I think it’s safe to talk about some Avengers physics now. I was inspired by an epic picture released by Marvel Studios, which you can see in the tweet below. (If Marvel puts it “out there,” I don’t personally consider it to be a spoiler.) The cool part is that you can see all these flying Avengers. There are a bunch of them.
Let me be clear: I’m a huge fan of super hero movies. The Marvel Cinematic Universe is great—it’s like the comic book world on the big screen. Also, I know this stuff is not real—trust me, I really know that. However, that doesn’t stop me from using physics to look at superheroes.
Now for the flying part. If you think of the Avengers, some of them run and some of them fly. The Hulk just jumps really far. Oh, Spider-Man swings and jumps, but he doesn’t fly. But for the other Avengers (I am just sticking with MCU Avengers—not ones from the comics), how do they fly? I am going break these into three categories. Really, there is just one category that has some fun physics.
Wing Flying
I can think of three wing-based flying Avengers: the Falcon, the Wasp, and Valkyrie. The Falcon is pretty straightforward: He has some wings and a jet pack on his back. He flies mostly by moving very fast so that the wings create lift. (Here is my video explaining the physics of airplanes.) But yeah, Falcon is basically just an airplane.
If you aren’t familiar with Valkyrie, she is an Asgardian warrior. (We first saw her in Thor: Ragnarok.) Technically she doesn’t fly. She rides on a pegasus—a horse with wings. If you like, you can say that the pegasus flies just like a bird. Of course something else must be happening here, since the wingspan wouldn’t be enough to generate a lifting force to carry both the horse and Valkyrie. But still—I am going to say she flies with wings (and maybe a little bit of magic).
The Wasp is really just using wings (and maybe some type of thrusters). Clearly she is wing-based.
Magic and Science Flying
This next group has the following heroes: Vision, Scarlet Witch, Thor, Dr. Strange, Captain Marvel. Yes, these are all very different in their flying—but they are also the same in some way. They are the same in that we don’t really have a physics-based explanation for how it works. It just works.
OK, maybe you could say Thor flies by throwing his hammer and holding on. However, that wouldn’t let him change direction midflight. Also, I imagine Vision can get off the ground by changing his density to some crazy low value—so low that he floats. Honestly, I don’t really know.
For the others, they can fly however they like, since there is no clear flying mechanism. I am totally fine with that.
Thrust Flying
Now for the last group. These are the Iron Man-like fliers. They fly with some type of rocket thrust out of their feet, hands, or both. This includes War Machine, Pepper Potts (SPOILER ALERT), and Star-Lord. Although I’m not sure exactly how these thrusters work, I’m going to assume that they produce a force by shooting some type of mass out of an engine. This is how normal rocket engines work—and how a jet engine works too.
But let’s just assume that these thrusters do indeed produce a force; now we can talk about flying. Let’s assume that you want to fly at a constant velocity, for now. Constant velocity flying means the acceleration would be zero and zero acceleration means a zero net force. Yes, flying at constant velocity is the same as standing on the ground—from a physics point of view. In two dimensions, we can use the following equations for net force.
Rhett Allain
Let’s consider a flying Star-Lord and how it would work with the net force. Here is a diagram showing him flying at a constant velocity along with the forces acting on him.
Rhett Allain
There are two significant forces on Star-Lord. There is the downward gravitational force and then the thrust force. The thrust is pushing in the direction of the rockets—I guess that should be obvious. Since we are just looking at forces (for now), I have put both of these forces as though they were acting at the center of mass (that red dot in the diagram).
But perhaps you can see the problem here. How can you make these two vector forces add up to zero in both the vertical AND horizontal direction? Oh sure, the net vertical force can be zero since there is an upward component of the thrust force to cancel the downward gravitational force. This is not true in the horizontal direction. There is only the forward-pushing thrust force component with nothing to balance it. If this is indeed the correct force diagram, Star-Lord would accelerate forward and not fly at a constant velocity.
Yes, the way Star-Lord flies is wrong (with respect to physics) but he still looks cool. Really, the problem is that there is a confusion about the nature of force and motion. Most people hold the idea that you need a constant forward-pushing force to move at a constant speed. It all makes sense in real life. If you want to drive a car at a constant speed, you need to keep your foot on the gas pedal. If you push a sofa across the floor, you need to keep pushing. We see it all the time—when you stop pushing things, they stop. This was the way Aristotle thought about forces, but he was wrong.
The problem is that we almost always have this other force on an object. That force is the frictional force. It’s a backward-pushing force that is an interaction between two surfaces rubbing together. If you remove the forward-pushing force, you still have friction and that causes the object to slow down and stop. Oh, if you are in the air there is the air resistance force—it also pushes in the opposite direction as the motion. So it just seems to make sense that if you don’t have a forward-pushing force, the object stops.
OK, so maybe Star-Lord has a significant air resistance force pushing on him. Let me jump to the answer here: No. That won’t work. In order for the air resistance to be a major factor, he would have to be flying at jet-like speeds, which would also produce a lift force. At slow speeds, the only way for this to work is to have a super low density. Here is a calculation of the density of a flying R2-D2, who suffers from the same flying flaw.
If you think it’s all about forces, you are mistaken. There is something else that we need to consider for a thruster-based Avenger flying at a constant velocity. In order to be in equilibrium, the superhero needs a net zero force AND net zero torque. What the heck is torque? At the simplest level, torque is like a rotational force. It depends on not just the force, but WHERE that force is applied. Here is a simple expression for torque.
Rhett Allain
In this expression, τ (that’s the Greek letter “tau”) is the torque. The distance from the force (F) to the rotation point is r and the angle between the force and the distance is θ.
So, how do you get a total torque of zero for an object (or a superhero) to be in rotational equilibrium? How about this—let’s try it with a pencil. Take a pencil and hold it at an angle. Now push up on one end with one finger. Notice that you need another finger somewhere else to keep it from falling over? Here’s what that might look like.
Rhett Allain
If you use the eraser end (the left end) as the point where you calculate torques, then there are two nonzero torques. There is the clockwise torque from the left finger pushing up and the counterclockwise torque from the gravitational force pulling down at the center of mass. You need a combination of at least two torques in different rotational directions to get a total torque of zero.
Now let’s go back to Star-Lord. Note: I am using Star-Lord since he only has thrusters on his feet. Don’t worry, I will get to the others soon enough. Here is an updated force diagram while he is moving with a constant velocity.
Rhett Allain
The only change was to move the thrust forces from the center back to his feet. But this creates a torque problem. If we pick the feet as the point of rotation (you can pick any point), then the thrusters produce zero torque since the distance to the rotation point is zero. That just leaves the torque from the gravitational force in the clockwise direction. With no counterclockwise torque, there is no way for Star-Lord to stay in that position and look cool.
Actually, there are two ways to use physics to make this work. The first method is to add air resistance. If he was flying fast enough, the air resistance could produce a large enough force (pushing to the left in the diagram above). This force would result in a counterclockwise torque that could keep Star-Lord in that cool position.
The second way to make this work is with acceleration. Yes, if we let Star-Lord accelerate everything will work with only two forces (the thrust and the gravitational force). The best way to explain this is with fake forces. Normally, forces are an interaction between two objects and the net force makes things accelerate. However, this only works in a reference frame that itself is not accelerating.
If you want to use an accelerating reference frame (like the reference frame that moves along with Star-Lord), you need to add a fake force. It’s fake because it’s only there to make the net force again be related to the acceleration and it’s not actually an interaction between two objects. The magnitude of this fake force is equal to the mass of the object multiplied by the acceleration of the frame, and the direction is in the opposite direction of the acceleration of the frame.
Honestly, you already know everything about fake forces since you use them all the time. Remember when you were in your car that one time? You hit the gas and the car started accelerating? What did you feel? Yes, you felt a force pushing you back into the seat. But that’s not a real force, that’s a fake force. Your mind put it there so that it could make sense of what was happening in the reference frame of the car. It’s still fake.
Now for an updated force diagram for the accelerating Star-Lord.
Rhett Allain
With this fake force, everything works. In the reference frame of Star-Lord there is now a backward-pushing force to balance the horizontal component of the thrust. Also, the fake force creates a counterclockwise torque to make a net torque of zero. Everything works.
But wait! How about I show a real version of this fake force? I can place a tilted ruler on an accelerating cart. In the reference frame of this cart, the ruler won’t “tip over.” OK, let me give a few details here. If you want to get this to work, you need a force to accelerate the cart but not the ruler. You can’t just let the cart roll down an incline—that won’t work. In this case, there is a large mass hanging down from a pulley. The string from this mass attaches to the horizontal cart to make it accelerate. (This is called a half-Atwood machine.) Based on the cart acceleration and the fake force on the ruler, you can calculate (for homework) the appropriate lean angle so the ruler won’t tip over. Hint: The acceleration of the cart was 5 m/s2.
Now for the experiment. There is a small piece of white paper on the cart. That doesn’t hold up the ruler (it’s way too flimsy), it was just an angle measurement so I could hold the ruler at the correct angle. Also, this is in slow motion.
Rhett Allain
Did I write this whole post just to show that experiment? Maybe. Did the cart go zooming off the end of the track? Absolutely—but don’t worry, I had someone there to catch it.
And what about the other superheroes? Iron Man and War Machine and Pepper use their hands for thrust too. They still have the acceleration problem such that they would need a significant air resistance force to make them move at a constant velocity. But maybe their hand thrust would fix the rotational equilibrium problem.
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