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Jeudi, 10 Novembre 2011 14:42

## Physics of the Yellow Angry Bird

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You have waited long enough. It is now time for another Angry Birds post. Today, it is the yellow bird’s time. To start, an Angry Birds haiku:

The Sun and sky, still.

Green pigs cackle with delight.

Smash wood from above.

Why did I wait so long to look at this yellow bird? Why? It is one of the first ones you get – and way better than the blue or red bird. I really don’t know. Oh, you don’t know about the yellow bird? You haven’t gotten past the levels that just use the blue bird? Ok. Here is the short version. You launch the yellow bird. When you tap the screen, it seems to zoom down and hit stuff. The yellow bird is especially good against wood blocks.

## How does it work?

When I first started playing Angry Birds oh so many years ago, I had this feeling that after tapping the screen the yellow bird just went at a constant velocity. Then one day, I accidentally shot it super high. The bird didn’t just keep going up, it looked like some parabolic motion. I guess I was wrong. What next? Collect some data.

Data collection in Angry Birds is much simpler now that you can play it inside your Google chrome browser (for free). This means that I can just use a screen capture tool along with Tracker Video Analysis (also free). All I need to do is to shoot a whole bunch of yellow birds and look for some type of relationship between the initial (before the tap) motion and after the tap motion.

Also, don’t forget to use the correct scale of things in Angry Birds. I found that the sling shot is about 4.9 meters tall.

## Constant acceleration during “tap”?

Right before you tap the yellow bird, it has some velocity. Clearly, it has a different velocity after the tap. Maybe there is some constant tap-acceleration in the direction the bird was moving. Here is a plot from Tracker that shows the x- and y-velocity of the bird both before and after the tap.

Just to check, let me make a plot of the magnitude of the velocity right before the tap vs. the acceleration during the tap. Oh, it looks like all of the shots have the yellow bird accelerating (due to the tap) for 0.067 seconds. Of course this acceleration could just be due to the screen capture frame rate.

It doesn’t look like there is a simple relationship here. It also doesn’t look like the tap-acceleration is constant. The magnitude of this acceleration ranged from 124 m/s2 to 336 m/s2.

## Looking at the change in speed

How about a plot of the magnitude of the velocity right before and right after the plot? I know I already showed that there seems to be no connection between the acceleration and the initial velocity, but I am going to do it anyway.

You look at this and it seems like there might be a correlation. But I am going out on a limb and I am going to say that the magnitude of the velocity after the tap is always 30 m/s. Yes, I see that one has a magnitude of around 25 m/s and there is one around 26 m/s. Most of them are much closer to 30 m/s. Remember, this graph starts at 24 m/s on the vertical axis. Here is plot of the distributions of accelerations.

This has an average of 29.06 m/s with a standard deviation of 1.86 m/s. Yes – I need more data to really see if the final velocity is constant. However, let me look at the distributions of vertical accelerations before the tap. This SHOULD be a constant near 9.8 m/s2. Here is that distribution.

This has an average of -10.23 m/s2 and a standard deviation of 0.73 m/s2. Comparing the ratio of standard deviation to the average for these two distributions show that they are similar. So, even something that I am certain is constant does not always measure as constant. Part of the problem is that the motion after the tap is usually pretty short – making it more difficult to get a good value of the final velocity.

I ran five more yellow bird shots (and just collected the final velocity data). For these last shots, I was sure to put the bird in a location that would have sufficient post-tap motion. Here is the new histogram (with all the speeds):

I am going to stick with 30 m/s. It is a nice number. Really, you can try this yourself. Shoot the yellow bird almost straight up. When the speed is close to zero, tap the dude – it will go just as fast as any other case.

## What about the angle?

If the yellow bird just jumps up to a speed of 30 m/s after the tap, what about the direction? Here is a plot of the angle (in degrees from the horizontal) of the bird’s velocity before vs. its speed after.

Looks like they are the same (this is a good thing).

## Weird acceleration

Check this out. This is the x- and y-motion of the bird for a case where the bird is moving upwards after the tap.

Notice that in the y-motion, it looks like a parabola both before and after the tap. This is because the vertical acceleration is the same in these cases. Now, here is a case where the bird is shot down. (this is a plot of the y-position and the y-velocity)

In this case, the acceleration of the bird is different after the tap. You can tell by looking at the position graph (which shows an almost straight line) as well as the velocity graph where the slope clearly changes.

What about all the other cases? Here is a plot of the distributions of the vertical accelerations for a variety of bird shots.

Hopefully, you can see what I see. It seems like there are two different accelerations. Just from playing around, it seems like the acceleration is much lower when the yellow bird is moving down before the tap.

How about a plot of the vertical acceleration vs. the final velocity angle. Here you go.

From this, it looks like for a velocity somewhere lower than -20°, the vertical acceleration changes from -9.8 m/s2 to maybe -3 m/s2 (or maybe the acceleration is zero – it is difficult to tell). Actually, I collected some more data and it looks like the transition of accelerations might not be sharp – there might be some function in here. This calls for further exploration.

## Summary

Oh, you don’t like all the graphs and equation? You just want the scoop? Ok – here it is: it appears that when you tap the angry yellow bird, two things can happen. First, it increases its speed to 30 m/s (in the same direction that it was going). Second, if its velocity is greater than 20°ree; below the horizontal the vertical acceleration will be lower than 9.8 m/s2.

If there is a chance a post can become popular, I like to include preemptive comments. This way, I can respond to your concerns before you even ask them.

• WHAT’S UP PHYSICS GUY! I am having trouble with level 11-3. Can you give me some tips? Sure. Try again, but this time aim better.
• Don’t you think you should have collected more data before drawing your conclusions? Yes. More data is almost always better – but so is sleep.
• Hello. My physics teacher somehow found out about this Angry Birds thing. He assigned us homework to find out how big the sling shot in the game is. Can you tell me? Yes. The sling show is 1.21 Gigawatts tall.
• Don’t you get tired of writing about Angry Birds? Surprisingly, no. I thought I wouldn’t enjoy this analysis, but this might have been my favorite bird to analyze.
• Analyze this bird! No thanks. I am good.
• You are a nerd. You must have no life. Well, that is a good point. I guess it depends on what you consider “a life”.
• Will there be even MORE Angry Birds posts? Probably.