Recoil calculus

[The Nomad]

In my current scifiverse, I'm trying to figure out how much recoil my Gauss guns ( electromagnetically accelerating guns ) would have... supposedly an EM accelerating weaponry system with the performances of an actual gun would have less recoil, since the bullet is progressively accelerated instead of being brutally propelled by a chemical explosion...

Anti-personnel guns fire 1 g explosive bullets at 5 kps, and have to accelerate it in about 0.1 sec...

I'm trying to calculate the recoil, using basic dynamics, but I'm not sure on how to do it exactly...

Given that the mass of a handgun is typically about, say, 800 g unloaded ( what's the average weight of a current handgun, by the way ? ), and the accelerating chamber is say, 10 cm in lenght, how would the recoil of the gun compare to that of a current weapon ?

[phongn]

F=ma. M=0.001kg, A=50000m/s^2, therefore force = 50N imparted on your gun.

I have no numbers on the recoil of a modern firearm

[Kuroneko]

In my current scifiverse, I'm trying to figure out how much recoil my Gauss guns ( electromagnetically accelerating guns ) would have... supposedly an EM accelerating weaponry system with the performances of an actual gun would have less recoil, since the bullet is progressively accelerated instead of being brutally propelled by a chemical explosion...

The momentum imparted on the projectile must equal the momentum imparted on the gun. The average force is then simply the momentum divided by the acceleration time.

I'm not well-versed in Gauss gun theory, but it is my understanding that the force imparted on the projectile is more or less uniform (unlike, say, with railguns, the force of which decreases as the projectile goes along the rails due to back-emf). But either way, I doubt you actually need to get overly technical with how the force is distributed, so simply knowing the momentum and average force should be sufficient.

Anti-personnel guns fire 1 g explosive bullets at 5 kps, and have to accelerate it in about 0.1 sec...

That would make them use a 250m barrel. There is nothing 'anti-personnel' about that sort of gun, although guns of comparative size have been attempted during World War II.

I recommend a barrel length of 10cm, which means for such speed will need to be reached in 40μs. But that means 1.25e5N of average force will be experienced on the gun, which is ridiculous for an anti-personnel weapon, so toning down the speed will be necessary as well.

[Sriad]

On the other hand, if you're using an assault rifle that's say, a meter long you've got a whole .0004 seconds to accelerate it... a=12,500,000 m/s^2 so... that's only one order of magnitude less than Kuroneko's handgun. Yea.

I guess that unless you've got inertial dampeners or acceleration after the projectile leaves the barrel you'll need to tone down the speed. That or have one hell of a back blast on a bazooka style gun.

[SPOOFE]

Dump the velocity down to 1 kps, or even 500 meters per, and it'd make more sense. Unless this anti-personnel gun is to be mounted on vehicles. If it's to be carried by soldiers, it makes little sense to give it such a high velocity, as their aim would be so inherently bad that travelling five kilometers in one second would be an utter waste.

[Darth Wong]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

[BlkbrryTheGreat]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

That would only be in atmosphere though, correct?

[Darth Wong]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

That would only be in atmosphere though, correct?

Right. I suppose I'm assuming that an anti-personnel weapon would be used on the ground or in air-filled starship corridors.

[BlkbrryTheGreat]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

That would only be in atmosphere though, correct?

Right. I suppose I'm assuming that an anti-personnel weapon would be used on the ground or in air-filled starship corridors.

Well, it could be a useful weapon for some sort of theoritical space trooper, or on a planet/moon with no atmosphere.

[Kuroneko]

I think you should forget Gauss guns completely if you want to deal with large forces in such a small profile. Although railguns are less efficient, they have the advantage of having two thicker rails to deal with it, whereas putting such a force on the solenoid coils of a Gauss gun would just destroy them.

Let's say you want a 2.5g projectile at 2.0kps, and you have 25mm² cross-area, 100mm length rails (this is already making a pretty big gun), so that the projectile has about 0.10ms of acceleration time, correspoding to a force of about 5.0e4N. That means the tensile strength of the material of the rails should be above 5.0e4N/(2*25e-6 m²) = 1.0GPa (145ksi). Although this is not particularly impressive when one considers the various steels available today, one has to realize that this material should also have a very low electrical resistivity and maintain that strength at high temperatures (obviously important for repeat shots without deformation of the rails). Well, this is a sci-fi universe, so you can get a lot of elbow room as far as fictional materials go.

Alternatively, you could go with Gauss guns anyway by introducing some adamantium-like, extreme-strength metal for the coils.

[Darth Wong]

Well, it could be a useful weapon for some sort of theoritical space trooper, or on a planet/moon with no atmosphere.

Except that in a low-G environment, the recoil would send him flying.

[Admiral Valdemar]

Forget using the gauss gun or railgun method, man portable EM guns aren't plausible no matter what universe it's in.

You could have a Steyr IWS 2000 which fires a 15.2mm, 20g tungsten dart at over 1450m/s that will take down helicopters and penetrate two walls of any modern APC armour at over 1km. That and it weighs around 18kg and is only 1800mm long.

[Kuroneko]

Except that in a low-G environment, the recoil would send him flying.

Well, it wouldn't be that bad, unless it's in very low gravity. The proposed 5kg·m/s is actually lower than an AK-47 round (7.9g at 0.71kps). With some footgear that's designed to cling to the ground, it should be quite manageable even on moon-sized bodies.

The idea should probably be thrown out simply due to such restrictions on usage, though. If one has the power to fire a 1g slug at 5kps, one would do much better with a 5g slug at 1kps.

[NapoleonGH]

no the proposal is for 5 KILOMETERS PER SECOND

[Kuroneko]

no the proposal is for 5 KILOMETERS PER SECOND

What exactly is your point? A 1g slug at 5kps and a 5g slug at 1kps have the exact same momentum--5kg·m/s. As the latter will not lose nearly as large a fraction of its velocity due to air friction, it will actually be much more effective.

[Admiral Valdemar]

no the proposal is for 5 KILOMETERS PER SECOND

What exactly is your point? A 1g slug at 5kps and a 5g slug at 1kps have the exact same momentum--5kg·m/s. As the latter will not lose nearly as large a fraction of its velocity due to air friction, it will actually be much more effective.

Typically a smaller projectile going faster is better since it means faster recycle rate and Mach's equation shows that a higher velocity projectile having the same KE as a slower one will retard faster thus delivering energy over a shorter area.

[Sea Skimmer]

Anti-personnel guns fire 1 g explosive bullets at 5 kps, and have to accelerate it in about 0.1 sec...

How exactly do you propose to fit an explosive and fuse inside of a 1 gram bullet? And what exactly do you think will be harmed by this round?

[Admiral Valdemar]

Anti-personnel guns fire 1 g explosive bullets at 5 kps, and have to accelerate it in about 0.1 sec...

How exactly do you propose to fit an explosive and fuse inside of a 1 gram bullet? And what exactly do you think will be harmed by this round?

Well throw it fast enough and a 1g slug of DU would be pretty nasty. It's also totally useless in reality as I showed, railguns rely on immense KE to kill, not shaped charge warheads (unless you were flinging them over the horizon). The explosive (even if it could fit) is superfluous, like putting a stick of TNT on an MIRV.

A modern anti-material rifle will suffice.

[Kuroneko]

Typically a smaller projectile going faster is better since it means faster recycle rate and Mach's equation shows that a higher velocity projectile having the same KE as a slower one will retard faster thus delivering energy over a shorter area.

That's true, but the higher kinetic energy of the faster, lower-mass bullet will be burned away pretty quickly--both the velocity and mass. It would only be more effective at very short ranges. I'd rather have a gun I could use in almost any situation.

[His Divine Shadow]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

Hmm, what if blasters work on a similar technology? Though it doesn't help given the lower speeds and red and gasp, green colors they display.
And other factors also, such as anti-gravity shit and whatnot, eh, I'm really reaching here.

[Admiral Valdemar]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

Hmm, what if blasters work on a similar technology? Though it doesn't help given the lower speeds and red and gasp, green colors they display.
And other factors also, such as anti-gravity shit and whatnot, eh, I'm really reaching here.

Elaborate.

[Sea Skimmer]

Well throw it fast enough and a 1g slug of DU would be pretty nasty. It's also totally useless in reality as I showed, railguns rely on immense KE to kill, not shaped charge warheads (unless you were flinging them over the horizon). The explosive (even if it could fit) is superfluous, like putting a stick of TNT on an MIRV.

A modern anti-material rifle will suffice.

The damage path of such an insanely tiny projectile isn't enough to make it effective, even if it didn't vaporize from friction. The explosives blast wouldn't harm anything, while 1 gram on its own is barely enough to make one decent fragment. Overall this is an ineffective and very stupid weapon.

[Darth Wong]

Typically a smaller projectile going faster is better since it means faster recycle rate and Mach's equation shows that a higher velocity projectile having the same KE as a slower one will retard faster thus delivering energy over a shorter area.

Actually, the exponential increase of aerodynamic drag with velocity means that hypervelocity shells are a bad idea. That's why incoming asteroids burn up harmlessly in the atmosphere unless they're huge.

[Admiral Valdemar]

Typically a smaller projectile going faster is better since it means faster recycle rate and Mach's equation shows that a higher velocity projectile having the same KE as a slower one will retard faster thus delivering energy over a shorter area.

Actually, the exponential increase of aerodynamic drag with velocity means that hypervelocity shells are a bad idea. That's why incoming asteroids burn up harmlessly in the atmosphere unless they're huge.

Naturally, they'd also make one hell of a bright tracer (and if made from DU we all know what that entails). People think railguns should only fire at many hundreds or thousands of km/s, (Erazer had Ah-nuld firing aluminium slugs at .99c!) like the movies. That's simply excessive and, well, short of a battleship, nothing is taking that recoil too well.

EDIT: Some have come up with the idea used in sci-fi to vape a pathway through the air with a laser first before the railgun fires. Of course, others argue whether just having that laser alone would negate the need for the railgun.

[His Divine Shadow]

At that velocity, it will be a surprisingly short-ranged weapon. The enormous air friction will create a plasma bow wave that will vapourize the insignificant 1g projectile before too long. It should look cool, though. Like a white-hot blaster bolt.

Hmm, what if blasters work on a similar technology? Though it doesn't help given the lower speeds and red and gasp, green colors they display.
And other factors also, such as anti-gravity shit and whatnot, eh, I'm really reaching here.

Elaborate.

Well blasters have been reffered to as both projectile and plasma weapons, so was thinking, what if it fired a projectile that turned into plasma? Ofcourse that still leaves the speed, antigravity and color issues and the fact that some bolts are opaque.