Physics Says Hollywood Shrank the Angry Birds for Their Leading Roles

[mashshare]

The analysis of a video game can be a game in itself. The process of trying to figure out the underlying physics engine in a game is just like science–but much cheaper. It’s been a while since I’ve explored the mechanics in Angry Birds (the game), but I have quite a few posts on the topic.

In my first Angry Birds post, I examined the trajectory of a bird after leaving the slingshot. The first thing I found was that the flight path was indeed a parabola. This means it had a constant horizontal velocity and a constant vertical acceleration–just like projectile motion (without air resistance).

Whenever you have a situation (like a game or a video) with projectile motion, there are three things to consider:

The vertical acceleration (on Earth, this would be -9.8 m/s^{2}).

The frame rate of the video (not all videos are play in real time–a slow motion video is a great example).

The size scale of the scene.

If you know two of these things, you can find the third. If you only know one of these things, you are going to have to guess at a second one. But here is the fun part. Assuming Angry Birds is on Earth and not in slow motion, I can solve for the scale of the video game–and therefore the size of the birds. From this, I found that red bird (his name is Red) has a diameter of 70 cm (over 2 feet).

But what about the birds in The Angry Birds Movie? How big are they? Here’s where we need to do some real science. Since this is a movie and not a video game, I don’t have any control over what happens. Instead, I have to watch the trailers and find something that looks like projectile motion. This scene with two birds spitting water was the only thing that would work. Yes, a water stream should behave like projectile motion.

I can assume the vertical acceleration is -9.8 m/s^{2} and that the frame rate is real–with that, I can determine the scale of things. Let’s do it.

Of course I will get the position of the front of the water in each frame of the video using Tracker Video Analysis. I will temporarily set a scale with the diameter of Bomb (the black bird) to a value of 1 b (using units of b for bomb). I used the size of Bomb instead of Red since Bomb is in the same plane of motion as the water–Red is a bit farther back. Now I can get the horizontal position of the water just to check that it looks like projectile motion (with constant horizontal velocity).

That looks pretty constant. You could even get the value of the horizontal velocity by looking at the slope of this line–but we don’t need that right now. OK, here is the vertical motion.

It’s not a perfect parabola, but it’s close enough. Actually, if you look at the front of the water stream it has a slightly different path than the rest of the water stream–but the deviation isn’t too much to worry about.

Once I fit a quadratic equation to the data, I can compare it to the kinematic equation for an object with a constant acceleration:

The coefficient in front of the t^{2} will be equal to half of the acceleration. Looking at the fit above, this gives a vertical acceleration of:

Remember this acceleration is in units of “b” and not meters since I don’t know the scale of things. Now I can set this acceleration equal to the expected free fall acceleration on Earth and solve for the unit conversion from meters to “bombs”.

The diameter of Bomb is 58 cm–smaller than the diameter of Red in the Angry Birds game. But what about Red in the movie? Here is an image showing Bomb next to Red.

Yes, there is a little bit of guessing here–but I am going to say the diameter of Red (he’s not circular anymore) is about 30 centimeters. That’s quite a bit smaller than in the video game, but still bigger than most birds.

But what about the rest of movie? Is there further evidence that this is indeed the scale of the birds? I will have to wait to see a new trailer or the movie so I can gather more evidence. It’s sort of like waiting for another set of black holes to collide so that I can gather further data on gravitational waves (but much cheaper).