I have to model the behavior of an electric car. For this, I use these equations and I can observe by "playing" with parameters that, when going downhill at constant speed, the car has a negative consumption (i.e. recovers energy). I was wondering if this is realistic?

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    $\begingroup$ regenerative breaking is the keyword you are looking for $\endgroup$ Commented Sep 14, 2017 at 10:59
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    $\begingroup$ Important to note that regenerative braking is an feature that must be intentionally incorporated into the EV design; it is not an automatic property of any vehicle capable of electric drive. For example, bicycles with electric assist motors do not typically have regenerative braking as a feature. $\endgroup$
    – Air
    Commented Sep 14, 2017 at 15:25
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    $\begingroup$ As a happy Model S90D owner, I can tell you that regen can pull enough energy to bring the car nearly to a halt even on a downhill. $\endgroup$ Commented Sep 14, 2017 at 15:34
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    $\begingroup$ @Air If you take an electrical engine as it is, it is indeed capable of doing both: play motor and play generator. But maybe the electronics around it make it incapable of being a generator, which is why that has to be added afterwards again. $\endgroup$
    – glglgl
    Commented Sep 15, 2017 at 9:47
  • $\begingroup$ I remember reading an account of a Tesla owner who lived on the top of a small range. He deliberately limited charging to 80% or 90% so that he could take advantage of regenerative breaking on his way to work. It both saved energy andbreak pads. $\endgroup$
    – NPSF3000
    Commented Sep 15, 2017 at 12:52

5 Answers 5


It depends on how steep the hill is. On a slight hill, the energy added by gravity is still not enough to overcome rolling friction and air resistance, so the car still needs power to maintain speed. On a steeper hill, the two may balance out, so no power is used, and no power is generated. On a hill that's steep enough to require braking to control the speed, the car recovers energy. It's called regenerative braking. If the car is going too fast, applying the brakes turns the motor into a generator and charges the battery.

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    $\begingroup$ To add to this, most modern combustion engined vehicles will also use no fuel on grades steeper than where the energy balance goes even. Vehicles will usually only add enough fuel to keep the engine turning at idle speed, if necessary, but when rolling downhill they can cut fuel flow completely. In the case of a combustion engine the break-even grade is a bit steeper, however, since the vehicle must also overcome the un-fueled braking effect due to engine compression. $\endgroup$
    – J...
    Commented Sep 14, 2017 at 13:55
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    $\begingroup$ @J... Is this completely true? I know diesel engines at least use the diesel for lubrication purposes. $\endgroup$
    – SGR
    Commented Sep 14, 2017 at 14:56
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    $\begingroup$ @SGR Yes, it's called Deceleration Fuel Cutoff (DFCO). I think even passenger diesel vehicles do this. The diesel doesn't lubricate the engine - it lubricates the fuel system. $\endgroup$
    – J...
    Commented Sep 14, 2017 at 15:03
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    $\begingroup$ @SGR confirmed. Fuel injected engines shut off completely unless throttle or Idle Air Control asks for power. IAC is a minimum speed governor whose job is keep the engine from stalling against varying loads, i.e. Power steering or A/C. Also, diesel fuel does not lubricate the fuel system. It used to, but then they removed the sulfur. Biodiesel does a great job, even 2.5% biodiesel will replace the lost lubricity. $\endgroup$ Commented Sep 14, 2017 at 16:30
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    $\begingroup$ Not counting the newer cars that actually shut the engine off during drives... Fuel injected Manual transmissions cars have been doing fuel cutoff during in-gear deceleration for a while (engine load with no throttle). $\endgroup$ Commented Sep 14, 2017 at 22:28

Yes, it can certainly happen. To recharge the battery when going down hill, the free roll speed needs to be greater than the speed you are trying to go. That means going down the same hill may result in a different outcome depending on speed.

For example, let's say you put the car in neutral and coast down a particular hill. For most of the hill, the car settles at 45 MPH. If you were to drive down the hill at 35 MPH, then the system should be charging the battery a bit. However, if you drive down at 55 MPH, then additional power is needed than just the gravity assist of the hill, power is taken from the battery to run the motor or motors.

I have a Honda Civic Hybrid, and charging the battery when going down a hill is not unusual at all.

  • $\begingroup$ @Harper Aero drag is polynomial, not exponential, and any increasing function of speed would give rise to a terminal velocity. Terminal velocity arises simply whenever the speed is high enough that the drag forces cancel out whatever force is driving the vehicle forwards. $\endgroup$ Commented Sep 14, 2017 at 17:53
  • $\begingroup$ Don't forget that at proportionately higher speeds, you are gaining kinetic energy faster. That being a linear factor, what saves you is that aero drag tends to be polynomial... giving you a terminal velocity... but that is at the whimsy of the wind. 20kt headwind turns to a 20kt tailwind, aero drag drops precipitously and you could find yourself with a problem. $\endgroup$ Commented Sep 14, 2017 at 19:23
  • $\begingroup$ Thanks, my point is, aero drag is not a reliable contributor to braking, nor are reliably straight enough for terminal velocity, so there better be a plan B that doesn't rely on a battery being mid-charge. $\endgroup$ Commented Sep 14, 2017 at 19:26

ABB train regenerative braking.

Some Swiss trains give back energy to the grid upon descending the mountain pass that they previously climbed. The article claims as much of 70% is recovered.

I rode the Jungfraujoch and the personnel mentioned for every 3 trips down the mountain enough electricity was recovered for a "free" trip up.


The basic equations governing an electric car are reversible, so a simple analysis would say that the battery is getting charged. In the real world, there are more complications. In the case of an electric bike, there is a ratchet that disengages the engine from the wheel when the wheel is going faster from the engine (just like how on a regular bike -- where "regular" doesn't include track bikes -- if you stop pedaling, the wheel keeps moving even though the chain isn't). In an electric car, the motor can be disengaged from wheels either mechanically or electrically. Electric motors generally can't handle as much power when being driven backwards as when going forward, so electric cars are built to limit how much power can be transferred from the wheels to the battery. Absent those modifications, any time the wheels are going faster than the motor, there's going to be electricity flowing "backwards". Whether that energy will be charging the battery or frying the motor is a different matter.

And if you include heat, all cars "recover" energy in some sense when going downhill, either through increased kinetic energy, or heating of brake pads.


Absolutely. That "recovering energy" will kill you.

Take the freight trains of yore. In the day, helper districts involved extra steam engines waiting at the bottom of a mountain to help trains up. Today, it's more important to help trains down the hill with their regenerative (dynamic) brakes. Some railroads require additional units be added for dynamic braking, even for a train that could climb the hill! Best practice is to plan to use mainly or only dynamic brake, which saves money too.

The steam trains would awkwardly drag brakes all the way down the mountain, filling the valley with gray smoke.

Automotive brakes (gas or electric) don't have enough gray smoke, so they need engine braking... except electric cars can't.

That's been a huge problem, especially for the early/homebrew DC conversions. Like the freight trains, they could go up hills they couldn't go down.

Even a regenerating car has an issue, if the owner tops up the battery at Summit.

That is to say, when an electric car loses the ability to regen because its batteries are full, its only fallback is friction brakes - and as discussed, those can't sustain a downgrade either. They're playing with locomotive-style "make heat" dynamic braking, but I don't know how far along it is. They need it.

By "don't have enough gray smoke" I mean automotive brakes are not designed nor rated to descend a continuous mountain grade.

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    $\begingroup$ Your claims about electric cars are also incorrect. While electric cars have regenerative braking, they use them in tandem with traditional frictional brakes. (Not only for the reasons you mentioned, but also because regenerative braking wouldn't provide enough braking power for an emergency stop.) $\endgroup$
    – user12915
    Commented Sep 15, 2017 at 4:02
  • $\begingroup$ @DavidRicherby your experience is not mine, but I've made some edits to try to accommodate your experience. $\endgroup$ Commented Sep 16, 2017 at 3:50
  • $\begingroup$ @duskwuff you may be missing a big part of the context, of course electrics have friction brakes (they're just unhelpful) -- but I see where I did breeze through the relevant points pretty fast. I've thickened it up. I've also asked the technical question about electrics here, I'm fairly sure I know the answer but we'll see. $\endgroup$ Commented Sep 16, 2017 at 4:31
  • $\begingroup$ @Harper Fair enough -- thanks. I've deleted my comments, since they're no longer very relevant. $\endgroup$ Commented Sep 16, 2017 at 13:54

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