# How to generate energy from recoil?

Yesterday I was reading through this question and it got me thinking: would it be possible on a ship or building mounted railgun to convert the energy from the recoil of the shot in order to partially recharge its capacitors for the next shot?

• This might be a question more suitable for physics.stackexchange.com – Philipp Aug 3 '16 at 18:46
• How about compressing a spring which then latches to stay compressed? A compressed spring can be later released against some resistance to drive some movement, doing work. (Think: wound-up watch). – Kaz Aug 3 '16 at 19:04

# No, you cannot

...or rather: you should not be able to do it. This is because if — after the shot — you have a significant amount of energy in the recoiling mass, then you have wasted energy that did not go into the shot.

But this is moot because your gun was attached to something really heavy, in your case a ship, or a building. This means there is no recoil energy worth speaking of.

Physics that explains why to follow...

## Conservation of momentum

Momentum is mass times velocity.

$p = m\times v$

Double the speed of an object, and you double the momentum. Halve the mass of an object, and you halve its momentum. And conversely: for any given momentum, if double the velocity, you halve the mass, and vice versa.

Recoil is a consequence of Newton's Third Law of Motion. In this context it means that whatever momentum you have imparted on the projectile, will also be imparted on the gun and whatever it is attached to, but in the opposite direction.

This means that in your scenario, immediately after the shot, the following applies:

$m_{shot} \times v_{shot} = m_{ship} \times -v_{ship}$

Since the ship is many times heavier than the shot, it means the recoil speed of the ship is the equal amount of times smaller compared to the projectile speed.

Say the projectile weighs 10 kg and the ship weighs about 50 000 000 kg (the heaviest battle ship in WWII weighed 72 800 tonnes, or 72 800 000 kg). That means that the recoil speed of the ship will be 5 million times smaller than the muzzle speed of the shot. So let us say this railgun lobs out a 10 kg shot at 2 500 meters per second.

This means the recoil velocity on the ship will be $0.5 mm/s$ (1/50 inch per second).

Using $E = \frac{mv^2}{2}$ to calculate the inertia of the ship, we find that the energy available for you to recover is...

drumroll

...$6.25 J$, or 0.0015 kcal. This is less than the energy required for you to stand up from a sitting position.

The corresponding energy in the projectile is 31 250 000 Joule. Those 6.25 Joule recoil energy are meaningless is comparison. The astute will notice that the ratio between these energies is the same as between the masses.

In case your railgun is sitting on a building, then the mass of the gun and its fixture is even higher (especially if you count the Earth itself as part of the fixture) and then the mass becomes so ridiculously large compared to the projectile that the recoil energy is so near nothing it becomes entirely irrelevant.

So in conclusion: no, there is no energy for you to recover. And that is good, because as much energy as possible should go into the shot. Putting energy into the recoil instead, and then trying to recover that — with the inescapable losses of energy that will follow — and then putting that into the next shot, would be nothing but a huge waste.

• However, if you take into account the hydraulic recoil mechanism used on the guns of the ships, you have way more energy to work with. – SMS von der Tann Aug 3 '16 at 14:02
• @SMSvonderTann That would not be applicable to the rail gun because the recoil dampener is needed to catch the energy from the mechanism that smooths out the recoil when using explosive propellants, taking the peak off of the recoil forces. In a rail gun the recoil is already smooth and even. And in any case the main point is still that as much energy as possible should go into the projectile and not be converted to recoil, then to electricity, then stored, then converted to inertia. You just lose energy in every step. – MichaelK Aug 3 '16 at 14:08
• @MichaelKarnerfors It may still be applicable if the force on the gun mounts from the rail gun firing is high enough to potentially damage them, or if there is enough force to cause barrel movement. In either case, a mechanism allowing a small amount of recoil could be helpful in prolonging component life or improving accuracy. – ckersch Aug 3 '16 at 14:21
• This is pure speculation, but I wonder if there might be value in using a recoil mechanism to avoid passing high frequency transients through the hull of the ship. Smoothing out the recoil before transmitting it to the ship (and thus giving a meaningful place to capture energy) might be beneficial from a maintenance perspective. – Cort Ammon Aug 3 '16 at 21:37
• @CortAmmon That is the general purpose of recoil dampeners, yes. – MichaelK Aug 3 '16 at 21:38

You can definitely recover kinetic energy using some sort of system, like a kinetic energy recovery system (aka KERS) used on some racecars when braking. That's called regenerative braking (thanks to @JohnDallman for the tip). If you have a racecar, you can store that recovered energy into a flywheel or a supercapacitor to reuse it later. If you're driving a Prius, it's most likely used to charge back to the battery a tad. Some cars can also recover energy on a down slope.

However, since we live in an imperfect world, you will only recover a fraction of the energy used to fire a shot. Firstly because some of that energy went into the projectile. Secondly because there's always waste, typically in the form of heat. Thirdly because converting one form of energy into another one (here kinetic to kinetic to electric) isn't 100% efficient either.

tl;dr: You can recover some of the energy, but you can most definitely not recover it all.

• The general kind of system used to do this is a regenerative brake. – John Dallman Aug 3 '16 at 12:04
• @JohnDallman I always only am able to remember KERS. I'll add that to the mix, thanks. – AmiralPatate Aug 3 '16 at 12:26
• Practically you can't. As explained in this answer. – Fermi paradox Aug 4 '16 at 6:20
• @Fermiparadox I'd say it's more that you may not have any significant amount of energy to capture. That largely depends on the gun, the gun carrier and how the former is mounted on the latter. In the absolute, you can, but YKMMV as to how pointless it is or isn't. – AmiralPatate Aug 4 '16 at 6:52
• @Fermiparadox But there's also a cost to that in terms of mechanical stress. – AmiralPatate Aug 4 '16 at 8:14

Using Michael Karnerfors' answer as a basis for the numbers, only instead of directly attaching the rail-gun to the ship so that everything moves as a whole, attaching the gun to a flywheel (or something similar), which is then connected to the ship so that only the gun moves (and the flywheel rotates) so that KERS can be used as in AmiralPatate's answer allows for the kinetic energy of the gun to be recovered:

Note: This answer takes the rail-gun to be intrinsically 'not the ship', so that the gun will move regardless of how it is attached. While it could also be completely built in to the ship (or built into the ground) so that it cannot turn/move independently of whatever it's on, in which case Michael Karnerfors' answer applies completely, we like our guns to be able to do things like turn and maybe even move independently of whatever it's placed on.

Taking the mass of the rail-gun to be $~1.5\times 10^5kg$ as in here, gives the speed of the railgun immediately after firing as $v = \frac{2.5\times 10^4}{1.5\times 10^5} = \frac{1}{6}m s^{-1}$, which gives a kinetic energy of $$KE = \frac{1}{2}\times 1.5\times 10^5\times \frac{1}{36} = \frac{6250}{3}J$$

At this point, there are two options: either the gun can be directly attached to the ship without any recoil and whichever method used of attaching it needs to withstand the large stresses that this creates or some recoil system can be used to help prevent these stresses. Using the recoil option allows for KERS as well as decreasing these stresses, which decreases damage done to the ship/the mechanism that attaches the gun to the ship. Otherwise, the resulting reaction force that exists as a result of the projectile leaving the gun will cause a torque that results in a stress on the mechanism that attaches the gun to the ship. Using something that decreases this force (something that dissipates recoil) decreases this stress and so decreases the damage done to this mechanism.

To forestall the argument about needing to put as much energy into the projectile as possible, I'll point out now that the momentum and energy of the projectile are already well defined and the mass of the overall system or how the gun recoils doesn't change this. It does increase the amount of energy needed to be put in the system in the first place, but we want the gun to move around a bit, so it'll have to have some recoil in this case anyway (as well as for the above reasons).

In any case, the energy required to fire said projectile is $3.125\times 10^7J$, about 4 orders of magnitude greater than the recoil of the gun, so, while KERS can be used in principle, in practice, there is no real point. Decreasing the mass of the gun is pointless as more energy is needed overall.

However, there are large amounts of excess heat generated and large amounts of electricity used in a rail-gun, so there may be other ways of regenerating some of the used energy. Having said that, rail-guns that have been created so far have a tendency to get heavily damaged, so allowing the guns to move might decrease the amount of damage caused to the guns.

## In summary:

It is possible to use energy from the recoil to partially charge the capacitors, but in practice, you're recovering less than 0.1% of the energy required to fire the next shot, so there's no real point unless it decreases damage done to the gun

• Note also that the only reason of using energy in a rail gun is to convert that energy into kinetic energy of the projectile. With this trick (assuming other efficiency factors remain constant), the increase in the kinetic energy that goes to the gun is essentially obtained by decreasing the kinetic energy that goes into the projectile by the same amount. (Michael Karnerfors's answer also refers to this in the beginning.) So not only you recover less than 0.1 % of the energy required to fire the next shot, you also increase the energy required to fire a shot by the same amount. – JiK Aug 3 '16 at 15:48
• @JiK Yes, more or less, but that's exactly why I've written the bit about the option of allowing for recoil or not - if you directly attach the gun to the ship without some form of recoil dissipation, you're just causing stress to the attachment mechanism, which just causes damage. To put it another way, if you don't explicitly put that in, then the energy's still going to be there, only it's going to be going into the mechanism that attaches the gun to the ship, unless the gun is 'intrinsic' to the ship. i.e. the only way to turn the gun is by turning the ship – Mithrandir24601 Aug 3 '16 at 16:04
• @JiK I've made an edit that hopefully makes this clearer, as it's the very reason I wrote this answer – Mithrandir24601 Aug 3 '16 at 16:16

Don't forget that the principle of the machine gun is to use energy from the recoil to move another round into the barrel. I imagine that future weapon designers will have that concept in mind as well.

• That amount of energy is tiny compared to the energy that goes into the shot. – MichaelK Aug 3 '16 at 13:15
• @MichaelKarnerfors Yes, that's because the amount of energy involved in recoil in general is tiny compared to the energy that goes into the shot. – Random832 Aug 3 '16 at 15:59
• @MichaelKarnerfors that is actually not correct. According to Newton's third law, For every action, there is an equal and opposite reaction. The amount of force applied to the projectile is also equally applied to the firing mechanism. The difference is that the firing mechanism has a great deal more mass, and therefore the force does not have the same effect. If a 1kg firing mechanism fired a 1kg projectile, both the firing mechanism and projectile would experience the same acceleration in opposite directions. – DVK Aug 3 '16 at 16:48
• That depends on how you count the energy. When you compare the kinetic energy of the projectile with the kinetic energy of the firing mechanism, then it will be exactly 1:1. But when you count the energy used to accelerate the projectile and that acceleration process is not 100% effective, then you will have less recoil energy than you invested. – Philipp Aug 3 '16 at 18:24
• @DVK and Philipp.... read through my answer above please. Right now you are either repeating or ignoring what I said in it. – MichaelK Aug 3 '16 at 21:06

It's possible, as other answers indicate, to convert kinetic force into electricity, so I won't repeat that. But what you should think about is the cost-benefit ratio. The truth is, it's not feasible to add the complexity of an extra subsystem to an already ridiculously complex system. Think of the amount of electricity it takes to accelerate anything to several times the speed of sound. Power savings from a kinetic converter would simply be insignificant.

you don't have to harvest the KE. the heat generated by rail guns is substantial. simply add peltier panels or use liquid cooling diverted to a sterling engine to harvest 30% of the waste heat. apparently because railguns can accelerate things to 3 km/s, the heat from friction of both the amount of electricity flowing through coils and the friction of the projectile is substantial.

• Railguns work by reducing friction using electro-magnetics. – Durakken Aug 4 '16 at 2:52
• welcome to SE! Technically, this isn't what the question is asking, but it is a much better idea than this argument over how things are mounted and damage done to these mountings and worrying about restoring small amounts of energy... @Durakken These electromagnets are what generates the large amounts of heat – Mithrandir24601 Aug 4 '16 at 8:31

I also read the question you're quoting. Well after reading it, I think that yes, you could generate some energy from recoil, however, not much.

It's quite easy to guess you can produce energy with it, just like our cars generates energy for the battery while we drive, or just like automatic/semi-automatic weapons use the movement when firing to load and fire another bullet. The difference with such gun, is that the recoil it generates can't be compared with a rifle's recoil, or a wheel movement.

As stated in that answer, to allow a 1 GJ tank with a small size in regard to a cannon like the German super heavy artillery, most of the recoil energy must be redirected somewhere. Some would be absorbed by the hull, some could be redirected into the ground, and some would be redirected in shock absorbers.

You might say "Then manage to make everything go into that shock absorber ?" Well we can do that, provided it can resist the recoil. Then we'll need to convert the recoil energy and here lies a problem, we can't convert 100% of that energy. The main problem is : you don't want what you use to convert recoil into energy to tear apart, destroyed by that energy, so you'll need to soften the recoil, or to spread the energy between multiple converters, losing energy in the process each time. If you had a continuous flow of energy, totalling 1GJ, converting it wouldn't be a problem, no, but converting at a time T a huge amount of energy is clearly harder.

Of course, on top of that problem, remember that a mechanical converter can't convert 100% of what it receives. As I imagine that gun, I think its shock absorbers could work somehow like pistons activating alternators, and that would imply a loss of energy at each movement.

Other kind of converters doesn't seem to me better suited for this, using the heat from that gun could work but wouldn't generate a lot of energy, same thing would apply to radiation or to the blast of the canon itself.

So perhaps you could use the energy from that gun to supply some systems like computers for a while, but it would most likely be negligible compared to what you need to fire with that beast.

• Really, that thing about being attach to a ship or building meaning there's not energy to gain... This is not true. Your canon is not attached to a fixed structure, otherwise the recoil would just damage that structure. Your gun need to be mobile, be it put on some rails, or have it something to absorb the shock. BUT it can't be fixed !!! Please, just try to shot with a rifle. If you do it the wrong way you'll break your arm. The same thing apply with a big 1 GJ gun, and a ship. – Kaël Aug 3 '16 at 13:12