Sabtu, 08 Oktober 2011

How tall is an Angry Bird?

Screenshot from Angry Birds on Google Chrome
The question from yesterday's post was, how big is an Angry Bird, really?  Using the screen shot to the right, and assuming we're on earth (so that g = 10 N/kg), we can figure this out.

The screenshot showed an elapsed time of 4.2 s, as I measured with a stopwatch.  I count 98 dots from launch to the ground, for a dot rate of about 23.5 dots per second.  (Be careful:  I don't believe that dot rate to be a general truth of the Angry Birds game.  In other firings I measured different frame rates.  I suspect that the game is designed always to produce a similar *distance* between dots rather than a steady dot rate.  But I digress.)

The bird hits its highest point at about the 47th dot.  At 23.5 dots per second, that's 2.0 s from launch to the peak height.  So, we can do vertical kinematics with a final velocity of zero, acceleration -10 m/s2, and time  2.0 s.  This gives an initial vertical velocity of 20 m/s, and a vertical displacement of 20 m.

The maximum vertical height of the bird's launch on the screenshot was 8.0 cm above the launch point, as measured with a ruler.  Now we know the scale of the picture:  8 cm to 20 m, or 1 cm to 2.5 m.  We're essentially done.

The piggy and the bird are both about half a centimeter high on the screenshot.  Knowing the scale, that gives a "real-life" height of 1.3 m, or about four feet.  The tower is 5 cm off the ground in the picture, or about 12.5 m.  

So, is the video reasonable?  NO!  The bird in the video hit the car window.  Car windows aren't anywhere near four feet tall top to bottom.  And, a man had to stoop in order to cower under the bottom floor of the tower next to a piggy.  In the screenshot, the bottom floor of the tower measures 2 cm, corresponding to 5 m.    Not even Kareem Abdul-Jabbar would have to bend his knees to duck under a 15-foot ceiling.

I was considering buying Burrito Girl, my wife and sidekick, some of the plush Angry Birds toys for Columbus Day.  But I don't think I have room in the house for a stuffed toy that's taller than my Siberian Husky.

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