What would I do without internet videos? It’s not just viral cat memes but also amazing humans like this guy, Xiao Qiang. In this short clip, the kung fu fighter appears to leap onto a bucket of water several feet off the ground—then bounce off the surface of the water like a trampoline. Whaaaat?
It’s an illusion, of course, but one that is made possible only by awesome strength and athleticism. Even when you know how it’s done, it still looks cool. So I’ll give you a clue right up front: As he flies through the air, watch a spot around the middle of his body.
Yep, once he pushes off the ground, his center of mass actually follows a normal parabolic trajectory. Just like when you toss a ball into the air, the only force acting on him at that point is the gravitational interaction with Earth. That means he has a constant downward acceleration, producing that familiar path. At this level, it’s normal projectile motion.
But he’s not just a rigid ball; his body is still working as he moves through the air, and that’s where the magic happens. To sort it all out, I ran this clip through my Tracker video-analysis app.
Plotting the Motion
Usually when I do video analysis to track the motion of something through space, I graph vertical position in each frame as a function of time. But there’s a problem in this case. Someone clearly messed with the frame rate in this clip to highlight the “water jump” portion. That means we can’t get a stable time scale.
Instead, how about we plot vertical position against horizontal position in each frame? If an object is moving through the air with only gravity acting on it, the horizontal velocity will be constant. This means we’ll still get a parabolic graph—it’s just a little harder to analyze.
What I’ve done here is trace the movement of three different parts of his body: his head, his feet, and his center of mass. Normally the center of mass would be around a person’s belly, but it changes as you move your arms and legs up or down, so this is a rough estimate.
So check it out: The center of mass (COM) follows the parabolic path we expect. But look at his feet. They reach the top and start moving down—then they bounce back up again, as if he really is jumping off the water. What’s really happening, as this graph shows, is that he’s pushing his feet hard away from his body near the top, then pulling them back up.
Remember the “invisible box challenge” from a couple of years ago? This is basically the water version of that trick.
But wait—can we model a crazy jump like this? Yes we can, because you don’t really understand something till you can model it. Now, modeling a whole human body in motion is crazy complicated, so we’ll go real basic: just two moving parts—a head and some feet. I can represent these two parts as balls and then find the center of mass between them.
Here’s what a jump might look like with a rigid body. I know, it’s impossible to jump with a rigid body, but just go with me here. The yellow ball is the head, the red ball is the feet, and the white ball represents the center of mass. Notice that everything moves in a parabolic trajectory. (Here’s the code for this animation if you want to see how it’s done.)
Now, what if we want to move the feet down and up to make that crazy water-jump move? This is a little trickier. Remember, the only external force acting on the guy once he leaves the ground is gravity, so the center of mass of the head-feet system (also known as a person) has to follow a parabolic trajectory. What we need, then, is an internal force inside that system.
Let me explain by starting with the momentum principle. This says that the net force on a system is equal to the rate of change of momentum. Like this:
Now, if we look at the body parts within the system of the whole person, suppose there is a force that pulls the feet toward the head. It might look something like this.
Remember, forces always come in pairs. Every force is an interaction between two objects, so the force with which the head pulls on the feet (Fh–f) is equal to the force with which the feet pull on the head (Ff–h).
Since these two forces are equal in magnitude but opposite in direction, they won’t affect the motion of the center of mass for the whole system. But if the head is more massive than the feet, the head will move less. That’s just how forces work.
Completing the Illusion
Now let’s build this into the model. I can put any force I want into the model; the only constraint is that it has to pull equally on the head and the feet. Springs do that! So imagine there’s a spring connecting the head to the feet. If it starts off in a stretched state, it’ll pull the feet toward the head on the way up, just like on the jumping guy.
Then, near the top, I magically replace that spring with another one that pushes the feet and head apart to model the motion of the fake water jump. Finally, I replace that spring with one that pulls the feet and head back together to complete the illusion. (Oh, here’s the code. You can go in and play with different parameters to see how it changes things.)
Again, It doesn’t matter that this spring-swapping thing sounds crazy—all that matters is that the forces on the head and feet are equal. That will keep the center of mass for the head-feet system in a parabolic trajectory. Setting my model in motion, here’s what I get:
Boom. It’s not perfect, but if you focus on the feet—which I think is what our eye tends to do as we watch the video—it looks like there are two jumps.
I also pulled out the location data and plotted the trajectory of the head, feet, and center of mass in the model. This is the real center of mass, not just an estimate:
This isn’t an impossible jump after all—at least not for somebody like Xiao Qiang. For most of us, though, it might as well be.
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