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Not a tank that could survive being shot with a 1 GJ railgun (pretty sure nothing can survive that), but a tank that can withstand the recoil of a 1 GJ railgun that's been mounted to it.

Obviously, a way to anchor it to the ground is in order to keep it from flying away is required, but what about the frame itself actually withstanding the force? Could the vehicle survive if the barrel and all of the tank's moving parts were made from sheets of a 2d supermaterial like graphene?

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ How about some sort of track the weapon mounts on? Give it 6' of recoil travel where the transfer could be transferred into the frame over time. This would drastically reduce the stress on the materials. $\endgroup$ – Nex Terren Aug 1 '16 at 19:09
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    $\begingroup$ For reference of answers, 1 GJ of energy is equivalent to roughly 0.25 tons of TNT. $\endgroup$ – Delioth Aug 1 '16 at 19:24
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    $\begingroup$ If the 1GJ is used with perfect efficiency to get a slug of negligible mass ( <10 micro grams ) to almost the speed of light the recoil force is 3Ns or 3*10^7 N ( 3000 tonnes) for 10^-7 s for a 15m rail. $\endgroup$ – Donald Hobson Aug 1 '16 at 19:55
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    $\begingroup$ Disposable barrel. The railgun shots comes pre-packaged with barrel and shot as one unit. $\endgroup$ – MichaelK Aug 2 '16 at 9:17
  • $\begingroup$ On the topic of a tank surviving a 1Gj railgun strike - if you ablated the round with a laser point defense system more powerful and fast than the ones we currently use to detonate mortars in-flight, and then equipped your tanks with skirt armor and high-performance electric ERA (en.wikipedia.org/wiki/Reactive_armour#Electric_reactive_armour) behind that, you'd probably be able to withstand the railgun strike. Unless, of course, the railshot was precipitated by a laser shot that blinded defensive ADS and ablated skirt armor and ERA... :DDDDD $\endgroup$ – Adam Wykes Aug 2 '16 at 21:07
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SCIENCE

The value with which you must be concerned when designing against recoil is not energy but momentum.

The Kinetic Energy of a projectile is formulated with the equation:

enter image description here

where E is the kinetic energy, m is the mass of the projectile and v is the velocity.

Momentum, on the other hand, is calculated using this similar equation:

enter image description here

where p is momentum (from the Latin petere, or impetus), m is mass, and v is velocity.

The change in momentum of an object is known as Impulse. The Impulse-Momentum theorem and the Conservation of Momentum are largely used to calculate scenarios involving Newton's Third Law of Motion (Equal but Opposite Reactions, or Recoil if you prefer).

So Kinetic Energy and Momentum are clearly very similar values, but they are not quite the same. Specifically, if you have two guns that fire different projectiles, one is fast and light and the other is slow and heavy, the energies might be the same but the recoil will not be the same, or vice versa. This is due to the velocity squared we see in the Kinetic Energy equation. This means we need to define our projectile exactly in order to properly analyze this problem.

HISTORY

Now, with that out of the way, we can look at some history. There have, in fact, been weapons (projectile weapons, even) that have delivered kinetic payloads on the same order of magnitude as your railgun. Specifically, the Schwerer Gustav railway cannon used by Nazi Germany could deliver a payload of about 1.8 gigajoules (v = ~720 m/s, m = ~7100 kg). The recoil the weapon would experience was about 5,112,000 newton-seconds (a unit we don't really need to care about too much).

The astonishing energy delivered by the Great Gustav was largely achieved due to the massive projectile, and not so much due to the speed of the projectile. In theory, we could definitely reverse those attributes and launch a small projectile at hypersonic velocities. If we had a muzzle velocity of 1% the speed of light, for example, the projectile would only need to weight like a milligram to deliver a gigajoule of energy. Unfortunately we have an issue in this regard.

It turns out there is an upper limit to velocity while inside the atmosphere. Atmospheric Heating will literally vaporize things travelling too fast (which is one of the many reasons you can't launch satellites into space with a railgun). The fastest you can reasonably go is about 7000 m/s. Even at this speed most materials will vaporize too quickly to be useful, but super dense materials like Uranium or Iridium will survive well enough. With this speed as the upper bound, if we wanted to strike with 1 gigajoule the projectile would have to weigh about 40 kilograms. That's not super unreasonable, especially considering Great Gustav's shells weighed 7 tonnes.

With these numbers in mind, we can figure out how much impulse the railgun will produce when it fires: 280,000 newton-seconds. Compared to Gustav's figure, that number is paltry. To compare some others, the Mark 7 16"/50 guns aboard the Iowa Class Battleship produce a little over 1,000,000 newton-seconds of impulse. The primary weapon of the Abrams MBT produces about 10,000 newton-seconds of impulse.

So what does all this mean? In my opinion, a 1 gigajoule railgun would need to mounted aboard a small ship, or perhaps a very large self-propelled artillery piece (I'm fairly confident weapons like the M110 Howitzer produce similar recoil, but I could not find any definitive ballistic data). Large stationary artillery would also work, but such weapons were never really effective.

If I forgot something, or there is data I missed, please let me know!

EDIT: Turns out the M110 Howitzer produces about 50,000 newton-seconds of impulse, so I was actually mistaken about the magnitude of the recoil involved. This suggests a self-propelled artillery piece with our hypothetical 1GJ weapon will need a carriage much larger than used with the M110. I doubt it will need to be 5x bigger to manage the 5x recoil, but it will need to be significant.

EDIT 2: Ok one more edit! I found a weapon with a very similar recoil value: the German 28cm/45 SK L/45 Naval Gun. It generates an impulse of about 260,000 newton-seconds, which is close enough for our purposes. That link contains most of the relevant ballistic and dimensional data, but the long and short of it is that a weapon that size is usually mounted on a large ship (in this case it was the primary armament of some of Germany's Dreadnought-era capital ships) or as a fixed artillery piece (shore defense or railway cannon). In my humble opinion, it would be very difficult to mount this cannon on a tank, but at least some of that difficulty will be a result of the gun's weight. Our railgun will not have the same kinds of weight restrictions as a traditional cannon, though, so I think it's still feasible, especially if we're using modern materials and techniques.

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    $\begingroup$ At 7000 m/s any impact will cause strange effects, like building up a plasma bubble at the point of impact out out of vaporized material from the projectile/target. This will have the effect of dissipating the momentum of the shot and making the damage more superficial. I suggest that a more effective rail gun would be weighted more to momentum, to carry the projectile into/through the target for maximum carnage. The Navy rail gun is targeting Mach 7, or 2500 m/s. At this speed, your projectile is 320 kg and has 800,000 N/s of impulse. Will need a battleship sized object to handle the recoil. $\endgroup$ – kingledion Aug 2 '16 at 16:35
  • $\begingroup$ @kingledion That's interesting. I couldn't find much data on impacts at that velocity. Thanks for the addition! $\endgroup$ – MozerShmozer Aug 2 '16 at 16:38
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    $\begingroup$ I said it like a fact, but the plasma thing is mostly theory, since there isn't much data on impacts that fast. Still 1 GJ is a hell of a lot of energy. My back of the napkin math says it is 0.7MJ to raise 1kg iron (close enough to steel) to melting point, 0.3MJ to melt, 1MJ to raise to vapor point, 6MJ to vaporize. I can't figure out hot hot exactly iron plasma will be, but to heat it to 15000K is another 6MJ. So 14MJ to make a sizable plasma bubble on impact; its easy to imagine at least 14MJ turning to heat out of a 1GJ impact. $\endgroup$ – kingledion Aug 2 '16 at 16:55
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    $\begingroup$ I do believe that it could be made mobile as a "tank" rather than being stationary. An Abrams, with it's 10,000 newton seconds of recoil, weights around 60 tons. The WWII era Panzer Maus weighed in at 280 tons. If we extropolate, something the size of the Maus should be able to handle 46,000 ns with equivalent recoil dampening technology to the Abrams. That's roughly 1/6 of your estimate for the railgun, but you have different factors, with recoil being more instant, not spread over the length of barrel travel with the conventional cannon. I think it could be mitigated. $\endgroup$ – JBiggs Aug 2 '16 at 18:07
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    $\begingroup$ There is a mismatch in your data. According to Wikipedia, the Gustav could fire 2 projectiles: High Explosive, which weights 4800kg at a velocity of 820m/s; or Armour Piercing, which weights 7100kg at a velocity of 720m/s. So for HE rounds, the kinetic energy would be around 1.6 GJ and AP about 1.8GJ. $\endgroup$ – Bruno Ferreira Aug 2 '16 at 19:46
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You might be surprised to hear this, but there are have been weapons IRL that have fired projectiles with 1GJ+ muzzle energy.

The best way I can think of to make something the size of what you're describing not get blown away by the recoil of its own weapon is to give it a VERY long barrel for the projectile to accelerate down. This is a losing proposition eventually, the velocity (assuming the same force pushing all the way down the barrel) only increases by the square root of the length.

The second option I can give you is that you could fire a VERY light projectile. muzzle energy increases with the square of the velocity, so if you halve the weight of the projectile, you could (in a perfect world) get double the muzzle velocity, which in turn gives you 4 times the muzzle energy.

Real world problems of having an extremely light projectile: drag will slow it down very fast so you wouldn't have very much effective range, secondly is that mass is very helpful to have when you want a projectile to penetrate material.

If you are content with just disintegrating smaller objects, the small projectile scheme works well since that energy gets converted into basically an explosion on whatever gets hit, but don't think that it would punch a hole through feet of steel, it would just wreck the outside of it.

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    $\begingroup$ "..there are have been weapons IRL that have fired projectiles with 1GJ+ muzzle energy.." Cite some examples. $\endgroup$ – RBarryYoung Aug 2 '16 at 14:15
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Build a shell that is a vacuum container, so the mass spins inside it. Put most of the 1GJ into projectile spin before you launch it. Then you can launch it with conventional velocities, so it hits the enemy 5 miles downrange instead of flying past the moon and hitting Jupiter's rings 3 years later.

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    $\begingroup$ This is basically a weaponized flyweel, while it is clever in the sense that it conveniently delivers large amounts of energy without the linear velocity problem, it needs some more effort put into it to actually work; with a single flywheel you will never be able to guide it as gyroscopic effects will put it off-course very (very) quickly at the slightest lateral acceleration. You can correct with two flywheels spinning in opposite directions, but there will be a residual higher-order effect you will need to account for, possibly with active guidance. $\endgroup$ – Thomas Aug 2 '16 at 6:34
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    $\begingroup$ just place some explosives as usual. 250kg tnt if roughly 1GJ $\endgroup$ – MolbOrg Aug 2 '16 at 13:31
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One nice thing about a railgun is that, unlike explosive propellant, the force is not transferred to the projectile all at once, but along the entire active length of the rail. So the longer the active acceleration distance, and thus time, the less force you need for the same ending velocity. (so less force per unit time on the tank)

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    $\begingroup$ I am sorry but what you just said is just not true. The projectile keeps accelerating down the length of the barrel, which means the recoil is there as well. And when the projectile leaves the barrel, you can use the hot gasses to dampen the recoil. If what you said was true, then the forces would be near infinite, which would break every gun that used explosive propellants. $\endgroup$ – MichaelK Aug 2 '16 at 8:00
  • $\begingroup$ @MichaelKarnerfors The recoil is there but it is not instant as you would get from a traditional explosively powered projectile. The impulse is spread over a longer time. $\endgroup$ – Trotski94 Aug 2 '16 at 12:10
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    $\begingroup$ @JamesTrotter As I just said: it is not "instant" with explosive propellants either. If it was the gun would be ripped to pieces. $\endgroup$ – MichaelK Aug 2 '16 at 12:12
  • $\begingroup$ Your statement not totally true, but even if it is - 1GJ means 100kg projectile at speed 3333m/s. So for 1sec redistribution of that force - it have to have 1500m launch track - not sure it fits in description of a tank - as a mobile system. $\endgroup$ – MolbOrg Aug 2 '16 at 13:24
  • $\begingroup$ @MichaelKarnerfors I didn't say in zero time, I said all at once. The explosive is a single event, the time rate of change of the acceleration is steeply downward; whereas a railgun has a continuous/constant acceleration the length of the barrel. $\endgroup$ – Seeds Aug 2 '16 at 18:16
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Having the frame survive the recoil is not such an insoluble problem, you basically have to transfer the recoil shock out to something external to the tank. Modern MBTs are usually made out of steel (covered in layers of other stuff) that approaches a foot thick. Historically, we have seen tanks and other vehicles made of significantly thicker steel than that. It is not impossible to make the frame effectively one piece, not deformable, and capable of transferring recoil away from the tank's body.

There have been tanks built that exceeded 100 tons, and mega artillery that was considerably bigger than that, so it is possible to build something that could carry such a gun, but it would obviously be very heavy and slow.

Large, self-propelled artillery (like the Russian 2s7 Pion SPG) use a blade like a bulldozer (Called a "recoil spade" -thanks, T) at the back of the vehicle to transfer recoil into the ground. The SPG stops, deploys the hydraulic blade, raises the barrel, and goes boom. Shock is transmitted directly into the ground below the vehicle. Your tank could do the same thing, but would obviously not be able to move and fire at the same time.

Alternately, you could devise some sort of rocket-like device that would fire on the back of the tank turret at the same time as the railgun. That would mitigate recoil but would have a limited fuel supply.

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    $\begingroup$ The word you are looking for is "recoil spade". $\endgroup$ – Thucydides Aug 2 '16 at 1:58
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    $\begingroup$ Ah HA! There you go. I was infantry, not artillery, so everything bigger than an 81 mm mortar is beyond my immediate experience. $\endgroup$ – JBiggs Aug 2 '16 at 17:36
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Odds are anything that has that much power will not be mobile...a tank that can handle that just can't exist as we currently understand the word tank.

The energy requirements and the impact/stress of such a weapon necessitate that it be stationary. A tank simply doesn't have the weight and structural integrity to handle that much force.

Additionally the power requirements mean the tank would have to carry around multiple times its weight in batteries/capacitors to fuel the cannon (I don't know the math specifically)

Something putting out 1GJ of force has to be able to offset that...a tank would go flying through the air from the recoil.

You could build artillery style and put the whole thing on some sort of modified train rails so it is held down and allowed to slide back after firing.

Graphene isn't a great idea. Strong yes, but relatively brittle. The frame materials will need toughness and strength. Steel for example has arguably the best balance of toughness and strength.

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    $\begingroup$ I seriously doubt that .25 tons of TNT would send a modern MBT "flying". Modern tanks get up to nearly 70 tons. Something built for a very large railgun would probably approach the size of the WWII Panzer VIII Maus (188 tons). Remember, we were able to make things close to 200 tons basically mobile back in WWII. We have much better suspension, materials, and power technology now. $\endgroup$ – JBiggs Aug 1 '16 at 19:33
  • $\begingroup$ @JBiggs I had an orders of magnitude brain fart...editing $\endgroup$ – James Aug 1 '16 at 19:34
  • $\begingroup$ As a side note: 1 GJ is a measure of energy, not force. $\endgroup$ – ckersch Aug 1 '16 at 21:48
  • $\begingroup$ With modern technology, it is possible to beam energy from an external source to the firing unit, so the mass of the tank (or drone aircraft, for that matter) could be quite reasonable. Probably the bigger issue is the length of the railgun itself, which will be difficult to reconcile with a traversing turret or even a moving vehicle (turning corners in a built up area or having the muzzle strike the ground in hilly or rolling terrain). $\endgroup$ – Thucydides Aug 2 '16 at 2:01
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For tanks, this will be tricky, as you'd want the gun to be loaded from the inside. This is clearly not going to be possible, due to the high currents involved in the initial burst. In fact, it'd probably be advisable to raise it well above the passenger area of the tank, to prevent accidental electrocution by induced currents.

Since you must mount it outside anyway, your vehicle becomes less like a tank and more of a motorized ladder. That being the case, to improve your stability, mount your ladder on a non-conducting surface on the ground.That way, as long as your gun is pointed above the horizontal, the reverse thrust will act to drive the non conducting base into the ground, from where it will have to be dug up. In short, you can mount a 1GJ railgun on a tank, and the tank won't break apart/fly away when the gun is fired, except that it will be more of a single shot rocket launcher. Apparently the rails can't take more than one shot.

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  • $\begingroup$ Good points. I do believe that conventional projectile propellants do not actually "explode", they are designed to burn. Cordite and similar chemicals are designed to burn very fast, which very rapidly fills up the firing chamber of a gun with gas, etc etc. Just a technicality, but I was once taught that if we used chemicals that ACTUALLY explode, it would be a whole other ball game to keep a typical rifle together. (Of course, I have heard of "dynamite guns" and even the use of a nuclear blast to propel a projectile in a super gun, so maybe it's semantics). $\endgroup$ – JBiggs Aug 2 '16 at 17:42
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    $\begingroup$ Two points, just because you are pulling instead of pushing doesn't mean there is no force acting backwards, please review Newton. Force is acting to move projectile in one direction, there is force equal and opposite. Secondly, there is no reason for a railgun to have a barrel, per se; just needs a track, keeps the projectile oriented, and some electromagnets to motivate it. $\endgroup$ – Seeds Aug 2 '16 at 18:37
  • $\begingroup$ @JBiggs: Not sure if there's a technical definition. I used explosion in the sense "loud noise caused by rapid expansion of gas" $\endgroup$ – nzaman Aug 2 '16 at 19:20
  • $\begingroup$ When the magnet pulls the projectile, the projectile will pull the magnet as well, with the same force (but opposite direction). Which means you still need to "fix" the tank to the ground sufficiently so it doesn't get blown or at least shoved away. $\endgroup$ – Guntram Blohm Aug 2 '16 at 19:37
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    $\begingroup$ @nzaman, As I said, no barrel is required, and that has nothing to do with the physics. The total force exerted backward will equal the force used to propel the projectile forward. Additionally, I am not sure why you think there is air rushing into a gun barrel. $\endgroup$ – Seeds Aug 2 '16 at 19:37
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Recoil is essentially impulse, and impulse is essentially Force/Time. To reduce recoil, I can reduce the force, or I can increase the time over which that force is applied. Twice the time, half the recoil, four times the time, quarter the recoil, and so on.

Suppose I apply, say, 1GJ of energy total to push my broken down car. If I apply that all at once (One mother of a punch) I'm going to explode both my hands and my car. If I apply that over a half hour, everything is fine.

Now Imagine mounting your railgun in a very long cradle. The tanks barrel isn't so much a barrel as it is a very, VERY long recoil dampener with the gun inside. Perhaps the barrel/cradle is 40 feet long and pokes out both ends of the turret. As it fires, the actual railgun slides backwards, 'gently' decellerating and slowly transferring its energy into the chassis instead of delivering a single earthshattering blow.

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