I've written some other entries on how superheroes fly but I didn't get into assisted flight. This is usually done with rocket boots, jet packs, flying belts, or, occasionally, rings.
The Rocketeer is a great example of flying with a jetpack. As portrayed in the movie, there are serious issues with control. The Rocketeer solved some of these problems with a fin on his helmet. The movie also had a few other nods to physics. He only flew in short bursts reflecting the fact that a pack like that couldn't have more than a few minutes of fuel. Landing was difficult. Finally, the whole thing ran on highly alcohol and could burst into flames if there was a leak.
More common in comic books are rocket boots. These are usually as light as hiking boots but contain enough fuel for extended flight. They also allow the wearer to hover, fly like a missile, or land. Obviously several laws of physics are being violated here.
The movie version of Iron Man addressed several of these. Stark's first attempt at flight gets him airborne for a few seconds but doesn't allow for any sort of soft landing. It's more a ballistic trajectory. Later Stark adds thrusters to his gloves so that he can balance. He also has flaps that pop out of his suit to assist banks and other maneuvers. Even with all of this, he still has some problems. This is probably the most realistic example of powered personal flight.
There is one big question about Iron Man's flight - how do those thrusters work? The movie drops the term "repulsor" early on. These might work something like the repulsor rays in the comic version. These were always represented as being different than his boot jets but jets that are only an inch or two thick (and still leave room for retractable skates) are impossible. Presumably the repulsors are similar to ion drive except with much greater thrust. They are powered by Stark's chest piece which represents a miracle in electrical power production.
The Legion of Super-Heroes has gone through a few generations of powered flight. They started out with backpacks then moved to flying belts. Finally they developed flying rings. These use an anti-gravity metal. Will-power is also required.
Meanwhile, in the real world, someone demonstrated a jet-powered flying wing. This has several drawbacks. You have to be dropped from an airplane in be high enough, you only have around five minutes of fuel, and you use a parachute to land. Control is accomplished by the flier's body movements. Still, this is getting close to the Rocketeer.
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