Like many other writers, I'm hoping to create some sort of justification for destroying the monopoly firearms have on the modern combat scene so that I can justify mixing things up with melee weapons, archery, slower-than-bullet magic, etc. I'm hoping to do this by using my story's magic system to knock guns down a peg, and after giving it a lot of thought, I've come up with a solution with potential. But I need to run it past some more knowledgeable people to see if this would actually work.
The gist is that, when the inciting event of the story renders nearly everyone on Earth low-level superhuman and capable of using magic, it also alters how the laws of physics interact with the human body in a few key ways, and one of those is that all solid objects colliding with the human body have an "effective speed limit" proportional to the object's mass, and any velocity beyond that speed limit is completely ignored once the object collides with the person and it's time to "calculate the damage" of the impact. To be clear: this doesn't change how fast objects move. It only changes how fast the human body acts like it's moving when it's struck.
For example, let's say, just to demonstrate the concept and not declaring this as the actual value, that the effective speed limit of an object, in feet per second, is equal to 100M, where M is the object's mass in pounds. This means that a 700 grain (0.1 pound) bullet, when shot from a gun, would only damage the human body it collides with as if it were traveling at 10 feet per second, instead of the staggering thousands of feet per second they usually get. Meanwhile, a sword, which weighs 3 pounds on average and is normally swung at speeds well below the sword's effective speed limit of 300 f/s, would be completely unhindered and be just as effective.
This changes the formula for momentum to p=mv, p(max)= Xm2, where X is the feet per second per pound that the mass-proportional speed limit is set to.
Since an object's mass now also 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.
The idea here is to force bullets to be big. Big, cumbersome and slow-loading enough that while they aren't completely nonviable and still have their advantages, guns are no longer the rapid-firing, compact bringers of instant death they were once allowed to be. Ideally, guns will be more like they were in the early days: cumbersome, slow to load, and barely more powerful than archery for the trouble.
I'm fairly certain this would make melee weapons relevant again, but the issue comes to archery. I've been informed of certain facts regarding the comparative weight of the heaviest calibers of bullet and the general weight of arrows. Apparently guns can fire some very, very heavy bullets, as much as 3000 grains, without much issue, and the heaviest bullets drastically outweigh most if not all arrows. While bows would be stronger here than in real life due to humans in my universe having the strength of two men, and thus arrows could be made heavier, this still calls into question whether or not a sweet spot weight even exists that would nerf guns but not render archery physically impossible. I'm willing to accept that in order to use this system I have to give up any prospect of including archery, but I'd like to see if it's still possible to make this work.
Is it possible to set a minimum weight projectiles have to weigh to achieve penetration that is too heavy for bullets to be fired more than once every few seconds, but light enough for arrows to be shot from bows with draw weights of double human strength or less?