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And I'm not talking about the wimpy 32 MJ kind we have in the real world, I'm talking about the superweapon kind. Anyone familiar with Knights of Sidonia and their flagship's Heavy Mass Cannons will know what I'm talking about (https://m.youtube.com/watch?v=D1GdoUDBsaE)

This is less of a "how it's done" question and more of a "am I understanding this right" question, because my rudimentary understanding of physics tells me that if your spaceship is firing a railgun projectile with megatons or gigatons of kinetic energy behind it, recoil from the weapon should also be destroying you as well as your target. Whatever asteroid you cobbled your ship together out of probably isn't going to survive that kind of abuse unless it's made from adamantium.

Or am I wrong? I get the sneaking suspicion there's some fundamental part of how a railgun works that I'm either ignorant of or don't properly understand. Can anyone help clarify this for me?

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    $\begingroup$ That's pretty easy, in an isolated system such as in space your railgun just need to accelerate fast in the opp direction meaning no fix mount to cancel the momentum of the projectile. The bigger the gun the more engineering issue you face any more just apply handwavium. $\endgroup$ – user6760 Oct 19 '16 at 1:49
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    $\begingroup$ You need two guns at the opposite sides of an object that can rotate. The first shot’s recoil turns into rotation of the object, the second gun’s shot will stop the rotation. Of course, you need an advanced targeting device that can compensate the rotation when aiming. $\endgroup$ – Holger Oct 19 '16 at 9:22
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    $\begingroup$ @Holger You cannot cheat Sir Isaac Newton. There will be recoil, always. No matter how many flywheels or rotating gizmos you have inside your ship, the system as a whole will recoil away from the projectile you shoot. You cannot cheat at basic physics. $\endgroup$ – MichaelK Oct 19 '16 at 9:54
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    $\begingroup$ @Holger How do you mean that a rotating impulse sink (i.e. recoil dampener) will help you? And sure, of you make the gun a one-shot disposable affair, sure, then the ship would not need to deal with the recoil at all. But I hardly think that is what OP had in mind. $\endgroup$ – MichaelK Oct 19 '16 at 10:27
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    $\begingroup$ @enkryptor: But if the vehicle is not in space - say an ocean-going ship, as that appears to be the first use for real-world railguns - the recoil is eventually spread to the whole Earth. E.g. a ship firing a railgun due north causes the ship to recoil to the south, but the motion is damped by the water. $\endgroup$ – jamesqf Oct 19 '16 at 17:30

11 Answers 11

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The conserved quantity causing the recoil is the product of mass and velocity. The projectile is a small fraction of the mass of the ship. The recoil will be the same fraction of the velocity.

E.g. if the projectile is 100g and shot at a million miles per hour, and the ship was 100 tons then its recoil would be 1 mile per hour.

The additional energy needed to correct the motion of the ship can be in principle much smaller than what you expended on the projectile, since that’s mass times the square of the velocity. (The real needs will depend on how your thrusters work: how much reaction mass you are willing to lose).

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    $\begingroup$ Velocity of the ship doesn't matter, it is effectively firing from rest. and 0.99c is a lot and it's gonna feel that. $\endgroup$ – John Meacham Oct 19 '16 at 1:28
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    $\begingroup$ I really like this answer, would have been what i had written. Please also take into consideration that the kinetic energy of a projectile is mass times velocity square... so a high velocity is much more important than a high mass. You can reduce the weight of your projectile to a level where your ship can still take it. Also, the gun is probably constructed in a way that it distributes the "recoil" over a large area, so it won't break the ship. compare to a stock rifle without recoil comp. Kills target, but doesn't brake your shoulder. $\endgroup$ – Andreas Heese Oct 19 '16 at 6:35
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    $\begingroup$ @JohnMeacham at 0.99c, the equations get a bit more complicated due to relativity. I would limit yourself to a "whimy 0.1c"; that is still world destroying sort of territory. $\endgroup$ – Aron Oct 19 '16 at 6:59
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    $\begingroup$ @Z.Schroeder i totally didn't see your numbers. A 100kiloton projectile fired at .7c would have a kinetic energy of... roughly 2.2 Exajoule. With .99c you would get...45 Exajoule. That's roughly 10714 MT of TNT. It's really hard to imagine what would happen if that thing hit earth. But it would probably kill all the dinosaurs or something like that. I am quite sure making your bullet a LOT lighter will still provide sufficient destructive power. Try a factor of 100-200. With your bullet at 0,5kTons, you'll still have 50 MT of TNT left... $\endgroup$ – Andreas Heese Oct 19 '16 at 8:05
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    $\begingroup$ @Aurast Basically the projectile would stop so much being a projectile as it would be basically just a large collection of particles. at least inferred from what-if.xkcd.com/20 $\endgroup$ – Jake Oct 19 '16 at 15:57
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Hardpoints

On military vehicles there are special locations called "hardpoints". A hardpoint is a specially reinforced location on the frame that is designed to support the weight of something heavy and/or withstand the force of something with a lot of recoil.

On null-grav vehicles, a hardpoint is also a specially reinforced section of the frame, but the design of the entire frame of the vehicle also takes the location of these hardpoints into consideration, due to the lack of constant acceleration (ie: gravity), and the potential variable acceleration effects inherent in an omni-directional environment. Otherwise any recoil of weapons (or engines) being fired might damage or warp the frame, or possibly impart acceleration in an undesirable way. In reality, weapon systems would either be axially located, or would consist of multiple matched weapons (pairs, triple-config, quad-config, etc.,) placed so that they do not impart spin in any given direction.

Acceleration

It is true that in reality, unleashing a weapon with a exa-joule or zetta-joule output would impart acceleration away from the direction of fire. Even smaller weapons would impart some fraction of acceleration which may result in deflection of angle of travel or even in spin.

Therefore, the frame of a vessel mounting such a capital weapon must be designed to not only withstand the acceleration force of the weapon itself, it must also be able to withstand the force of all the weapons it mounts, plus the engines, plus any impact (armor) it is designed to take, plus any gravitational stresses it may come under during travel near massive objects such as planets, stars, or maybe even stations.

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    $\begingroup$ While hardpoints let you spread the force properly through your structure, it's also worth noting that you with a railgun you can accelerate the projectile gradually over a long track or barrel, thus reducing the force that the structure has to support at any given moment. On the other hand, the impact of that projectile against a target will be attempting to bring the projectile to rest in a much shorter time, resulting in much higher peak forces. This explains how your ship can be made of the same stuff as theirs, but theirs breaks and yours doesn't. $\endgroup$ – anaximander Oct 19 '16 at 10:09
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    $\begingroup$ The problem is the same as with any projectile weapon: how deliver lots of energy into the hull of your enemy, and this 1) without breaking your own vehicle and 2) breaking the enemy vehicle. The trick is time. The forces depend inversely on the time it takes. You want the launch to take enough time to spread out the impulse. The first you achieve by having a really long barrel, and you can also tack on recoil dampeners which further extends the time it takes for you to soak the recoil. And the second you achieve by having the projectile deliver all its momentum as quickly as possible. $\endgroup$ – MichaelK Oct 19 '16 at 12:14
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    $\begingroup$ @MichaelKarnerfors many (most?) projectile weapons that are designed to be effective against any sort of armour rely less on kinetic than on chemical energy in the projectile, particularly shaped charges. $\endgroup$ – leftaroundabout Oct 19 '16 at 21:01
  • $\begingroup$ @leftaroundabout A projectile, by definition, is moving. How is this not a dependency on kinetic energy? Regardless of the generator, the energy must eventually become kinetic in order to move the thing. $\endgroup$ – jpaugh Oct 20 '16 at 16:54
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    $\begingroup$ @leftaroundabout Oh, I get it. You mean, it carries a payload to the target, and causes an explosion there. Yes, but a weapon relying more on kinetic energy could compensate by having a longer barrel and more gradual acceleration. The real question is, How well would this scale up to the energies of a rail gun? $\endgroup$ – jpaugh Oct 20 '16 at 16:55
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How long does it take to accelerate the projectile?

If you have a really long launcher, you can fling lumps of metal around at great speeds and not have ship-shattering recoil. What the ship feels instead is a continuous push from the launcher over a length of time.

Let me explain that will some simple maths.

The product of $Force\times Time$ is going to be the total amount of energy imparted into the projectile. You can push really hard for a short length of time, or you can push gently for a longer period of time, and the results will be the same.

When designing your railgun/mass-driver/doomsday-weapon, this is one of the factors you need to consider.

Why?

Newton's Third Law: for every action, there's an equal and opposite reaction.

If you push hard against something, the something pushes back hard. If you push against it too hard, you'll damage yourself.

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    $\begingroup$ As I've said in a comment on another answer, the trick here is that the shooter gets to "push gently for a longer period of time", while the target is pushed "really hard for a short length of time". You've said the result is the same, but that's only true in terms of final velocity. There's a limit to how hard you can push without damaging the material your ship is made form (which you alluded to later). The fact that the shooter gets to push gently while the target is pushed hard is a large part of what makes it more damaging to get shot than to do the shooting. $\endgroup$ – anaximander Oct 19 '16 at 10:11
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    $\begingroup$ This is the only answer that actually addresses the real issue at hand. The answers above comparing the relative momentum of the projectile and the momentum of the ship would seem to imply that you can't actually damage your enemy's ship because you'll only impart a small delta v. $\endgroup$ – Shufflepants Oct 20 '16 at 15:55
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    $\begingroup$ I'm pretty sure this comment by anaximander is the only one that fully addresses the issue. @anaximander, Why not throw an answer in the mix? $\endgroup$ – jpaugh Oct 20 '16 at 17:00
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It's not specific to railguns. Railguns aren't magic. Rocket engines work exactly the same way - they throw mass at (relatively) huge velocities. So why doesn't a rocket engine break your ship apart?

First, there's the issue of momentum and inertia. Your is much more massive than the projectile, so the recoil only causes a tiny amount of change in the velocity of the ship - a small acceleration. This is extremely important in weapons like railguns (and impulse engines of any kind) - the energy of the projectile goes up with the square of the velocity, but the momentum only goes up linearly. And the conserved quantity here is momentum - so you can increase the energy of the projectile while keeping the recoil identical "simply" by making the projectile less massive. Mind you, energy isn't the only thing you care about with a projectile, but most sci-fi railguns don't care too much about the momentum of the projectile. Lasers are an extreme example - they fire "rounds" that move at the speed of light, but impart only an absurdly tiny amount of momentum (though not zero - you can use this to construct photonic drives or solar sails and the like).

Second, the force of the launch is much more spread out over time. You're accelerating the projectile through a barrel - and the length of the barrel is the difference between the impact of the projectile on the target and on the firing ship. If you have a barrel that's ten meters long, that gives you a lot lower acceleration than when the projectile hits a piece of armour.

Third, the force of the launch is a lot better spread over area as well. The guns are mounted in specially hardened parts of the hull, in their own weapon mounts which may have some sort of recoil compensation - for example, electromagnetic "springs", or throwing something heavy with the same momentum in the opposite direction of the launch. The biggest rail-guns in sci-fi are invariably in something called a "spinal mount" - basically a massive hardpoint going through the whole core of the ship. It's not a gun mounted on a ship anymore, really - it's more that the ship is just a few bits around the gun. Which also means that most of the mass is the gun itself, and the recoil is quite tiny in the rest of the ship (all that inertia stuff :)). There's a reason why those superweapon-kinds of railguns are so huge, and often spinal-mounted - that's how they can be so powerful in the first place. And mind you, a "superweapon railgun" might as well be a weapon that redirects asteroids to inhabited planets :D

In the end, you don't even have to think about railguns and spaceships, really. When you throw a rock at someone, you can cave their skull in easily, while your arm doesn't really get any damage. It's all about making the stress as small as possible on the attacker, while maximizing it on the defender - concentrating the round's impact in time and space.

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The basic run down of what's happening is that there is recoil, but the difference is in time.

Let's say you shoot something at a speed of 10.(obviously the numbers and units don't matter so ignore that.) The recoil is also 10. This is the same no matter whether you're using a normal cannon or rail gun.

With a cannon the 10 recoil is all delivered at T1 (or instantly) where as with a railgun, because of how it works, the recoil is delivered at T1, T2, T3, T4, T5, etc based on the number of magnets the round which equates to 10 divided by the magnets... to Recoil / Time.

So you still get the same recoil, it's just not felt because it is divided temporally, just like how ion drives work vs chemical thrusters. You can get the same velocities. It just takes longer with one over the other which impacts how you'd use them.

also, I didn't fully read it, but this should give a more in depth answer than I could ever: https://humanlegion.com/authors-notes/railgun-recoil-pt1/

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    $\begingroup$ What is conserved is momentum, not speed. What is different between the firing ship and hit ship is impulse, or change in momentum over time which determines the force of the interaction. The firing ship spreads it out along its firing tube, the hit ship instantly has to absorb the momentum. $\endgroup$ – John Meacham Oct 19 '16 at 1:36
  • $\begingroup$ True. I couldn't remember the words and I just was trying to answer the question of why the ship doesn't explode from the same force being experienced as another ship that does explode... $\endgroup$ – Durakken Oct 19 '16 at 2:11
  • $\begingroup$ So if the projectile is launched with zettajoules of kinetic energy, how long would the ship need to "cook" it to make firing it safe? Can the projectile continue to circle around a closed loop to build up speed, or do you need to loop thousands of kilometers of rail around the ship? $\endgroup$ – Z.Schroeder Oct 19 '16 at 2:27
  • $\begingroup$ @Z.Schroeder the magnets turning on and off is when the recoil happens. Each magnet has it's own small amount of recoil that boosts the velocity of the round. The recoil is minimizd even more by this looping because you are getting a recoil in each direction until it is launched which then has a small amount of thrust. The amount the ship that it can "cook" doesn't change, because you can accelerate to any speed without difference in that. The problem is in individual recoils from the magnets but railguns generally wont be using magnets that are that powerful. $\endgroup$ – Durakken Oct 19 '16 at 2:40
  • $\begingroup$ @Z.Schroeder imagine that each magnet is like an explosion when it comes on. This force will create a thrust. Each thrust will speed up the round and push the ship a small bit. The magnet on the opposite side will counter the push on the ship and speed the round up more. So long as this "thrust" isn't too much you're ok. The problem is that you need bigger thrusts to control faster speeds and the bigger the thrust the quicker the round gets to the launching velocity. Too big or too small and it won't work and the round will destroy the railgun. Look up the LHC and how it works. It's a railgun. $\endgroup$ – Durakken Oct 19 '16 at 2:47
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Because the ship is so much more massive than the projectile.

In Newtonian Physics, momentum is mass times velocity. Recoil is determined by the momentum of the projectile being fired and the momentum of the gun carriage (in this case, the whole ship). This is Newton's Third Law: for every action there is an equal and opposite reaction. Expressed in terms of recoil...

mpvp = −msvs

Rearrange it and you can see the ratios.

mp/ms = vs/vp

So a 1 kg projectile fired at 1000 m/s will cause a 1000 kg ship to recoil back at 1 m/s.

So if a ship with a mass of 5.5 teratons and a velocity of .1c fired a 100 kiloton projectile at .7 or .99c, the recoil felt by the ship wouldn't disturb it to any great degree?

Let's do the math. We need to solve for vs (recoil velocity of the ship).

mpvp = −msvs

mpvp / ms = −vs

Plug in the numbers...

ms = 5.5 × 1015 kg (5.5 teratons)

mp = 108 kg (100 metric kilotons)

vp = 2.1 × 108 m/s (.7c)

And we get vs of −3.818 m/s. The ship will hardly move.


BUT WAIT! That's Newtonian Physics. Momentum being mass times velocity is actually a simplification for speeds much slower than the speed of light. We're working at significant fractions of the speed of light so we need to account for the Lorentz factor. This changes things. Momentum increases exponentially as you approach the speed of light.

The full momentum equation is: mv / sqrt(1−v2/c2). How much of a difference does this make? Let's look at our projectile in both. Newtonian momentum says a 100 kT projectile at .7c has a momentum of 2.1e16 kg·m/s. But its relativistic momentum is 2.94e16 kg·m/s. A 50% increase.

At 0.99c the momentum is almost 10 times greater! 3e16 kg·m/s vs 2.1e17 kg·m/s.

Buuuut the ship is so massive compared to the projectile that means a change of roughly −30 m/s.

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  • $\begingroup$ The question doesn't ask how much would a hypothetical ship would move. The question, paraphrased, is; why wouldn't a spaceship rip itself to bits when firing? $\endgroup$ – user6511 Oct 19 '16 at 4:29
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    $\begingroup$ Isn't this an adequate answer though? Or does this answer not necessarily mean the ship won't be destroyed? $\endgroup$ – Z.Schroeder Oct 19 '16 at 4:34
  • $\begingroup$ I agree, this is only part of the answer. How quickly the projectile accelerates is the other. I should have noticed when the resulting units were expressed over time. Well, the momentum equations are still useful. $\endgroup$ – Schwern Oct 19 '16 at 4:39
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    $\begingroup$ Sidenote: The momentum equation is a slightly incorrect. $\Delta v_p m_p = -\Delta v_s m_s$ is more correct. Though it doesn't change the outcome of the maths by much. Edit I made a mistake too (fixed)! $\endgroup$ – user6511 Oct 19 '16 at 5:04
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    $\begingroup$ @JDługosz I thought it would be interesting to run the specific numbers from the OP's comment on your answer. I started to do it as a comment, but it got cramped, and I wasn't sure how it would turn out especially with the relativistic considerations. I thought it would have a greater effect. $\endgroup$ – Schwern Oct 19 '16 at 7:37
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Yes, most such weapons as depicted in fiction won't be viable.

The firing ship has a few advantages. They get to pick where the momentum and kinetic energy is deposited, while the target ship gets hit somewhere random.

They also get to accellerate the projectile over a slightly longer period and over a wider area; the length of the ship, if it is a axis-mount weapon.

But as the KE and velocity of the projectile grows, the time it has to cross the length of the ship goes to zero, which reduces the period it has to "soak" the momentum and KE of the projectile. It still can soak it over a longer distance.

Chemical bonds are limited in strength, and our conventional "matter" based engineering is limited by the strength of chemical bonds. If you accellerate a projectile to a significant fraction of c over the length of your ship, the time it takes is going to be bounded, hence the amount of momentum/energy required to be transferred per second will be bounded below.

Given the strength of chemical bonds, the amount of solid matter the projectile must be coupled with will be bounded below.

A magnetic launcher somewhat helps here, as you can push on/pull on the projectile from far away. However, there are falloff problems with magnetic fields, and near the projectile the slope of the magnetic field is going to be strong enough that no "stationary" matter is going to be permitted.

Eventually the competing "magnetic field slope falls off with distance" and "the field has to be very steep to get the accelleration we need" and "nothing can be close to the projectile and survive while stationary" are going to render the problem unsolvable, probably long before a large-fraction-of-c gun with a barrel modern-naval-ship-length order of magnitude could exist. Let alone finding a way for the crew to survive near the magnetic fields involved.

This then reduces you to fantasy physics.

One way to solve this problem is to spread accelleration over a longer period. Do a high velocity magnetic launch, then use lasers to keep on adding impulse over extremely long distances. Or, have gun barrels that are not single solid objects, but spread over an area of space the size of a planet or solar system or larger.

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Three reasons:

  • Recoil dampener / recoil buffer / shock absorber: We add a moving element on the ship, possibly inside the gun, which changes the lots-of-force applied by the gun over a millisecond to lots-of-force/1000 over 1 second.
  • Armor: We know where the lots-of-force/1000 is applied, so we design the ship to withstand it.
  • Mass: Compared to the mass of the weapons platform, the mass of the projectile is very small, which cancels out the high velocity. Thus, while the gun can serve to accelerate the ship, it's likely an inefficient drive (unless you select a big enough gun).
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Spread the force...

When materials are subjected to forces, what happens to them is determined by their properties - their strength (sheer, tensile, compressive, etc.), their brittleness, and other factors. If the force is below the threshold they can handle, then they can transmit that force externally, onto other things; if the force is too great, it causes changes internally, and the material fails.

In other words, if you push something gently, then it can pass that on to what's behind it; push too hard, and it breaks.

Spread across space

Weapons are mounted on hardpoints, which have two main properties:

  • They're made of something strong.
  • They're constructed in such a way as to spread any force applied to them across as much of your craft's structure as possible.

This reduces the amount of force that any one part of your craft takes, helping to keep it below that critical threshold. The important part, however, isn't spreading the force over more space - it's time that's key.

Spread across time

With a weapon like a cannon or railgun, you can accelerate the projectile gradually over a long track or barrel, applying force the whole time by the expansion of gas, a magnetic field, or some other means. This means you can apply a (relatively) gentle force, which adds up over time to give the projectile a very large velocity. This reduces the force that the structure has to support at any given moment while that projectile is being accelerated.

On the other hand, when that projectile strikes a target, the material of that target will be attempting to bring the projectile to rest in a much shorter time. Force is defined as the rate of change of momentum, and the time you spent giving the projectile its momentum is much longer than the amount of time it spends punching through an armour plate - the peak forces are much higher, and therefore more likely to exceed the threshold at which the material fails. This explains how your ship can be made of the same stuff as theirs, but theirs breaks and yours doesn't. By keeping peak forces low, your ship can spread the force out and experience the weapon fire as a slight push applied to the whole ship, while theirs has the force concentrated and experiences it as a hole being punched somewhere.

Spread across mass

Conservation of momentum says that the total "nudge" your ship experienced has to add up to the same amount of momentum as the shove that their armour felt, but because your ship spread it over more mass, it's less noticeable. A weapon whose recoil changes the velocity of a multi-tonne ship by a few metres per second might send chunks of debris flying out at hundreds of metres per second because the chunks have so much less mass. Of course, their craft may have similar mass to yours - or even more - but because they couldn't spread the force, that didn't help them:

  • Because the projectile came in at great speed, they weren't able to spread the force over more time. This meant that they exceeded the peak forces of their materials.
  • Because their materials failed, they were unable to transmit the forces further through the ship and spread them over space.
  • Because they couldn't spread the forces across more space, they couldn't affect a large enough of the ship to add up to much mass.
  • Because they couldn't spread the force over more mass, the pieces that were affected ended up with greater velocity, which means that those pieces will then probably hit other bits of the ship at great speed...

And so the whole thing happens again until the pieces are small and/or slow enough that the materials they're hitting can stop them. This is particularly important in space, where you're likely to be in vacuum:

  • There's no air to slow the pieces down, so this knock-on process is particularly effective
  • There's no air to carry a shockwave, so this process is your most effective means of spreading damage through the enemy ship.

This process of generating as many fast-moving chunks as possible so as to spread the damage is called fragmentation. Sometimes your projectile might be designed to shatter on impact, or even explode beforehand; other times it's just about striking in such a way that you maximise the fragments thrown off (perhaps by having a round that will tumble erratically as it passes through the target rather than punching through pointy end first).

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While both the firing ship and the target will experience the same change in energy (roughly, as there is still a minimum amount of friction in space), the way this energy is transferred is radically different.

On the receiving end, the transferral of energy is abrupt and near-instantaneous. This means that the applied Force is very large indeed.

On the sending end; the energy is applied over a trajectory, and therefore over time. This makes the Force at any instant much lower. Although it will definitely cause a backwards acceleration for the whole vessel, the material impact is much more limited.

The two material factors to keep in mind here when it comes to measuring the destruction of either party are Strain (Bend until it breaks) and Impact (punching a hole in a sheet of paper). Both of these are mostly uncorrelated. The defending ship will benefit most from a high Impact Resistance, while the firing ship will survive through its Strain Resistance.

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If you simultaneously fired another shot in the opposite direction the motions would cancel out and the shooter would not be perturbed.

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    $\begingroup$ No, the accelerations would cancel out, but the force would remain. It'd be like smashing a soda can with two hammers simultaneously rather than with just one hammer. $\endgroup$ – Telastyn Oct 19 '16 at 13:57
  • $\begingroup$ Well, it solves the issue of the railgun shot pushing your ship into a different orbit (which could, incidently, work as a propulsion mechanism too). As to the shot destroying the craft, I think thats a separate issue more related to material strength, structural integrity, barrel length, projectile mass etc. which others have addressed. There are many limiting factors on the size of the weapon, but it simply scales up when you add more handwavium in these areas. The issue of knocking yourself out of orbit is only solvable by counter shots, which hasn't been mentioned in other answers. $\endgroup$ – Innovine Oct 19 '16 at 17:36

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