Common feat: Air attacks

[Floxy178]

Introduction
This will be for kind of feats where character causes an air attack with punch, finger flicking, sword slash, etc.

Since KE of object causing this attack is greater, we can upscale it knowing energy of air attack.

Assumption
While it's hard to find how much part was transferred, we can lowball things. For example, air's KE physically can't be more than lost KE due to air resistance. So we'll assume them being equal.

That'll be lowball since we're trying to find object's KE knowing air's, so taking air KE as maximum gives us a lower bound (the greater part of initial KE air has, lower the result).

Formula

Values:
Density of air(ρ), cross sectional area of object(A), drag coefficient(Cd), distance(d), mass of object(M), speed of object(v)

Air resistance =
0.5 * ρ * A * Cd * v^2

Energy loss =
0.5 * ρ * A * Cd * v^2 * d

So here ρ * A * d is whole displaced/interacted air mass, and ρ * A * d * Cd (let's call that m) is effective resisting mass, the part of mass that actually effectively resists the object.

KE = 0.5 M * v^2

KE / energy loss = M / m

Then:
KE = energy loss(air KE) * M / m

For potential questions:

What about feats where such destruction needs relativistic speeds and thus relativistic KE formula?

That won't affect the method since both formulas will be affected in the same way. Only thing that matters for their ratio is energy being proportional to mass at constant speed. Method itself doesn't rely on speed since they'll share same speed after momentum transfer.

So ratio of their individual energies will be equal to ratio of their masses regardless of how energy behaves compared to speed at that level.

To put it simply, the work done by air resistance corresponds to the kinetic energy that the air would gain in a scenario of perfect transfer (which is the assumption we made in the beginning, even though in reality, it's only a fraction) so:

(γ-1) * M * c^2 / (γ-1) * m * c^2 = M/m

Will every feat fit?

If feat is done through physical force, yes. However if feat is portrayed as a kind of "ability", like character doing this with some air manipulation or something similar, method will not work. Factors like those should be taken into consideration.

Conclusion

Formula = E * M / (ρ * A * d * Cd)

 

[DontTalkDT]

Problem is, to quote wikipedia, Cd is "not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity."
Or one can express it as a function of Reynolds number and Mach number, with the Reynolds-Number also being dependent on velocity.

This produces problems, the key ones being:

1. You need the velocity of the object, but as we all know, calculating velocity from KE is a big no no for us. (It's also not trivial to actually find the speed, but that aside)
2. Finding the appropriate constant from velocity is usually a lab test thing. You probably won't be able to find it for any of the scenarios you are looking for, since obviously you would need to punch at insane speeds.
3. I'm fairly sure the formula breaks down at a certain point becoming unusable. You definitely won't be able to use it for relativistic cases, no. I'm sceptical about your whole ratio argument actually being sound, but actually the premise of there even being air drag just is faulty. At sufficiently high speeds there is no such thing as air flow anymore, there is only atoms performing nuclear fusion against your fist.

 

[Floxy178]

• You need the velocity of the object, but as we all know, calculating velocity from KE is a big no no for us. (It's also not easy to actually find the speed, but that aside)

• Finding the appropriate constant from velocity is usually a lab test thing. You probably won't be able to find it for any of the scenarios you are looking for, since obviously you would need to punch at insane speeds.

I don't see problem with using Cd based on regular speed. Because with greater speed/Reynolds number Cd will be smaller, which again makes the method lowball.

I'm fairly sure the formula breaks down at a certain point becoming unusable. You definitely won't be able to use it for relativistic cases, no. I'm sceptical about your whole ratio argument actually being sound, but actually the premise of there even being air drag just is faulty. At sufficiently high speeds there is no such thing as air flow anymore, there is only atoms performing nuclear fusion against your fist.

Yeah but then we wouldn't see air just being pushed in the first place. Given how this type of feats are portrayed, environment should behave like fluid. Otherwise object will just compress and ionize air in its path as you pointed out, which these feats clearly don't acknowledge/show.

Since this point is just contradiction of feats with what'd happen in real scenario, I'll just let you to decide if it's appeal to reality fallacy or we should left these as incalculable.

 

[DontTalkDT]

I don't see problem with using Cd based on regular speed. Because with greater speed/Reynolds number Cd will be smaller, which again makes the method lowball.

How do you know that it will be smaller for a Mach 1000 object? It's not monotonous as far as I am aware.

Yeah but then we wouldn't see air just being pushed in the first place. Given how this type of feats are portrayed, environment should behave like fluid. Otherwise object will just compress and ionize air in its path as you pointed out, which these feats clearly don't acknowledge/show.

Since this point is just contradiction of feats with what'd happen in real scenario, I'll just let you to decide if it's appeal to reality fallacy or we should left these as incalculable.

The problem is not just nuclear fusion in itself, but also the fact that at these speeds air doesn't move out of the way of the fist. I.e. at that point air just behaves like a elastic collision, even ignoring nuclear fusion. And that doesn't contradict what we see anymore than such feats generally deviate from prediction.
In general, you can't use air drag in a realm in which the premise for the equation is not applicable, just as we don't do FTL KE. If you want to use air drag at high speeds you would need to find the actual formula of high speed air drag.

 

[DontTalkDT]

Actually, if this random webpage is anything to go by, it seems the drag coefficient goes up with speed (within the limited dataset and for spheres specifically), seemingly approaching 1.

 

[Floxy178]

How do you know that it will be smaller for a Mach 1000 object? It's not monotonous.

I couldn't know normally, but afaik its reason for increase is effects like shockwave formation, air compressibility, ionization(which makes Cd not even applicable), etc. Which most of feats simply ignore.

The problem is not just nuclear fusion in itself, but also the fact that at these speeds air doesn't move out of the way of the fist. I.e. at that point air just behaves like a elastic collision, even ignoring nuclear fusion. And that doesn't contradict what we see anymore than such feats generally deviate from prediction.
In general, you can't use air drag in a realm in which the premise for the equation is not applicable,

But that's a contradiction. You can't both ignore nuclear fusion(also other effects) happening and treat air as many number of tiny inelastic collusions. That's why I said that it's intended to behave like fluid medium. If feat doesn't show effects which that environment would, then what's point of appealing to reality?

just as we don't do FTL KE. If you want to use air drag at high speeds you would need to find the actual formula of high speed air drag.

Method doesn't literally rely on air drag formula, that's just simplified explanation for lower speeds. Existence of air drag is needed for usage of Cd, high speed air KE formula will be just relativistic KE formula.

 

[Floxy178]

Actually, if this random webpage is anything to go by, it seems the drag coefficient goes up with speed (within the limited dataset and for spheres specifically), seemingly approaching 1.

Ah, nevermind then. Even if we go with my version, feat is still unquantifiable. Formula is useless if we don't know Cd.

 

[Floxy178]

Actually, if this random webpage is anything to go by, it seems the drag coefficient goes up with speed (within the limited dataset and for spheres specifically), seemingly approaching 1.

Btw, what do you think about using whole interacted mass for ratio? If I'm not missing anything, air can't have more KE than "using A * d * ρ mass and object's speed" . This won't need classic air drag or usage of Cd to work.

 

[Floxy178]

.

Btw, what do you think about using whole interacted mass for ratio? If I'm not missing anything, air can't have more KE than "using A * d * ρ mass and object's speed" . This won't need classic air drag or usage of Cd to work.

Bump

 

[KLOL506]

Btw, what do you think about using whole interacted mass for ratio? If I'm not missing anything, air can't have more KE than "using A * d * ρ mass and object's speed" . This won't need classic air drag or usage of Cd to work.

@DontTalkDT

 

[DontTalkDT]

Btw, what do you think about using whole interacted mass for ratio? If I'm not missing anything, air can't have more KE than "using A * d * ρ mass and object's speed" . This won't need classic air drag or usage of Cd to work.

I don't know where mass ratio comes in there.
It sounds to me like you ask whether it's ok to calculate the KE of the projectile using the mass and velocity of the projectile.

 

[Floxy178]

I don't know where mass ratio comes in there.
It sounds to me like you ask whether it's ok to calculate the KE of the projectile using the mass and velocity of the projectile.

As long as neither air's speed exceeds object's nor pushed air by object exceeds mass of whole interacted air (which both are physically impossible), object mass / whole interacted mass could be used to find absolute minimum difference for KEs.

Since we're taking "how much KE could the air at most receive compared to the object's KE".

 

[DontTalkDT]

Not sure if your assumption that the pushed air can't be faster than the object pushing it is correct. In an elastic collision, that would be technically possible. Not that air is an elastic collision (at least at low speeds), but who knows how exactly things really work in the high speed realms.

That aside, if air is pushed that is not part of the projectile (I think that is what you mean by the "whole interacted air"-thing, right?) then the KE of that air that is not part of the projectile would indeed come on top of the KE of the projectile in a KE calculation.
However, I say KE of the interacted air that is not part of the projectile, and not its mass, on purpose. Because obviously the other air doesn't need to move at the same speed as the projectile. (And could be differently compressed which can make calculation hard)
So, like, you would need to calculate the KE of that stuff, too, so you don't get anything out of it that wasn't already obviously included.

 

[Floxy178]

That aside, if air is pushed that is not part of the projectile (I think that is what you mean by the "whole interacted air"-thing, right?) then the KE of that air that is not part of the projectile would indeed come on top of the KE of the projectile in a KE calculation.
However, I say KE of the interacted air that is not part of the projectile, and not its mass, on purpose. Because obviously the other air doesn't need to move at the same speed as the projectile. (And could be differently compressed which can make calculation hard)
So, like, you would need to calculate the KE of that stuff, too, so you don't get anything out of it that wasn't already obviously included.

No, I didn't mean it. Whole interacted mass is just amount of air that actually was affected by object, and therefore gained energy, doesn't matter even if projectile ends up having more mass than that as making that through air affecting other air would result in speed decrease, since object is the only source in the system, projectile won't have higher energy than energy gained from object.

It also doesn't matter if projectile has smaller mass(like some pushed air not being a part of projectile as you mentioned) as that'd mean only fraction of our "highest KE" is this level (so real ratio would be higher). Sum of projectile KE and KE of air is still <= highest KE we assumed, just projectile having all of it is assumed for lowball. In short, projectile KE + additional KE case won't be higher than just projectile case since ratio is using whole energy, not just projectile, only value of it is used for whole energy.

Not sure if your assumption that the pushed air can't be faster than the object pushing it is correct. In an elastic collision, that would be technically possible. Not that air is an elastic collision (at least at low speeds), but who knows how exactly things really work in the high speed realms.

I'm fairly sure that it's not elastic even at high speeds. Kinetic energy isn't conserved after all. I'll still do research on it tho.