Hi Jason. What you're describing (and would make your question clearer) is momentum. You're saying that the velocity component of the momentum is 'capped', but the mass component is not. Explaining it that way might actually draw more scientific answers.

@TimBII Thanks for the advice. I'm a bit confused though: what part should I change, and what would you recommend I rephrase it as?

The paragraph that starts in bold and has For Example is describing what you're asking, but this could be greatly simplified by saying something like 'the velocity of a 700 grain bullet is capped at 100m/s in terms of momentum, but that's multiplied by the mass (regardless of value) to determine momentum of impact. So, a sledge hammer hitting you at a slower speed but at or above the velocity cap (but weighing a thousand times as much) has a momentum at point of impact of 1000 times, meaning that the speed is taken to be the same'. Something like that.

@TimBII Just to be clear, the effective velocity limit is proportional to the mass of the object, not fixed. Heavier objects are allowed to apply more of their velocity to the momentum equation before the excess is ignored.

Well yes, that's one way to put it, but your math looks differently the way you've expressed it. What your math shows is that mass can be anything, but there is an upper limit to velocity. By using a constant (100), you're effectively putting a limit on speed, meaning that momentum is increased through mass, not velocity past the speed limit of 100

@TimBII No, what I'm saying is that when a .1 pound bullet hits the human body at 2,000 fps, the body reacts as if it were hit at 10 fps, and thus the momentum is 10 feet per second times .1 pound. But when a 3 pound sword hits the human body at 70 fps, the human body reacts to the full 70 fps because 3 pounds allows for 300 fps, and thus the momentum is 70 fps times 3 pounds. The limit on speed gets higher the heavier the object is.

Alright.

Alright; M=mass x Velocity, and you're saying that the upper bound of momentum is Mass x 100. That means, that the maximum momentum is governed by the mass only. Any velocity past 100 (of whatever unit, I prefer SI) is discounted. Your example actually agrees with this

No, the upper bound for VELOCITY is mass times 100.

That's what I'm saying

Well, that's not velocity

It's a mass-proportional effective speed limit.

That's momentum.

Yes, but like I said, magic changed the equation so that mass counts both for how fast an object is allowed to go AND for how much that speed is multiplied by.

Is that not clear in my explanation?

No. It's not.

I thought paragraph 2 explained it pretty well, and then paragraph 3 elaborated on it. What should I change to make it clearer?

Not to me anyway. What you're describing is a massive change to some of the constants in general relativity, and any velocity times a mass is a momentum because you're multiplying things of different units

I think I understand what you're trying to say, but you're effectively changing the speed of light.

Another way of putting this is that you'd have to convert mass to a unit compatible with speed and direction before you can create a mass-dependent velocity, unless you change general relativity

Well as I said, this doesn't change how fast the objects actually move. It's how fast they can move before any additional velocity is ignored upon collision with the human body. Until they hit a human, everything is exactly as it was before.

So you're saying that a bullet twice the weight can travel twice as fast as the first bullet and have that velocity factored into the upper momentum limit?

So the second bullet (twice as heavy) is effectively 4 times the momentum?

Yes

As long as it's moving at or above the new speed limit, a doubling of mass quadruples momentum

Why not just say that momentum is now equal to mass^2 times velocity?

Much simpler

Something tells me that simplifying it to that would have nasty unintended side-effects on colliding with large objects, making them even worse than they were in real life.

This way magic only changes the impact if it would lessen it.

Right. So you're saying that this only provides an upper bound, so to speak?

Yes

Hmm. More thought required on my part for this

Why not say that the upper limit of momentum is mass^2 x 100?

Hmmm

Is that the same thing?

That still meets the spirit of your question, makes it a bit clearer in terms of the difference between momentum and upper bound of momentum

Well, yes I think so. I was struggling because you're talking velocity when in fact the problem (to me at least) is a momentum one.

What you're really trying to do (if I understand correctly) is limit the momentum of an impact by proportionally limiting the upper bound based on the mass and a theoretical speed limit

Yeah. I want to emphasize heavy projectiles rather than fast ones, to make projectiles more cumbersome

Without making anything hit harder than it already does

Ah. Well if you're looking to nerf impacts based on speed, this still works I think. I'd have to do some more math, but it could work

Basically, dealing with the upper bound equation of M^2 x 100 means that you're not automatically applying that much momentum, you're still using it as a cap

Sorry, I didn't realize this complicated the math so much.

No it's all good.

I'm just trying to help

And it's not the math you complicated - it's the value types

The unit types actually

If you multiply a velocity with a mass, you always get a momentum

Maybe I should clarify what the new formula for momentum is?

Well, it might be a good idea

Mass times velocity or mass times mass in pounds times 100 feet per second, whichever is slower?

Pretty much

Just call that a momentum equation rather than a velocity equation

Or, you can still put in the M^2 x 100 for momentum if you like, so that heavier things can still go faster and have it count

Do I have to specify units of measure in the equation, or can I say "If v > 100mv, momentum = 100v(M^2)"? Doesn't multiplying mass by velocity in that simplified way put the two sides of the equation in unequal units of measure and invalidate it?

Well no, because momentum IS mass times velocity. Your previous equation was invalidated by the fact that you were adding units of mass to velocity, which is only speed and direction. It's actually your first equation that's invalidated because of unit crossover.

Yeah that's what I was saying

Hmm.

I'm having difficulty working out how to simplify the equation mathematically when not explaining it in words

I'm thinking your new momentum equation looks like Momentum = min(mass x v, mass^2 x100)

I think you need two equations. The first, momentum, stays the same as it is now, but the new equation is simply an upper bound test

Yeah

So, you're saying that if the momentum calculation gives a value that exceeds mass^2 x 100, then it's capped at that level

Also, 100 f/s/lb isn't fixed, as I don't know yet what value I'd need to sufficiently cripple guns. I just need to know if a value can even exist, and if it's possible to make a minimum missile size large enough to hinder guns that a bow would even be capable of shooting.

Good point

The thing is, it's a place to start.

Right

Take a look at what mass^2 x 100 will do for your various projectiles as an upper bound, and then adjust the 100 constant to taste

Well, looks like someone upvoted your first comment, meaning you weren't the only one confused. I'll try to change it now.

Right-O.

I'll keep an eye on it, I plan to upvote the question because it's a good one, just needs a bit of clarity. Hope I was helpful

Thanks

You're very welcome

Does this help?

"Since an object's mass now determines its effective velocity, this means that, until an object becomes heavy enough that its effective speed limit exceeds its actual speed, a doubling of the mass of a bullet results in a quadrupling of momentum, which suddenly makes small projectiles much, much, much less viable."

I like it. That makes sense to me. But, I'd recommend putting the equation in to explain it as well as some people like me will benefit from taht

that

But it's good

What's the symbol for momentum?

I think it's commonly p

alright

so p=Mv, p(max)= M^2 x 100

(with the units in there)

Alright

The p_(max) will make sense to the math heads; it means maximum possible P

(I might also recommend you convert to SI units as this being a science question will attract that comment)

So this?

"This changes the formula for momentum to p=mv, p(max)= X(m^2), where X is the feet per second per pound that the mass-proportional speed limit is set to."

Sounds good to me.

That way, you're not actually changing how momentum works; you're just putting a proportional upper bound on it based on mass.

Which, unless I've missed my guess, is exactly what you were trying to do...

Yes

Updated.

And I upvoted

Thanks, I appreciate that, not familiar with all the code on this site yet