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Suppose a person has the ability to cast fire, water or wind, using the hands and feet. This person gets the idea of using such ability to fly, from ground to sky. This person could get off the ground using any of these three, but as the main intention is to use such ability to fly, and it's only allowed to choose one, it's needed to be sure of which one of them is the most efficient for this goal, i.e., that is possible to reach high speeds and altitudes anywhere.

So the question is: what would be the implications of each one, and which one would be the best for flight?

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  • $\begingroup$ I don't really want to make a different question for this, but what is there to prevent the forces involved from harming the caster? Jets of water leaving a persons hands could possibly break their arms with too much force being put on them, in fact, this applies to any of the three if it has enough force to guarantee liftoff. Thoughts? $\endgroup$ – Jonathan Sep 22 '16 at 8:18
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So how is flight actually achieved? In an airplane, lift is created by the wings traveling through a fluid (hopefully air), but in something a bit less elegant like a rocket or jetpack lift is generated by shooting stuff toward the earth really fast. The "stuff" is usually some extremely hot gas, maybe steam or exhaust vapor, that is ejected downward (read: against gravity) at ridiculous speeds. In general, if you want to fly without wings you need to generate enough thrust to counteract gravity.

Thrust is calculated by taking the product of two values: the rate of ejection of mass (the "stuff"), and the speed of the mass being ejected.

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where T is Thrust, v is the velocity of the mass being ejected, and dm/dt is the amount of mass being ejected over time. So, we need to know these two values.

Water has a mass density of 1000 kg/m^3, air a density of 1.225 kg/m^3, and fire is massless (it's more of an expression of energy than an actual "thing"). So if mass-ejection rate were held equal for both water and air, then water would provide the most thrust because it is the most massive.

But that's only half the equation. The speed of ejection of the propellant is just as important as the mass of the propellant. In theory, if we could expel air 1000x faster than water, air would be just as good a candidate for propellant as water. In practice, however, if you can manage to spew air out a nozzle at extreme speed, you will also be able to manage that same speed with water. We're forgetting our massless third element, though.

By itself, fire is useless as a propellant because it isn't an actual thing. As an expression of energy combined with air or water, however, we get to go very interesting places. Using fire to heat the propellant at high speeds is easily the most effective method of thrust. Many rockets use a fuel of Liquid Oxygen and Liquid Hydrogen, which when burned produce water. The extremely hot water (technically steam) is ejected out the nozzle at extreme speeds by its own pressure, and produces thrust. Jet engines, on the other hand, produce thrust by burning fuel and heating air. The heated air is ejected out the rear of the jet at high speeds and produces thrust.

So what about our aeronautic castor? If he can cast only a single element at a time, his best bet will be water since it is the most massive option and thus able to project the most thrust as he casts it. If he can cast multiple elements, he could either use fire + water creating a steam rocket (like many modern rockets) or use fire + air to create an air-breathing jet. It is also possible that some combination of the three might be even more efficient if his powers limit the amount of mass he can cast at once (though that will require some discussion of specific impulse and some other more complicated subjects).

I hope that helps!

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Assuming they just create:

  • A blob of water
  • A blob of (compacted) air
  • A flame

The winner easily goes to the air, since none of the other imply any exerted force that would accelerate the caster. It's pretty cut and dry.

On the other hand assuming they create:

  • A blast of water
  • A blast of air
  • A fiery blast

It very much depends on how much force each blast provides, how easily they can be controlled, and how focused the blast is. The more (potentially) forceful, the more control the caster has over the blast, and the more focused the blast can be, the better they will be for flight. These factors are really up to you, so mold them how you see fit.

Ultimately these methods produce momentum by simply following Newton's third law either directly (as the air/water/fiery blast) is expelled, and possibly indirectly as the expelled force impacts a solid surface. To this end, water jetpacks already exist, and you might research them to get a feel for how the flight might look like.

Beyond these concerns, specifically touch on the fiery blast. Obviously a giant flame leaping out of one's hands and feet will... set things on fire and normally you don't want this. Water and air dumped into environments tend to be less damaging, but both can be turned into means to cut or destroy material if focused and powerful enough.

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