of the grid and adjusted the camera aperture and the position of SPOT
and repeated this as needed until the exposure looked good.

     After positioning SPOT, we needed to create a triggering
mechanism to make SPOT strobe when the BB impacted the glass.  The
idea behind this is that a beam from the beam break trigger will be
reflected off of the glass into the detector.
When the BB impacts the glass, the beam is reflected away from the detector
and the trigger is triggered.  We set up the beam as in
Figure~\ref{f:altG}.  The output of the trigger was put into the Time
Machine.  The Time Machine was set up with a timeout of 4 seconds and
the output of the Time Machine was fed into SPOT\@. SPOT was set up
with no delay.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{diagramG}
\parbox{6in}{\caption[Setup diagram of reflected beam break for glass
     deformation]{Setup for triggering strobe SPOT\@.  The output of the
     trigger was put into the Time Machine.  The Time Machine was
     set up with a timeout of 4 seconds and the output of the Time
     Machine was fed into SPOT.}\label{f:altG}}
\end{figure}

     In order to capture the images, we repeated the following
procedure for each sheet of glass:
\begin{enumerate}

\item Tape glass to the apple boxes.

\item Confirm the trigger is functioning by tapping the glass
      and making sure SPOT flashes.

\item Pump the BB gun to the correct pressure, and chamber a BB.

\item Place the gun in the wooden shooting harness
(see Figure~\ref{f:altF}).
\item Aim the gun.
\item Ensure everyone is wearing safety glasses.
\item Deactivate the gun's safety.
\item Turn off the lights.
\item Open the D200's shutter.
\item The shooter hears the shutter click and fires the gun.
\item The shutter is closed when strobe flashes.
\item Turn lights back on.
\end{enumerate}

We repeated this over several trials.


\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Schlieren Imaging}

\begin{table}[!ht]
\centering
\small
\caption{Materials for Schlieren imaging experiment.}
\begin{tabular}{l|l|l|l}
\hline
\emph{Item}
&	\emph{Manufacturer}
&	\emph{Model}
&	\emph{S/N} \\
Heat gun
& 	Accupro
&	1500 Watt 
&	--- \\
Tripod (for Phantom camera)
& 	Manfrotto
& 	3021BPRO
& 	--- \\
Titration device
& 	DNR
& 	DNR
& 	--- \\
Lab Stand, clamps
& 	--- 
&	---
& 	--- \\
Water
& 	---
& 	tap water
& 	---\\
Schlieren Setup
&	---
&	---
&	---\\
Light source & ---
&	DNR
&	``1''\\
Roscolene gels & Rosco & 2001,89,70,310 & ---\\
NTSC video camera
&	Sharp
&	XC-900D
&	211325\\
DV camera & Panasonic & PVGS-400 & H5HG50513\\
Digital multimeter
&	Fluke
&	179
&	93810559 \\
Type K thermocouple & Fluke & --- & ---\\
\hline
\end{tabular}
\label{t:MaterialsHeatShockSchlieren}
\end{table}

For Schlieren experiments, we used the Schlieren setup\footnote{the
``setup'' includes parabolic mirrors, adjustable knife-edges,
tabletop, etc.}  in lab.  The projector is designed to work as shown
in Figure~\ref{f:schlieren-photography}.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{schlieren_hires}
\caption{Diagram of a Schlieren Photography System \cite{schlieren}}
\label{f:schlieren-photography}
\end{figure}

For our experiments, we suspended a piece of glass within the
Schlieren field of view with a ring stand clamp.  The glass was held
from one side.  We then heated the glass with the heat gun.  Once the
temperature of the glass, stopped
increasing, we removed the heat gun and dropped a droplet of water
from a titration device onto the glass.  The specific used materials
are listed in Table~\ref{t:MaterialsHeatShockSchlieren}.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\clearpage
\section{Results}

As mentioned under ``Procedure,'' there were a number of pieces to this
lab, each with a distinct set of results.  To recapitulate, we looked at the
impact of thermal shock, at the beam break and optical trigger
mechanisms, at means for breaking sheets of different thicknesses, and
at different lighting techniques.


\subsection{Thermal Shock} %results
For the testing of thermal shock, as described under ``Procedure,'' we
determined that neither a heat gun nor a soldering iron alone were
sufficient to crack glass.

Heating the glass and then rapidly cooling it with water, however, was
able to break glass under certain conditions.  The initial height
of the water-dropping mechanism, as well as the volume of water
dropped, both appeared to be important. This effect can be seen in
Figures~\ref{f:CrackCalc1} and \ref{f:CrackCalc2}.


\begin{figure}[!ht]
\centering
\includegraphics[width=5in]{crack1}
\newline
\newline
\includegraphics[width=3in]{crack1settings}
\parbox{4in}{\caption[Crack moving through slide (1)]{The first of two
images showing a crack propagating through glass.  HSV settings are
shown.}\label{f:CrackCalc1}}
\end{figure}

\begin{figure}[!ht]
\centering
%\includegraphics[width=5in]{crack2}
\includegraphics[width=5in]{slide-fixed}
\newline
\newline
\includegraphics[width=3in]{crack2settings}
\parbox{4in}{\caption[Crack moving through slide (2)]{The second of
two images showing a crack propagating through glass, taken 93
$\mu$seconds after the first frame.  HSV settings are shown.}\label{f:CrackCalc2}}
\end{figure}


\clearpage
\subsubsection{Trigger Mechanisms}
We had relatively good results with the beam break trigger but
relatively poor results with the optical trigger.  The beam break
trigger seemed to fire relatively consistently when water was dropped
through its beam, though during setup and testing, we did
experience droplets that failed to cause a trigger.

The optical trigger, however, frequently failed to trigger at all in
the presence of a drop of water.  We were not able to gather useful
data on it because we were unable to get it to work reliably.

Experimentally, it seems that lighting has a significant impact on the
optical trigger.  If a light was pointed directly at the trigger's
sensor mechanism, it was likely to not trigger at all, whereas it
seemed to work when only in the presence of ambient room light.
Adjusting the sensitivity of the Time Machine that interfaced with the
trigger helped, but did not entirely resolve the problem.


\clearpage
\subsubsection{Lighting Techniques}
For testing different lighting techniques, the goal was to find the
most visually effective form of lighting rather than to calculate any
specific data.  Towards that goal, we generated images from backlit
and side-lit slides, as shown in Figures~\ref{f:LightingTechniques2}
and \ref{f:LightingTechniques3}.

\begin{figure}[!ht]
\centering
\includegraphics[width=5in]{lighting_sidelit}
\newline
\newline
\includegraphics[width=3in]{mark1-Fig10settings}
\parbox{4in}{\caption[Water falling on a hot slide]{This image was
captured with a side-lit microscope slide, lit against a black
background.  The displayed settings were used.}\label{f:LightingTechniques2}}
\end{figure}

\begin{figure}[!ht]
\centering \includegraphics[width=5in]{lighting_backlit}
\newline
\newline
\includegraphics[width=3in]{mark1-Fig11settings}
\parbox{4in}{\caption[Image captured with a back-lit microscope
slide.]{This image was captured with a back-lit microscope slide.  The
displayed settings were used.}\label{f:LightingTechniques3}}
\end{figure}

We found that standard lighting was not particularly effective.  Both
side- and back- lighting were effective.
Shooting a slide from underneath, however, produced images that were
surprisingly unclear. We quickly discontinued this strategy as we
could not easily tell what was going on in the images that it produced.

\clearpage
\subsection{Mild Impact}
We found that the thicker $\nicefrac{3}{32}''$ sheet glass was much harder to break
than the thinner microscope slides.  We tried dropping objects from
various different heights onto the glass.  Based on this data, we
gathered the glass-breakage data listed in Table~\ref{t:ResultsGlassImpact}.

The pendulum used for these experiments was a piece of PVC pipe
roughly $12''$ long and $1''$ in diameter, hinged at the top so that
it can swing freely around one axis and with an exposed bolt head on
its end facing in the direction of swing.  This pendulum was used in a
previous lab for popping balloons.

\begin{table}[!ht]
\centering
\small
\caption{Glass Impact Data}
\begin{tabular}{l|l|r|l}
\hline
\emph{Glass}	&	\emph{Implement}&\emph{Height}&\emph{Break?} \\
Slide			&	Pendulum	&	$1''$	&	Yes \\
Slide			&	Screwdriver	&	$1''$	&	Yes \\
$\nicefrac{3}{32}''$	&	Pendulum	&	$1''$	&	No \\
$\nicefrac{3}{32}''$	& 	Pendulum	&	$3''$	&	No \\
$\nicefrac{3}{32}''$	&	Pendulum	&	$12''$	&	No \\
$\nicefrac{3}{32}''$	&	Screwdriver	&	$2''$	&	No \\
$\nicefrac{3}{32}''$	&	Screwdriver	&	$4''$	&	No \\
$\nicefrac{3}{32}''$	&	Screwdriver	&	$8''$	&	Yes \\
$\nicefrac{3}{32}''$	&	Screwdriver	&	$12'$	&	Yes \\
\hline
\end{tabular}
\label{t:ResultsGlassImpact}
\end{table}

While our control experiment was able to break $\nicefrac{3}{32}''$ glass
at a height of $8''$ with a screwdriver, later tests were unable to do
so consistently.

\clearpage
\subsubsection{Glass Flexing on Impact}

We intend to see if the glass flexes when impacted with a blunt
object.  In order to analyze this we will use the below two
frames.  One right before impact and one right after
impact (Figure~\ref{f:altH}).

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{flexing_results}
\parbox{6in}{\caption[Screwdriver impacting glass]{Two consecutive
     frames of the glass being broken by the impact of a screwdriver.
     Phantom camera. 28 mm lens.  Frame rate 47,000
     fps. $8\times{}2\times\nicefrac{3}{32}''$ glass
     sheet.}\label{f:altH}}
\end{figure}

\clearpage

%========================================

\subsection{BB Rifle Fired at Glass Slides and Sheets}
\subsubsection{Crack Formation}

We did several trials to see the crack formation as a BB impacts
glass.  Figures~\ref{f:altI} and \ref{f:altI2} are a set of ten
consecutive frames that show how cracks form when a BB impacts glass.


\begin{figure}[!ht]
\centering
\includegraphics[height=6in]{BB_thru_slide_results1}
\parbox{6in}{\caption[BB impacting glass slide, multiple HSV
frames]{Parts A through E. The first five frames of a BB impacting a
glass slide. Phantom camera with aperture f/1.8 and 50 mm
lens. 75,000 fps.}\label{f:altI}}
\end{figure}


\begin{figure}[!ht]
\centering
\includegraphics[height=6in]{BB_thru_slide_results2}
\parbox{5.5in}{\caption[BB impacting glass slide, multiple HSV frames
(continued)]{Parts F through J. The second five frames of a BB
impacting a glass slide. Phantom camera with aperture f/1.8 and 50 mm
lens. 75,000 fps.}\label{f:altI2}}
\end{figure}

\clearpage
\subsubsection{Deformation with HSV --- Our First Try}
\label{s:dwh1}

In our first attempt to do the projected grid method described in the
background, we obtained the following results.  Figure~\ref{f:badgrid}
is five consecutive frames of a BB impacting glass, captured using the
grid reflection method.

\begin{figure}[!ht]
\centering
\includegraphics[height=6in]{bad_grid}
\parbox{6in}{\caption[Five consecutive frames of BB impacting glass
with projected grid.]{Five consecutive frames of BB impacting glass
with projected grid.  This glass piece was
$8\times{}1\nicefrac{1}{8}\times{}\nicefrac{3}{32}''$.  The Phantom
camera was used with f/2.8 and 75,000 fps.  4 pumps on the BB gun.  28
mm lens.  Exposure time 18.25 $\mu$seconds.}\label{f:badgrid}}
\end{figure}


\subsubsection{Deformation with HSV --- Our Second Try}

We ran several trial runs of this experiment.  A number of trials were
run with mirrors.  However, in many of these trials the mirrors did
not shatter.  It was found that the silver reflective mirror surface
held the cracked glass together, preventing it from shattering.

We present 2 trials of grid deformation with this setup.

In one trial with the $\nicefrac{3}{32}''$ glass, we obtained the two
images shown in Figure~\ref{f:grid_test1_frames}.  The two consecutive
frames shown in this figure illustrate the glass deforming
substantially on impact with the BB.  This deformation can be seen
more clearly in the charts shown in Figure~\ref{f:grid_test1_graphs}.
These charts show plots of the positions of the vertices of the wire
mesh that are visible in the image.

\begin{figure}[!ht]
\centering
\includegraphics[width=3.2in]{grid/grid_test1_frame1}
\includegraphics[width=3.2in]{grid/grid_test1_frame2} \\
\includegraphics[width=4in]{grid/grid_test1_videodata}
\parbox{6in}{\caption[Grid projection, first trial, HSV]{Two
consecutive frames of the ``projected grid'' method from Trial 1.  The
first frame is immediately prior to the BB's impact; the subsequent
frame is immediately after the BB's
impact.}\label{f:grid_test1_frames}}
\end{figure}

\begin{figure}[!ht]
\centering
\includegraphics[width=3.2in]{grid/grid_test1_graph1}
\includegraphics[width=3.2in]{grid/grid_test1_graph2}
\parbox{6in}{\caption[Grid projection, extracted data]{Graphs of the
grid vertices from Trial 1, as shown in Figure
\ref{f:grid_test1_frames}.  Units are in ``image pixels.''  The image
that we worked with was scaled up to a resolution of $512\times{}256$ prior to
gathering the data for these charts.}\label{f:grid_test1_graphs}}
\end{figure}

The glass deformed in a circular region surrounding the impact point
of the BB.  The amount of deformation decreased with distance from the
BB, up to a certain radius at which the magnitude of the deformation
rapidly dropped to zero.

\clearpage
In a subsequent trial with the $\nicefrac{3}{32}''$ glass, we obtained
the series of images shown in Figure~\ref{f:grid_test2_frames}.  The
images show a similar deformation.  The third image in the series
exhibits a number of irregular deformations; it appears that, in this
frame, the glass has begun to crack.  Interestingly, these odd
deformations do not show up effectively in the vertex graphs in
Figure \ref{f:grid_test2_graphs}.  The cracks manifest themselves as
disjoint lines, which are very visible to the naked eye but which
don't necessarily have a large or consistent effect on the positions
of grid vertices.





\begin{figure}[!ht]
\centering
\includegraphics[height=2in]{grid/grid_test2_frame1}
\includegraphics[height=2in]{grid/grid_test2_frame2}
\includegraphics[height=2in]{grid/grid_test2_frame3} \\
\includegraphics[width=4.5in]{grid/grid_test2_videodata}
\parbox{6in}{\caption[Grid projection, second trial, HSV]{Three
consecutive frames of the ``projected grid'' method from Trial 2.  The
first frame is immediately prior to the BB's impact; the second frame
is immediately after the BB's impact, and the third frame shows the
glass beginning to crack.}\label{f:grid_test2_frames}}
\end{figure}


\begin{figure}[!ht]
\centering
\includegraphics[width=4.2in]{grid/grid_test2_graph1}\\
\includegraphics[width=4.2in]{grid/grid_test2_graph2}\\
\includegraphics[width=4.2in]{grid/grid_test2_graph3}
\parbox{4.5in}{\caption[Grid projection, second trial, extracted
data]{Graphs of the grid vertices from Trial 1, as shown in Figure
\ref{f:grid_test2_frames}.  The image that we worked with was scaled
up to a resolution of $512\times{}256$ prior to gathering the data for these
charts.}\label{f:grid_test2_graphs}}
\end{figure}

%========================================
\clearpage

\subsubsection{Deformation with Still Images}

Figure~\ref{f:alt1} is a still image obtained using sync-and-delay and
the Nikon D200 camera.  The photo depicts a BB hitting a glass sheet.
that is $8\times{}2\times{}\nicefrac{3}{32}''$.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{d200/pic1}
\parbox{6in}{\caption[Still image of glass deformation using D200
camera.]{Still image of glass deformation using D200 camera.  Camera
aperture f/3.  Shutter speed set to ``bulb.''  4 pumps on the BB gun.
No added delay in the system.}\label{f:alt1}}
\end{figure}

\clearpage
%%%%%%%%%%
\subsection{Schlieren Imaging}

Our Schlieren imagery did not provide frames showing the deformation
of glass.  We were able to acquire relatively few good video images of
glass cracking.  Figure~\ref{f:schlieren_video_frames} shows our
best captured recording of glass cracking.

\begin{figure}[h!]
\centering
\includegraphics[width=2.25in]{schlieren/schlieren_heating}
\includegraphics[width=2.25in]{schlieren/schlieren_crack}\\
\includegraphics[width=2.25in]{schlieren/schlieren_crack2}
\includegraphics[width=2.25in]{schlieren/schlieren_done_cracking}
\caption[Frames from a captured Schlieren video of glass cracking
under heat shock.]{Frames from a captured Schlieren video of glass cracking
under heat shock.  The video was taken at 30 fps with an NTSC camera; a
frame counter is included in the bottom left corner of the frames.}
\label{f:schlieren_video_frames}
\end{figure}

%%%%%%%%%%


\clearpage
\section{Discussion}

\subsection{Thermal Shock} % discussion
We found that, while we do not yet fully understand how thermal shock
causes glass to crack and shatter, we are able to shatter
it consistently. 


As mentioned in ``Results,'' the inconsistency of the optical trigger
seemed to be correlated with ambient light.  We suspect that the
sensor was flooded with too much light.  It might work better in
a darker room (though such a setup would not work for HSV recording).
Because the sensor is infrared-based, and because the HSV camera is
monochromatic and sensitive to an array of different light
frequencies, we might also be able to run the experiment with a strong
monochromatic visible-spectrum light.  We could also use a still
camera in a dark room with a flash.  However, since the beam break
trigger works most of the time, we decided to use that trigger.




We found both the back-lighting and side-lighting techniques to be
effective.  They tend to produce inverted images: white-on-black
vs. black-on-white.  We do not have an immediate use for this fact, but
it may well prove useful in future analysis and so is worth keeping in
mind.

Based on the high-speed video that we captured and on the images shown
in Figures~\ref{f:CrackCalc1} and \ref{f:CrackCalc2}, we calculated a
crack propagation rate of 430 m/s in microscope slides.

\clearpage
\subsection{Mild Impact}

\subsubsection{Glass Flexing on Impact}
Glass is a hard material, however it is known to flex before
breaking.  We wanted to test this assertion as well as see if we could
capture this flexing.  In order to analyze this, we will use the
images presented in Figure~\ref{f:altH} in the Results section.  To
see the change in motion of the glass from one frame to another, we
will overlay the two images and measure in pixels the change in
displacement.  Figure~\ref{f:altH2} shows the two frames side by side.
The images are placed next to each other where the screwdriver impacts
the glass, which is the point that will flex the most.  The left side
is the first frame.  The right side is the second frame.  Red lines
are placed to show where the glass from the non-flexed frame would
extend if the glass had not been contacted by the screwdriver.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{flexing_disc}
\parbox{6in}{\caption[Screwdriver, successive HSV frames]{Overlay of
two consecutive frames from Figure~\ref{f:altH}. Phantom camera with
28 mm lens.  47,000 fps.  $8\times{}2\times{}\nicefrac{3}{32}''$ glass
sheet.  The left is the first image and the right is the subsequent frame.
The red lines extend the edge of the non-flexed glass to show
visually how the glass has flexed.}\label{f:altH2}}
\end{figure}

     To analyze this, the image is calibrated using the known
thickness of the glass of $\nicefrac{3}{32}''$, which is $0.094''$.
We measured the thickness of the glass in the screenshot at 23 pixels.

\[ \frac{\frac{3}{32}}{23} \Rightarrow \frac{3}{736} \textrm{ inches/pixel} \]

The image displaces by 15 pixels.  Changing this back to inches gives
us $0.061''$, or roughly the thickness of the glass.

One problem with light-based triggers in this experiment
is that drops of water are clear.  They act as lenses, distorting
light passing through them; but they do not block light.  We
hypothesized that using a darker-colored fluid (such as water
containing a great deal of food coloring) might lead to better results
with both trigger mechanisms.


We established that glass that is 2.4 times as thick requires an
impact with much more than 2.4 times the energy in order to shatter.
This is not terribly surprising. Mechanics \cite{Mechanics} teaches us
that the resistive moment $M$ is

\begin{equation}
M = \int_A \rho \cdot y dA = \rho \frac{h}{2}^2 \cdot w
\end{equation}

This means that the strength of the glass varies with both its width
and with the square of its thickness.  Dividing these two, we get that

\begin{equation}
\frac{(h_1)^2 \cdot w}{(h_2)^2 \cdot w}
\end{equation}

is the ratio of the moments.  Calculating the ratio between a
$75\times{}25\times{}1$ mm slide and a $203\times{}51\times{}2.4$ mm pane of glass, and assuming that
the two different panels of glass are made from the same glass
compounds so that their $\rho$ constants are the same, we get

\begin{equation}
\frac{(2.4)^2 \cdot 51}{(1)^2 \cdot 25} = 12
\end{equation}

which would predict that the thicker glass can withstand 12 times the
moment of the thinner slide.  Our experiments were not targeted at
calculating this moment; nonetheless,
comparing our data from thin slides to our data from much-harder-to-break
$\nicefrac{3}{32}''$ glass, our results do seem to support this
calculation.

\clearpage
\subsection{BB Rifle Fired at Glass Slides and Sheets}
\subsubsection{Crack Formation}

     From Figure~\ref{f:altI} in the results we can see the
progression of what happens to a glass slide when a BB hits it.  It is
apparent in Figure~\ref{f:altI2}, parts F through J that the BB goes
through the piece of glass.  We can look at this glass and
characterize the types of cracks that form.  In Figure~\ref{f:altX},
we can see that there are radial or concentric cracks that form.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{slide_circular}
\parbox{6in}{\caption[Crack propagation, BB on slide]{This image
     extracted from Figure~\ref{f:altI}, part D.  Here, we overlay a
     circle showing the concentric cracks that form.}\label{f:altX}}
\end{figure}

In Figure~\ref{f:altY}, we can see that radial cracks also form.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{slide_linear}
\parbox{6in}{\caption[Crack propagation, BB on slide, cracks
     highlighted]{This image is extracted from Figure~\ref{f:altI}, part D.
     Here, we overlay lines to show the major radial cracks that have
     formed.  The cracks are labeled 1 through 6.}\label{f:altY}}
\end{figure}

By looking at Figure~\ref{f:altI}, parts B through D, we can
trace the crack formation over time and calculate the average
crack speed.  In Figure~\ref{f:altZ}, we placed blue dots at the end of
each crack in the first of the three frames, a green dot at the
end of the crack in the second frame, and a yellow dot at the end
of the crack in the third frame.  Then we overlaid the cracks
from Figure~\ref{f:altY} and the dots indicating crack endings to see the
progression of the slide breaking.

\begin{table}[!ht]
\centering
\small
\parbox{30em}{\centering
\caption{Distances traveled by cracks in pixels}
(pixels from BB impact)
\label{t:altC}
}
\begin{tabular}{l|l|l|l}
\hline
\emph{Crack \#}  &  \emph{Blue dot} &  \emph{Green dot} &  \emph{Yellow dot}\\
1         &  ---      &  133       &  189\\
2         &  30       &  118       &  ---\\
3         &  34       &  143       &  ---\\
4         &  ---      &  121       &  136\\
5         &  37       &  113       &  142\\
6         &  ---      &  129       &  ---\\
\hline
\end{tabular}
\end{table}

\begin{figure}[!ht]
\centering
\includegraphics[width=6.0in]{slide_form_cracks}
\parbox{6in}{\caption[Successive HSV frames, crack formation]{This is
     using the frames from Figure~\ref{f:altI}, parts B through D.  Here we have
     traced the crack formation, placing dots at the ends of cracks at
     this particular stage in the breaking process.}\label{f:altZ}}
\end{figure}

Using the image at the bottom of Figure~\ref{f:altZ}, we can
measure the distance the crack has moved in pixels.
Table~\ref{t:altC} illustrates the results obtained by finding the
pixel distances.


We can also measure the apparent slide width in the image. It is 178 pixels
wide.  This allows us to calibrate the image so that we can find
actual displacements.  Using the actual slide width of 25 mm, we can
see that the we have a ratio of 25 mm per 78 pixels which is 0.32
mm/pixel.  Using this ratio, we can make Table~\ref{t:altD} with the
actual displacements from the pixel displacements.

\begin{table}[!ht]
\centering
\small
\parbox{30em}{\centering
\caption{Distances traveled by cracks}
\label{t:altD}
(millimeters from BB impact)
}
\begin{tabular}{l|l|l|l}
\hline
\emph{Crack \#}  & \emph{Blue dot}  &   \emph{Green dot} & \emph{Yellow dot}\\
1         &   ---       &   43        &     61\\
2         &   9.6       &   38        &     ---\\
3         &   11        &   46        &     ---\\
4         &   ---       &   39        &     44\\
5         &   12        &   36        &     45\\
6         &   ---       &   41        &     ---\\
\hline
\end{tabular}
\end{table}

     Using the data in Table~\ref{t:altD}, we can calculate the change
in distance from the point of impact of the BB.  We can use this
information to calculate velocities.  Table~\ref{t:altE} has the changes in
distances.

\begin{table}[!ht]
\centering
\small
\caption{Change in distance from BB impact (in mm)}
\label{t:altE}
\begin{tabular}{c|c|c}
\hline
\emph{Crack \#} & \emph{Blue dot to Green dot} &
\emph{Green dot to Yellow dot}\\
1         &      43             &  18		\\
2         &      28             &  0		\\
3         &      35             &  0		\\
4         &      39             &  5		\\
5         &      24             &  9		\\
6         &      41             &  0            \\
\hline
\end{tabular}
\end{table}

     From Figure~\ref{f:altZ}, we can see that only crack 5 expands in
all frames.  It is important to note that, for all other cracks besides
crack 5, we cannot be certain that the crack has been forming for the
entire duration between each frame.  For example, if we look at crack 1,
we see that the crack did not start to form and therefore has no blue
dot in Figure~\ref{f:altZ}.  This same logic holds for
cracks that do not have a yellow dot in Figure~\ref{f:altZ}.  We do
not know when the crack stopped moving, so the crack may have reached
the location of the green dot before the Phantom captured that image
for the second frame in Figure~\ref{f:altZ}.  For this reason, the
time between frames represents the maximum time taken for a crack to
travel a specified distance.  Thus, the velocity
calculations in Table~\ref{t:altF} are a lower bound.  In order to
make the calculations in Table~\ref{t:altF}, we multiply by 75,000
fps, the frame rate of this sample.
\clearpage

\begin{table}[!ht]
\centering
\small
\parbox{30em}{\centering
\caption{Velocities from one point to another (m/s)}
\label{t:altF}}
\begin{tabular}{c|c|c}
\hline
\emph{Crack \#}&  \emph{Blue dot to Green dot} &
\emph{Green dot to Yellow dot}\\
1       &        3200             & 1350\\
2       &        2100             & 0\\
3       &        2600             & 0\\
4       &        2900             & 380\\
5       &        1800             & 680\\
6       &        3000             & 0\\
\hline
\end{tabular}
\end{table}

     Using Table~\ref{t:altF}, we can see the average velocities of
the crack formation for different cracks at different times.  As
stated earlier, we must use logic to figure out which values are
valid.  Cracks 2, 3, and 6 do not have yellow dots so the crack
stopped moving before the green dot or before the second frame in
Figure~\ref{f:altZ} was analyzed.  Looking back at
Figure~\ref{f:altI}, we can see that after part D, the cracks appear
to stop forming.  This suggests that the cracks stopped well before
the frame part D was taken by the Phantom camera.  For this reason the
velocities found that represent cracks forming between the blue and
yellow dots should be the valid values.  The range that we have found
from this data for the velocity of crack formation is 1800 to 3200 m/s
with an average of 2600 m/s.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsubsection{Deformation with HSV --- Our First Try}

Figure~\ref{f:badgrid} (\S\ref{s:dwh1}) is extremely blurry.  We can see
that there is deformation in the glass, but beyond that there is not
much analysis that we can do.  The grid lines are blurred to the point
where they are hard to distinguish.  The reason for the blurring is
motion blur caused by too long of an exposure time.  For this reason,
in future grid trials discussed later in this report, we
increases the amount of light and decreased the exposure
time.  This information is presented to illustrate how important the
short exposure times were and that we learned through trial and error
that they were necessary.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage
\subsubsection{Deformation with HSV --- Our Second Try}

Looking at this data, we were unable to make many generalized
conclusions.  Based on the data from the grid-vertex location graphs,
we calculated the distance that each vertex moved between its rest and
deformed positions, and graphed this distance against the vertex's
initial distance from the point of impact of the BB.  Not
surprisingly, we found that pixels closer to the impact site had a
strong tendency to move a greater distance within the first few
$\mu$seconds of the impact.  This effect is illustrated nicely in
Figure~\ref{f:grid_test1_dist_v_dist}, which shows two nodes, one at
around 80 pixels ($1.3''$ from impact) and one at around 140 pixels
($2.8''$ from impact).  The first node appears to be the expected edge
of the deformation as the bullet pushes the glass inwards.  We are not
certain what causes the second node.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{grid2/grid_test1_dist_v_dist}
\caption{Graph of Point Displacement vs. Point Radius. 50 pixels $= 1''$.}
\label{f:grid_test1_dist_v_dist}
\end{figure}

With our two-frame trial run, we were able to compare two consecutive
sets of position changes.  As can be seen in
Figure~\ref{f:grid_test1_dist_v_dist}, in the first 13 $\mu$s after the
impact of the BB, the glass deforms as in the first trial; but in the
second 13 $\mu$s, the glass near the BB doesn't show much deformation
(probably because it has begun to crack), but there is a ring of
deformation at a radius of around 100 pixels ($2''$ from impact).  We do not know
if this is caused by a shock wave propagating outwards at some
velocity or by a secondary local deformation caused by the cracking of
the glass.

\begin{figure}[!ht]
\centering
\includegraphics[width=3.25in]{grid2/grid_test1_graph1}
\caption{Graphs of the grid vertices from Trial 1, as shown in
Figure~\ref{f:grid_test1_frames}}
\label{f:XXgrid_test1_graphs}
\end{figure}

If we make the assumption that the second peak in the second chart is
caused by a shock wave propagating outwards, we can attempt to
estimate that shock wave's velocity.  In
Figure~\ref{f:XXgrid_test1_graphs}, we examine the radial distances of
the pixels that moved the greatest distance within the specified time
windows, and take their distance from the impact site to be the radius
of the shock wave.  Making this assumption, we have two radii
(measured at $23$ and $87$ pixels, respectively), and a time delta
(13 $\mu$s).  This gives us a velocity of 1,530 m/s.

As noted in Table~\ref{t:glass_wave_propagation_rates}, waves
propagate at speeds that are on the same order as 1,530 m/s.  The
slowest propagation rate is roughly 1.5 times the number that we
calculated for a possible propagation velocity.  This is far enough
off that it is unlikely that what we are seeing is strict wave
propagation, but it is close enough that what we are seeing is likely
a related phenomenon.

\begin{table}[!ht]
\centering
\caption{Speed of sound in glass}
\small
\begin{tabular}{l|l|l}
\hline
\emph{Glass Type}	&
\emph{velocity of longitudinal waves (m/s)}	&
\emph{velocity of shear waves (m/s)} \\
Fused Silica			&	5968	&	3764\\
Glass, heavy silicate flint	&	3980	&	2380\\
Glass, light borate crown	&	3980	&	2380\\
Glass, pyrex			&	5640	&	3280\\
\hline
\end{tabular}
\label{t:glass_wave_propagation_rates}
\end{table}


\paragraph{Sources of Error}

There are a number of possible sources of error in this data.  One
error source is the resolution, both pixel resolution and time
resolution, of the Phantom HSV camera.  Capturing video of an event as
quick as the deformation that we are interested in is at the edge of
the Phantom's range. We had to use a frame rate near its maximum, and
as a result an image resolution near its minimum, to get any
deformation imagery at all.  This has two effects: first, we are only
able to view at most two frames of deformation prior to cracking, so
we have very few frames and relatively little timing data to work
with.  Second, there are only about 10 pixels between each vertex in
the grid that we are watching, so an error of a single pixel has a
substantial impact.

Additionally, the software that we used to find the pixel locations of
the grid points was quite simplistic, and depended on a lot of human
interaction.  It was easy for a point measurement to be off by one or
two pixels.

Based on these factors, we expect the position error to be on the
order of $\pm2$ pixels, or $\nicefrac{1}{12}''$.  We are interested in
time estimates on the order of two or three frames, so time error may
be as much as half a frame duration, or 7 $\mu$s.

We feel that the experiments that we ran were approximately as
thorough as possible given the limitations of the Phantom HSV camera.
Were we to repeat the experiments, we would follow the same procedure.
However, there would be substantial benefit to a future group with
more sophisticated analysis software and an HSV camera capable of
higher frame rates at a higher resolution, re-running these
experiments to attempt to gain data with greater accuracy.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage
\addtolength{\parskip}{-1ex}
\subsubsection{Deformation with Still Images}

Looking at Figure~\ref{f:alt1} (found in the Results), the image
appears to be blurry.  We are unsure what caused this to occur.  Some
of our hypotheses include:
\begin{itemize}
\setlength{\parskip}{0pt}\setlength{\itemsep}{0pt}
\item the duration of SPOT's flash creating too
long of an exposure to image the speeds of the shock waves without
blur
\item the aperture of the lens being large enough that the deformed
glass was out of the depth-of-field of the camera
\end{itemize}
It was
difficult to confirm if either or both of these were factors
leading to this phenomenon.

We do learn some things from this D200 still image.  In
Figure~\ref{f:alt2}, which is copied from Figure~\ref{f:alt1}, we have
drawn an ``x'' to indicate where the BB impacts.  Around this ``x,''
we can see circular waves emanating out from this location as one
might see in water if a rock is thrown into the water.  This
phenomenon is consistent with what we saw with the high-speed video
camera.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{d200/pic1_waves}
\parbox{6in}{\caption{Figure~\ref{f:alt1} with wave lines added.}\label{f:alt2}}
\end{figure}

In the D200 image we can see that the grid lines are not continuous in
many places.  Figure~\ref{f:alt3} has arrows that show some examples
of this.  When the grid lines are not continuous, this indicates that
cracks have started to form, because the glass no longer has a curve
that would cause a distorted but continuous line.  For this reason, it
is apparent that there is so much delay in the sync-and-delay system
that we cannot capture the glass deformation before breaking that we
successfully captured with the Phantom high-speed video camera.

\begin{figure}[!ht]
\centering
\includegraphics[width=6.5in]{d200/pic1_arrows}
\parbox{6in}{\caption[Figure~\ref{f:alt1} with arrows showing grid
line discontinuity.]{Figure~\ref{f:alt1} with arrows showing grid
line discontinuity. This shows that cracks have already started to
form.  }\label{f:alt3}}
\end{figure}

The main reason we used the D200 was to capture a higher resolution
image that is esthetically pleasing.  We did succeed in this goal,
however we were not able to extract useful data from the resulting
image.  We can see that we can capture higher-resolution images.  We
can also see that there are circular waves that form on the glass.
This is consistent with what we saw on the high-speed video of a BB
hitting glass.

%%%%%%%%%%%%%%%%%%%%
\subsection{Schlieren Imaging}
The Schlieren experiment led us to the conclusion that Schlieren, at
least at regular video speeds, does not produce useful data about the
process of glass breaking under heat stress.  We were ultimately
unable to gather any useful data.  We did determine that glass does not
deform interestingly as it is heated; the glass does not change color
in the imager.

Future experiments with Schlieren could try high-speed video.  If
available, a color high-speed video camera might provide more
information about the deformation, because of the importance of hue in
Schlieren imaging (hue indicates the direction in which light is being
bent).

Additionally, taking Schlieren video of a BB breaking glass could
provide useful data.  In our other experiments, we found that BBs were
more effective than heat expansion at providing both interesting crack
patterns and initial glass deformation.  BBs travel at a high-enough
speed that viewing them with either a high-speed video system or a
synch-and-delay system (with a still camera) would produce more-useful
data.\footnote{Because of resource limitations, we performed the
Schlieren experiments without the BB gun while the BB gun was being
used for other high-speed video of glass breaking.}

%%%%%%%%%%%%%%%%%%%%


\clearpage
% \section{Future Work}
% 
% Our future goals will be to capture an array of images of glass
% breaking using the techniques described above as well as other
% techniques such as BBs and Schlieren imagery.  The long-term goal is
% to produce measurements of the rate of flexing and crack propagation
% in glass.
% 
% Based on this preliminary data, we feel that the thicker glass is
% likely to produce more interesting results than the thinner glass.  We
% would also like to try a broader array of lighting techniques and
% camera angles since these factors will be key in making data
% extrapolation and analysis possible.
% 
% Another method that can be used to calculate fracture speed is the
% electrical grid method.  This can be done by using electrically
% conductive paint or wires that lay in the path of the glass fracture.
% When the fracture severs the wires or painted connections, it creates
% an open circuit.  The voltage readings can be obtained by putting
% different load resistors with different paths so the change in voltage
% can be read as the fracture breaks this path \cite{fracture}.

% \section{Project Plan}
% 
% We plan to proceed along the following timeline:
% 
% 
% \emph{Week 1 (of Nov. 3)}
% \begin{itemize}
% \item Shoot glass with a BB gun, try to obtain HSV and still images of
% the glass breaking
% \item Test grid reflection: obtain several images of the glass
% breaking with a reflected grid, see if deformation can be observed.
% \item Measure for consistency between slides/sheets, pendulum break of
% slides; see how consistently these break under the same amount of
% force.
% \item Apply heat to the sheets (hotter than heat gun, flame); obtain
% high-speed video of sheet glass breaking.
% \item Rotate the glass, break it on-end.  Obtain high-speed video of
% the glass breaking on-end.
% \end{itemize}
% 
% \emph{Week 2 (of Nov. 10)}
% \begin{itemize}
% \item Try Schlieren imaging to capture heat distribution and flexing
% when breaking.  Obtain high-speed video of glass flexing and breaking
% in the Schlieren imager (or determine that flexing or breaking glass
% does not produce interesting diffraction as displayed by the Schlieren
% imager)
% \end{itemize}
% 
% \emph{Week 3 (of Nov. 17)}
% \begin{itemize}
% \item Run lots of trials of what we found works well during Weeks 1
% and 2.  Gather multiple sets of video of any imagery that we found
% effective for analyzing the glass.  Do this analysis.
% \end{itemize}
% 
% \emph{Week 4 (of Nov. 24)}
% \begin{itemize}
% \item Capture still photos of all interesting events for which video
% was captured during Week 3.  Analyze more data.
% \end{itemize}
% 
% \emph{Week 5 (of Dec. 8)}
% \begin{itemize}
% \item Write-up -- do whatever we need in lab to finish the final lab
% report
% \end{itemize}
% 
% 
% 
% We plan to work as a group in lab.  We have not allocated specific
% tasks to specific people at this point.  We expect one member of our
% group to keep lab notes each week, with the position rotating for
% fairness and balance.  For portions of the lab where this makes sense,
% we expect one member of the group to manage the HSV camera, including
% its trigger; one to drop the water or object on the glass; one to take
% notes; and one to supervise and manage lighting.  The person handling
% lighting could deal with a still camera should one come into play.  If
% we have sufficient equipment, we can have two tests running
% simultaneously, in which case at both test sites, one person will drop
% the water or object and record results, and the other person will
% manage the camera.
% 
% We will divide up lab write-ups and manufacturing of hardware that we
% find we need, as such things come up.

\clearpage
\appendix
\setlength{\parskip}{0ex}
\section{Appendix}
\begin{thebibliography}{Ravi-Chandar}

\bibitem[2.001]{Mechanics} ``Mechanics.'' Course 2.001. Massachusetts
Institute of Technology. Spring 2008.

\bibitem[IM3-JWB]{lab3} Bales, James W. ``Laboratory 3: Multiflash
Photography.'' 6.163 Strobe Project Laboratory. Massachusetts
Institute of Technology, Cambridge, MA, 24 September 2008.

\bibitem[Jones02]{Jones} Jones, Allison PhD. ``Forensic Handbook 2 ---
Trace Evidence.'' May
2002. \url{http://www.channel4.com/science/microsites/S/science/society/forensic_trace.html}.
Retrieved 11 Dec 2008.

\bibitem[Socrate]{Socrate} Socrate, Simona. \emph{A Roadmap to 2.001},
Massachusetts Institute of Technology. p.168. 2007.

\bibitem[Bhuyan89]{impacts} Bhuyan, Sanjeeb, Sarah Longenbaker, and
Dmitry Portnyagin.  \emph{Impacts on Glass --- Final
Report}. Massachusetts Institute of Technology Strobe Lab (6.163).
December 10, 2004.

\bibitem[Ravi-Chandar]{fracture} Ravi-Chandar, K. \emph{Dynamic fracture of
nominally brittle materials}. International Journal of Fracture 90,  1998.

\bibitem[Jeronimo]{schlieren} Jeronimo, A. and V. Van Der
Haegen. ``Schlieren Technique --- Lab Notes.'' EUROAVIA Symposium ---
Mission to Mars. November 2002. Von Karman Institute for Fluid
Dynamics. \url{http://www.vki.ac.be/event/euroavia/slides/lab1exp.pdf}.
Retrieved 12 Dec 2008.

\end{thebibliography}


\small
\clearpage
\listoffigures
\clearpage
\listoftables

\clearpage
\section{Point-Capturing App}

We developed a simple software tool to speed up the identification of
vertex points in an image.  The software was quite simple: It loaded
an image; then whenever the user clicked on a location in the image,
the program would log the location of that click.  It accumulated a
list of click locations that could be imported into a data analysis
program such as Microsoft Excel.

The tool was written as a Web page using HTML augmented with
JavaScript.  It ran within the Mozilla Firefox 3.0 Web browser.

%\vspace{-4ex}
{\footnotesize\begin{verbatim}<html>
<head>
<title>Image Pos Calc</title>
<script language="JavaScript">
function onImgClick(event) {
  txt = document.getElementById('text_out');
  txt.value += event.layerX + " " + event.layerY + "\n";
  txt.scrollTop = txt.scrollHeight;
}

function onImgMouseover(event) {
  x = document.getElementById('xcoord');
  y = document.getElementById('ycoord');

  x.innerHTML = String(event.layerX);
  y.innerHTML = String(event.layerY);
}

function updatePhoto() {
  document.getElementById('scan_image').src =
    document.getElementById('target_img_file').value;
}
</script>
</head>
<body style="margin: 0">

<img src="" onclick="onImgClick(event);"
     onmousemove="onImgMouseover(event);" id="scan_image" />
<br />

<label for="target_img_file">Image to View:</label>
<input type="textbox" id="target_img_file" />
<input type="button" value="Update" onclick="updatePhoto();" />
<br />

(<span id="xcoord">0</span>, <span id="ycoord">0</span>)
<br />
<textarea id="text_out" cols="80" rows="24"></textarea>

</body>
</html>
\end{verbatim}}


\clearpage
\section{Lab Notes}

%\includepdf[pages=1-2]{mark1-notes1.pdf}
%\includepdf[pages=1-1]{mark1-w2.pdf}


\end{document}