# Why can electric cars recoup energy from braking, but a spaceship cannot?

It is said that in a spaceship, you need to spend as much energy to brake as you spent for accelerating. An electric car, however, charges its batteries while braking, thus it actually recovers energy by braking.

Both facts somehow seem intuitive to me, but aren't these two observations contradicting each other?

Looking at the answers, I realize the quastion might not have been clear enough. So let me pose the question in a different way:

Do you absolutely need an outside object moving at a different speed (the road for a car, slamming into an atmosphere as a space ship) to convert kinetic energy into another form? What is the fundamental principle?

• Mar 9 '17 at 9:52
• Just a reminder: Comments are not for giving answers. If you want to say something that answers the question, type it into the answer box. Comments are for clarifying and improving the question. Mar 9 '17 at 13:54
• Spaceships in the Star Trek simulation game Star Fleet Battles could recoup energy when decelerating, if they were equipped with a "positron flywheel" device, though it was an optional rule. ;-) Mar 11 '17 at 21:45
• Mar 11 '17 at 23:36

## The main point is that the space-ship is a closed system and the car is not

Consider that to conserve momentum we need to give something else the momentum our decelerating object had before.

• In the case of the space-ship this requires ejecting something in the opposite direction to the direction of travel. We need to put energy in to do this.
• In the case of the car we have been connected to the road the whole time and because of this friction we need to continuously provide energy in order not to decelerate. So our wheels are turning and because of the connection with the road friction will decelerate us, what electric cars do is to add an extra resistive force to the turning of the wheels (which is needed to keep going) and make use of the energy gained from this.

So because space-ships don't require any further thrust to maintain a constant speed we have no process to steal the energy from. If you could provide a resistive force on the space-ship you could regain some of the energy but it would have to be outside the space-ship (a magnetic field emitted from a series of space stations for example).

You have to be moving relative to something else which you can impart energy to.

• By the way, some satellites actually do use the Earth's magnetic field in this manner, except in reverse: by running electricity through a coil, they can generate torque for attitude control. Mar 8 '17 at 22:09
• "So because space-ships don't require any further acceleration to maintain a constant speed we have no process to steal the energy from" I'm not sure this is correct. Assuming a car travelling in a vacuum with no rolling resistance (i.e. perfect axels but still high resistance between the wheels and ground), are you saying that car could reclaim zero energy when breaking. I believe its more about having something to lend and reclaim the energy from/to; the earth Mar 9 '17 at 13:37
• What about gravity assists? Can't you use them both for braking and acceleration? Mar 9 '17 at 16:18
• @RichardTingle, I am sure it is incorrect. Whether there is some force when not decelerating is irrelevant (and when decelerating, you need it either way); it is only relevant where you can transfer the momentum. Mar 12 '17 at 21:26
• @Jan Possibly it's British over-subtley. What I meant was "I have a masters in Physics and this is definately wrong" (although has elements of correctness, drop all the stuff about "requiring further thrust to keep going being neccisary and it would be much improved) Mar 12 '17 at 21:57

There is one particular omission in the existing answers that I'd like to rectify.

It is that there is a very special context in which you can do the problem, which answers the question in the affirmative with very little actual effort. In this reference frame the travelling spaceship appears to start at rest and then starts moving backwards.

# Reference frames

Modern physics generally recognizes that you can do the same physics in a bunch of different frames of reference which are related by some sort of transformation group. You may choose any frame you like, they all give the same physics. In classical physics this is done by the Galilean transformation $$(\vec r,~~ t) \mapsto (\vec r - \vec v~t,~~ t),$$ for any constant velocity vector $\vec v.$ As you can see, anything which is moving forwards with velocity $\vec v,$ having $\vec r(t) = \vec r_0 +\vec v ~ t,$ is suddenly stationary with respect to us after performing this transformation: that is a nice way to see "oh, this corresponds to moving forward with speed $v$ relative to my prior situation."

Since we're talking about a spaceship you might wonder if the strange rules of relativity will mess with this explanation, but in fact they won't. Actually, for small velocity changes special relativity only changes this an insignificant bit: instead of that Galilean transform we instead must use$$(\vec r,~~ t) \mapsto (\vec r - \vec v~t,~~ t - \vec v \cdot \vec r /c^2).$$ The only catch is that any "big" acceleration needs to be made out of a lot of these little accelerations, which didn't matter for classical physics when the $t$ component kept its fixed identity, but now matters a lot more when you have both components intertwining. But I promise we won't be using these strange little simultaneity shifts in the following talk.

# Our special reference frame

Anyway, the point is: all of the laws of physics are perfectly valid in the reference frame that travels alongside the spaceship once it is moving at its cruising speed, and they are perfectly valid in the reference frame that travels alongside the car. And the laws that we're interested in are the laws of conservation for energy and momentum.

Now think of what "braking" looks like in this reference frame: it looks like the spaceship/car which was at rest, now starts moving backwards. So it gains kinetic energy where it previously had none, and gains momentum where it previously had none.

But what do the conservation laws state? They state that in this reference frame, something can only brake (get negative momentum) by causing other things to move "more forwards" than they were moving before (get positive momentum). The usual way to do this is to fire a rocket engine forwards: this takes rocket fuel which was "not moving" and propels it "forwards," and this will always cost energy: you now have two moving entities (your spaceship, the spent fuel) moving opposite to each other with some kinetic energy. In our special reference frame we can see that this demands energy expenditure: first we have 0 kinetic energy, then we have nonzero kinetic energy.

But if you're slowing down with an atmosphere or braking against a road, that looks subtly different in this reference frame. In this reference frame, that means that there is something (let's say it has mass $M$, though of course that's an idealization for a road or an atmosphere) coming towards you with velocity $-\vec v$, and you are going to grab hold of it or perhaps (like with solar sails) bounce it off of you, in order to gain momentum in the $-\vec v$ direction.

If you think about that for a second, you'll realize that you're not necessarily sure where the energy will end up. This big thing $M$ is going to be moving backwards slower, say at velocity $-v'$ and your little spaceship/car $m$ is going to be moving backwards faster, say at velocity $-u$. Since $v' < v$ it's not clear whether $\frac 12 M (v')^2 + \frac 12 m u^2$ is going to be greater or less than $\frac 12 M v^2$, corresponding to either requiring your input of energy or else allowing you to siphon off some energy and "regeneratively brake". So let's derive the condition.

# Some formulas

So our car/spaceship has mass $m$ and starts off with speed $0$ and it ends up with velocity $-u$, and the object it interacts with has velocity $-v$ and mass $M$, and ends up with velocity $-v'.$ Conservation of momentum says that $M v' + m u = M v,$ so that $v' = v - \frac mM u.$ The resulting change in kinetic energy is $$\frac 12 M \left(v - \frac mM u\right)^2 + \frac 12 m u^2 - \frac 12 M v^2 = - m v u + \frac 12 m \left(1 + \frac mM\right)u^2.$$If this change in kinetic energy is negative then that means that the missing kinetic energy could be collected, having a magnitude $$E = mu\left(v - \frac12 \left (1 + \frac mM\right) u\right).$$ Taking the limit as $M \gg m$ we see that this condition is actually $u < 2v$ for the possibility of energy regeneration. This threshold $u =2v$ has an intuitive explanation back in the reference frame that moves along with the ground, where it says "you cannot possibly regenerate any more energy if you stop your car regenerating 100% of that energy and then use it to drive yourself in reverse, so you were going at speed $+v$ and now you go at speed $-v.$" But for any velocity $u$ (relative to the road) where $-v < u < v$ it is hypothetically possible to regenerate some energy. The same applies to the spaceship, it could hypothetically grab enough energy to hurl itself in an arbitrary direction at the same speed as it came in.

So: we see from the co-moving reference frame that yes, regenerating energy is possible, but only if you slow down (by some tiny fraction) some massive object which is moving through the space. You can also see this principle applied for example in gravitational slingshots: to complete a gravitational assist, you want to pass behind a planet as it follows its orbit about the Sun; this means that your gravity will pull backwards on that planet, and its corresponding gravitational pull on you is going to give you a lot more kinetic energy. If you tried to get a gravitational assist going in front of the planet (again, in terms of the direction it is going in its orbit), you would find yourself exiting with much less speed than when you went in.

• -1. It is not at all clear to me what you are saying. Are you saying that you can use the atmosphere to slow down as in re-entry? Mar 9 '17 at 2:55
• @sammygerbil I'm saying that there are many ways to slow down, but all of the ones which can "recoup energy from braking" must necessarily involve colliding with something coming towards you: and with those you only have a certain latitude to extract energy. This is to answer the question "Do you absolutely need an outside object moving at a different speed" to extract energy while slowing down in the affirmative. Mar 9 '17 at 3:36
• This is much clearer. I think this message is lost in the detail of your answer. Mar 9 '17 at 3:56
• @sammygerbil: rewritten a little bit. Is that better? Mar 9 '17 at 21:13

Technically if the space ship could find something to brake against, it could regain some energy. You would need a braking system devised to take advantage of resistance or drag where ever you could find it. Maybe in a planet's atmosphere or gravity in some way, or even a large contraption designed to catch the spaceship and extract energy from the process. You could go on and on. For every action there is an opposite action.

• Yes. In an atmosphere you could use the heat generated by re-entry to boil water to turn an engine to generate electricity. It would be inefficient and maybe a little silly, but you could do it. Mar 9 '17 at 20:05
• Well, that might be getting a little hung up on the "how," from an intentionally self-limiting viewpoint. The bottom line is that where there is energy transfer going on (forces such as acceleration being experienced), there is an opportunity to figure out how to extract part of that energy, maybe through some electromotive mechanism, maybe via some other mechanism (possibly one not yet devised), and store it as potential energy in a capacitor or battery or a spinning flywheel or something else for later use. Mar 11 '17 at 7:30

There is some work on systems that could recoup energy from slowing a spaceship down. Here are two of the main ideas.

One is called an electrodynamic tether. It requires a magnetic field and a very long wire. The field and wire act a bit like a generator/motor and is able to turn mechanical energy into electrical energy and vice versa.

The other idea is a momentum exchange tether. Here a pod could be tethered to another craft (the craft would be probably much more massive than the pod) and both rotating about their common center of mass. When the pod is released, the rotational kinetic energy is changed to translational kinetic energy, and the pod is flung into a new orbit. It could then be captured by a similar craft at the end of its journey, and when the return trip is needed, released again to be flung into the orbit it came in.

• but then it will slow down in relation to what? Mar 9 '17 at 8:12
• @SargeBorsch The magnetic field in the first case, and the other spacecraft in the second. Braking and accelerating are still symmetric of course. The main point is still that just like the car transfers momentum to and from the Earth, the spaceship would have to do the transfer to and from something else. Mar 9 '17 at 12:48
• My answer addressed the first part of the question, because I don't think the second part was there. I may have just missed it. For the second part, the answer is no, conservation of momentum is about as iron-clad as you get in physics, so in order to change your momentum, something else must also change its momentum. On the Earth we don't notice those changes since the reaction force on the Earth produces such a miniscule change, that the Earth's change in momentum can be ignored for practical purposes. Mar 10 '17 at 5:59

To brake a car and generate energy out of it, you have two systems interacting: the drive shaft of the car and the electric generator. The linear kinetic energy of the car is converted into rotational kinetic energy of the shaft due to the friction between the wheels and the floor.

The configuration on the spaceship is different: you don't have anything analogous to the floor that could convert the linear kinetic energy of the spaceship into a rotational kinetic energy that could turn your electric generator. To brake the spaceship, you have to eject matter out of it, and this matter goes away together with the energy you used to accelerate it.

• Thank you for mentioning not having the floor, i think that goes in the direction I was thinking. Do you have to have a "floor" or can you convert kinetic energy into a different form without it? I edited my question to reflect this wording.
– Jens
Mar 8 '17 at 20:52
• @Jens: The only way to get a "floor", or something that imparts friction like the road does, would be something like a giant non-powered propeller. As the craft enters atmosphere, the air would hit the fan blades and spin the shaft (like how a windmill generates power). But in space, this would be useless. Mar 9 '17 at 0:39

An electric car wth DC motor can slow itself via regenerative braking, in which voltage applied to the motor is reduced to less than back EMF Eb. Armature current and torque are reversed, the armature slows, speed falls, and the motor acts as a DC generator, powered by inertia of the vehicle's turning wheels. Power then can be stored in a battery for future use.

A spaceship does not propel itself by rotating wheels or rotating armature. If a spaceship is slowed, the process must involve reverse thrust, not reversal of current. Thrust is generated by ejecting matter from the spaceship, which is an irreversible process, as toliveira points out in his answer.

• Ernie, thanks for your nice explaination of the working principles of the two types of decceleration. I had something a bit different in mind though and edited the question.
– Jens
Mar 8 '17 at 20:51

You seem to be comparing apples and bricks. A spaceship absolutely can, and DOES, gain energy from braking, but it's not useful. The advantage the car has is that it runs on energy we know how to generate from the braking process.

Spaceships don't run on electricity. Nor do they run on heat, which is the most obvious energy gain, if you look at our current state of spaceflight. If we could turn that heat into more rocket fuel, you would have your equivalence, but we can't.

There are all kinds of ways we could capture energy during braking or reentry of a spacecraft, but we can't turn that energy into rocket fuel. In order to do that we'd need to be able to create matter from energy but, so far, we only know how to turn matter into energy. Not the other way around.

• Actually one could conceive an endothermic chemical reaction, or just a Peltier element creating electric energy to power an ion drive later, driven by the temperature differential between the heat shield and other parts of a space craft going through an atmosphere. Although that would be terribly inefficient. And it also assumes a body to brake against, whose necessity was part of the question. Mar 9 '17 at 12:55

Thinking about it some more you could break it down to: Do you absolutely need an outside object at different speed (the road for a car, slamming into an atmosphere as a space ship) to convert kinetic energy into another form. What is the fundamental principle of this fact?

Inertia. An object in motion will stay in motion will stay in motion unless acted upon by an outside force. For a car, the "outside force" is the friction of the air on the body and the road on the wheels. Instead of turning that energy into heat with conventional brakes, regenerative braking turns it into energy by using the wheels to rotate an electrical generator which slows the wheels which drag against the road.

For a spaceship in an idealized vacuum there is no such outside force... but in reality there are. For example, a spaceship in orbit around a body with a strong magnetic field could use their movement through that field to generate power via an electric generator. This would also have a braking effect and lower its orbit.

Vacuums are not perfect, even in outer space. A spacecraft is usually moving through some sort of very wispy gas and solar wind. They can use this medium to brake against, like a car brakes against the road, just very, very, very, very slowly. For example, let's say our spacecraft is moving at 10km/s relative to the medium.

     ==>                           . . . . .
10km/s -->                       0 km/s


Or, if we use the spacecraft as the reference point.

     ==>                           . . . . .
0 km/s                        <-- 10 km/s


The spacecraft has all these particles flying at it at 10 km/s. Their bouncing off the spaceship's hull will apply a small "braking" force depending on their overall momentum. It's very small, but it will add up over time. But remember, braking is acceleration. So in this reference frame "braking" is accelerating in the direction of the medium.

      ==>                           . . . . .
<-- 0.000001 km/s                  <-- 10 km/s


If instead the spacecraft captured these particles and used them to turn a generator they'd gain both electricity and reaction mass as well as braking.

The surface area of a normal spacecraft is too small, and the medium too thin, for this to be used as a significant source of power or thrust (unless you're in LEO where drag is significant). But expand your surface area and you have a solar sail. Combine the two together, using electromagnetic fields to collect the interstellar medium, and you have a Bussard ramjet.

• In the external magnetic field the spaceship would have to expend more energy to move forward while storing energy. It would waste more energy than it generates. ... Capturing particles : You cannot turn the vacuum on and off at will. The particles will still be there when you accelerate, requiring more energy to be expended. Mar 9 '17 at 2:44
• @sammygerbil Yes, the question is about regenerative braking; ie. using the process of slowing down to recover some energy. The ship in orbit is trying to slow its orbital velocity, using the magnetic field of a planet allows it to do that without expending fuel. The ship moving through the thin medium of outer space is using those inevitable particle collisions to generate some power; like if I threw a tennis ball at you and instead of letting it bonk you in the face you caught it on a turbine wheel. Note, I don't think these are practical. Mar 9 '17 at 2:50

Think about the momentum in the two situations. In any closed system, momentum must be conserved. When you accelerate a car, you push the Earth in the opposite direction with exactly the same momentum. When you want to slow down (which again is acceleration, just in direction opposite to motion), you again push the Earth, and it will be accelerated in the opposite direction. Since the Earth is much more massive than the car, the acceleration on the Earth is tiny, which makes Earth easy to push from (compare jumping on concrete with jumping on a bit of foam - the concrete is almost unyielding, which gives you a lot of leverage).

The braking and acceleration are symmetric in this case - when accelerating, you make the car move faster relative to the ground, when braking, you make it slower relative to the ground. Slowing a fast thing down on a slow thing allows you to extract useful work, pretty much the same way you can extract work from, say, an interface between a high temperature and low temperature object, or high pressure and a low pressure system.

But that's not the case with a spaceship in free space (i.e. where we can safely ignore gravity, space dust etc.). There's no simple way to "push off" anything in space - so you carry your own "pushing mass". Momentum is still conserved - if you look from a frame of reference where the original spaceship is motionless, accelerating will make you see the spaceship moving in one direction with a given momentum, and the propellant (the mass you throw backwards) will have exactly the opposite momentum. Together, the total momentum is still zero - but relative to the fixed point, both masses have been accelerated, and both have their own momentum. That's how we can get to other planets, despite having no roads to push off - that's the difference between a jet airplane (which uses ambient air as propellant) and a rocket (which needs to carry both fuel and propellant).

Now imagine what would have to happen if you were to brake similar to a car. You'd somehow need to get the already expelled propellant back - imagine something like having two balls connected by a string. When the string snaps taut, the balls will "recoil", their direction of motion reversed, and they will collide at some point; if you are careful enough, you can accelerate one ball by throwing the other ball in the opposite direction, and when the string runs out, they will stop again. The problem is, just like the momentum is conserved, so is the center of mass - somewhere between the two balls, the center of mass is at exactly the same position as before the acceleration and subsequent deceleration (or rather, it's where it would have been if you didn't accelerate in the first place, as long as we can assume interference with e.g. the atmosphere or gravitational field etc.). The only reason rockets can move in space is that the propellant is not connected to the rocket anymore.

If you could have a magical string that allowed you to connect your rocket to its propellant and draw it back, you could brake the rocket "for free". But you'd also pull the rocket back to where it started. Now, mind you, in a planetary system, this could still be used for transportation, and it would be a revolution in spaceflight - you'd use gravitational maneuvers with your target planet to steal some of its momentum, which would allow you to draw the propellant back with more "leverage". But we have no such magical string, and no other way to move in free space.

We do have a few tricks, though. Aerobraking and gravitational assists are both ways of exchanging momentum with planets (and other massive bodies), and as such, they are very different from the rocket engine itself. Momentum is again still conserved - each such "push" changes the motion characteristics of the body in question; it might slow down its orbit, or make it faster, or slow down its rotation or make it faster. But since we're again dealing with objects much more massive than your spaceship, we're back to "essentially free". And indeed, we use these maneuvers extensively - our capabilities are so limited that we can scarcely afford not to. Remember those brutal reëntry videos of the space shuttle and similar craft? Huge speeds, huge temperatures, huge stress on the spacecraft? They are only necessary because we don't have spaceship engines efficient enough. If we had rocket engines that would use half the propellant/fuel mass for the same amount of momentum produced, spaceflight would get much easier, and we could easily avoid the dangerous reëntry with existing spacecraft (though it might be that we would simply build smaller spaceships to do the same thing).

Okay, so if we have something to push off, we can recuperate energy. Indeed, we can even recoup more energy than we originally used, if we just use the right trajectories between the right kind of massive bodies! But there's little you can reasonably do with that energy. We do have spaceship propulsion systems that run on electricity (they still need some propellant, they just need far less mass for the same amount of velocity change); but those are powered either by solar cells or RTGs - they have no benefit from recuperating the energy, even if it were practically possible. With our technology, energy isn't the biggest problem - propellant is. As long as we keep throwing mass out the backside of a rocket to produce a change in velocity, we'd need some way to get that mass back. The kinetic energy of the spacecraft is tiny compared to the mass-energy of the propellant. And the fun is, the less massive the propellant, the higher the efficiency, but the more energy input you need for the same momentum (momentum increases linearly with velocity, while kinetic energy increases with a square of velocity), and the lower the thrust. Most of the energy cannot be recuperated, since it's in the propellant, not your spaceship - and the more efficient your engine, the more energy is in the propellant as opposed to the spaceship. So in the end, the systems which would have the most benefit from recuperating the energy also need far more of it.

The holy grail of spaceflight would be a magical device that allows you to push off any object you want with as much force as you want - this would make spaceflight almost as easy as driving a car. Want to accelerate? Push off the planet you're leaving. Slow down? Recuperate the energy as you push off the target planet. It would work just like the electric engine in your car! Sadly, we have little reason to believe we'll ever be able to make such a device; it's not technically impossible in theory, but we know of no mechanism that would be adequate. One could imagine some orbital infrastructure that would allow us to exchange the momentum of planets with spacecraft being flung out from one planet to another, but certainly not for independent spaceships zipping along willy-nilly around the system.

One key principle underlying this is the reversibility of processes.

Reversibility is tied in with entropy : a reversible process does not increase entropy, while a process that increases entropy is not reversible.

The processes involved in regenerative braking are reversible :

• Electrical energy can be translated to kinetic energy by an electric motor - and vice-versa.
• Chemical energy can be translated to electrical energy in a battery - and vice-versa if the battery is rechargeable.

Both processes involve losses, creating some entropy, but as second order effects such as resistance, not fundamental to the process.

The processes involved in rocketry are irreversible, entropic processes :

• Chemical energy is translated to heat through combustion - by the second law of thermodynamics, this is an irreversible process, increasing entropy
• That heat energy is used to emit reaction mass. Converting an organised state of matter in a propellant tank to an unorganised exhaust plume is again an increase in entropy, and not reversible.

(Strictly speaking you CAN reverse both processes - but only by the application of further energy, increasing overall entropy further, which negates the point of regenerative braking).

So for regenerative braking a spaceship, you have to abandon rocketry and find reversible processes you can apply to the problem. Interaction with an external magnetic field or solar stream may be possible - as the currently leading answer suggests, this implies the spacecraft ceases to be a closed system.

Small satellites (like cubesats) already interact with Earth's magnetic fields to spin, de-tumble, and orient themselves, through magnetorquers. These are in principle reversible - though the field is so weak and the winding resistance is so high that the energy generated in insignificant. Perhaps superconducting magnetorquers could generate some energy.

For another example : sailing away from one sun, accelerating towards the speed of its solar wind, and parachuting down towards another may be possible.

I propose that regenerative braking of a spacecraft is indeed possible, and by a similar means to that of a car. Linear momentum of the vehicle is countered by influx of energy sapped from the angular momentum of the braking system. The solution, carry a circular road/ring into space along with the craft. It matters not that the road isn't attached to a planet, only that it have sufficient angular momentum and sufficient time to transfer the energy. Whether it is practical, is a different question.

Regenerative braking is not a free lunch. The energy to stop ultimately comes from the fuel used to accelerate. Whether car or spacecraft, upon launch, the vehicle converts chemical energy into kinetic energy. The vehicle carries that kinetic energy with it.
The vehicle also must carry with it the machinery to couple to the kinetic energy and change it into a different direction or form.
At the end of the journey, the 'friction' between this rotating machinery and the non rotating vehicle, which has been low and continuous, suddenly increases causing the kinetic energies to be redirected.

The space vehicle I envision has take off rockets mounted on 1 or more large concentric rings which can rotate freely in relation to the fuselage of the craft, as well as slide along the length of the fuselage. The rockets are slightly angled so that both lift and spin are imparted simultaneously on takeoff. These spinning rings could be used to generate artificial gravity, but such use limits the practical angular velocity available to braking. The ring to fuselage friction must be sufficiently low to still be spinning at the end of journey. If the fuselage exterior consists of a spiral inclined plane (screw thread), a breaking pin, extended from the ring into the thread of the fuselage would suddenly engage the thread and thrust the fuselage rearward in relation to the rings. when the ring reaches the end of the fuselage, impact occurs. Retracting the pin, imparting some of the rearward fuselage momentum into the ring, slowing the whole craft somewhat, and resetting the relative positions of spinning rings and fuselage ready for another go. The operation is similar to that of a rotary hammer massively scaled up. Not pleasant perhaps, but theoretically plausible.