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I have a superhero setting where one guy, when fully powered up, is a flying-brick type with energy blasts who I think of as being able to lift about 1000 tons (about 10 million Newtons), and this lifting power translates directly into flight. Now, the superpowers in this setting are basically magic, coming from a source outside of the laws of physics. That being said, as defined right now, this is a potentially world-busting power. If the only limitation to his flight/lifting ability is '10 million Newtons', then the amount of power he can generate is arbitrary. He could simply fly directly away from earth at an acceleration of about 100km/s^2 for a few days, come back at relativistic velocity, and hit with the energy of the Chicxulub asteroid. This would be bad, for several reasons.

I think it would be more convenient for me to think about his capabilities in terms of power generation. To pull a ridiculous number out of the air, say that his personal peak power generation is about 75 GW, about 5% of the U.S.'s total energy consumption. That enables me to figure out how much destructive power he can output via his energy blasts, but there's no way to directly convert this into force, making his lifting strength and flight acceleration arbitrary.

So, I figure that I'm giving him a specific power output (75 GW, generated via magic nuclear reaction), and his flight works by telekinetically 'pushing' against every atom within a 1 km radius of himself, and equivalent force is applied back to him, satisfying 'every action has an equal and opposite reaction'. If he's in the air, that's a little over 4 billion cubic meters of air, and air density at sea level is about 1.22 kg/m^3, so let's assume that he's pushing against 4 billion kilograms of air.

What equations do I use here to determine his flight acceleration, or how much he can lift? By how much does he push the air around him? I can use the rocket equation and kinetic energy equations to figure out how much acceleration a spaceship can get, but I don't think I can apply them here.

EDIT: Also, let's assume that the guy masses 100 kg, just so we have nice round numbers.

EDIT2: To clarify, telekinetically pushing against an object in his area requires as much energy from him as is determined by the kinetic energy equation (1/2mV^2), the same way that expelling reaction mass from a rocket requires, at minimum, the kinetic energy imparted on the reaction mass to give it its speed.

FlyingLemmingSoup
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  • Does your superhero need to be able to fly in space? If he does need to fly in space, does he need to go beyond LEO / geostationary / lunar orbit? – KerrAvon2055 Apr 12 '21 at 02:24
  • I believe this is effectively a duplicate of https://worldbuilding.stackexchange.com/questions/160846. Alas, I never got a decent answer; maybe you will fare better? – Matthew Apr 12 '21 at 02:53
  • @KerrAvon2055 He doesn't need to be able to fly in space. The limit that he 'pushes' against matter in an area around him would logically impair his ability to fly in space - though it doesn't completely remove it. I suspect that his acceleration would be dramatically reduced by having the available reaction mass reduced from billions of kilograms to a handful of grams. – FlyingLemmingSoup Apr 12 '21 at 03:25
  • What is his reaction speed like? Can he think fast enough to, say, fly inside a building at mach speeds? – Dragongeek Apr 12 '21 at 06:03
  • But wait, when you're talking superhero universe YOU, the creator, make the rules, no? So just don't make him that powerful(?) – Len Apr 26 '21 at 16:27

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What equations do I use here to determine his flight acceleration, or how much he can lift?

For flight along the vertical you can use the relationship that links Power to force and velocity $P=F\cdot v$, where F will be the weight they lift at lift off, which could be their own weight plus whatever load they are carrying, P is given and then you get the velocity as outcome.

More generally they need to overcome drag, and I guess that here you have to proceed by iterations, since there are various relationships according to the velocity: first estimate the velocity using the linear relationship between velocity and drag, and if you get a velocity out of the regime where that approximation is valid, move to the next approximation.

L.Dutch
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    I don't think this is useful to my specific scenario, because if all he's doing is holding up a weight without moving it, then 'v' is zero, and then he can lift infinite weight with an arbitrarily small amount of power, which obviously doesn't make any sense. – FlyingLemmingSoup Apr 11 '21 at 17:40
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    @Draft85 Yeah, but this equation only deals with velocity. I think I'm missing some fundamental understanding of basic physics somewhere. – FlyingLemmingSoup Apr 11 '21 at 17:45
  • @FlyingLemmingSoup, holding a weight against gravity makes no work, because there is no displacement. Lifting a weight instead makes work, because there is a displacement. – L.Dutch Apr 11 '21 at 18:17
  • ♦ Well, then I'm at a loss as to how to quantify what this guy's capabilities are. Should I just define his energy generation and force generation capabilities separately? Like, he can generate 10 million Newtons of force, OR 75 GW of energy blasts? – FlyingLemmingSoup Apr 11 '21 at 18:25
  • Wait... what equation do you use to convert the power generated by an aircraft engine into thrust? Because that's basically what he's doing; borrowing reaction mass from the environment around him. – FlyingLemmingSoup Apr 11 '21 at 18:26
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Magic with constraints

Let's work through some of the issues here, using Flying Brick as the working name for the superhero:

  1. Structural strength - from the wording of the question, I am assuming that the Flying Brick's body has effectively infinite compressive strength and that his body does not ablate when travelling at insane speeds in atmosphere. This is, of course, impossible.
  2. Application of reactive force to all atoms within 1 km. This is, of course, also impossible. Nice idea though, one of the results of this is that it is much easier to fly (lifting heavy loads) with minimal observable effects when within 1 km of the ground (or even water) compared to at altitude. Given the masses involved, Flying Brick will only have a noticeable effect on the air at very high altitudes where no one will be particularly inconvenienced by his activities.
  3. Acceleration and force - apparently this is where you want science to nervously poke its head back into the room and look around. If Flying Brick can lift 1000 tons including himself, accelerating at a modest 0.2 m/s^2 (since round numbers are easy to work with and gravity can be safely treated as 9.8 m/s^2) then he needs to be able to output 10 million N, as you observed. This means that he can accelerate himself, within the confines of the atmosphere, at 1000 G. He needs 1G of thrust to cancel out gravity, leaving 999 G to play with. This is a truly insane level of acceleration, which leads to some interesting consequences and limits...
  4. Drag is not (much of) an issue - Looking at the density of air at sea level, a speed of 10 km/s (ie approaching Earth's escape velocity), a drag coefficient of 1 (???) and a head-first cross-sectional area of 0.1 m^2 and plugging this into the drag equation drag equation we find that the force of drag is around 6.5 million N. This is significant, but it allows for sustained flight at sea level ten times faster than the vast majority of speeding rifle bullets with thrust to burn on changing direction. This means that...
  5. Important limit - interplanetary space is not Flying Brick's friend. At higher altitudes with less air resistance the Flying Brick actually needs to be applying downwards force to himself or he will slip out of the atmosphere at escape velocity. Once he is out of the atmosphere, the chances of encountering sufficient mass within a 1 km radius to allow him to significantly change his vector and return home are negligible, even assuming that radiation, asphyxiation, dehydration and starvation are not threats to him. It also means that Flying Brick cannot become a planet-busting impactor - in practice the fastest he can go is about Earth escape velocity, and the planet takes hits from 100 kg meteors coming in at that speed with barely a shrug.
  6. Considerations - Does Flying Brick need to breathe at all - if he has a conventional human airway and lungs then he cannot fully utilise his speed without asphyxiating. Does Flying Brick have extra-sensory abilities that allow him to see over the horizon and through fog / smog / cloud - if not then his speed will be limited to one at which he can see and react to objects in his path. Does Flying Brick have a payload (or costume) that cannot survive insane acceleration and/or atmospheric speed without sustaining unacceptable damage? It is very easy to come up with reasons why Flying Brick cannot travel at 10+ km/s while still being able to lift 1000 tons when necessary. Although...
  7. Maximum load lifted - have a look at the kind of payloads that can be lifted using a single attachment point. If the object would break apart instead of being lifted intact (eg most buildings) then Flying Brick does not need to be able to lift that much mass in 1G and reduce the required strength accordingly. A quick look at what the largest cranes in the world can lift suggests that the ability to lift 100 tons is probably sufficient, which lets you reduce Flying Brick's maximum airspeed to less than escape velocity. Of course, if Nemesis-Of-Flying-Brick is crushing the innocent under a 1000 ton solid steel sphere with a convenient attachment point, ignore this advice.

Finally - if you are worried about the effect of Flying Brick on the energy market, there is fortunately an obligatory xkcd What If.

KerrAvon2055
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  • (Does Flying Brick have a payload (or costume) that cannot survive insane acceleration and/or atmospheric speed without sustaining unacceptable damage?) I read somewhere where spider silk can withstand 109,000 gees. Amazing, there's his super suit. – catsteevens Apr 12 '21 at 16:33
  • This is useful, but is there any way to calculate how much power this would require? Aircraft need power in order to accelerate air to push themselves forward. The faster they push the air, the more power they use for less thrust gain, (which is why airliner engines are so huge, they're trying to move a lot of air a little, rather than a little air a lot.) This guy is basically doing the same thing, except that he's moving an absolutely stupid amount of air. – FlyingLemmingSoup Apr 12 '21 at 21:39
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Flight

Maximum Speed How does flight work?

The four forces on flight: Lift and Gravity. Thrust and Drag.

We will achieve maximum speed when the drag force equals the thrust of the super hero. We don't need to worry about gravity, I will explain why after I show the maximum speed we will achieve.

The equations

Drag equation is Force = 1/2 * Drag coefficient * Density of fluid * Area of object * Velocity^2

The power equation is Power = Force*Velocity

The drag coefficient (1.1), density of the fluid (1.22 kg/m^3), area of the object (0.18 for head down human), and power (75 GW) are all constants. We plug those in

Force = 1/2 * 1.1 * 1.22 * Velocity^2 * 0.18 this simplifies to

Force = 0.12078*Velocity^2 This is the effect of drag at any speed for this person.

The power equation is

75 GW = Force * Velocity or Force = 75 * 10^9/Velocity

Combining the solves for Force

We now have two equations that solve for the same variable, so we can set them as equal.

We can then say the drag equation = the force equation. 75 * 10^9/Velocity = 0.12078 * Velocity^2 or (7510^9/0.12078) = Velocity^3 or Velocity = cubic root of (7510^9 /0.12078) This makes the velocity.

Final speed

8531 meters per second

But wait, what about lift?

Your super hero doesn't need lift at this speed. Orbital velocity at sea level is 7905 meters per second, which your super hero exceeds. Your hero isn't flying, your hero is orbiting the planet. Your super hero will fly straight, and realize that unless they purposely pitch down they will rise due to the fact that they move vertically due to the curvature of the earth faster than gravity can pull them down.

How fast does the air get moved?

Every action has an equal and opposite reaction, so the force applied to the hero is also applied to the air. So 0.120788531^2 = 8,790,122 newtons of force. Distributed over 4.1910^9 cubic meters of air with 1.22 kg per cubic meter is 5.111*10^9 kg. This will accelerate the air at a rate of 1.719 millimeters per second^2. That isn't much, but it is accelerating every atom by that much.

Acceleration of the Hero

With roughly 8,790,122 newtons of force, the rough acceleration is 87901 m/s^2 which mean that you should hit the maximum speed in under 100 milliseconds, this isn't actually the case since air resistance will cause you accelerate slower.

That is fast but seems slow in comparison to the relativistic speed

For reference:

The ISS orbits the earth at 7660 meters per second, and orbits the earth once every 1.5 hours. It is slower than your hero at sea level.

The Lockheed SR-71 Blackbird travels at 980 meters a second at top speed. It does so at higher altitudes, and is Less than one eighth as fast.

Your super hero is moving at nearly Mach 25.

your super hero does New York to Los Angles in less than half an hour.