Motion Model

What is a perfect pancake toss?

To flip a pancake, two things need to happen. The pancake must be moved airborne, and the pancake must have some sort of angular momentum applied to it in order to get it to flip. An easy way to do this with a standard pan is to "take advantage of the curved side" (Nihaan 2012). To do this, you can "push it away from [you], and then pull it back quickly." (Nihaan 2012). This front to back motion sometimes is not enough energy to lift the pancake off the pan, so it is often supplemented with a flicking motion. This motion can be seen on the right on Fig. 6.

The forces involved in a pancake flip change throughout the toss. This means that the vertical force (exerted from the flick and/or the push of the pancake from the edge of the pan) coupled with the change from the push to pull force leads to a torque that flips the pancake (Hadley 2020). You can see this movement and the torque that flips the pancake in the GIF on the right.

Since we are measuring the movement of the pan, we don't care about the specific torque, but more about the movement that causes it. These movements create accelerations in the vertical and horizontal planes, but not the depth plane. We will explain what this means for our sensor in the next section.

Figure 6

Motion Model

The physics of the actual pancake flip are complex, but the chef does not have actual control of the pancake, they have control of the pan, so we are measuring the movement of the pan. For our calculation, we are using three degrees of freedom even though there are technically six (since its a three dimensional space). The reason we are choosing three degrees instead of six is because the pancake flip has no lateral movement, it all horizontal and vertical, meaning the differences in the x-axis would be so minimal that they would only complicate the simple movement. It also has rotation in only one axis, the one in line with the flip. The other two axes have no ration, thus we have a total of only three degrees of freedom we use. In our model, the rotation ends up translating to more movement in the Y-Z plane, since its parallel to it, meaning we end up with practically only two degrees of freedom.

Figure 7

Figure 8

The frequencies of the movement are not extremely crucial for our model, but we are using them in a very unique, and important, way. We are calculating the frequencies of both the "perfect pancake toss" and the pancake toss we are testing. Then we find the differences in these frequencies and use that determine what the color of the trial plot is, meaning we are not plotting position, with velocity seen in the separation of the points, and the frequencies being compared by the colors. Thus, in one simple graph, we can compare three different characteristics of the same toss.

Knowing this, we chose to use an iPhone for our data collection, placing it on the bottom of the pan as shown in the image on the left. Above, you can see how the phone recognizes its axes of movement.

Frequencies and Fast Fourier Transformation (FFT) Graphs

One of the important things about the frequency of the pancake toss is that not only does the frequency matter, the amplitude of each frequency also matters a lot. In the case of the Z-axis, the frequency should be around 5 +- 0.1 Hz, with the Y-axis one being around 1.6 +- 0.05 Hz. It is important to note that in this case, since the movement isn't perfect, it will not be only that frequency, it will probably also be the frequencies around it, so the frequencies included should actually be +- 1Hz around the values we are looking for. Besides that, once we do the FFT graph, we should look for a max amplitude of around 4 and 0.65 for Z and Y respectively. You will notice we don't mention the X-axis, as we explained before the motion in the X-axis should be zero, and in so many of the trials we did it is, so we decided to not test it.

Another important aspect is that the tosser should look for the frequencies to be two triangle, and avoid really big peaks (besides the main one). You can see the two FFT graph graphs for our "Perfect Toss" below.

Figure 3

Figure 2

Resources:

Hadley, Mark. "Pancake Tossing". Warwick.Ac.Uk, 2020, https://warwick.ac.uk/fac/sci/physics/staff/academic/mhadley/pancakes. Accessed 7 Dec 2020.

Nihaan, Titli. “How to Toss (Flip) a Pancake. ” YouTube, hosted by Titli Nihaan, 19 Feb. 2012, https://www.youtube.com/watch?v=mTsXuPCZbRY.

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