# Could a mass-proportional physical speed limit on projectiles "nerf" guns but not ruin archery?

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?

• 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. Mar 25, 2019 at 0:52
• @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? Mar 25, 2019 at 0:55
• 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. Mar 25, 2019 at 0:58
• @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. Mar 25, 2019 at 1:00
• 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 Mar 25, 2019 at 1:02

The effect you're describing could at least in part be achieved by greatly increasing the atmospheric pressure of a planet, or even adjusting it so humans live in a liquid without them realising. Yes, this part requires a liberal dose of handwavium sprinkled about, but ultimately the greater the wind or atmospheric resistance, the more lowering the mass of an object is going to have an effect because it's taking the same amount of energy out of every object passing through it at a similar rate, aerodynamics notwithstanding.

This last point is important, because your melee weapons and the like are going to work better if they are thin and sharp, like swords or axes, not hammers. It's also going to work better for arrows, which are heavier but also aerodynamic and therefore more likely to retain as much of their momentum as possible while moving through the thicker air.

Bullets in their current form will suffer, but their current design (blunt lead projectiles) is to maximise damage in an environment where their velocity counts. In this new situation, bullets may well survive as a combat measure, but they'll have two major modifications;

1) Convert to harder metals and a sharp point, and
2) Only be used as high velocity (long range) rounds, think snipers.

The reason for this is that the harder metal and sharper point means that the bullet does more penetrative damage when it hits, maximising what momentum it can still retain, but becomes less lethal in the process. With the exception of head shots, the bullet won't cause as much damage by deforming and spreading the kinetic energy out over a wider impact area, so it's now restricted to a long range wounding weapon in most situations.

Your arrows in this situation will also now have very sharp tips, and will be designed to wound as they currently are. Bullets in this scenario are effectively constrained to being long range arrows, although the arrow is probably in most instances the better and more effective weapon at short and medium range by virtue of its mass.

The real winner out of this will be your melee troops, who will have swords and spears for slashing and wounding across a broader surface area than arrows or bullets which have to keep their contact surfaces constrained as a sacrifice for longer range. Despite this, arrows will continue to be effective as a wounding weapon as it's unlikely that this 'upper bound of momentum' effect will be strong enough to constrain the momentum at impact of the arrow, and a sharp point would actually do more to make the arrow effective in any event.

I don't think this works, because it would effect the gun as much as the bullets. You would feel no recoil because the gun can't gain more momentum than the bullet does. So there isn't much preventing you from using a gun with large bullets. If you needed 10x as much mass as a normal bullet to be lethal, but also felt 1/10th the recoil, every soldier would just carry 20mm rifles. They don't even need to be as big as they were historically, because you don't gain anything from additional speed. You only need the projectile to be fast enough to be accurate, speed doesn't help you penetrate anymore. So no need to bother with high enough pressure and a long enough barrel to hit 2000fps when 600fps is plenty. I think you would be looking at having everyone carry bolters, not swords.

See S. M. Stirling's Emberverse, starting with "Dies the Fire". In an instant, all electricity stops, high speed chemical reactions (gunpowder) fizzle, and it's impossible to get useful work with air pressures over about 150 psi.

Interfering with the speed of chemical reactions is a good bet. It would mean that you might be able to make steam powered cannons if you can get high enough pressure steam (thousands of PSI) Guns would be very cumbersome. Mechanical siege weapons would come into play: Trebuchet, mangonel, catapults, as well as both bow and arrow, and slings, atlatls, throwing sticks.

A physical change such as tripling the air pressure, by adding extra argon would allow guns to work, but the velocity drop from air friction would be

As a kid I played LaCrosse. This is a dangerous game played with a rubber ball. (A lacrosse ball is about the same weight and only slightly softer than a baseball hardball) A lacrosse stick, some training, and potato sized rocks could be bad news. A sling is more efficient -- most of the energy is in the stone, where with a throwing stick of any form you have energy in the stick that you have to stop for your next throw. But you can train a peasant in a day to be effective at putting rocks into a massed charge.

This opens the possibility of a "Pedal powered anti-personnel catapult." where some sort of wheel with cups, grooves, etc throws a rock at the enemy. Would require a well balanced wheel and good bearings. Given the relative strength of legs vs arms, I would think you could be about 5-15 times as efficient at transferring energy from your legs to the enemy's armour that arm powered projectile (You still need to concentrate the energy on a small enough area to inflict damage.

With a conventional sling, consider the effect of lead pellets the size of a robin's egg instead of a stone.

A boy's rubber band style wrist rocket slingshot used with 1/2" steel bearings can be deadly

• "Interfering with the speed of chemical reactions is a good bet." Well, assuming you overlook the part where everything dies because chemistry doesn't work right any more. Jul 16, 2019 at 22:18

What you are describing would work. I would simply restate the kinetic energy formula with a Log function on the velocity bit so that it receives a maximum kinetic energy from velocity. This would have massive consequences for much of your world though.

But I think you can do it simpler: introduce runes. A rune would be a minimum size. Armor can be enhanced to be nigh impenetreable and its cheap and easy... But a counter rune is easily made on weapons. Problem is that bullets of sufficient size are so cumbersome and the recoil so great that you are better off using swords and arrows. This also limits what kind of ammo everyone uses, since an artillery shell that explodes also destroys its runes and becomes ineffective unless it hits you directly.

An alternative to runes is that each magic user can use its magic to Block enemy fire. An opponent can bypass this jf he concentrates magic in his weapons... But only if he can actually see and focus on it. High velocity projectiles regrettably are too fast so a slower projectile or melee weapon it is then. Another alternative is that mass is what carries the magical potential, but this magical potential leaks away the moment it leaves proximity with the wearer, the farther away the faster this goes. A bullet has lost almost all its magical potential to penetrate someone's armor while an arrow still has enough to do damage. And melee weapons become even more universally used as they lose no energy and stay close enough to be powered.

• love the runes. you can even still have anti-materiel rifles (speed limit is only against humans, right?) and guns (you'd be able to charge through a barrage, because the shrapnell won't get you). you could also still have elite snipers (using ultra expensive rune-inlayed bullets). Very cool! Mar 26, 2019 at 15:25

Many other answers already state the parts where this would screw up physics and not actually prevent firearms by just making them use bigger bullets; so, I'll skip the reasons why this does not work, and just try to focus on fixing the idea in a way that it could work.

Instead of reinventing the universal laws physics to make bullets not work, this kind of problem is usually addressed best by adding new ways of stopping attacks that bullets don't counter well. This way you can avoid the collateral effects of completely flipping Sir Newton the bird.

For this I suggest you add some kind of protective runes or personal shields (depending on if you want to go more fantasy or sci-fi). These shields can stop incoming attacks based on their kinetic energy. Bullets actually don't have a lot of force for their killing power. Consider that even a high calibre handgun like a 44 magnum delivers about ~1200 joules of kinetic energy, but a 10 lb sledgehammer can deliver ~2500 joules. If an opponent's shield can block 1000 joules, then the high calibre handgun becomes little more than a pea-shooter while the sledgehammer still hits like a very fatal 6 pound hammer.

While this makes heavy weapons useful, it's still not good for bows, short swords, etc. which gives us a need for a second technology: shield disruptors. A disruptor would be a device or rune designed to penetrate a shield. Disruptors would be effective based on their size meaning you could fit one well into a sword or arrow, but not a bullet. So let's say you can cancel 50 joules of shielding per cubic centimeter of disruptor. The above listed 44 magnum could only cancel ~60 joules of shielding if the whole slug was replaced with a disruptor. In contrast, an average arrow shaft could easily hold a disruptor with 1000 joules of shield penetration, and a melee weapon like a broad sword could cut right through a 6,000-10,000 joule shield.

Because these interactions are only between the weapon and target; you don't need to spend your whole story having to worry about if you remembered to account for weird physics.

• "In contrast, an average arrow shaft could easily hold a disruptor with 1000 joules of shield penetration" - wouldn't a bigger gun still be superior to a bow? An arrow can be stopped by conventional armor, a 20mm round... not so much. Jul 17, 2019 at 10:19
• By not changing physics you still need to contend with the gun's recoil. A 20mm cannon is artillery not a bow. A vulcan 20mm cannon fires shots with ~52,600 joules of kinetic energy. Various styles of a roman ballista can fire 20,000-60,000 joule javelins with 1,600,000-4,800,000 joule disruptors. Since the OP seems to want to balance guns and ancient tech, this would make superiority a case by case solution of where do you need more RoF vs more penetration If you want guns to be totally useless, just make shields and disruptors even stronger. Jul 17, 2019 at 17:28
• though past a certain size, missiles will beat both cannons and ballistas as the heavy weapon of choice, swords and bows would still be competitive weapons in comparison to assault rifles, and handguns. Jul 17, 2019 at 17:35

I'm offering a frame challenge to your question.

I think that making the universe constrain motion or momentum in mass-dependent ways is problematic for all the reasons cited in the other answers.

But, since everyone is now magical, they could individually generate a personal shield that is always active against attack. It can be consciously made more powerful, but people keep it at a reduced level normally so they can carry out everyday activities.

For instance, at too intense a level, they'd suffocate since the air couldn't circulate around them. The everyday brownian motion of gases would trigger the shield and they'd soon consume all the oxygen. Similarly, riding a horse could be a problem since your butt bounces on the saddle. Bounce too hard, and the shield pushes back really hard on your mount, breaking its back. So, to keep life manageable, unless someone is really paranoid, they keep the shield powerful enough and a subconscious level that it makes bullets useless.

If you want most everyone to be vulnerable to melee weapons and arrows and stuff, then make it an instinctual reaction that everyone has -- a subconscious use of magic -- but very accomplished mages, witches, wizards, and magi can consciously control the shield.

In many ways, it would be like a magical version of Frank Herbert's personal shields in the Dune novels.

Again, FRAME CHALLENGE!!