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How does MPG change vs. speed? How "aggressive" is the regenerative braking?

How does MPG change vs. speed? How "aggressive" is the regenerative braking?

Hi all --

Some engineering questions for the knowledgeable ones out there -- just curious about the energy efficiency of the motor and brakes at different speeds?

Context is that I'm familiar with driving my Prius, where:

1) I try to keep acceleration as much on electric as possible when starting from stopped, because MPG of the gas engine clearly changes with the effective gear in use, and
2) when braking, I try to brake as early as possible because (I believe) if too heavy brake is applied, it will revert to mostly mechanical braking.

So my questions are:

1) For a purely electric motor, is MPG basically flat at all speeds? Therefore, no need to start off slowly and "get into higher gears" as soon as possible?
2) What's the balance of mechanical vs regenerative braking balance vs. brake pedal actuation? Is it possible to set the balance to more regen? Will I still need to brake early and lightly to maximize the regen, and not send it into purely mechanical braking?

Thanks for helping my curiosity!

tobi_ger | July 18, 2013

1) certainly not flat at all, see for example the MS dashboard energy scaler (right part of odometer dash); the faster you accelerate or drive, the more power you draw. Or did I misread your question?

tobi_ger | July 18, 2013

Also see William Calvin's great presentation which includes a chart for mileage vs. speeds:
http://www.teslamotors.com/forum/forums/showoff-slideshow-smartphones-and-ipad

soma | July 18, 2013

Well, I guess the first question really is, "neglecting air resistance, is the engine equally efficient (in kwh/mi) at all speeds?"

tobi_ger | July 18, 2013

Hmm... the chart with torque over rpm, which was posted in other threads, may be more relevant to your 1st question?
(* waits for the Pros to answer *)

dtesla | July 18, 2013
PaceyWhitter | July 18, 2013

I would love to know the answer to this question.

On a related note, I have always thought that slowly accelerating from stop improves MPG, would this be the same in the MS? For example, after a tollbooth on the highway would I use a different number of watts if I floored it, got to 65 and then stayed there, or slowly accelerated to 65 and then stayed if I travel the same distance for both?

Mathew98 | July 18, 2013

Flooring it always consume more energy then gradual acceleration. This rule is no different than ICE vehicle.

However, who cares about the efficiency when you can floor it and ENJOY it every single time? How much is that Telsa grin worth??? I would gladly pay the differential on my electric bill for every bolting opportunity.

Now when you had your fill of the joy ride, then you may resume driving with brisk acceleration and cruise control under 60 to maintain the optimal EV efficiency.

Flaninacupboard | July 18, 2013

Slowly accelerating to target speed may use less power than accelerating hard to target speed, because your average speed will be lower. However, travelling below ~20mph is non-optimal due to constant loads, such as the computers, displays, illumination, climate control, battery/inverter cooling systems etc.

The good news is it really doesn't matter how you accelerate in the S, or other EV's, it's about how you brake, i.e. best is to never brake at all and gently roll to a stop where you want to, second best is regen, and then mechanical braking is right at the bottom.

dirkhh | July 18, 2013

The question was about "low gears" and the comparison to a Prius.

The Tesla has no transmission. One single fixed gear, it's all done via rpm of the motor.
The torque of the motor is nearly constant for big part of the RPM range. At some point you no longer have enough current to feed the beast and it tapers off.
And at every RPM level, the more aggressively you accelerate, the more current the engine draws, the lower your efficiency.

So while this has nothing to do with the "low gears" vs "high gears", it has to do with physics.

Driving like a hyper-miler: best range. So if you have an S60 (208 mile rated range) and need to go to a place 200 miles away, I'd go really easy on acceleration, keep it under 60mph and watch for every opportunity to avoid hitting the break pedal and using just the engine instead (and make sure you are in standard mode for regen)

Driving like a drag racer: if you floor it at every traffic light the cost will be significant. Not so much in electricity, but in tires and wear and tear on the car. We had the threads here about people with worn rear tires in 5k miles. No offense to those, but I wonder how much they are enjoying their Tesla's acceleration capabilities.

Most everything in between: there's a correlation between how quickly you pull away and how much electricity you consume; for example on my commute (20 miles, half neighborhood roads with lights, half freeway) the difference between "really softly" and "woooo this is fun" is something like 6kWh vs. 8kWh. Or 22 cents. I think I'll go with "woooo this is fun".

PaceyWhitter | July 18, 2013

"And at every RPM level, the more aggressively you accelerate, the more current the engine draws, the lower your efficiency."

I don't think anyone would disagree with that, however it is also true that maintaining highway speed is more efficient than accelerating toward highway speed.

In an ICE with multiple gears, the effeciency hit for rapid acceleration is larger than the effeciency gain from the time maintaining highway speed so it is more advantageous to gradually accelerate (or that is always what I have been told).

I was just wondering if that was the same in the MS with the single gear.

rdrcrmatt | July 18, 2013

@ dirkhh

Regen on low?

I've heard this both ways, that regen to max and modulating it with your foot is best, and i've heard keeping it on low is best.

Why do you suggest keeping it on low? Is there a technical advantage you can expand on?

bcimae.co.us | July 18, 2013

Without referring to other posts with graphs, the speed of the motor is determined by the frequency of the alternating current. Except for frictional losses, fairly independent of power. The power of the motor is determined by watts ( the product of amps and volts). There are some other components (climate, computers and such) but at highway speeds the major factor is air resistance which goes up at the square of the speed. For example,
50X50=2500 and 70x70=4900 so it takes nearly twice as much energy to travel 70 mph as it does 50 mph. As for stopping, the most efficient thing is to coast to a stop by placing the car in neutral (not very safe) or feathering the go petal to make the needle on the energy meter go away but you will roll 'forever'. The second efficient thing is to use regen braking which will convert motion into electricity. The least efficient is to use your brakes, that converts motion into heat which is not recaptured.

ye | July 18, 2013

soma, about your second question: The brake pedal controls only the mechanical brakes. Regenerative braking is accomplished simply by letting up on the accelerator sufficiently far.

soma | July 18, 2013

Ah, one of the answers I was looking for - thank you, ye. This is different from the Prius, where I can feel and hear the effects of the regen when using a small amount of brake (like 2" worth of pedal depression). More than that, and I believe the mechanical brake kicks in.

Is the regen very strong by itself? Why doesn't Tesla allow you to control the regen and turn on more by pressing some of the brake?

kback | July 18, 2013

Regen is definitely strong. It feels like you are actively braking when you lift all the way off the accelerator. It feels strange at first, but once you get used to it, it's great. One pedal driving most of the time.

jbunn | July 18, 2013

Regen is fairly strong. Settings are configurable.

Mathew98 | July 18, 2013

Regen also kicks in when you press on the brake pedal.

Try this out for yourself: stomp on the brake, the regen will definitely kicks in first, then the mechanical brake will bring the car to a stop.

soma | July 18, 2013

Ok, thanks -- if this is correct that the brake also turns on some regen, does applying regen brake aggressively "at the last minute" regen just as much as braking early and gradually?

This would change my habit from being a "Prius" driver to being a more sporty driver, enabled by the technology.

It's the reverse question of the accelerating slowly vs. quickly from start.

Mathew98 | July 18, 2013

@Soma - Try to drive the MS primarily using the go pedal and only engage the brake for stopping. Once you release the pressure on the go pedal, regen will kick in and slow down the momentum of the MS until it is less than 5 mph, then you should use the brake to bring it to a complete stop.

It is a much easier driving dynamic than driving a hybrid. It took me a few days to adjust to the one pedal driving...

If you are looking for efficiency, then speed up brisky without flooring it and maintain speed around 60-65 using cruise control if possible.

However, do this at your own risk. I usually just bolt it from stop or merge to speed limit + 10 mph and then maintain speed. This is how you get the Tesla grin without getting the tickets...

ye | July 18, 2013

Mathew98, are you sure? When you press the brake pedal, how can you tell the difference between increased regenerative braking and application of the friction brakes? Does the power meter to the right of the speedometer indicate more regenerative braking than before?

I've never driven the car myself, but I've read the manual, and it just says, "Regenerative braking - when you take your foot off the accelerator when driving, regenerative braking slows the vehicle and feeds energy back to the Battery." (p. 14 of the Model S Owners Guide, available at https://www.teslamotors.com/mytesla/manuals/)

jonerickson1 | July 18, 2013

I watched a drag times video where they did the 1/4 mile and then let the max regen go until they reached 15mph. They used 1.1 Kwh in the first 1/4 then took 3/4 of a miles to slow to 15. The net was around .5 KWh used so 500-550 wh/mile which is about twice the normal usage. Does that help?

GuyDormehl | July 18, 2013

This is an interesting thread - even though I can only dream of a Tesla living in South Africa (small connection thru Elon..!)

I was wondering if anyone can answer the following:- if three Teslas of varying power motors and battery size completed exactly the same route at the same speed at the same time, would there be any difference in electrical consumption? Does a larger motor use more (or less?) juice to achieve the same performance in a similar way that various capacities of ICE engine may do?

soma | July 18, 2013

I guess what I would do when driving is apply the brake up to the point that it "maxes" out the regen green indicator. After that, you must be getting significantly into mechanical braking.

But I would still like to know what the balance of regen/mechanical braking is, within the green zone.

PaceyWhitter | July 18, 2013

@Ye

The brake pedal has nothing to do with regen. When you lift of the go pedal (can't call it gas) regen kicks in, the regen meter goes into the green and you can definitely feel it. It feels alot like engine braking in a manual transmission ICE. (at least when regen is set to standard)

When you press the brake pedal you are engaging the friction brakes so you should try to do that as little as possible (and once you get used tto it, you only have to push the brake to come to a full stop)

@GuyDormehl

Electric motor power has absolutely nothing to do with efficiency, the p85 would get exactly the same mileage as the standard 85 in your situation.

create | July 18, 2013

@soma. Don't loose sleep thinking about this. Once you get your s you'll get the hang of it rather quickly. What you will find is that you really only need to hit the brake when you want to come to a complete stop. For most slowing down situations, taking your foot off the go pedal will be enough to slow you down. It really slows you down a lot. I have a 50mi commute 90% freeway and a handful of lights and the most I use the brakes is about 10 times in a commute, usually less. This includes some heavy traffic on the 880 in the Bay Area.

HenryT2 | July 18, 2013

The brake pedal is purely mechanical. Those who claim that there is regen when they stomp on the brake are seeing the results of having taken their foot off the accelerator (I'm going to assume no one is "stomping on the brake" without reducing their acceleration).

Mathew98 | July 18, 2013

Hold the sarcasm...

i was explaining to a fellow hybrid driver that regen works quite differently in an MS vs a hybrid. Hybrid regen only kicks in while the brake pedal is engaged whereas the MS regen kicks as soon as the pressure is off the go pedal.

Try and put my comments in this context. I did encourage only using the go pedalfor regen...

jbunn | July 18, 2013

Matthew was correct. Lift off the go pedal and regen kicks in. You might never need to kick the brake. But if you do, regen kicks in even more.

Regarding acceleration - Does it take more power?

Hmmm... So question is more complex that it seems.

Let's say I take off fast from a stop. My watts per unit of time are higher than if I take off slowly. On the other hand, my watts per unit of distance are not as high. I'm moving much faster, so I travel a greater distance even though I use more power. I also have converted more potential energy into kinetic energy on a fast start. So if I start to coast I'm going to cover more ground.

As an experiment, if you accelerate briskly, then put the car in neutral and measure the distance covered and power used, I suspect that it won't consume significantly more power than if you creep to a speed then put the car into neutral and end up at the same distance.

Electric cars do not follow the same "rules" as gas cars, as they are not "engines", but are motors.

cfOH | July 18, 2013

Matthew was correct. Lift off the go pedal and regen kicks in. You might never need to kick the brake. But if you do, regen kicks in even more.

That's not my understanding because the MS would have to have regenerative energy capture in the brakes (like a Prius does) and it does not. All the regen comes from using the car's inertia to force the motor's rotor to turn inside the coil (via the drivetrain), thereby generating current back into the battery. So, if you let your foot off the GO pedal, the forward motion of the car creates regenerative recharging until the car stops. If you use the brakes, you transfer some of that kinetic energy (momentum) into heat (via friction between the brake pads/rotors) rather than into current for the battery via the motor and inverter.

At least that's how every authoritative explanation I've seen describes it.

nickjhowe | July 18, 2013

@jbunn - what's the source of your "kicks in even more" comment.

Like cfOH this statement is the opposite of everything I've ever seen and heard about Model S (and Roadster behaviour). Braking does NOT affect regen beyond the fact that regen varies with speed and since braking affects speed...

Back to the original question...
Assuming (and it is a big assumption) that the efficiency of the motor does NOT vary under different load conditions, then using distance as a basis (energy used per mile), accelerating hard to a speed and then staying there uses more energy (because you are spending longer at a higher speed so higher wind resistance). If you do enter a measured mile at 35mph, immediately accelerate to 60 in 3 seconds and then stay at 60 for the remainder of the mile you will use 0.3% more energy than if you'd accelerated over 6 seconds, and 3% more than if you'd taken 30 seconds.

The extra energy is purely down to spending longer at a higher speed.

This is VERY different to an ICE engine where engine efficiency varies dramatically over the rev range.

But - repeated, constant hard acceleration (like at a racetrack) DOES cause heating in the battery and motor and efficiency does decrease.

So - hard acceleration in an S uses slightly more energy per mile than lesser acceleration due to higher average speed.
And regen is purely on the motor, so avoid the brakes when possible.

But if you are tending towards hypermiling then you need to turn off regen and start coasting. But that is a whole different discussion.

Brian H | July 18, 2013

goose pedal. "Goose it!!" Honk!

jbunn | July 18, 2013

Nick, cfoh,

Regen on the brake pedal is based soley on my own observation. While there is a mechanical braking system, it may be a faulty assumption to think that the brake pedal does not trigger regen on mild braking, or in addition to mechanical braking.

As an experiment, get to speed, and put the car in neutral. Foot off the go pedal, no cruse control. Car should display no regen. Now use the brake. Repeat at different brake pressures. My guess is the car will regen.

If I drive her tomorrow, I will test. If you guys do first, let us know.

Brian H | July 19, 2013

No, in neutral no regen under any circumstances. The motor is not linked to the wheels in neutral. That's what it means.

rch1708 | July 19, 2013

Question: if I understood correctly, a couple of posts have said that the most efficient way of slowing down is coasting to a stop, second most efficient is using regen, third is braking. How come coasting is more efficient than regen? In terms of energy dissipation, coasting to a lower speed/stop dumps the excess energy into the environment, whilst regen effectively "recycles" it. Or am I missing something?

Jolanda | July 19, 2013

I would like to ad some details to the discussion.

Accelerating:
When you draw a lot of current, the resistance in the battery, the cabeling, the inverter and the motor will cause a voltage (U) drop. That means that you need extra current (I) to get the same performance (P = U x I). That extra current makes it worse, because the voltage will drop even further. At the same time all the parts with resistance are getting hot. This makes the situation worse again, because heat raises the resistance.

So yes, moderate acceleration is more efficient from that perspective.

But there is more.

To accelerate, the electric motor needs to rotate the magnetic field in the stator in an angle to the field in the rotor. When you try to accelerate fast, the angle in the field wil be larger and the efficiency of the motor then tends to drop. I don't know the specific data of the Tesla motor, but most electric motors tend to be more efficient when in the middle of their performance range.

Also when accelerating fast, the traction control will try to minimize wheel spin. But you will get a small difference between the rotation of the wheel and the amount of distance travelled. This is due to deformation of the tyre and a bit of dynamic friction of the tyre to the road. This will also hurt the efficiency.

End conclusion: yes, accelerating fast uses more energy but it brings a huge advantage "The Tesla Grin!"

Constant speed:
A constant speed between 20 and 50 miles an hour is efficient. If you go higher than 50 m/h the air resistance will build up fast. So if your range is not sufficient, slow down... Wind will eat up efficiency even faster, head wind (12 o'clock) is bad but 9 and 15 are even worse.

Braking:
Braking with friction brakes is highly effective but the efficiency is zero. All the energy is converted to heat and dumped in the environment.

Braking using regeneration is effective but limmited to the amount of power that you can put back into the battery without doing harm to the battery. The efficiency of the proces is high, but you are losing energy in the generator (10%?), resistance in the cabeling and gears (5%?) and in the chargeproces of the battery (10%?).

Coasting to a halt by using "Neutral" or by "feathering the go pedal", is the most efficient by avoiding any losses. Braking effectivity is nearly zero, you will need tons of space to get to a halt.

rch1708 | July 19, 2013

Jolanda: when you coast to a stop, all the energy, (1/2 MV^2), is lost, surely. When you stop using the regen, this energy is not lost, it's (partially) put back into the battery pack, is it not? Certainly there's hysterisis, ie losses in the total system, but this has to be better than just bleeding all the energy away using air/motion friction to coast to a stop.

Or do I misunderstand something about how the MS coasts to a stop in neutral?

Jolanda | July 19, 2013

You are dismissing the distance traveld during coasting to a halt. When you would have kept constant speed for that distance and would have used regenarative braking for the last meters to come to a halt, you would have used more energy to travel the distance. So, the energy is not lost, but used to travel the distance.

The difference is small, but you can measure it.

On the other hand, I would never use coasting to a halt to get this small amount of extra efficiency. It is annoying for other drivers, needs lots of space and is dangerous behavour.

Regenerative braking is designed to recap the energy that otherwise would have been wasted in friction brakes.

rch1708 | July 19, 2013

Duh, of course. Was a long time ago that I did school physics.

docdac | July 19, 2013

Just as a minor technical point, most of the energy from braking is not transferred into heat. It is transferred into the rotational inertia of the earth. (This, of course, is counterbalanced by cars traveling in the opposite direction).

Mathew98 | July 19, 2013

@Jolanda - Good summary of what most MS drivers experienced.

For those posters who regurgitate everything they read online, please let the actual owners experiment and proof or disproof the statements posted.

Go pedal rules and avoid using brake and use regen as much as possible.

Bolting every chance you get to obtain that constant silly Telsa grin.

NICE | July 19, 2013

The Teslas are different than other Electric cars or Hybrids in that they have big batteries with long ranges.
In other cars you need to drive like a Grandma to maximize your range because their batteries are small. In a Tesla you can floor it all the time, have a blast doing it, and still have plenty of juice left. You can drive like Grandma on long road trips.

tsx_5 | July 19, 2013

Lots of interesting discussion here... A number of references to wind resistance being the largest factor, which it's not -- terrain is (for or against). Anyone want to comment on best strategies when dealing with non-flat terrains?

ye | July 19, 2013

Brian H, I'd guess you're right about the lack of regenerative braking in neutral, but I'm not sure what you mean by saying that "the motor is not linked to the wheels in neutral." Does the Model S have a clutch? I don't think so. Probably it would be more accurate to say that, in neutral, the motor is electrically disconnected from the battery.

docdac, are you thinking of momentum, perhaps, instead of energy? When a car brakes to a stop, its momentum is transferred to the earth, but its energy is not. Its energy turns into heat in the brakes.

hsadler | July 19, 2013

Not a physicist, but I believe it is much safer to institute Regen that is 'not' disengaged when the brake pedal is applied. If it were, the rate of stopping would be unpredictable during the Regen disengage.

@dodac Also, in addition to cars going the opposite direction, earth rotational inertia is counterbalanced when a car accelerates.

Jolanda | July 19, 2013

@tsx_5: at normal speeds (0 - 70 mile/hour) you are right. Above 200 mile/hour you need far more than 320 kW to keep your speed.

That is driving at top speed with a very strong headwind. It wil drain your battery in minutes....

Going up also uses a lot of energy, but you wil get some energy back when going down.

jbunn | July 19, 2013

I believe Ye is correct in that there in no mechanical disengagement between the motor and the wheels. I think the gearbox is a simple reduction. Disengagement is easy enough, but to reengage you'd need to synchronize the gears, which makes the gear box overly complicated.

Rolling resistance is very very low in neutral though. I was at a car wash, and had to put the car into neutral on level (I thought) ground. Apparently not. Any tiny slope and she wants to roll off. I think that's a great testament to the Tesla engineers efforts to reduce rolling resistance.

I'll still try the neutral experiment to see if even in neutral regerative braking works in conjunction with mechanical braking just for (Tesla) grins.

docdac | July 19, 2013

@ye. It's a long time since college physics for me. But the kinetic energy of a moving car is primarily transferred to the earth, changing its momentum ( which is what I meant by changing rotational inertia). Only a small part of the kinetic energy is transferred to heating the brakes. If you look at how much kinetic energy is lost (1/2 mass*velocity squared?), that would be a whole lot of heat!

wcalvin | July 19, 2013

Much carryover Prius thinking here. Once the common rotation shaft of motor and inverter slows via initial braking, energy is recaptured as DC charging.

Here's that range curve again:

That erased curve faintly seen below the Model S curve is the Roadster curve: same slope but reduced capacity.

soma | July 19, 2013

I think this is all getting a bit more complicated / misunderstood as we go. I'd just like someone with simple electric engineering background, or real knowledge of the vehicle systems to explain.

I think the root of my question is relatively straightforward, and for the moment, I wish to neglect air resistance at relatively low speeds. I want to take all the confusion about the car out of it.

1) Energy expended per rotation of an electric motor -- is it constant versus the speed/rpm of the motor? Or does low speed rotation use more energy per revolution (under some steady load)?

2) Does pressing the brake cause an inductive / regen circuit to be engaged, or not? (i.e. additional over the regen setting you have chosen when there is no brake and no throttle applied) How much, up until mechanical braking action kicks in?

Thank you, to anyone who can answer these engineering questions!

Alex K | July 19, 2013

@soma | JULY 19, 2013: 2) Does pressing the brake cause an inductive / regen circuit to be engaged, or not? (i.e. additional over the regen setting you have chosen when there is no brake and no throttle applied)

Short answer: No.

The brakes and the regen are decoupled. This is Telsa's philosophy of regeneration. You drive mostly with one foot, letting up on the accelerator to engage regen and slowing down. You can press on the brakes at any time, but they do not add any more regen. This way, Tesla does not have to balance the amount of regen vs. friction braking that other manufactures have to do.

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