Efficiency versus hard acceleration

[conman]

Something I've been trying to get my head around is the effect of relatively hard acceleration on efficiency on our vehicles. In an ICE vehicle the efficiency takes a nosedive with hard acceleration for many reasons, but with our electric motors at 93%/97% efficiency (depending on model) and only one gear ratio, how does this translate? Does the efficiency change according to how hard we accelerate? Assuming you don't lose traction then the extra losses are in flexion of the tyres, which doesn't amount to much. Does the energy efficiency otherwise change at different levels of acceleration? If you maintain traction, and only accelerate hard to the speed limit, is it really that much less efficient than accelerating slowly to the speed limit? Does anyone know of any relevant graphs that can portray this?

 

[Babaron]

Assuming efficiency decreases as speed increases, due to wind resistance, and assuming a single drive motor, and assuming a set final speed:

Fast acceleration to that speed would be about as efficient as slow acceleration to that speed.

The picture changes if you end up going faster with hard acceleration with efficiency loss due to increased wind resistance.

Or if you increase and decrease speed as regenerative recapture of energy has inherent inefficiency.

Or if you have dual motors, the motor with the higher gear ratio would be used more for hard acceleration and would use more energy than with lower acceleration.

 

[beatle]

My anecdotal evidence shows that there isn't much of a difference in consumption based on how hard you accelerate. All the more reason to enjoy all that power!

 

[ewoodrick]

Just accelerate as the cars around you do.

 

[conman]

Assuming efficiency decreases as speed increases, due to wind resistance, and assuming a single drive motor, and assuming a set final speed:

Fast acceleration to that speed would be about as efficient as slow acceleration to that speed.

The picture changes if you end up going faster with hard acceleration with efficiency loss due to increased wind resistance.

Or if you increase and decrease speed as regenerative recapture of energy has inherent inefficiency.

Or if you have dual motors, the motor with the higher gear ratio would be used more for hard acceleration and would use more energy than with lower acceleration.

Thanks, that was my impression based on my understanding. Dual motors with a less efficient rear more powerful motor would be the only real reason faster acceleration would compromise efficiency.

 

[takedownca]

Your battery's capacity for work (W) is relatively constant and equal to it's electrical storage capacity (E) times system efficiency (c).
W = cE

Ignoring drag, work is calculated by applying a force (F) to move a mass (m) over a distance (x). W = Fx. And the force is equal to mass times acceleration (a).
F=ma

So if your accelerating twice as hard, then you're applying twice as much force, and using twice as much energy. Mind you, this is only during the acceleration. Once you level out you're using the same force to overcome friction and drag, regardless of the acceleration it took to reach that speed. So your overall Watts/mile efficiency will definitely be lower if you accelerate hard, but depending on how often you accelerate the difference may or may not be noticeable.

 

[conman]

Ignoring drag, work is calculated by applying a force (F) to move a mass (m) over a distance (x). W = Fx. And the force is equal to mass times acceleration (a).
F=ma

So if your accelerating twice as hard, then you're applying twice as much force, and using twice as much energy.

Twice as much force, but for half the duration, no?

 

[plumazul]

My anecdotal evidence shows that there isn't much of a difference in consumption based on how hard you accelerate. All the more reason to enjoy all that power!

Depends on what you are worried about consuming. You WILL consume your tires, with regular hard acceleration.

 

[takedownca]

Twice as much force, but for half the duration, no?

Good point. It's been a while since kinematics. Yes, assuming you double acceleration, acceleration time is cut in half, and so is acceleration distance. I stand corrected.

Anecdotally, I get fewer miles per kW when I feel like zooming around, but that's probably because I'm also driving at a higher top speed.

 

[Spacey73]

I’ve often thought about this, going up a hill doing 50 mph using 50kw of energy for 1 mile vs 25 mph using 25kw of energy for 1 mile is going to be pretty close no?

 

[conman]

I’ve often thought about this, going up a hill doing 50 mph using 50kw of energy for 1 mile vs 25 mph using 25kw of energy for 1 mile is going to be pretty close no?

I was specifically looking at acceleration, all else being equal. In your case, the extra drag at higher speed means you will be better off at the slower speed. There is an "optimal speed" and it's usually chosen when people hypermile and it's around 46km/h (29mph). I'm not sure how they come to that value, but perhaps mirrors unfolding at 50km/h is part of it.

 

[BigNick]

Depends on what you are worried about consuming. You WILL consume your tires, with regular hard acceleration.

I now have a picture in my head of a blue, hairy Michelin Man/Cookie Monster hybrid muppet eating tires. With the voice saying "TIIIRES!! Om nom nom!"
I must be weird, because I'm thinking of this while completely straight and sober.

 

[Spacey73]

I was specifically looking at acceleration, all else being equal. In your case, the extra drag at higher speed means you will be better off at the slower speed. There is an "optimal speed" and it's usually chosen when people hypermile and it's around 46km/h (29mph). I'm not sure how they come to that value, but perhaps mirrors unfolding at 50km/h is part of it.

I get it, and understood your point. But with efficiencies being as high as they are I think the same thinking applies up to a certain speed. When building hi-power Ebikes the golden rule is to keep speed under 30 mph for efficiency as the quadrupling of power needed for the doubling of speed rule really starts to hit after 30mph on a bike.

I think that a quick not over the top acceleration to get you up to speed which you would then hold is almost as efficient as a prolonged acceleration. With both options not giving huge benefit/negatives over the other energy-wise the only other factor is time.... and I would rather spend less time travelling.

 

[TIppy]

The amount of useful energy you can extract from the battery is a function of how fast you extract it. There is energy dissipated in the internal resistance of the battery. Power is current squared times the internal resistance. The wasted energy goes up with the current squared, whereas the torque generally goes up linearly with current. If you double the acceleration (thereby requiring twice the torque and current), four times as much power is lost to heat in the battery. So even though you accelerate for half the time, you are still dissipating twice as much energy as heat in the battery. This is true also for all other sources of resistance in the drive train like stator windings and semiconductors. Yeah, so accelerating hard is less efficient, but who's counting?

The best speed for max distance is a balance between the constant power required to operate the car even while stopped vs the non-linear increase in power required with speed.

 

[AlanSubie4Life]

The amount of useful energy you can extract from the battery is a function of how fast you extract it. There is energy dissipated in the internal resistance of the battery. Power is current squared times the internal resistance. The wasted energy goes up with the current squared, whereas the torque generally goes up linearly with current. If you double the acceleration (thereby requiring twice the torque and current), four times as much power is lost to heat in the battery. So even though you accelerate for half the time, you are still dissipating twice as much energy as heat in the battery. This is true also for all other sources of resistance in the drive train like stator windings and semiconductors. Yeah, so accelerating hard is less efficient, but who's counting?

The best speed for max distance is a balance between the constant power required to operate the car even while stopped vs the non-linear increase in power required with speed.

One other factor to account for is efficiency of the motor & inverter under load. If you accelerate very slowly or crawl between stoplights at 5mph, you may end up operating the motor in an inefficient low load and/or low RPM condition. So there may well be a happy medium of “normal” acceleration.

We don’t have these curves for Model S/3/X; this just illustrates how it might look. It would be cool to see someone with a CAN reader and dyno generate them...

 

[TIppy]

One other factor to account for is efficiency of the motor & inverter under load. If you accelerate very slowly or crawl between stoplights at 5mph, you may end up operating the motor in an inefficient low load and/or low RPM condition. So there may well be a happy medium of “normal” acceleration.

We don’t have these curves for Model S/3/X; this just illustrates how it might look. It would be cool to see someone with a CAN reader and dyno generate them...

View attachment 482734

When accelerating from zero to 4000 rpm at 200 Nm the efficiency starts at dark blue or around 70%. At 25 Nm it starts at about 80%. You have to get down to about 10 Nm before the efficiency falls back down to 70% at the start. This is because of the magnetization flux which generates no torque. I don't think anyone is going to be accelerating at these low torque values.

When accelerating using ludicrous, the car pulls 1850 amps and the voltage drops from 400 volts down to ~310 volts. So 90 volts times 1850 amps is ~167kw. The power to the motors is about 310 volts time 1850 amps, or 574kw. That means about 23% of the energy from the battery is being dissipated as heat.

There is enough info on the canbus to generate this plot.

 

[conman]

The amount of useful energy you can extract from the battery is a function of how fast you extract it. There is energy dissipated in the internal resistance of the battery. Power is current squared times the internal resistance. The wasted energy goes up with the current squared, whereas the torque generally goes up linearly with current. If you double the acceleration (thereby requiring twice the torque and current), four times as much power is lost to heat in the battery. So even though you accelerate for half the time, you are still dissipating twice as much energy as heat in the battery. This is true also for all other sources of resistance in the drive train like stator windings and semiconductors. Yeah, so accelerating hard is less efficient, but who's counting?

The best speed for max distance is a balance between the constant power required to operate the car even while stopped vs the non-linear increase in power required with speed.

Thanks, that's the kind of informative response I was looking for!