The Physics behind “Angry Birds”

Photo credit: https://d1guvqt7k9h5xe.cloudfront.net/AcuCustom/Sitename/DAM/005/red_400x400.jpg

Photo credit: https://d1guvqt7k9h5xe.cloudfront.net/AcuCustom/ Sitename/DAM/005/red_400x400.jpg

by Emily Lehman and Meghan Nay

We are avid Angry Birds fans, so when our physics teacher offered us the opportunity to analyze the validity of physics principles underlying the game, we accepted eagerly. We conducted an analysis to determine whether the mobile application “Angry Birds” followed the principles of physics – specifically, principles of projectile motion.

We videoed the game from the initial launch of a bird to his collision with the pig pedestal. Then, we used Tracker software to collect data of the bird’s motion. Here’s our procedure:

1) We uploaded the video of the red angry bird into the software,Tracker.

2) Using Tracker, we found the horizontal and vertical position vs. time graphs. From there, we found the equation of the best fit line/curve.

3) After obtaining the equation of best fit for the position vs. time data, we took the derivative in order to find the velocity vs. time equation.

4) Then to find the acceleration vs. time equation, we took the derivative of the velocity vs. time equation.

5) Using the position, velocity, and acceleration equations, we were then able to analyze the bird’s motion and compare it to the laws of projectile motion on Earth.

6) Since we don’t know any of the measurements in the video, we established an arbitrary unit of length using the pig pedestal in the video. All equations are based on a unit of length we have called a “pig pedestal.”

Data and Analysis:

Position vs. time data using Tracker. The straight line is the horizontal position vs. time, and the concave-down parabola is the vertical position vs. time.

The graph above shows the position of the bird in the x and y directions. The best fit line for the graph in the y direction is the equation y = -1.882t² + 6.833t + 1.993. To find the velocity of this position graph we took the derivative and found the equation of the velocity in the y direction to be v = -3.764t + 6.833. Also, to find the acceleration in the y direction we found the derivative of the velocity equation and found the acceleration in the y direction to be a=-3.764 pig pedestals/s².

We repeated these steps to find the equations of the position, velocity, and acceleration graphs in the x direction. Which in subsequent order the equations of these graphs are x = 4.637t – 0.0668, v =4.637 pig pedestals/s, and a = 0 pig pedestals/s².

X-Direction

Position vs Time: s(t) = 4.637t – 0.0668

Velocity vs Time: s'(t) = v(t)= 4.637 pedestals/s

Acceleration vs Time: s”(t) = v’(t) = a(t) = 0 pedestals/s²

Y-Direction

Position vs Time: s(t) =-1.882t² + 6.833t +1.993

Velocity vs Time: s'(t) =v(t) =-3.764t + 6.833

Acceleration vs Time: s”(t) = v'(t) = a(t) =-3.764 pedestals/s²

We assumed that the Angry Birds game takes place on Earth where the acceleration due to gravity is -9.8 m/s². Using the vertical acceleration from the best fit line, we  set -3.764 pig pedestals/s2 equal to -9.8 meters/s2  which determined the height of the pig pedestal to be 2.603 meters.

Conclusion:

Based on our findings, we were able to determine that “Angry Birds” follows the rules of physics for a number of reasons. The acceleration of the bird in the x direction was zero, which is characteristic of an object launched as a projectile on Earth, assuming no air resistance. Also because the position vs. time graph in the y direction closely followed the kinematics position equation, we determined that the Angry Bird is subject to a gravitational force.

We also made some strange or odd discoveries about the game. Using the unit conversion discussed in the Analysis section, we found that the actual size of an Angry Bird is 1.019 meters tall, which is around 3.3 feet. We derived this number from the position vs. time graph in the y direction. We found the acceleration to be -3.764, but this was not meters/second2; the units for this was pig pedestals/second2. By assuming gravity in “Angry Birds” was -9.8, we used conversions to find the height of the pig pedestal. Then, we were able to find the height of the bird, which was 1.1019 meters. Certainly, a bird of this size would be subject to air resistance; however, the data show no force in the horizontal direction!

Photo credit: http://resources0.news.com.au/images/2012/09/16/1226475/242180-rheinmetall-039-s-simulators-in-use.jpg

Photo credit: http://resources0.news.com.au/images/ 2012/09/16/1226475/242180-rheinmetall-039-s-simulators-in-use.jpg

Determining that one video game followed the rules of physics on Earth opens up many possibilities for real world applications. Virtual simulations have the potential to revolutionize society and many fields of work. For example, virtual simulations are extremely helpful in pilot training or training for warfare. The analysis that we undertook could be used to assess the validity of these simulations and thus gauge their acceptability as effective training tools.

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