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A meta-human, let's call him "Arnim", possesses the power of flight. In accordance with Einstein's law of conservation of energy, this superpower does not draw power from nothing or some nondescript alternate dimension. Rather, the way the ability works is by converting whatever energy is available in the user's direct vicinity directly into momentum. It's essentially the power to transmute energy but limited to serve only for locomotion.

Unlike Superman, this power cannot store energy for later use like some sort of battery. Instead it always uses whatever energy is immediately available to power its function. Think of it as a sort of 'funnel' that sucks whatever energy is around to propel the user.

His power sources would include Arnim's own metabolism a.k.a. the ATP breaking down in his cells at any given second, his body heat as well as the thermal energy in the air around him, the sunlight hitting his body as well as his surroundings and any ambient radiation. It goes without saying that drawing power from these sources will remove it from where it was taken: Arnim's cells will tire, his body cools down, the lights will dim and ambient radiation will be gone. There's some leeway with the exact range of absorption but that can be adjusted depending on the energy demands according to your answers. It should be noted that Arnim CAN carry around a battery to draw extra power from it... but I'd rather find out if he could fly unassisted before resorting to that very unsexy option.

Is there enough energy for Arnim to fly?

Arnim weighs a healthy average of 196.9 pounds or 89 kilos. He lives on the planet earth so 1g of gravity. The temperature is a warm 77 fahrenheit or 25°C. No clouds in the sky. No wind either.

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    $\begingroup$ This is going to require some handwaving; there's no direct conversion from energy (potential or otherwise) to momentum. Example: a bullet and bowling ball have similar energy, but the bowling ball has far higher momentum. $\endgroup$
    – Zeiss Ikon
    Feb 13 at 20:22
  • $\begingroup$ Momentum is momentum and energy is not momentum. You cannot convert energy, or anything else for that matter, into momentum. $\endgroup$
    – AlexP
    Feb 13 at 20:40
  • $\begingroup$ @AlexP thankfully, this is a superpower $\endgroup$
    – M S
    Feb 13 at 20:56
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    $\begingroup$ @MS: It may be a superpower, but it is an incalculable superpower. There is no relationship between momentum and energy, so that there is no way to say how many kilogram meters squared per second squared (= energy) are needed in order to get one kilogram meter per second (= momentum). Maybe the superpower is such that 1 microjoule of energy is enough for a million kilogram meters per second. Maybe the superpower is a cheap Chinese counterfeit and one would need one megajoule for a measly microgram micrometer per second. Incomputable. $\endgroup$
    – AlexP
    Feb 13 at 21:00
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    $\begingroup$ For a site based around encouraging creativity, you people really lack imagination. I'd spank you all but since joules apparently can't be converted to momentum my hand won't move. $\endgroup$ Feb 14 at 14:14

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I wouldn't recommend drawing the energy from internal sources, as cooling your core or stealing cellular energy will very quickly have negative consequences. Your body may be able to simply increase metabolic activity to counteract the drop in temperature or cellular energy, but I don't know enough about biology to make a definitive statement.

Instead, lets see whether or not your character could fly using the energy from the sun.

During the summer, the surface of Earth receives roughly 6 kW/m^2 of insolation. You say he can draw energy from things around him. I'll assume he can do so in a sphere around himself with a radius of 2 metres.

A sphere of that size has a surface area of about 50 m^2, but what we really want is the area of a circle with a radius of 2 metres, as all the absorbed light will be coming head on. That gives us a surface area of 12.5 m^2, which translates to 75 kW of available solar power.

Your 90kg character will need roughly 900 W of power to hover in the air, which gives us another 74.1 kW of power to use for directional flight. Using a kinetic energy calculator shows that 74.1 kJ of kinetic energy would have a 90 kg person moving at about 40 m/s (144 km/h), and since your character has 74.1 kJ of energy available to them every single second, they could achieve an acceleration of over 4 Gs, which means they could reach a speed of 144 km/h in a single second (ignoring air resistance).

That means your characters maximum flight speed will be limited not by the energy available to them, but by the ability of their skin to not tear at extreme airspeeds. I would expect your character to wear goggles while flying at an absolute minimum, and perhaps have a mask created that covers his face and head.

That is very impressive, but it's worth noting your character will be completely blind when he's at maximum acceleration, as all light within a bubble around him will be absorbed. That said, you can see inside perfectly fine with only a 10 watt LED, which means your character could ease up on the acceleration just slightly and still see just fine.

Another note is that your character will actually have more than 75 kW of solar power available to them, as light from the environment will reflect onto the sphere, but I'm not willing to calculate how much additional energy that would provide. At a guess I'd say something like 10%.

Another note is that this assumes clear skies. Overcast skies will significantly reduce your characters maximum acceleration, and at night they may have to carry around a bottle of gasoline to extract chemical potential energy from.

TL;DR:

Using just solar energy, your character could accelerate to over 100 km/h in a single second, and could fly around at blistering speeds.

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    $\begingroup$ You managed to put together an eloquent answer without getting hung up on nitpicking my wording and for that you have my most sincere respect. $\endgroup$ Feb 14 at 14:05
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    $\begingroup$ @LiveInAmbeR you're most welcome. Unfortunately I've come to learn that this stack is really not a great place to ask worldbuilding questions, people are much more focused on pedantry than they are on helping. $\endgroup$
    – M S
    Feb 14 at 17:00
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We know that normal human muscles can generate enough power for flight because human-powered flying machines exist. If your superpower was limited to only metabolic energy, it would function as a replacement to the aircraft. Since these aircraft reach 30 mph, if you assume your superpower is at least as efficient as the real-world aircraft, then your human can also fly at that speed on metabolic energy alone.

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  • $\begingroup$ The caveat there is that human-powered aircraft rely on aerodynamics for lift, which this character cannot do unless he wears a wingsuit. $\endgroup$
    – M S
    Feb 13 at 20:32
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    $\begingroup$ Based on the OP, I am pretty sure the character superpower is the ability to generate lift without relying on aerodynamics. $\endgroup$
    – E Tam
    Feb 14 at 3:42
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I suggest your metahuman be able to internally convert mass to energy, in particular minute amounts of the waste building that would otherwise be excreted. Poo-powered Superman for the win!

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I weigh 265#. I can also dead-lift 265#. If I strap my hands, I can hold the weight for about 30 seconds before muscles (arms, shoulders, legs...) start giving out. Let's use this as implicit proof that I could, being a meta, lift myself off the ground for about 30 seconds. Not move, just float there.

But let's be more robust. 9.8 joules are required to lift 1kg to a height of 1m.

$$E = Fd = (ma)d = mgd = (1 kg)(9.8m/s2)(1 m) = 9.8 kg m2/s2 = 9.8 joules$$

And that's 9.8 joules of energy just to hold that 1kg mass 1m off the ground against the pull of gravity. Ignoring the change in the force of gravity as you get further away fro the surface of the earth, it takes 9.8 joules for each meter we lift the mass, but only 9.8 joules to hold it at the final altitude.

But F=mA, so if we're moving laterally in the sky at 1m/s then it costs us 9.8 joules to move horizontally.

So, 89kg metahuman wants to fly 1km off the ground. 872,200 joules to get to altitude and 872 joules to move horizontally. We'll assume 872,200 joules to get back to the ground. Technically it can be done with 0 joules, other than the energy needed to scream during the descent. We're going to fly horizontally for 30 minutes or 1800 seconds so 872,200 + 1,569,600 + 872,200 = 3.3 megajoules.

Online estimates vary wildly as to the energy output of a human. It depends on a LOT of factors, some of which aren't controllable (like what kind of metabolism you're born with), while some are (how lean you are). But the average appears to be 30 megajoules in 24 hours or 625,000 joules for 30 minutes.

Answer: No, your metahuman can't fly on internal energy alone.

Although when you scale that down to my weight lifting experience, it suggests that your metahuman could leap over trees... but your metahuman would tire very quickly and be constantly eating high-energy foods.

Curiously, a day or two ago I left a comment for a question that was asking how a superpower could be justified scientifically that basically said that one of the reasons trying to base superpowers on science is painful is that the consequences must also be justified by science and can usually only be avoided with magic.

Like getting tired and having to constantly eat (and defecate...).

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  • $\begingroup$ "That's 9.8 joules of energy just to hold that 1kg mass 1m off the ground against the pull of gravity": That's absolutely not true. The amount of energy required just to hold 1 kg mass 1 meter or 10 meters or 100 meters or 1000 meters off the ground is zero. It is true that one must expend energy to lift the mass, but once lifted, with proper arrangements it can stay there indefinitely with no consumption of energy. For a practical example, consider a computer sitting on a table. The table does not consume energy to hold the computer 1 meter above the floor. (And sailplanes do fly.) $\endgroup$
    – AlexP
    Feb 13 at 20:53
  • $\begingroup$ @AlexP the power of flight is almost always portrayed as the flyers body experiencing a force in a given direction, in which case the flyer would need to create a force equal and opposite to the force of gravity, which would constantly consume energy. It is less like standing on a table and more like wearing a jetpack. $\endgroup$
    – M S
    Feb 13 at 21:00
  • $\begingroup$ @MS: Gliders, also called sailplaines, do exist, and they do fly. Without engines. The table in the example does indeed create a force equal and opposed to the force of gravity, without consuming energy; and so do the wings of the sailplane, except that the wings being of finite size there is a small consumption of energy which lost to drag. (The general rule is that work is equal to the displacement times the force in the direction of motion. A force perpendicular to the direction of motion does no work.) $\endgroup$
    – AlexP
    Feb 13 at 21:03
  • $\begingroup$ @AlexP In this case though, the power of flight requires force parallel to the direction of motion, not perpendicular to it. $\endgroup$
    – M S
    Feb 13 at 21:14
  • $\begingroup$ @AlexP Wait... did I miss something? If I lift a 1kg mass with my hand and try to hold it 1m off the ground, it becomes obvious in about ten seconds that I'm expending energy. Or do you mean by "proper arrangements" the idea that someone built a stand for the mass to sit on? The question is about trying to fly my friend. That means keeping oneself in the air without the providence of a table (which is experiencing compressive force...). $\endgroup$
    – JBH
    Feb 14 at 4:30

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