E=MC^2 ? wtf??

[Thomas Shey]

Though I should note damage to a target is more than simple energy transfer, and that's even more true when dealing with complex structures like living creatures and machines. A lot of firearm systems in a lot of games where someone tried to use energy transfer as the only or primary damage category basis without looking at some other things come a cropper on that.

 

[Umbran]

The formula in the title doesn’t apply to simple punches. The correct equation should be Force = Mass x Acceleration. So a very fast punch from a small guy can have the same force as a slower punch from a brute.

With respect, punches are mechanically pretty complicated. F=ma is an easily measurable quantity for a free body, but fists are attached to arms, thence to bodies, legs, and finally the ground. When in complicated mechanical events happen, the resultant force is not so simple.

 

[Jack Daniel]

With respect, punches are mechanically pretty complicated. F=ma is an easily measurable quantity for a free body, but fists are attached to arms, thence to bodies, legs, and finally the ground. When in complicated mechanical events happen, the resultant force is not so simple.

Not to mention, the time that the fist is in contact with its target matters for Δp.

J = ∫ F dt

 

[kigmatzomat]

With respect, punches are mechanically pretty complicated. F=ma is an easily measurable quantity for a free body, but fists are attached to arms, thence to bodies, legs, and finally the ground. When in complicated mechanical events happen, the resultant force is not so simple.

Nah, the connection to the ground isn't a pinned connection, its a friction contact patch.

F=Ma is pretty easy to measure these days because we can capture F and a with sensors to back into the applicable M. Although this is force when in reality we probably want kinetic energy.

From memory, KE=E * sin(⊙)(FM'ad + 0.5*M"v^2), with a ceiling of the lowe of uN and the breaking point of the limb in question.

The E portion is the elasticity of the contact surfaces, ⊙ is the angle of impact, FMad is Force of punch, M' is the mass of of body in punch,a is acceleration of punch and d distance accelerated. The v is the relative velocity of the two bodies, with M" being the total mass of the punch-er.

Force in excess of ground friction (uN) is split between accelerating the puncher and adding force to the punch-ee. Although if at any time the breaking point of the limb is exceeded, that energy is mostly spent on the arm, although in most cases the target will suffer comparable failures. The general incompressibility of liquids should eliminate the need to calculate deformation distances.

Given the number of variables that are situational plus most creatures' innate ability to use natural weapons correctly, a typical punch force that adequately represents combat situations should be pretty easy to back into, with a ceiling for maximum applicable force under extreme situations (i.e. punching a target falling towards you.)

Dang, been a long time since I set up a dynamics formula. I will have to check later to see how close this is to my text books.

 

[kigmatzomat]

it should mean that Str ( Mass, like what Brutes share ) is far less effective than Speed ( say Acrobats, Monks ? , Illusionists ? )
if so, then BodyBuilders wouldn't find their food would they ?

This is the matter-> energy conversion. Oddly, the usable E is actually similar to kinetic energy (kE=0.5 mv^2) where v=c , if you are combining matter + antimatter, because roughly half of that energy gets turned into neutrinos, which are (currently) unharnessable.

So if a bodybuilder can spontaneously convert a tricep to pure kE, well, they could split a continent right down the middle. (0.5kg of energy is suuuuper destructive)

 

[Umbran]

Nah, the connection to the ground isn't a pinned connection, its a friction contact patch.

If you know enough to throw that terminology around, you also know enough to know that a "pinned connection" is merely an approximation. You can rivet steels beams together, and call that a "pinned connection"... until the forces are great enough to shear steel, and then those bets are off.

So, to first approximation, that contact point is a pinned connection. It will cease to be so when the forces get high enough - but that also speaks to how this is not a simple interaction, but a complex one.

F=Ma is pretty easy to measure these days because we can capture F and a with sensors to back into the applicable M.

You have not identified the applicable M.

Although this is force when in reality we probably want kinetic energy.

This is not a simple instantaneous elastic collision between two free bodies, and cannot really be approximated with one - heck, if you want to hurt someone, you need the collision to be inelastic - to deposit energy within the body, not just bounce elastically.

From memory, KE=E * sin(⊙)(FM'ad + 0.5*M"v^2), with a ceiling of the lowe of uN and the breaking point of the limb in question.

The E portion is the elasticity of the contact surfaces, ⊙ is the angle of impact, FMad is Force of punch, M' is the mass of of body in punch,a is acceleration of punch and d distance accelerated. The v is the relative velocity of the two bodies, with M" being the total mass of the punch-er.

So, you mention M, M', and M", but your equation only has M' and M". You do not clearly identify what object M' "the mass of of body in punch" is, especially when you then also refer to the "total mass of the punch-er" separately.

FM'ad appears to have a units problem: F*d has units of work (so energy), but M*a has units of force, so the product FM'ad then, is not energy.

Next, a is not constant in real body mechanics. You don't identify what the distance d is. Depending on what d is, we may need to talk about how the angle is not a constant either.

Also, in a real application the fist continues to receive energy from the body after contact is made with the target. This isn't an instantaneous interaction.

And finally, we note that the total kinetic energy delivered doesn't really tell us much about the punch, because exactly how that KE is delivered matters - I can deliver it so that it breaks your jaw, or I can deliver it so it gently pushes you back, and one is a hard punch and the other is not.

Dang, been a long time since I set up a dynamics formula. I will have to check later to see how close this is to my text books.

I'm a physicist who used to teach basic mechanics to college students. I have noted my thoughts above.

What it comes down to is that the overall mass of the puncher doesn't mean much of anything unless they are flying through the air and come to a complete stop when they hit you, which is very anime.

 

[Sir Brennen]

With respect, punches are mechanically pretty complicated. F=ma is an easily measurable quantity for a free body, but fists are attached to arms, thence to bodies, legs, and finally the ground. When in complicated mechanical events happen, the resultant force is not so simple.

Yeah, I realize it’s an oversimplification, but it’s a heck of a lot closer than Einstein’s famous equation. In a gaming context, I don’t think the additional factors would be terribly useful.

But then, I’m not even sure what use of applying any of these physics equations is in a gaming context, but such is often the nature of the OP’s threads.

 

[kigmatzomat]

If you know enough to throw that terminology around, you also know enough to know that a "pinned connection" is merely an approximation. You can rivet steels beams together, and call that a "pinned connection"... until the forces are great enough to shear steel, and then those bets are off.

So, to first approximation, that contact point is a pinned connection

So, you mention M, M', and M", but your equation only has M' and M". You do not clearly identify what object M' "the mass of of body in punch" is, especially when you then also refer to the "total mass of the punch-er" separately.

FM'ad appears to have a units problem: F*d has units of work (so energy), but M*a has units of force, so the product FM'ad then, is not energy.


Also, in a real application the fist continues to receive energy from the body after contact is made with the target. This isn't an instantaneous interaction.

And finally, we note that the total kinetic energy delivered doesn't really tell us much about the punch, because exactly how that KE is delivered matters - I can deliver it so that it breaks your jaw, or I can deliver it so it gently pushes you back, and one is a hard punch and the other is not.



I'm a physicist who used to teach basic mechanics to college students. I have noted my thoughts above.

What it comes down to is that the overall mass of the puncher doesn't mean much of anything unless they are flying through the air and come to a complete stop when they hit you, which is very anime.

I posted at 1am local time on a gaming board from a phone to comment on why E=Mc^2 was completely inapplicable to a punch (A fact that got lost in an edit and was added in a follow up) while having a BAC of "happy glow". Not really going to be concerned about failing to fully describe a term given that the "punch" in question could come from an 18" pixie or a tentacled otyugh.

So first off, F=M*a. Work (energy)= F*d. Ergo W=M*a*d. Both have units of kg*m^2/s^2. You probably got hung up in named units. I always decompile joules, newtons and such to fundamental units as quickly as possible. Makes it easier to find which components of a formula will be irrelevant at the scale in question so I can ignore it sooner.

I am a licensed engineer. If I need to deal with a collision, the energy to turn a human body into a 50m smear isn't even a round off error on the last significant digit. Not something I have had to do in the last 20 years, though, as I am a retired engineer.

Overall this is normally a "spherical cow" scenario, where tons of hand waiving is applied. Although engineering doesn't like to say it uses "assumptions" like those ivory tower academic physicists, we call them statistically significant multipliers for safety factors. Same diff. (You would be stunned at the amazing oversimplifications done as part of engineering best practices that let us reduce a ginormous physics problem to a simple 2-term approximation. We get away with it because they are based on empirical test results within the energy/mass tier in question, always errs on the conservative (safe) side, and then we add another large (~40%) safety factor. As long as you choose the right "tier", its easy peasy. That transition between tiers? Ugh, we hate that. Sometimes there are differential equations to solve and they're the worst.)

If you are throwing a punch, the best case scenario is already gone, its now all shades of bad. First shade of bad is terrain. Ever gotten in a fight in mud or on loose gravel? Yeah, totally not a pinned connection to the ground.

As to the terms I didn't define, M' is the "limb mass", as punch style will change that. Could be as small as the arm below the elbow a quick snap punch, arm+ fraction of shoulder, +component of torso on a roundhouse, etc. Add tentacles and such and its all messy.

Total mass is relevant. From my minimal martial arts experience decades ago, it is much easier to break a board starting at walking speed than while keeping the center of mass essentially stationary. If two fighters move towards each other, the collision forces can increase significantly. Or I can just point at head on collision energies between cars if you want something less anecdotal.

I did make a nod towards the time of collision, though I referred to it indirectly through assumptions of the incompressibility of fluids.

And did you actually try to say flying is irrelevant in a gaming concept? In d&d it becomes available at 5th level and magic items can make it show up at 1st even for humanoids. That ignores flying opponents, like the aforementioned pixie.

So ultimately, this was all a flying incompressible spherical cow used to explain why the cow is not spontaneously converting its mass into a planet-shattering explosion.