F = m * a

There's some loss of efficiency due to tire flexion, I don't have the formula for it but intuition tells me it's a scary curve like wind speed pushback is.

Discussed several times before on TMC, good discussion if you search for it.

In short:

In theory: no difference between accelerating quickly or slowly (power is higher but energy used to achieve a given speed is the same).

In reality: more losses with higher acceleration. Heat losses due to higher current draw (inductive heat loss), heat losses in drivetrain (friction) and tires (slip, wear, heat).

Debate: how far off is theory from real life.

Consensus so far: Difference is smaller with EVs than ICEs.

Some say the difference is small (I'm in this camp), some say the difference is still big and will result in a large "range penalty" in real life conditions.

(My view is that the difference people find is mainly due to other, related factors such as more braking and going faster in general).

I have attempted to measure the amount of energy consumed during slow acceleration vs. fast acceleration for an EV. Fast acceleration used more energy. The following chart shows my analysis. The dashed lines are fast acceleration and the solid lines are slow acceleration. In both cases, I travel a distance of 0.25 miles and end up at 40 mph at the end of the 0.25 miles. For fast acceleration, I reach 40 mph after 0.05 miles. For slow acceleration, I reach 40 mph after 0.25 miles.

The red lines show the energy consumed from the battery. The difference is small, about 0.009 kWh. The green lines show how much of the energy consumed is due to friction, i.e. aerodynamic drag, tire rolling resistance, and internal frictions. About 0.006 kWh of the difference is due to friction. The remaining difference 0.003 kWh is due motor/inverter efficiencies. This difference is hard to measure.

Johan said:

Some say the difference is small (I'm in this camp), some say the difference is still big and will result in a large "range penalty" in real life conditions.

(My view is that the difference people find is mainly due to other, related factors such as more braking and going faster in general).

Click to expand...

I think your view is correct. The difference is large for me because my "base energy use" is low (250). if my base energy use was high (370), I would probably think the difference was low. My experience is that the slower you accelerate and the longer it takes you come to a stop, the less energy you use. At the P85D drive event I saw the energy use was around 700, and that's probably a worst-case as the idea was to accelerate as fast as possible over a very short course. That makes is close to 3x for me and less than 2x for the high use case.

@iphe -- it's not immediately obvious, do you normalize for the much greater mean speed in your high-acceleration runs? It seems as though it would be improper to account those as "lower efficiency" when what you're really doing is going faster on average.

jgs said:

@iphe -- it's not immediately obvious, do you normalize for the much greater mean speed in your high-acceleration runs? It seems as though it would be improper to account those as "lower efficiency" when what you're really doing is going faster on average.

Click to expand...

The green lines take into account the additional friction (aerodynamic drag, rolling resistance, internal friction) associated with higher average speeds during fast acceleration vs. slow acceleration. The difference at the end of 0.25 miles is about 0.006 kWh more energy consumed from the additional friction

Motor efficiency refers to the motor is more efficient when outputting higher power. Its outputting higher power longer for slow acceleration because you are accelerating longer.

lphe said:

The green lines take into account the additional friction (aerodynamic drag, rolling resistance, internal friction) associated with higher average speeds during fast acceleration vs. slow acceleration. The difference at the end of 0.25 miles is about 0.006 kWh more energy consumed from the additional friction

Motor efficiency refers to the motor is more efficient when outputting higher power. Its outputting higher power longer for slow acceleration because you are accelerating longer.

Click to expand...

So how much of the extra energy used is due to the fact that you are traveling the same distance in a shorter period of time? I.e. going faster on average (unrelated to going quicker)?

The batteries will be less efficient at a 4c output vs 1/2c or whatever slow acceleration uses. You should be able to draw more total power at a lower output

This is what it feels like as it can be hard to remember or plan ahead enough to coast after hard accelerations. Even more so in Insane mode

Johan said:

So how much of the extra energy used is due to the fact that you are traveling the same distance in a shorter period of time? I.e. going faster on average (unrelated to going quicker)?

Click to expand...

Of the total 0.009 kWh of additional energy for fast acceleration, 0.006 kWh is due to traveling the same distance in a shorter period of time. This is the difference between the dashed and solid green lines. But it is very difficult to measure such small differences accurately.

But note, that even though the motor is more efficient outputting higher power, the battery provides less total energy when outputting higher power (Peukert's Law).

The efficiency pulling energy out of the battery is better at lower output levels.
See page 4 from this presentation http://naatbatt.org/uploads/Arch-Padmanabhan.pdf where it shows that the efficiency is significantly better at C/4 than C/2.

How does it change when you go from C/4 in your car ( ~22kW ) to 2C ( ~170kW )? No idea, but the difference could be large.

Edit: I see Zextraterrestrial beat me to the point while I was finding the PDF via google.

lphe said:

Of the total 0.009 kWh of additional energy for fast acceleration, 0.006 kWh is due to traveling the same distance in a shorter period of time. This is the difference between the dashed and solid green lines. But it is very difficult to measure such small differences accurately.

But note, that even though the motor is more efficient outputting higher power, the battery provides less total energy when outputting higher power (Peukert's Law).

Click to expand...

Thanks, now the graphic makes sense to me

Yes resistance increases squared with a doubling of current draw from the battery and through the wiring. So the same does electric heating losses. Drawing 300 kW during heavy acceleration is very different from drawing 80 kW during lighter acceleration. The current has to increase even more than the simple power=voltage x current equation would suggest, since there's a voltage drop on heavy draw.

But in cold climates, with the need for cabin heating, quite a bit of that heat can go to the cabin.

The charts were not made driving a Tesla. But I would expect similar results. The max power output of the battery in my car is 68 kW. I don't know how things would change for a P85D. You would probably need a racetrack to properly measure the effects of fast acceleration. I'm doing this over short distances in a residential neighborhood on a level section of road. I didn't try maximum acceleration. In fact, I have never tried max acceleration in my car

The theory:
You are at a stoplight on a 55 mph road. Light turns green. You accelerate slowly to 55 mph or quickly to 55 mph. The energy difference is negligible.

The reality:
You are at a stoplight on a 55 mph road. Light turns green. You accelerate slowly to 55 mph or floor it and hit 70 mph before you realize it and slow back to 55 mph. The energy difference is significant.

While the theory is true, in practice the reality supercedes.

The following is an explanation of why fast acceleration less efficient than slower acceleration.

The plot below is the Electric Motor Map for a Prius. The x axis indicates rpms. The y axis indicates torque. The contour lines indicate efficiency. So at 20 Nm of torque and 3000 rpms, the motor is about 93% efficient in converting electrical power to mechanical power.

If you accelerate quickly, you operate the motor along the top line labeled fast acceleration. You are operating the motor for a long time in some of its most inefficient regions. You start out at less than 73% efficiency and you will inefficiently consume high power from the battery for quite some time before efficiency reaches 90%. You have consumed most of the energy required to accelerate while the motor is operating inefficiently.

If you accelerate more slowly, you operate the motor along the line labeled slow acceleration. You again start out at less than 73% efficiency. But this time, you inefficiently consume less power from the battery for less time before efficiency reaches 90%. You are consuming more of the energy required to accelerate while the motor is operating more efficiently.

This is a rather small motor. But the principles behind this analysis should also apply to the much larger Tesla motor. If only someone had a map for the Tesla motor, we could determine how much faster acceleration impacts efficiency.

Johan said:

Thanks, now the graphic makes sense to me

Click to expand...

For a more detailed analysis of how fast acceleration impacts my car, see the posts I made in this forum:

EV Dynamics Physics Experiment - Page 2 - Energi Driving Tips & Tricks - Ford Fusion Energi Forum