I haven’t seen The Defenders yet, but it’s high on my list of things to watch. I am super excited about it, and why not? It brings Luke Cage, Iron Fist, Daredevil, and Jessica Jones together to save … oh, never mind. No spoilers!
That said, I consider trailers fair game, and this one from Netflix features an amazing scene in which the four Defenders fight a horde of bad guys in a hallway.
Of these four superheroes, all but Daredevil can throw a superhuman punch. I considered analyzing this scene to determine who hits the hardest, but I’m not going to do that. Not yet, anyway. Instead, I thought of another question: What is the best way to punch someone if you possess superhuman strength?
I hear you saying, “I am a superhero! I will punch villains in whatever way looks coolest.” You might have a small problem with that. I like to call it “physics, and the nature of forces.” Suppose that I, a mere mortal, punch my brother on the arm. Sure, I might exert a force of 100 newtons or so, but that same force also is exerted on me. The one thing you ought to know about forces: They are an interaction between two objects. If object A (my fist) pushes on object B (my brother’s arm), object B pushes back on A with an equal and opposite force. This explains why Thor punching the Hulk in mid-air might not turn out the way he likes.
Pause. Yes, I just pressed the blog pause button. Now is the appropriate time to say I don’t hate superhero movies. In fact, I love them. I think they are awesome. And it doesn’t bother me in the slightest that they sometimes get the physics wrong. The No. 1 goal of any movie is to tell a story. If that means the science is squishy, so be it. If Hollywood made completely realistic superhero movies, they’d all be about first grade teachers and sanitation workers (because both groups put up with serious stuff for lousy pay.)
OK. Back to the physics.
Let’s see what happens with a superhero punch. This was easier in my analysis of Thor and The Hulk because they threw their punches while leaping toward each other. The only forces acting on them were the punch force and the downward gravitational force. But what happens if a superhero is standing on the ground? Two more forces act on him or her: The force of the ground pushing up (we call this the normal force), and a frictional force. This means four forces (or more, if you count both feet) act on our hero. The sum of these forces changes the hero’s momentum, with momentum being the product of her mass and velocity.
Finding the change in momentum isn’t too terribly difficult. However, you also must deal with rotational motion. Each force that acts on the superhero also exerts a torque. In essence, torque is like the “rotational force” in that it changes how an object rotates. The torque that a force causes depends upon its magnitude, direction, and location. A quick example: Open a door by pushing on the handle. Now try pushing near the hinge. Much harder, right? Pushing near the hinge requires a much larger force to get the same torque as pushing on the handle.
I bet you never realized so many forces act on a superhero throwing a punch. Now let’s take a look at two different kinds of punches.
First, we’ll look at what I call a straight punch. It’s like a jab, but with much greater force than a normal human. We can assume the guy on the receiving end will go flying into a wall or something, so we’ll focus on the motion of the hero. This diagram shows all the forces:
With so much going on here, I identified the forces by color. Gravitational force pulls down (the red arrow). That seems fairly straightforward. You also have the force of the punch (green arrow), which exerts a force on the bad guy and on the hero. And don’t forget the force of the ground on the hero. There’s actually two parts to that. First, a force perpendicular to the ground pushes up against the superhero. We call this the normal force, and it is whatever force might be necessary to keep the hero from moving through the ground. Without it, he’d sink. And then there’s the frictional force parallel to the surface. It is proportional to the normal force such that it increases as the hero is pushed into the ground.
To examine the motion of the superhero during this punch, I must look at the total forces and the total torque. Now, it should be clear that the vertical forces are boring. If the superhero punches horizontally, you won’t see any significant vertical motion. Ah, but you could see a problem in the horizontal direction: If the punch force exceeds the frictional force, the hero will increase in velocity to the right. In other words, the hero will be pushed backward by hitting someone (or something) too hard.
Torque presents a bigger problem. Using the example I diagrammed above, a large punching force by itself would cause the hero to increase in rotational velocity in a clockwise direction. The frictional forces also would cause a clockwise rotation. Even if the normal forces have a counterclockwise effect, the total will clearly be a clockwise rotation. So, a significant super-powered punch would make the hero slide back and tip over. It’s hard to look cool when you are falling over.
Now consider a case in which the hero swings a fist with a force that pushes up (and to the side). This punch throws the villain back and up, as you might expect. Meanwhile, the hero moves down and to the right. Here is a diagram:
The upward punch exerts downward (and still somewhat horizontal) force on the hero. Two things keep the superhero from sliding backward. First, a small horizontal component to this punching force means you don’t need much friction to stop a slide. Second, the increased normal force leads to greater frictional force.
But what about the rotational motion of the superhero? Again, it won’t be as severe as what you see with a horizontal punch. Since the punch force is downward and aiming toward the center of mass,…