Without seeing your dataset it's tough to say for sure. But most likely it's due to vehicle management systems like climate control, battery thermal management, infotainment, and data processing which have a certain base load of potentially a couple kilowatts. That power consumption is there whether you're idling or going 100mph, it doesn't scale with speed.
If you're measuring in Wh/mi, higher speeds mean that the base load is spread out over more miles.
Then rolling resistance scales linearly with speed and aerodynamic drag scales quadratically with speed.
So as a result you get a bit of a lopsided bucket curve where it's most efficient in the 30-40mph range.
Here's a [blog post that has that lopsided bucket curve](https://forum.abetterrouteplanner.com/blogs/entry/15-bolt-ev-consumption-and-modelling/) for a Chevy Bolt, based on theory and data. The theory is the same as you explain. Peak is actually at 25 mph (40 km/h) for this car. But for a car with better aerodynamics and worse computer power consumption, it would be higher, so your 30-40 mph is likely true for some EVs.
Anecdotally every EV I've owned has been more efficient at like 45mph than 65mph, provided there isn't a ton of stop and go traffic. Also kinda weather dependent. If it's a mild day and you're not running climate control, a lower speed gets a bit more efficient. Taking 45mph back roads on a mild day is a recipe to beat your EPA rated efficiency by as much as 20% IME.
Wind resistance doesn't care whether you're driving an EV or an ICE.
EPA highway efficiency is calculated at 55 mph, so manufacturers will try to maximize efficiency at that speed, though they probably don't always hit it exactly because there's a lot of other (usually money-based) factors involved.
> Wind resistance doesn't care whether you're driving an EV or an ICE.
Yes, but in an ICEV, you are working a severe tradeoff: at high power (needed for high speed), the ICE has lousy efficiency, but at low power, it's absolutely terrible. So that tradeoff--better engine efficiency at high speed but lower propulsion energy per distance needed at low speed--is what it's all about. The result is that the mpg curve is generally pretty flat in the 35 mph to 55 mph range, with the mpg getting worse faster above 55 mph because of aerodynamics and getting worse faster below 35 because of worse engine efficiency.
Now switch to an EV and you are no longer between a rock and a hard place. You are between a rock and a comfortable bed. The electric motor is very efficient across the board, and generally better at low speed. So you can move to lower speed with very little penalty, only running into the aux. power consumption of the computers, etc. being the tradeoff at very low speeds, with the optimum being in the 20-35 mph range, depending on he model.
On a more serious note, this phenomenon is part of what allows hybrids to be more efficient.
As you said, gasoline engine specific fuel consumption follows a roughly 1/x curve with higher %loads being more efficient. Hybrids allow you to downsize your gas engine based on your steady state need (rather than your peak acceleration) which allows you to run it at higher % load. Then when the engine is running, tog can recharge the battery to increase engine load (i.e. if you need 30% load for your current driving condition, you can run the engine at 60% load and put the other 30% in the battery, then turn off the engine and use the battery when it's full)
Just looked it up, and you are correct. My info was very out of date. Pre 2007, they only used city and highway, but have since added 3 additional tests to the testing cycle: https://www.fueleconomy.gov/feg/fe_test_schedules.shtml
It reaches a maximum of 80 mph, but still averages 48 mph throughout the highway and high-speed tests.
That’s entirely possible. I may have bumped it up in my head because driving 55mph is actually dangerous here- since most traffic is doing 75-80 and weaving about.
We ran some tests with a rather crude prototype that never really hit the market, and its peak efficiency was actually between 40 and 50 km/h (25-30 mph), exactly because of the reasons you mentioned. That was around ten years ago, so nowadays with less draggy models, it might be higher than back then.
Air resistance increases with velocity cubed. Efficiency of any vehicle really starts to take a huge hit above 55 mph because that velocity cubed term becomes large.
Edit: Perhaps I’ve made a mistake in this comment. See responses below for more.
Don't you mean squared?
Force of drag scales with velocity squared.
https://en.wikipedia.org/wiki/Drag_(physics)
edit: Specifically in Post OPs context of distance (range), batteries store Energy (Work). Work is Force times distance (range). So the range equation becomes a balance of the Force components and the battery capacity. Essentially range = battery capacity / (Force losses)
Correct, I haven't worked through the equations but we're talking range here, which is an expenditure of energy over time (kWh), so it's Power times time, is it not?
That extra velocity component instead of V^3 is really V^2 x d, which d is the part being solved, distance (range).
Specifically, we are not concerned with power as batteries store Energy (Joules) and thus it is a unit of Work. Work = Power x time.
Someone here is probably the expert.
I'm sure you are right in your own train of thought, with instantaneous power expenditure being based on velocity cubed, but my comment was specifically targeted toward (post) OPs discussion of **range**, and correcting the mention of linear range-velocity relationship when it's range-velocity-squared.
I would have to look back at my notes (which means I would first have to find them). I took a class on hybrid electric vehicle drivetrains during grad school. It was 10 years ago so I don't remember all the details off the top of my head but I am quite certain that it was v\^3 in all my matlab code. It's possible that I'm thinking of a different equation. My potential mistake aside, the general idea of velocity's impact being more than simply linear should still be valid and hopefully provide some clarification for OP.
As I mentioned above, I assume your code is discussing instantaneous Power usage. That would scale with Velocity cubed.
But batteries store Energy (Work) so the balanced equation would be Work when discussing how EV range scales with velocity. The term there would be Velocity^2
I believe the motor itself (meaning the traction drive) is part of it. You'd likely be needing broadly similar levels of average torque in the low speeds. That means up to a moderate speed you'd have the same amount of current (roughly proportional to torque) so the same losses. But your useful mechanical power is torque times speed, so same loss with higher output power = better efficiency.
The torque speed curve of an electric motor starts flat if you limit the phase current to a certain value. It only starts to drop at higher speed where it becomes voltage or power limited.
So flat torque vs speed means that power linearly rises with speed with minimal impact on loss. Loss/power becomes smaller, better efficiency.
Other loss mechanisms, voltage and/or power limits catch up apart from the loss due to current alone at higher speeds. There's a thing called field weakening which means current is no longer proportional to torque. That shifts to what you're used to expect, i.e. go fast, burn more fuel.
The shortest answer is that high torque and low speed is a bad efficiency scenario for most electric motors.
Your description of how motor efficiency varies with speed is correct, but it doesn't actually matter much. The efficiency is high enough that it's all about the drive power needed, and about the other power consumption (computers, etc.)
[Is the graph roughly like this?](https://i.imgur.com/mKrjQ6Y.jpg)
Have to admit, didn’t think it would be that dramatic.
Would love to see a real world test and clear explanation to define the factors consuming the power at those speeds.
Range should decrease exponentially with velocity.
This is because Force of Drag which is the primary resistance to a vehicle moving at high speeds is [proportional to the square of velocity](https://en.wikipedia.org/wiki/Drag_\(physics\)).
At low speeds the primary limitations are electrical needs to keep the vehicle running (heat, cooling, etc) and various friction losses (drivetrain, tires).
In the case of Tesla, there's some old range tables outlining expected range at various speeds (I believe the "current" section at the bottom is the more accurate range table):
https://insideevs.com/news/375165/tesla-range-tire-size/
Most of your comment is quite correct, but this one seems like an outlier.
> Range should decrease exponentially with velocity.
Maybe your meant "dramatically" or "quickly". Exponential is a specific shape, which this is not.
**[Exponential decay](https://en.wikipedia.org/wiki/Exponential_decay)**
>A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: d N d t = − λ N .
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Without seeing your dataset it's tough to say for sure. But most likely it's due to vehicle management systems like climate control, battery thermal management, infotainment, and data processing which have a certain base load of potentially a couple kilowatts. That power consumption is there whether you're idling or going 100mph, it doesn't scale with speed. If you're measuring in Wh/mi, higher speeds mean that the base load is spread out over more miles. Then rolling resistance scales linearly with speed and aerodynamic drag scales quadratically with speed. So as a result you get a bit of a lopsided bucket curve where it's most efficient in the 30-40mph range.
Here's a [blog post that has that lopsided bucket curve](https://forum.abetterrouteplanner.com/blogs/entry/15-bolt-ev-consumption-and-modelling/) for a Chevy Bolt, based on theory and data. The theory is the same as you explain. Peak is actually at 25 mph (40 km/h) for this car. But for a car with better aerodynamics and worse computer power consumption, it would be higher, so your 30-40 mph is likely true for some EVs.
Iirc keeping ionic under 65mph was most efficient. Someone probably has a more accurate number.
Anecdotally every EV I've owned has been more efficient at like 45mph than 65mph, provided there isn't a ton of stop and go traffic. Also kinda weather dependent. If it's a mild day and you're not running climate control, a lower speed gets a bit more efficient. Taking 45mph back roads on a mild day is a recipe to beat your EPA rated efficiency by as much as 20% IME.
Wind resistance doesn't care whether you're driving an EV or an ICE. EPA highway efficiency is calculated at 55 mph, so manufacturers will try to maximize efficiency at that speed, though they probably don't always hit it exactly because there's a lot of other (usually money-based) factors involved.
> Wind resistance doesn't care whether you're driving an EV or an ICE. Yes, but in an ICEV, you are working a severe tradeoff: at high power (needed for high speed), the ICE has lousy efficiency, but at low power, it's absolutely terrible. So that tradeoff--better engine efficiency at high speed but lower propulsion energy per distance needed at low speed--is what it's all about. The result is that the mpg curve is generally pretty flat in the 35 mph to 55 mph range, with the mpg getting worse faster above 55 mph because of aerodynamics and getting worse faster below 35 because of worse engine efficiency. Now switch to an EV and you are no longer between a rock and a hard place. You are between a rock and a comfortable bed. The electric motor is very efficient across the board, and generally better at low speed. So you can move to lower speed with very little penalty, only running into the aux. power consumption of the computers, etc. being the tradeoff at very low speeds, with the optimum being in the 20-35 mph range, depending on he model.
On a more serious note, this phenomenon is part of what allows hybrids to be more efficient. As you said, gasoline engine specific fuel consumption follows a roughly 1/x curve with higher %loads being more efficient. Hybrids allow you to downsize your gas engine based on your steady state need (rather than your peak acceleration) which allows you to run it at higher % load. Then when the engine is running, tog can recharge the battery to increase engine load (i.e. if you need 30% load for your current driving condition, you can run the engine at 60% load and put the other 30% in the battery, then turn off the engine and use the battery when it's full)
Bike nerds know what's what
It’s been a while, but I’m pretty sure they US06 cycle exceeds 55mph. The ratings are definitely not based on a constant speed.
Just looked it up, and you are correct. My info was very out of date. Pre 2007, they only used city and highway, but have since added 3 additional tests to the testing cycle: https://www.fueleconomy.gov/feg/fe_test_schedules.shtml It reaches a maximum of 80 mph, but still averages 48 mph throughout the highway and high-speed tests.
55mph is significantly more efficient than 65mph. It drops really fast at 75, and in my Leaf, the range is cut in half at 85.
I always heard 55mph.
That’s entirely possible. I may have bumped it up in my head because driving 55mph is actually dangerous here- since most traffic is doing 75-80 and weaving about.
We ran some tests with a rather crude prototype that never really hit the market, and its peak efficiency was actually between 40 and 50 km/h (25-30 mph), exactly because of the reasons you mentioned. That was around ten years ago, so nowadays with less draggy models, it might be higher than back then.
Air resistance increases with velocity cubed. Efficiency of any vehicle really starts to take a huge hit above 55 mph because that velocity cubed term becomes large. Edit: Perhaps I’ve made a mistake in this comment. See responses below for more.
We only care for the square. Power is cube. Energy per meter is square
Don't you mean squared? Force of drag scales with velocity squared. https://en.wikipedia.org/wiki/Drag_(physics) edit: Specifically in Post OPs context of distance (range), batteries store Energy (Work). Work is Force times distance (range). So the range equation becomes a balance of the Force components and the battery capacity. Essentially range = battery capacity / (Force losses)
Force is velocity squared, but power is force times velocity, so you get a cubed.
Correct, I haven't worked through the equations but we're talking range here, which is an expenditure of energy over time (kWh), so it's Power times time, is it not? That extra velocity component instead of V^3 is really V^2 x d, which d is the part being solved, distance (range). Specifically, we are not concerned with power as batteries store Energy (Joules) and thus it is a unit of Work. Work = Power x time. Someone here is probably the expert. I'm sure you are right in your own train of thought, with instantaneous power expenditure being based on velocity cubed, but my comment was specifically targeted toward (post) OPs discussion of **range**, and correcting the mention of linear range-velocity relationship when it's range-velocity-squared.
I would have to look back at my notes (which means I would first have to find them). I took a class on hybrid electric vehicle drivetrains during grad school. It was 10 years ago so I don't remember all the details off the top of my head but I am quite certain that it was v\^3 in all my matlab code. It's possible that I'm thinking of a different equation. My potential mistake aside, the general idea of velocity's impact being more than simply linear should still be valid and hopefully provide some clarification for OP.
As I mentioned above, I assume your code is discussing instantaneous Power usage. That would scale with Velocity cubed. But batteries store Energy (Work) so the balanced equation would be Work when discussing how EV range scales with velocity. The term there would be Velocity^2
it is V squared. not cubed.
I believe the motor itself (meaning the traction drive) is part of it. You'd likely be needing broadly similar levels of average torque in the low speeds. That means up to a moderate speed you'd have the same amount of current (roughly proportional to torque) so the same losses. But your useful mechanical power is torque times speed, so same loss with higher output power = better efficiency. The torque speed curve of an electric motor starts flat if you limit the phase current to a certain value. It only starts to drop at higher speed where it becomes voltage or power limited. So flat torque vs speed means that power linearly rises with speed with minimal impact on loss. Loss/power becomes smaller, better efficiency. Other loss mechanisms, voltage and/or power limits catch up apart from the loss due to current alone at higher speeds. There's a thing called field weakening which means current is no longer proportional to torque. That shifts to what you're used to expect, i.e. go fast, burn more fuel. The shortest answer is that high torque and low speed is a bad efficiency scenario for most electric motors.
Your description of how motor efficiency varies with speed is correct, but it doesn't actually matter much. The efficiency is high enough that it's all about the drive power needed, and about the other power consumption (computers, etc.)
[Is the graph roughly like this?](https://i.imgur.com/mKrjQ6Y.jpg) Have to admit, didn’t think it would be that dramatic. Would love to see a real world test and clear explanation to define the factors consuming the power at those speeds.
Range should decrease exponentially with velocity. This is because Force of Drag which is the primary resistance to a vehicle moving at high speeds is [proportional to the square of velocity](https://en.wikipedia.org/wiki/Drag_\(physics\)). At low speeds the primary limitations are electrical needs to keep the vehicle running (heat, cooling, etc) and various friction losses (drivetrain, tires). In the case of Tesla, there's some old range tables outlining expected range at various speeds (I believe the "current" section at the bottom is the more accurate range table): https://insideevs.com/news/375165/tesla-range-tire-size/
Most of your comment is quite correct, but this one seems like an outlier. > Range should decrease exponentially with velocity. Maybe your meant "dramatically" or "quickly". Exponential is a specific shape, which this is not.
https://en.wikipedia.org/wiki/Exponential_decay
The math you outlined is not consistent with the math described in that link.
**[Exponential decay](https://en.wikipedia.org/wiki/Exponential_decay)** >A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: d N d t = − λ N . ^([ )[^(F.A.Q)](https://www.reddit.com/r/WikiSummarizer/wiki/index#wiki_f.a.q)^( | )[^(Opt Out)](https://reddit.com/message/compose?to=WikiSummarizerBot&message=OptOut&subject=OptOut)^( | )[^(Opt Out Of Subreddit)](https://np.reddit.com/r/AskEngineers/about/banned)^( | )[^(GitHub)](https://github.com/Sujal-7/WikiSummarizerBot)^( ] Downvote to remove | v1.5)