In this clip from Ant-Man, we get to see Ant-Man in action. But do tiny humans run the same as normal humans? Not really. Why? In short, the problem is that big things aren't the same as small things. Oh, sure everyone knows that a big hamburger is different than a small hamburger, right? Yes, but it's worse than that. If you shrink down a human to a tiny size, running doesn't look like a full size human. Let's see why.

Falling Ball Example

Let's take a ball that is dropped from a 1 meter tall stick. I know that sounds like it has nothing to do with running, but just hang on. Here is a picture.

After the ball is dropped, there is only the gravitational force on the ball and it will have a vertical acceleration of -g (where g = 9.8 m/s2). Since it has a constant acceleration, I can write the following kinematic equation and solve for the time it takes to hit the ground (the initial velocity is zero).

With a height of 1 meter, it would take the ball 0.45 seconds to fall and hit the ground. Ok, now let's make a small version of this ball and stick. Let's make everything half the size.

Dropping from just 0.5 meters, the ball would only take 0.32 seconds to hit the ground — which is NOT the same as 0.45 seconds. What does this have to do with running? Just wait. Let's look at a slightly different example — a bouncing ball. Instead of an actual running person, let's consider a ball that is both bouncing and moving horizontally. I can model this without too much difficulty by using basic ideas of projectile motion and just reverse the vertical velocity of the ball when it "hits" the ground. Here's what that looks like for a ball with a 0.5 meter radius (assume a spherical human) and a horizontal velocity of 2 m/s (4.5 mph).

If you want to play with the code, go for it. You can change the above code and rerun it.

Ok, now let's do the same thing for a small Ant-Man. Of course, he is going to be smaller in his small form. This also means that each step will cover less distance. Suppose I shrink him by a scale factor of a. In order to make his run look like normal sized human, I would also have to decrease his velocity by the same factor a. So, for a Ant-Man a tenth the size, a = 0.1 and his horizontal velocity would be 0.2 m/s. Oh, I would also make the spherical human smaller and the surface he is running on smaller by the same factor. Here is what that looks like.

If everything is smaller, shouldn't it look the same? No. There is one thing that isn't smaller — the gravitational field. This means that if tiny Ant-Man jumps with a lower speed, he won't go as high and he won't be off the ground for as long of a time. He is still taking hops, but the hops are super tiny — and yes, this is a tiny man on a tiny surface. Everything is scaled down.

So, a tiny Ant-Man wouldn't run like a full sized human. It would look really weird. Maybe this is why humans and big animals (like horses) run and leave the ground when they move fast. Insects just use multiple legs to move fast but don't get off the ground. That's just a guess.

Oh, there is one way to make Ant-Man run in a normal looking fashion — decrease the gravitational field (g) by the same scale factor. Try changing the code above to see if you can make it look better.

Video Analysis of Ant-Man

Now let's look at a clip from the Ant-Man movie. What kind of vertical acceleration does tiny Ant-Man have in these moves? The first step is to determine the actual size of the tiny Ant-Man. Fortunately, he appears next to an object of known size — the hand gun held by the security guard. Using my lack of handgun knowledge (really, I know nothing) and my excellent Google-fu (I am a black belt), I am fairly certain the weapon is a Glock 19. From that, I can get a size estimate for Ant-Man.

Assuming the full sized Ant-Man is 1.8 meters tall, this would make the tiny Ant-Man smaller by a scale of 0.0066 (151 times smaller). Now let's look at a plot of his position vs. time while jumping on the pistol.

The last two data points are a little messed up since the camera angle changes a lot. However, for the first few I should be able to use a quadratic fit to get his vertical acceleration. After Ant-Man "jumps" from the barrel of the pistol, he has a vertical acceleration around 1.2 m/s2. Clearly that's not what it should be — but also, it's not very good data. How about a plot of the Ant-Man as he jumps on the guy's shoulder and then punches him. Here is just his vertical position.

There's not much data, but during that first leap Ant-Man has a vertical acceleration of about -4.5 m/s2. That's not too bad — just about half of the normal vertical acceleration of -9.8 m/s2. But what about that jump punch? Check out Ant-Man's horizontal motion during this punch.

He goes from a horizontal speed of 0.19 m/s to 2.1 m/s. That's a crazy fast punch. It's a cool scene — but I just wish the camera showed a little bit more spit coming from the guard's mouth. I could have used that to get another estimate of the vertical acceleration.

Conclusion and Homework

The moral of this story is that small things are not the same as big things. Ant-Man would run weird, but the movie seems to show him running with a lower vertical acceleration to make it look more like a full sized human. Overall, I think the Ant-Man movie (at least in this clip) found a good balance between small and looking like a normal human (it's a tough thing to do).

Now for some homework questions. What? You thought this was just for fun and there would be no homework? Wrong. It's homework time.