Why does accelerating fast use more energy than accelerating slowly?

[stopcrazypp]

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

I think we are talking past each other. All the examples in response to you come with the caveat of assuming no frictional/heat losses, in which case integrating force over distance is exactly the same result in both cases of acceleration. For example, in the slow acceleration case, say the force is 50 and distance required to accelerate to a given velocity is 50 (made up numbers). In the fast acceleration case it'll be something like 100 and 25, with 250 as the end result of both. After you reach the target speed the energy consumption is 0 (so it's not a factor).

I took the kinetic energy approach, ItsNotAboutTheMoney completely derived the formula for kinetic energy straight from your example of integrating force over distance, and others described it with conservation of energy.

Of course if you consider frictional losses, there will always be additional losses, but how significant is not that clear.

I did some math about the frictional losses from the higher average speed. The assumptions I made is 0-60 in 10.6 (acceleration of a Prius C, one of the slowest cars in the US market) vs 0-60 in 4.2 (acceleration of P85) and a target speed of 60mph (for easier math). From the graph from the following Tesla blog, I got 193Wh/mi for 30mph and 287Wh/mi for 60mph.
http://www.teslamotors.com/blog/model-s-efficiency-and-range

My results show only 6Wh more is used:

0-60	dist to 60mph (ft)	dist after 60mph (ft)	Wh to 60mph	Wh after 60mph	Wh Total
10.6	466.4	0	17	0	17
4.2	184.8	281.6	7.7	15.3	23

Of course the losses from the higher power output has to be thrown in too, but the additional frictional losses from higher average speed don't appear to be significant.

- - - Updated - - -

From my perch, it seems the misunderstanding here wasn't reaching the same velocity, but the same distance.

The same distance doesn't matter. This is because in the theoretical friction-less case (which is what most people are talking about here), traveling a distance at a certain set velocity doesn't use any energy. Only the acceleration part uses energy.

 

[Brass Guy]

...
My results show only 6Wh more is used:

0-60	dist to 60mph	dist after 60mph	Wh to 60mph	Wh after 60mph	Wh Total
10.6	466.4	0	17	0	17
4.2	184.8	281.6	7.7	15.3	23

...

Only 6Wh? That's a 35% increase in that scenario. I'd call that a lot.

But I think the OP was simply opening a discussion of the efficiency of the drive train under different load levels. So without a lot more real data, we won't know just how much the efficiency changes.

As AndreyATC's informal experiment seems to show, the increase in losses are not significant; as long as you aren't flooring it. Remember that just a little less than flooring it draws half the power - and therefore much less of an efficiency hit throughout the drive train. The power capacity of the system is so great, I bet there'd be insignificant difference in efficiency between conservative and 3/4 go-pedal.

 

[stopcrazypp]

Only 6Wh? That's a 35% increase in that scenario. I'd call that a lot.

6Wh is what typical 110W car headlights would use in 3 minutes or what you would use travelling 110ft at 60mph. It's not significant, esp. if we are looking at the scenario of an on ramp.

Looking at percentage in this case doesn't make sense because you can't realistically continuously repeat such acceleration (so the cost is not going to be anywhere near 35%). For example, if you travel 1 mile on the freeway afterwards at 60mph, that cost will go down to 2%, 0.2% for 10 miles, and so on.

 

[wycolo]

@Stuart - The spring is a much more efficient transformer of potential energy. The losses might be entirely in whatever mechanism is used to perform the slow release of the trap so a comparison can be measured.

In an EV example one must sum all those separate losses that have been listed.

A related but simpler question would be: Is my practice of slowing down on hills really worth doing to save battery, aside from being safer or not?
--

 

[Brass Guy]

@stopcrazypp - I should have paid a little more attention to the units. 6Wh is not a lot of energy as the miles go by. I was thinking about if one were to repeat this a bunch of times like between badly timed lights, but it would take a lot of them (about 50?) to eat up even 1 extra mile's worth.

 

[TEG]

EV Acceleration Efficiency | PriusChat

Ford Focus Electric Forum What acceleration curve is most efficient?

 

[arsharpe]

(Health Warning: I am new to the forum and have only scanned this thread, so apologies if have I missed or duplicated anything from elsewhere)

The following is a slightly view of the question gained from gliding and real world measurements

For a long time when trying to get maximum range I would lightly accelerate to what I thought was most efficient. However, from my gliding experience, when pilots are travelling through sinking air (i.e. coming down quickly because of the air) they adjust their speed (so called the speed-to-fly) to travel faster and minimise the effect of the sinking air (ie spend less time in it) even though the glider will be less efficient at the higher speed. So for each situation of sinking air there is an optimum speed-to-fly.

For EVs they have an optimum speed and torque value. Anything outside this is less efficient and is equivalent to sinking air in the glider and it would therefore seem sensible to trade off inefficiencies in power train, tyres, etc to get back to near optimum speed and torque.

Although I am an experienced electronics engineer I do like to work from practical measurements as they take all the factors into account. Some time ago I tested this theory with a 2011 Leaf accelerating (on the flat) at different rates from 0 to 30 mph and logging used energy with a LeafSpy CANbus tool. In summary they indicated that, in the scenario indicated accelerating harder actually uses less total energy. The optimum acceleration power was never found (stopping the test at 40kw, ie 50% power) because it was uncomfortable to accelerate harder. However, the expectation is that there is an optimum power to accelerate and when getting near the optimum speed this power should be decreased proportioinally.

Applying the same thinking to hill climbing showed (see results) that climbing a hill quite swiftly also minimises energy use. This was a steep hill on a single track road and the speed was limited by road conditions. I hope to repeat the test on significant motorway hill some when.

I must clarify the gliding technique and theory indicates that there is an optimum power to accelerate and an optimum speed to climb each slope of hill. So flooring the accelerator is probably not good.

In summary when extending range I just accelerate quite swiftly to around 30 mph and tail off to the normal cruising speed of (e.g. 40-45 mph). On hills I keep the normal cruising speed.

Hope this helps,
Rob

 

[wndrful]

I think AlexKiritz's current chart explains the reason for higher consumption.
If one steps on the "gas" then the motor is drawing a large current. Drawing large current (1c = 85/60 2c = 170/120 4c = 340/240 and so on) drops the voltage which is due to bringing a resistance (equivalent) in the circuit in series. Current through extra resistance = extra heat generated = additional loss of efficiency.

All one has to do is to look at the % voltage drop and that's roughly equivalent to loss in efficiency. Most range estimates are done around 0.5C or less which has much less voltage drop and higher efficiency.

However this explains the comparison between flooring the pedal v/s driving at average speed. If we are comparing slight more acceleration and then glide v/s constant speed then we will have to start looking at differences between power-train efficiency and drag coefficients.

 

[simonog]

Very high level: heat generated is resistance time the square of current so any resistance in the entire system creates rapidly increasing (much worse than linear) losses as current rises

 

[wndrful]

Very high level: heat generated is resistance time the square of current so any resistance in the entire system creates rapidly increasing (much worse than linear) losses as current rises

True. One can treat (in a crude way) motor as an equivalent resistance ( say Rm) and let's say battery internal resistance is Rb. Then we have motor energy I^2*Rm and heat energy is I^2*Rb. Efficiency is then I^2*Rm/I^2(Rm+Rb) = Rm/(Rm+Rb)

Note efficiency = Rm/(Rm+Rb) has no I (current) component so efficiency will remain same for all current levels( as long as Rb doesn't change). If more current is drawn then heat energy goes up and so does the motor energy consumption but the ratio or efficiency remains the same.

However in real world, as more current is drawn, Rb in the lithium battery increases, ratio goes down ( and we get lower efficiency).

 

[David_Cary]

My take on this - of course accelerating very quickly has an efficiency hit from heat generated. Forget the higher speed since that is easily compensated for by driving style. The real issue is how much heat is generated and is that even significant?

There is very little comparison with full throttle ICE driving. With an ICE you do well at relatively high throttle inputs and low RPM for reasons that don't factor in with an EV at all. If "full throttle" EV acceleration has a 10% hit on efficiency during the acceleration phase, is that significant? I doubt anyone would care.

What is surprising to me is how many people thinking driving like Ms Daisy is the most efficient in an ICE vehicle. The most efficient is to accelerate briskly up to target speed. Not full throttle, not high RPM, but brisk. Ms Daisy was never right. Multiple reasons for this but decreased pumping losses at relatively high throttle inputs and getting to a higher gear as quickly as possible are the main reasons.

Of course in an EV, there are no transmissions and no pumping losses. So heat generated by resistance is the primary issue. That has to be coupled with all the background uses of energy. So accelerating relatively quickly to 25 mph is the most efficient....

 

[commasign]

You're all missing the point! It takes less energy to smile than to frown. The energy saved from having a Tesla grin during rapid acceleration should more than offset the energy losses from motor inefficiencies, friction, etc.,

Does It Really Take More Muscles To Frown Than To Smile?

 

[dhrivnak]

Here is a simple analogy most should understand. Are you more tired if you run a 7 minute mile or a 10 minute mile? For me sprinting fast wears me down FAR faster than an easy jog. Going fast, accelerating fast uses more energy.

 

[David_Cary]

Here is a simple analogy most should understand. Are you more tired if you run a 7 minute mile or a 10 minute mile? For me sprinting fast wears me down FAR faster than an easy jog. Going fast, accelerating fast uses more energy.

Except that is wrong. Biologic does not equal electric or mechanical of any kind. Humans do better and live longer with exercise and for the most part mechanical things wear out.... (so do humans eventually of course)

Going fast certainly costs more energy. Accelerating fast (to the same final speed) is a different set of parameters.

And in general, even humans use about the same amount of calories to cover a certain distance. It is about 100 calories per mile for an average person. Walk a mile burns about the same amount of calories as jogging. When you sprint really fast, you waste a lot of energy so you would spend a lot more per mile.

Sprinting is more analogous to full throttle in an ICE.

What I think is a very rational discussion is how much less the energy penalty is for rapid acceleration in an EV vs an ICE and I think the difference is dramatic. So if you are a lead foot, you really should be driving an EV.

 

[steve_rolfeca]

Fascinating discussion, but I'm astonished that you've gone 3 pages without aerodynamics entering the conversation.

All the calculations about energy losses presented thus far, seem to be working on the premise that you drive your electric car in a vacuum chamber.

Nothing could be further from the truth.

If you switch gears for a moment (pun intended), by far the highest draw on the power plant of a car with increasing speed, is wind resistance.

Two factors to consider:

At freeway speeds and higher, aerodynamic losses dwarf all other considerations. Anyone who follows Bonneville speed records understands this. For a given vehicle that needs 100hp to do 100mph, you need more than 1,000hp to do 200mph, even if all other factors (mass, frontal areas, rolling resistance, etc.) remain the same.

Even at lower speeds, aeorodynamic drag starts to be a consideration much sooner than you might think. To experience this for yourself, stick your hand out the open window of your car at about 45mph. Now try it while holding up a piece of cardboard about the size of an iPad...

Alternatively, look up the data that has been gathered by various parties when designing recumbent bicycles, bike fairings, competition vehicles for solar or gas power efficiency competitions, etc.

 

[steve_rolfeca]

Sorry, meant to say I was surprised that the conversation WENT that far without...

I hope no-one minds my resurrecting a zombie thread, but this subject interests me.

 

[TIppy]

I believe most of the increased losses come from the battery. At max acceleration, 1600 amps, 77% of the power is going to the motor and 23% is heating the battery. At lower acceleration, 160 amps, 98% of the power goes to the motor.

 

[Rashomon]

This is why you have to have efficiency maps and drive cycle models to simulate what the actual losses are. The MEs here are correct in that theoretically it takes the same energy to reach a given speed regardless of acceleration rate, but real powertrains are rate dependent. For ICE vehicles, best efficiency is generally to apply 80-90 percent throttle in a relatively tall gear, as best brake specific fuel consumption (BSFC) is generally reached with an ICE running nearly unthrottled. Accelerating slowly by feathering the throttle in that case takes more energy, ignoring the extra amount of time you spend at speed and the increased aero losses that causes. For electric vehicles in general, the efficiency maps are much flatter, with less variation. Below is an efficiency map of a Parker Hannafin GVM e-vehicle PMAC motor; the dark red is the highest efficiency; the blue/purple is the awful region. You can see that high load at low rpm isn't good, but as speed increases, there's a large region where efficiency is pretty constant -- unlike the extreme variation with an ICE. Really low loads are bad as well. It means in practice you can accelerate relatively quickly with an e-vehicle without it having much effect on your range, unless you're playing urban warrior in city driving and the quick acceleration followed by rapid braking just means you spend more time at maximum speed, where the aerodynamic losses get you.

 

[sorka]

Resistive power losses in the battery pack, drive inverter, motor, and associated wiring are proportional to the square of the current. So doubling the motor current doubles the torque but quadruples the losses.

This is the only valid answer but the effect is a small fraction of why a gasoline engine is less efficient to to get x mass up to y speed.

The primary thing that kills efficiency when accelerating hard with an ICE is air fuel ratio. The harder you accelerate, the richer the fuel mixture in order to prevent detonation. If you accelerate very lightly in an ICE, the AFR can remain near stoichiometric (14:1). The more load the engine placed under during acceleration, the richer the fuel mixture. I have a wide band O2 monitor that I used for years for post pre dyno tuning. Depending on the state of tune, the amount of power, boost, and other factors, the AFR can go as low as 10.5:1.

 

[sorka]

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.

My wh/mile is exactly the same whether I accelerate nice and slow up to x speed or do full on ludicrous launches. What kills my wh/miles is braking...even regenerative braking only recovers about 60% of the energy. That's why I start coasting as long before a stop as I can so that energy is scrubbed off in air resistance and tire resistance.