Why does accelerating fast use more energy than accelerating slowly?

[David99]

Does anyone know what the most efficient acceleration is for the Model S?

I've read that for ICEs at low speeds, say 30 mph, a very efficient (presumably somewhat unpleasant) style of driving is pulse and glide - rapid acceleration at the ICE's optimal acceleration followed by gliding. I doubt this technique would buy one much for the Model S, but it does make me wonder what the most efficient acceleration is.

You mean acceleration or cruise speed?

The Model S is most efficient at around 25 mph.

 

[martinwinlow]

Nope. He means acceleration...!

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No. Simple kinetic energy change. Doesn't matter how fast/slow you accelerate. ...

I can't fault your maths/physics (I have forgotten it all) but what you are saying sounds utterly counter-intuitive… It also irks me to think that there is no economical benefit to driving like Miss Daisy's driver compared to driving like a loon. How depressing (if your are sensible/middle-aged/old) or… *GREAT* (if you are… a loon).

 

[snooper77]

I can't fault your maths/physics (I have forgotten it all) but what you are saying sounds utterly counter-intuitive… It also irks me to think that there is no economical benefit to driving like Miss Daisy's driver compared to driving like a loon. How depressing (if your are sensible/middle-aged/old) or… *GREAT* (if you are… a loon).

I don't find it counter-intuitive, because if you accelerate hard you need more power on one hand, but only for a correspondingly shorter time on the other hand. These two facts cancel each other out.

 

[JohnQ]

Nope. He means acceleration...!

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I can't fault your maths/physics (I have forgotten it all) but what you are saying sounds utterly counter-intuitive… It also irks me to think that there is no economical benefit to driving like Miss Daisy's driver compared to driving like a loon. How depressing (if your are sensible/middle-aged/old) or… *GREAT* (if you are… a loon).

Just to clarify; that's assuming in a vacuum with 100% efficient energy transfer. As discussed above, efficiency varies by power input so it appears that it is indeed more efficient to accelerate more slowly.

 

[Jeff Miller]

Nope. He means acceleration...!

Yes, I meant acceleration.

I definitely get the ohmic losses ~ I^2 point that people have made above, and can also believe the point that others have made that the battery delivers power
less efficiently at higher power draw. But is there some load on the motor/inverter/battery which is optimal in terms of efficiency?

This article says that motors become much less efficient at low loads and that peak efficiency is at around 75% of the motor's rated load:

https://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/10097517.pdf

I'm not an engineer so maybe this isn't relevant to the Model S's type of motor.

 

[Brass Guy]

Your average speed will be higher too. This will be more noticeable with more stops like between lights. But I suppose the OP isn't discussing total energy use.
The best level of acceleration is the amount that invokes the biggest grin.

 

[ElSupreme]

You both nailed it. I tend to disregard these factors and go just with the the theoretical physics and hence always accelerate as fast as possible to my target speed

I tend to follow this philosophy as well! Forget trying to go sub 300Wh/mi. And just embrace the 350+ Wh/mi trips.

I tried to use a simplification, but I think if you integrate force over the same distance you still get more energy required for the more aggressive drive cycle.

GSP

If you just do the energy calculations they exactly cancel each other out (as they should because you can't destroy energy). But there are losses in the drive train and they do increase with more power. The motor will change efficiency over its speed range (and efficiency will go down after you hit peak power, but without real curves it is really hard to say where peak efficiency is). But motor efficiency is always really high. Mostly you are getting losses in the battery, increase amperage gives you increased losses. Which heat everything up and give you even more increased losses. Not to mention your power electronics also put out more losses with amperage increasing.

And thus do the electrical engineers continue to trump the mechanical engineers in this new era ... I've got no skin in the game, I was nuclear.
Thanks for the info, I didn't know the efficiency curve.

I am a mechanical (so obviously biased). I can tell you lots of these power electronics stuff is done by MEs learning some EE stuff. It really is the interface between the two disciplines and you see both. Dealing with field forces, and heat generation is a big factor when designing power electronics and motors.

Your average speed will be higher too. This will be more noticeable with more stops like between lights. But I suppose the OP isn't discussing total energy use.
The best level of acceleration is the amount that invokes the biggest grin.

This is my best reasoning behind increased energy usage. I think battery current losses is significant, but probably minor. But if you accelerate faster you have a higher average speed, and thus incur more aerodynamic losses. That coupled with over shoot you get your main losses.

 

[mnx]

No one has mentioned spinning tires or traction control kicking in yet. I do a lot of both, and yes it is obviously less efficient.

 

[digitaltim]

I think the theory of special relativity has to kick in at some point once the velocity approaches the speed of light.

At least that has been my experience...

 

[AndreyATC]

I was actually experimenting with this recently
I have the same commute every day, with very little differences in speed or time, with identical milage
I come home with 285whm reading pretty much all the time
Speed limit is 30-55, depending on the leg of the route, all local roads
So i decided to have some fun using power of this fine vehicle in the last few days
I accelerated hard or ramps and of the traffic light up to the speed limit an then cruise
Guess what?
The same 285-290whm
I never floored it, but it was pretty solid acceleration nevertheless

 

[MikeC]

No one has mentioned spinning tires or traction control kicking in yet. I do a lot of both, and yes it is obviously less efficient.

Now I'm no engineer, but I'm pretty sure if you do the equation, you'll see that the loss of energy from tire spin is exactly cancelled out by the decreased rolling resistance of the now worn tire.

On a serious note, I'm glad that it sounds like there is not a huge penalty incurred for driving like a "loon", provided no overshooting. Another advantage of EV over ICE?

 

[brianman]

I can't fault your maths/physics (I have forgotten it all) but what you are saying sounds utterly counter-intuitive… It also irks me to think that there is no economical benefit to driving like Miss Daisy's driver compared to driving like a loon. How depressing (if your are sensible/middle-aged/old) or… *GREAT* (if you are… a loon).

The only choices are old or loony? Lame. Why can't someone be neither (or both)?

 

[RDoc]

I think the theory of special relativity has to kick in at some point once the velocity approaches the speed of light.

At least that has been my experience...

Absolutely, but only for family members outside the car, particularly for very close family members, the ones that are really special to you.

 

[HankLloydRight]

On a semi-related note: :scared:

A constant speed is good for gas mileage – and for some reason that seemed important at the time. Indeed. On a trip like this one must be careful about gas consumption. Avoid those quick bursts of acceleration that drag blood to the back of the brain.

 

[metafor]

I think an EV will be less effected than a gas car. A gas engine will adjust things like fuel/air ratio for maximum power when accelerating quickly, and that's never the same as for maximum efficiency. I don't think an EV would have any analogous behavior.

I would be interested in seeing some scientific tests of this for some gas cars and EVs to measure the difference under different acceleration scenarios.

I once tried to do the calculations to determine how much energy was required to accelerate at different rates to a certain speed and was surprised to discover no significant different at different acceleration rates. But perhaps much of the losses are due to resistance/friction which I didn't account for, or maybe I just did it wrong. I don't know.

You're not wrong. In an ideal case (no friction/resistance), the energy used is exactly the same. Potential energy in the battery becomes kinetic energy of the car. Conservation of energy. Ideally, when you decelerate using regenerative braking, you'd gain back all of the energy you used; kinetic energy of the car becomes potential energy in the battery.

In real life, there are losses in the motor due to friction in the gears, motor coil, etc. and resistance in the electrical wiring, battery output, inverter, etc. All of this loss increases as current and spinning speed of the motor/gears increases.

 

[GSP]

No.
Work = integral(F(t)v(t) dt, 0 to T) where F(t) is Force, v(t) is velocity at time t, T is total time of acceleration. But under constant acceleration, v(t)=Ft/m where m is mass and force F is constant.
= integral(F^2 * t/m dt, 0 to T)
= F^2 * T^2 / 2m
But, F=ma, so T is inversely proportional to F, T = V/a = Vm/F where V is target velocity.
= F^2 * (Vm/F)^2/ 2m = F^2 * V^2 * m^2 / (F^2 * 2m )
= mV^2/2
This is independent of rate of acceleration.

Hmm, now where have I seen that last equation again?
Yes, it's kinetic energy. The simpler way of saying it is that in a perfect system the work is all coverted into kinetic energy, so rate of rate of acceleration would be irrelevant and we can leave the calculus as an exercise for the reader.

If you just do the energy calculations they exactly cancel each other out (as they should because you can't destroy energy). But there are losses in the drive train and they do increase with more power. The motor will change efficiency over its speed range (and efficiency will go down after you hit peak power, but without real curves it is really hard to say where peak efficiency is). But motor efficiency is always really high. Mostly you are getting losses in the battery, increase amperage gives you increased losses. Which heat everything up and give you even more increased losses. Not to mention your power electronics also put out more losses with amperage increasing.

As Brass Guy points out, average speed over the drive cycle is higher with quicker acceleration. This has to require more energy to cover the distance than for slower acceleration. Not in outer space, but on Earth it does. If you integrate force over distance it takes more Nm, ft-lbs, kWh, or whatever your favorite energy units are.

GSP

 

[gregincal]

On a serious note, I'm glad that it sounds like there is not a huge penalty incurred for driving like a "loon", provided no overshooting. Another advantage of EV over ICE?

Except that theory aside, from pure empirical evidence I can tell you that there is a large difference. Several people have mentioned why that could be, but for people to claim that they don't think it would make much difference flies in the face of my personal experience. Flooring it when you accelerate causes your wh/mile to go through the roof and even if you then travel at a constant speed for a few miles the average stays elevated.

 

[TEG]

Along with everything else... If you are slipping the tires you are wasting energy. (Heating the tires and the road.)
And if traction control engages the braking system... Further losses.

Plus that giant smile on your face isn't as aerodynamic...

 

[Stuart]

As Brass Guy points out, average speed over the drive cycle is higher with quicker acceleration. This has to require more energy to cover the distance than for slower acceleration.

No it doesn't have to require more energy. Imagine an old-fashioned mouse trap. When you prime the trap, it take a certain amount of energy to bend the spring into the loaded position. The spring under tension is storing energy. If the spring is allowed to fire suddenly, or gently released, the same amount of energy is released from the spring. The speed makes no difference to the amount of energy released. This is basic high-school physics.

When you factor in inefficiencies like non-linear heating in the wires then it becomes an interesting calculation, but it is absolutely incorrect to suppose that quicker acceleration to a given velocity necessarily and always takes more energy than slower acceleration to the same velocity.

 

[ohmman]

When you factor in inefficiencies like non-linear heating in the wires then it becomes an interesting calculation, but it is absolutely incorrect to suppose that quicker acceleration to a given velocity necessarily and always takes more energy than slower acceleration to the same velocity.

From my perch, it seems the misunderstanding here wasn't reaching the same velocity, but the same distance. So from A to B, if you accelerate faster and are traveling faster for a larger portion of the journey. If you're talking about reaching the same velocity, then I think it's a lot closer of a match.

While I used to be gentle as a feather on my ICE pedal, I find that I don't have any hesitation enjoying what the MS has to offer in acceleration. In my P85, I still average < 300 Wh/mi. I think mostly this is due to living in a place where the maximum speed limit is 45 mph (and I don't test that very often - I just get there quickly.)