Analysis

Our analysis included two different components.  The first part was calculating velocities of popcorn kernels.  We utilized our high speed photographs and high speed videos to determine the initial velocity of the popping kernal.

To calculate the velocity of a popcorn kernel popping using the high speed photograph, a scale is needed.  Initially, we took multiple exposure pictures of the popcorn actually popping.  Later, using the same zoom, we took a picture of a ruler positioned at the same point as the kernel would be, to use as a scale.  The ruler allowed us to know the ratio of the “real” length of the pop and the apparent length in the picture.  With this scale factor, we can figure out the distance the popcorn traveled.  The only other variable that is needed to find velocity is time.  We know the time between the two images on the multiple exposure popcorn pictures; it is the flash delay of the Intervalometer program.  Below is a sample of our work to find velocity with one photograph. 

This is our scale shot.  The known distance, the one we measured on the printed photograph, is 12.21 cm.  The distance on the ruler in the picture is only 7 cm.  Using this ratio and the picture of the pop, we can calculate the velocity.  In our calculation x is the actual distance covered by the kernel.  7.13 cm is the distance measured on the printed photograph.  The flash delay was 20 ms or 0.020 seconds.

The calculated velocity for this pop was 2.044 m/s.  We did the same process as shown for six photographs. 

We also calculated the initial velocity of the kernels in our high speed videos, which we took using a MotionScope 8000s High Speed Video Camera.  This required the use of a point-tracker program called Tracker.  In the the tracker program, we found an easily recognizable point on the popcorn, such as the top of a puff, and used that point as a point-mass.  We then tracked the point-mass and marked its position in each frame.  Then the tracker program uses a pre-defined set of axes to graph the change in position of the point-mass over time.  By importing these data points into Graphical Analysis, a graph analysis program, we could obtain a graph of position vs. time for the kernel.  We then fit a curve to the data and using physics equations determined the initial velocity.  A sample frame from the tracker program and a graph is included below.

 After examining all of the velocities that we found, our results were varied and there was a wide range of velocities.  The velocities ranged from 1.282 m/s to 4.235 m/s.  There wasn't a single velocity that most kernels centered around, but rather each kernel was different.

The second part of our analysis was to find patterns in the pops.  We chose to look at the size and shape of the kernel and compare it to the size of the pop.  On our data sheet that we kept during the experiment, we recorded before each pop whether the kernel was small or big and whether it was flat or round.  After it popped, we recorded whether it was a big or small pop.  Here are tables showing the relationship between size and shape of kernel and the size of the pop. 

Based on this information, we concluded that the round kernels have bigger pops, and the flat kernels have smaller pops.  Also, smaller kernels generally had smaller pops and bigger kernels had big pops.  However, since the relationship between the size of the kernel and size of the pop was close to even, it is safer to guess the size of the pop based on shape of the kernel.