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Sunday, June 16, 2024

Could Namor’s Ankle Wings From 'Black Panther 2' Really Work?

In the trailer for the upcoming Marvel movie Black Panther 2: Wakanda Forever, you can spot something cool: A character who flies using little pairs of wings on his ankles. In the shot, he’s seen descending slowly at an angle as the wings flutter to keep him from falling.

Right off the bat, it seems like this would be a clear violation of the laws of physics. After all, the character, Namor, is human-sized and shouldn’t be able to fly upright with such a tiny flying apparatus. (Technically, he’s not a human. Also known as the Sub-Mariner, he's a captain in the kingdom of Atlantis.) This is literally a problem waiting for an analysis.

But before we dig into the physics of whether or not these ankle-wings would really work, I think it's a good idea to give a quick review of the different ways heroes fly in the Marvel Cinematic Universe. (Yes, I am limiting this discussion to just the MCU—if we included all flying superheroes, there are just too many options.)

Flying Like an Airplane

A wing is basically a large flat surface that moves through the air at a slight tilt. When you stick your hand out of the window of a moving car and let the air push it up and down, that's the same thing that happens with an airplane’s wing. The air molecules deflect off the angled surface and get pushed down. But since forces are always an interaction between two objects, the wing pushing down on the air means that the air pushes up on the wing. We call this upward-pushing force the lift. The value of this force depends on the amount of wing tilt, the size of the wing, and the speed of the aircraft.

Since this wing is tilted up somewhat, there is also a backwards-pushing force from the air. This effect is called drag. With this drag force, an aircraft can't fly in still air for long without something pushing it forward—this is why it needs jet engines.

That's the physics of airplane flight in just a few sentences. If you want more details, here's an example of flying physics that explains why airliners can't take off in extremely hot weather.

Birds, of course, do all of this without engines. They use their wings to produce lift (and create drag)—but they flap their wings to counteract the drag force. (OK, it's a bit more complicated than that. The aerodynamics of bird wings isn't quite the same as that of an airplane wing because of the turbulent vortexes those wings create. This is especially true for birds that can hover in place, like a hummingbird.)

Who uses a wing method to fly in the MCU? Two examples come to mind: Falcon (from Captain America: The Winter Soldier) and the Vulture (from Spider-Man: Homecoming). Both of these characters wear artificial wings on their backs, along with some type of engine to provide thrust.

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But you don't have to be a superhero to experience this kind of flight. If you have a set of carbon-fiber wings and four engines, you can fly like Yves Rossy, also known as “Jetman.”

Flying Like a Rocket

Iron Man doesn’t have wings. He doesn’t need them. Instead, his armored suit (which is most likely not made of iron) gives him augmented strength, some type of blaster fire from his hands, and most importantly—flight. Iron Man appears to fly using something like rockets located on his feet and hands.

I'm not exactly sure how his suit produces thrust, but it seems to work like most rockets do, in that mass—the exhaust—shoots out of the thrusters. Since this expelled exhaust has mass and velocity, it also has momentum. But to change the momentum of an object (like the ejected exhaust mass), you need to apply a force. If the suit pushes on the ejected mass, then the mass pushes back on the suit, creating a basic thrust force. This is the same way a rocket flies through Earth’s atmosphere on its way to space. (Here's way more detail about the "rocket equation" than you probably ever wanted.)

But there's an important difference between a rocket and a jet engine. Both of these push mass out the back to produce thrust. An airplane’s jet engine scoops up air from outside the plane and uses fuel combined with the air as the ejected mass. However, a rocket engine only uses fuel. It doesn't need air. That’s why rockets work in outer space, but airplane engines don’t.

In my opinion, the Iron Man suit is more like a rocket than a jet engine—but I should point out that Gravity Industries made a flying suit that’s a lot like Iron Man’s but uses jet engines.

Floating

Vision, from Avengers: Age of Ultron, is a synthetic life-form. He has many of the classic superpowers (like strength, speed, durability), but he can also change his density. For that reason, when Vision flies, I assume it’s because he’s actually just floating in the air.

Is it physically possible to get a superhero to float? The answer is yes. Anything will float as long as it has a density equal to air, at about 1.2 kilograms per cubic meter. For example, if you need to build a floating metal sphere that can serve as your supervillain lair, you can—as long as it’s big enough that the density of the air inside is equal to the density of the air outside.

In the real world, this is the principle behind flying machines like blimps. Basically, air has mass. If you take a cube 1 meter on each side and fill it with air, that air will have a mass of 1.2 kilograms (2.6 pounds). Since air floats in air, that 1 cubic meter of space must have an upward-pushing force equal to the weight of that air. If you replace the cube of air with anything else, the outside air still pushes up on it with a force equal to the weight of the displaced air. And if you replace it with something lighter than air, like helium, the air pushes the cube upwards and it floats—just like a blimp.

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Most human-sized beings couldn’t float without a blimp, of course. Humans have a density very close to 1,000 kg/m3. In order to float, you would need to have a mass of just 75 grams, or 0.17 pounds. You see the problem. But for Vision, it’s no problem at all.

Other Methods

Some MCU characters don’t technically fly, but they do something like it. Let’s take the Incredible Hulk. He really only has three superpowers: He’s mostly indestructible, he’s extremely strong—and he can jump really far. When the Hulk uses his super strength to jump as high as a building, it’s not flying because there is no force keeping him in the air. He just starts with such a large upward velocity that it takes some time for the downward-pulling gravitational force to slow him down and bring him back to the ground.

Then there’s Thor, the Norse god of thunder and the hero of his eponymous movie franchise. Of course, he’s super strong, but he also wields a magic hammer called Mjölnir. Thor can sort of fly by spinning the hammer around in a circle really fast and then throwing it while holding on. The hammer pulls him off the ground in such a way that it looks like he’s flying.

If you want to say that he flies because of the magic powers of Mjölnir, that's cool and I totally accept that theory. But I think what he’s doing is pretty similar to the Hulk’s jump. In both cases, the hero uses their muscles to increase the speed of some massive object to get them off the ground. In Thor’s case, the object is the hammer. In the Hulk’s case, it’s his own mass that gets accelerated for the jump.

How Does Namor Fly?

Now let's get back to Namor and his tiny ankle wings—two per ankle. While they look like bird wings, his flight is actually similar to that of a helicopter. At a very simple level, a helicopter flies using a similar method to a rocket—they both push stuff down to produce an upward-pushing force. But instead of expelling exhaust fuel like the rocket, the helicopter takes air from above the rotors and pushes it down to create lift.

But Namor’s got two problems with his wings. First, they are much too small for his human-sized mass. To get a human off the ground requires giant wings, something more like a wingspan of 7 meters.

It also requires a colossal amount of energy. My new favorite unit of energy for superheroes is measuring how much food—specifically peanut butter and jelly sandwiches—they’d have to eat to perform their feats of strength. (Here are estimates I previously made for the Hulk and She-Hulk.) For Namor, I'm going to estimate how long he can fly using the energy from eating one PBJ.

How do you estimate the energy needed to hover? Fortunately, I already did similar calculations for a human-powered helicopter, and I can use the same basic idea here. Namor’s tiny wings need to push air down in order to create an upward lift force from the flapping. The speed of this downward thrust depends on Namor’s mass and the approximate surface area of the wings.

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First, here's how you would calculate that air speed (which I’ll use later to get the energy needed to hover):

In this expression, m is the mass of Namor. We also have the total area of the wings (A), the density of air (ρ), and the gravitational field (g). For the mass, Namor appears to be a normal-sized human with a normal mass.

That means I just need to estimate the size of the wings. I'm going to say each of the four wings has a length of 10 centimeters and a width of 5 centimeters. That means the total area will be four times the length multiplied by the width. With this, I get a downward air speed from the wings at a value of 247 meters per second, or 552 miles per hour. That's very fast.

Next, I can calculate the power required to hover. We define power (P) as the energy per time. Why does hovering require energy at all? When the wings flap, they push the air down. This makes the air go from a speed of zero to 247 m/s. But since the air is changing speed, there is a change in kinetic energy (1/2mv2), so that requires energy. It's actually easier to deal with this in terms of power, which gives the following expression:

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Putting in all my values, it would take 91,000 watts. Just to give you some perspective, an overhead LED light bulb uses around 10 to 20 watts. A typical car has a power output of 150 horsepower, or 112,000 watts. So Namor is more like a car than a light bulb.

But what about the sandwiches? If he eats just one sandwich, then he would get about 380 food calories, which is 1.59 million joules. (Both joules and calories are units of energy.) So I have the power and I have the energy (ΔE). I just need to solve for the time interval (Δt) using the definition of power:

This means that the energy from one PBJ sandwich would give a flying time—in hovering mode—of 17.48 seconds.

Let's say that Namor wants to hover for five minutes while he makes some epic speech. How many sandwiches would he need to eat? Plugging that into my equation, we get 17 whole sandwiches. And if he wanted to fly indefinitely, he would need to eat three and a half sandwiches every minute. Good luck with that.

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