…well, but what's the drag coefficient of Flappy Bird? What's the glide ratio of Flappy Bird?

This is one of the things that bugs me about armchair physicists - they forget that the real world is actually armchair engineering. If we do a Free Body Diagram for our bird, we have two vectors - force of gravity pulling down and force of air resistance pushing up (the lateral direction doesn't matter in this case as it's perpendicular, but we could deal with it using another FBD if we had to).

The analysis linked supposes an FBD with one arrow - force of gravity pulling down. This works if we're on the moon - like the famous Apollo footage:

Down here on the world, though, air resistance matters. I won't get into it too much because Hubski markup renders equations like shit, but basically, your 1/2mV^2 becomes

1/2 (mass density of fluid being traveled through) x (Velocity of fluid being traveled through)^2 x (Coefficient of drag) x (Area you're pushing through the fluid)

http://en.wikipedia.org/wiki/Drag_equation

So that's if Flappy Bird just tucks his wings in and falls - abnormal behavior for a bird attempting to fly. Even if we presume the drag coefficient of Flappy Bird is that of a badminton shuttlecock, we're still looking at a drag coefficient of 0.5-0.6. In other words, even if Flappy Bird has the aerodynamics of a feathered thing designed to fall, he's falling too fast.

But even that goes out the window if we consider Flappy Bird's glide ratio. Glide ratio is kinda complicated - for one thing, it's a ratio of two numbers that are quadratically linked (if I recall correctly - aero/astro weren't my thing). What you need to know, though, is that an aerodynamic body that, well, flies generates lift and suffers drag as a consequence. "Drag" is what we just talked about. "Lift" is something that bowling balls don't have.

If you drop a bowling ball, it will fall straight down. If you drop a paper airplane above its stall speed, it will glide. The amount it glides depends on a lot of things, but the big one is glide ratio. A bowling ball has a glide ratio of zero (zero on the top, that equation above on the bottom). It generates no lift for its drag. On the other hand, the glide ratio of a "house sparrow" is 4.

So if Flappy bird clamps his wings to his sides and plummets when you aren't making him fly, he should be dropping slower than a bowling ball because of the coefficient of drag. On the other hand, if Flappy Bird sticks his wings out and tries not to crash when you aren't making him fly, he should be gliding downward at approximately the same rate as, well, a bird. From the game, it appears he does neither of these.

I like that they went to the trouble of attempting to model exactly what force of gravity Flappy Bird is experiencing, but they should have gone all the way to model all the other forces. It's a side-scroller; there aren't that many.

It should be pointed out that not only have I never played Flappy Bird, I'd never heard of it before this post.