There are quite a few characters who fly one way or another in the MCU, and Thor’s ability might just be one of the most plausible. We’ll get to him in a moment, but first let’s explore the others in descending order of how physically justifiable their abilities are.
There is very little about Vision that has any basis in reality at all. He’s an A.I. placed into a bio-mechanical constructed body and brought to life with the Mind Stone (The Infinity Stone that was in Loki’s Septer in The Avengers). His ability to fly, is just… well he… he just kind of… does? Also he shoots energy beams out of the Mind Stone which is embedded in his forehead, also just because.
6. Wanda Maximoff A.K.A Scarlet Witch
Wanda’s superpowers also come from the Mind Stone, except instead of it being part of her, it just imbued her with powers, again… somehow. In Wanda’s case, it gave her telepathic and telekinetic powers, which I suppose makes slight more sense than energy beams given that it’s the Mind Stone, not the Shoot-Lasers-Out-of-Your-Forehead Stone. If you accept that Wanda has Telekinetic Powers, then, I guess her ability to fly is explainable. Seeing as I have no real-world frame of reference for how telekinesis works, I can’t assess it’s use as a means of flight however.
5. Carol Danvers A.K.A Captain Marvel
Danvers got her superpowers by absorbing a huge energy discharge from an experimental energy/propulsion system powered by the Tesseract which is the Space Stone (those Infinity Stones are just constantly causing superheroes apparently). Absorbing energy discharges seems to be a very common method of gaining superpowers in comic books (see Hulk, Fantastic Four, Dare-Devil, Dr. Manhattan, etc.). As a result, Danvers has some sort of energy discharge type powers. She can sheath her whole body or parts of her body in some kind of of plasma, and shoot it out in beams, or just, sort of, explode, but without exploding? Plasma discharges are a pretty reasonable way to fly once you accept that she can generate plasma discharges.
4. Hope and Janet Van Dyne A.K.A The Wasp
Ok, we’re starting to transition from the more “Fantasy” side of superheroes to the “Sci-Fi” side. The primary superpower of The Wasp along with her partner Ant-Man (Janet Van Dyne and Hank Pym in the 60’s and Hope Van Dyne and Scott Lang in the 21st century) is their ability to shrink down to the size of insects (or smaller) using specially designed suites powered by Pym Particles (which are fictitious molecules that control matter). This aspect is pretty fantastical and there is no real explanation of how it’s supposed to work (especially the part about keeping their mass/momentum when they change sizes). However, once you accept that the Wasp can change size, her ability to fly is pretty sound scientifically. The Wasp’s super suit has a set of insect wings, but, and this is the part I really appreciate, she can’t fly when she is normal human size, she can only use them to fly when she is shrunk down to insect size. This is all about Reynolds numbers. Reynolds number is a quantity in fluid mechanics that describes the relationship between the size of an object, the speed it moves, and the viscosity of the fluid it’s moving through. It essentially explains why we can swim just by moving our arms around in water, but in air, we have to use some sort of propulsion system. the viscosity of the water is much greater than that of the air and so we can generate a lot more force by moving our arms through the water than the air. Insects are small enough that their Reynolds number in the air looks a lot more like our Reynolds number in the water. So they are effectively swimming through the air. This is why you might have heard people say (erroneously) that bumble bees shouldn’t be able to fly. What they really mean is that their wings aren’t big enough compared to their mass to generate enough lift to fly like a bird or an airplane, but it doesn’t need to fly like a bird, because it can swim like a squid, and so can The Wasp, when she is the size of an insect.
3. Tony Stark A.K.A. Iron Man (And James Rhodes A.K.A. War Machine)
This is a tough one for me, because I love Tony Stark. As an Engineer it’s so inspiring to see a superhero who basically built their own superpowers using their ingenuity. A lot of people compare Tony Stark to Bruce Wayne because they are both billionaires who own technology companies they inherited from their parents that they use to outfit themselves as superheroes. However, the difference is that whereas Bruce Wayne just has people who design his superhero tech for him (I know i’m being reductionist, he worked very hard on his fighting and detective skills), Tony really is an engineering genius who designs all of the technology not only for himself but for all of the Avengers. And it’s not just that he has an incredible lab with all of the state of the art equipment imaginable. He built the first Iron Man suit in a frickin’ cave out of spare missile parts and an improvised forge. His superpower is literally that he is a superhuman engineer. I love it. The Iron Man suit is an incredible piece of technology that mostly makes a lot of real world sense. You can totally fly using rocket engines strapped to your body like the Iron Man suit. But if you watch that video linked previously, those are some big honkin’ engines and there is a big obvious fuel tank, and he can mostly just hover and scoot around (maybe reaching 30-60 miles per hour) and only for about 4-5 minutes with the fuel he can carry with him. Therein lies the problem with iron man’s suit. Where is the fuel? I’ll concede that the arc reactor is a phenomenally advanced piece of technology that can meet the incredible power demands of the Iron Man suite, but you still need rocket fuel for the rockets. The Rocket Equation states that
ΔV = Isp*g0*ln(Mfull/Mempty)
where ΔV is the total change in velocity a rocket can make under ideal conditions, Isp is the specific impulse of the rocket fuel (essentially the efficiency), g0 is the Earth’s gravitational acceleration, and Mfull and Mempty are the full and empty mass of the rocket (which in this case is Tony and the suit). Now assuming that the suit is using a Liquid Hydrogen/Liquid Oxygen bipropellant (which his what the space shuttle used), and every crevice of the suit is housing fuel, he might just be able to get up to the speeds we see him achieve in the movies if there were no aerodynamic drag and he was flying in a straight line before he runs out of fuel. Even with Hydrazine (a much more energy dense fuel, though not as efficient), he would get at best one good turn at supersonic speeds, but you would absolutely never want to get into a fire fight wearing a tank full of Hydrazine because if your exposed to direct contact with it, it LITERALLY MELTS YOUR DNA! For Iron Man to fly at supersonic speeds for hours at a time maneuvering and fighting drag and gravity? Not possible. Alas.
2. Sam Wilson A.K.A Falcon
The Falcon suit design actually makes a lot more sense than the Iron Man suit design from a practicality stand point. The Falcon suit has a wingspan of about 5 meters (~15 ft), even making a conservative assumption of a fairly modest lift coefficient of around 1, and assuming Sam weighs around 400 lb with the suit on, he only needs to be traveling around 30 m/s (65 mph) to stay aloft. Totally acheivable even with no power at all just by pulling out of a dive into a glide. Add in a small propulsion system and he could easily take off from the ground. Speaking of propulsion systems, this is another win in Falcon’s column over Iron Man. Falcon uses an air breathing jet engine (like most commercial and military airplanes use) which makes a lot more sense than rockets if you’re spending your time flying in the atmosphere. Rockets use a combination of fuel and oxidizer from tanks that mix together, combust and exhaust out a nozzle. They can generate a LOT of thrust, and they work in a vacuum, which is why you mostly see them in space crafts. Jets on the other hand, only carry the fuel, and they use the air flowing through the engine as the oxidizer. Because you don’t have to carry your oxidizer with you, and rocket propellant typically has a 4-to-1 oxidizer to fuel ratio, you can get a lot more burn time out of the same volume of fuel in a jet than a rocket. Additionally, since he only needs to occasionally use the jet engine for a boost or a maneuver, gliding with his wings the rest of the time, Falcon’s flight suit is pretty plausible.
Thor’s method of flying may seem crazy, but spinning a heavy object up to high speeds and then using it’s angular momentum to do work is actually a tried and true, time tested method of energy transfer. it’s called a flywheel, and the concept has been around and in use for almost 1000 years. The basic concept is that you can build up more and more energy into the flywheel over time by simply spinning it faster and faster. Then you can bleed energy off as needed to do useful work… or, if the thing catastrophically fails, bits of it go flying off at ridiculous speeds as the huge amount of angular momentum stored in the flywheel is suddenly converted to linear momentum. Thor takes advantage of this particularity of flywheels. he spins up the hammer as fast as he needs to, then let’s it go, but the strap catches on his wrist after the momentum has been converted from angular to linear. Now, the physics is sound, but to work out the particulars, we’re wading into murky waters because we’re dealing with, as Arthur C. Clark would say, science that is sufficiently advanced as to be indistinguishable from magic. We’ll do our best though. Thor is a big dude, like Defensive Linemen big, let’s call him 250 lb conservatively. Mjolnir (that’s the hammer) is a little bit harder nut to crack, it’s made out of a mystical cosmic metal called Uru and forged by the Dwarf Eitri (Peter Dinklage in Avengers: Infinity War) which is what imbues it with its magical properties (you know, the whole “worthy” thing). but for the purposes of this physics thought experiment, let’s say it’s made out of meteoric iron, that is, iron refined from meteorites. Typically, meteoric iron has a density of around 8000 kg/m3 so the head of the hammer probably has a mass of about 45 kg (100 lb). When Thor is spinning it by its leather strap, the head of the hammer is about 0.5 meter (20 in) away from the center of rotation. in order to pull Thor along at, let’ say 100 mph, the Hammer needs to fly off initially at about 450 mph before the strap catches his wrist and pulls him after it based on conservation of momentum. to get Mjolnir to achieve it’s initial launch velocity of 450 mph, Thor needs to spin it up only to about 4000 RPM which is basically what a typical car engine runs at under normal conditions. That seems reasonable for someone with literal Godly power (why not?). the hardest part would be not dislocating your wrist/elbow/shoulder when the hammer pulls you off the ground. Most importantly, though, the physics here is totally sound.