I’m not sure there is any way to figure this out, but assuming someone is a normally proportioned 6’ tall and 200 lb man, approximately how much energy would it take to levitate him and then fly him ay 50 miles an hour.
Depends on how you do it, of course. Gliders can move around and gain altitude without consuming any of our energy.
If you generally want to do it the way airplanes and jets do it (without worrying about how to convert from fossil fuel to electric), divide the power of an aircraft by its passenger load. I figure a few hundred kilowatts.
There are solar cell powered aircraft, aren’t there? But those probably just barely work - that is, they work under ideal conditions for demonstration purposes.
There are plenty of small plane designs that use something on the order of 40 horsepower. One horespower is about 750 watts. So about 30,000 watts, or 30 kilowatts will do it.
Now, an efficient glider can stay aloft using a fraction of that power. So, you could use a “glider” with a signifcantly smaller motor than 40 horsepower. The main problem would be your runway would have to be quite long and pretty smooth to allow you to get airborne.
A cyclist (depending on size and how aero their position is) requires 200-300 watts to maintain 25 mph. Quadruple for 50.
You can launch aircraft with special takeoff needs to get around the takeoff roll problem. Aircraft carriers do it but the technique started with the Wright Flier I which was launched into the wind from rails. Once airborne, the energy requirements to stay aloft aren’t very high under good conditions even if the goal is 50mph cruise.
The best place to look for the current state of the art semi-practical flight based on these requirements is to look at experimental ultralights. Ultralights in general can carry a 200lb person at 50mph with fairly small engines and fuel requirements but there are competitions to see how far the idea can be pushed based on current engineering. As of a few years ago, the most efficient ultralights could carry such a person in a reasonable configuration (similar to a very small plane) at least 30 miles on just one liter of fuel which is pretty impressive. You can do the energy conversion yourself. There are electric powered ultralights that have 30Kw motors but they don’t have to be used much of the time in flight because of the outstanding soaring capabilities of the planes that use them.
You can read more here.
Actually, we can’t, without also knowing the speed.
Well, as a lower bound, it took .3 HP to cross the English Channel at 17 km/hr.
If you don’t want wings and just mean “levitate as in jet pack”, it’s going to take a lot. The Mythbusters tried to build aducted fan jetpack that had a 60HP engine and failed to get off the ground.
And if you don’t want fans and just want to levitate in the Earth’s magnetic field, then it would take a ridiculous amount, if it’s even possible.
On the other hand, it wouldn’t take any energy at all to levitate via buoyancy, with a sufficiently large balloon.