This may have been discussed before, but I haven't seen anyone lay this out in one place. Reading up on EVs, range is one of the top concerns if not the top concern. Of course some of this is down to the shorter range of BEVs, but there is a lot of discussion about driving slower with EVs to extend the range, and that isn't as big a concern with ICE cars. The information is all out there in different places, but I had to dig out the pieces from various places. Before I started looking for efficiency curves, I suspected the efficiency curves for EVs was narrower than for an ICE. I found the efficiency curves here: http://blog.automatic.com/cost-speeding-save-little-time-spend-lot-money/ https://www.teslamotors.com/blog/model-s-efficiency-and-range This also has some Model S curves: http://insideevs.com/heres-how-speed-impacts-range-of-the-tesla-model-s/ For ICE cars, the Y-axis is MPG and for the Model S it's miles of range, but they will work for this discussion. The peaks of the curves and width of the peaks is most important. On the ICE/hybrid chart, the Prius gets 50 MPG or better between about 33 mph and 72 mph, with 55 MPG or better between about 35 mph and 65 mph. If you discount the small peak at 60 MPG, the range for top 10% gas mileage is about 40 mph wide. The BMW 328i, Honda Civic, and Subaru Outback have narrower curves, but the top 10% curves for these cars are: Outback - 35-70 mph 328i - 40-78 mph Civic - 35-78 mph There are a number of Model S curves out there and all of them vary a bit but all of them peak around 20-30 mph. The top 10% range is above about 405 miles, which extends from about 12 mph to about 38 mph. That's not only a less useful speed range for maximum range, but only about 2/3 as wide. I was wondering why the peak efficiency is so low and narrow for EVs and higher and wider for ICE. ICE cars have transmissions and EVs generally don't. The major productions BEVs: Leaf, BMW i3, and Model S all have 1 speed transmissions. Why is this? Wouldn't a multi-speed transmission help with the efficiency curves on an EV? Due to the nature of electric motors vs ICE, the answer isn't that simple. Multi-speed transmissions loose some of the energy going through the transmission. With an ICE, which is only about 30% efficient to begin with, the losses aren't very noticeable. Plus an ICE needs a transmission because the range of useable horsepower and torque is pretty narrow band of RPMs. A single speed ICE geared to get started would rip itself apart as it approached highway speeds and one geared for highway speeds would stall out trying to get started. A transmission with multiple gears is needed to keep the engine in that narrow band. ICE cars are getting more and more gears and CVTs to try and squeeze out a little more efficiency. ICE engines have 0 torque at 0 RPM, which is why they need to idle. Put a load on an ICE that is running too slow and it dies. Electric motors are the opposite, they have maximum torque at 0 RPM. This is the reason there are all those drag race videos out there of P85Ds and P90Ds blowing away fancy sports cars in drag races. A drag race favors the electric motor car. Get up to highway speeds and those fancy sports cars will usually win. A multi-speed transmission on an EV might be able to boost that efficiency range up a bit, but there are drawbacks, which is probably why it isn't being done. Electric motors can change torque much faster than an ICE. This puts massive loads on a transmission and people who have experimented with transmissions on EVs have often reported the transmission tends to rip itself apart in a very short period of time. Beefier transmissions can be made to handle the beating an electric motor will put on it, but that will add weight and complexity and take up more space. For designs so far, it's easier to just live with the trade offs. There is talk of transmissions for EVs out there, but so far no idea has made it into production as far as I can tell. Tesla experimented with a two speed transmission for the Roadster, but it had reliability problems. I suspect it ripped itself apart from the sudden torque changes. As a sort of aside the energy density difference between gasoline and batteries is pretty staggering too. The Model S's battery pack is 96 gallons in volume. That's less than 1 KWH/gallon, less than 30X lower energy density than gasoline, which has 33 KWH/gallon. Even at 30% efficiency, an ICE is getting close to 10 KWH/gallon out of the car. A 30 MPG car is consuming 1100 KWH/Mi, but since 70% of that energy is being wasted as heat and noise, the actual energy being used to turn the wheels is around 330 WH/Mi. Right in the range you see with a Model S. A 15 gallon tank gets a 30 MPG car 450 miles of range. If the Model S had a battery that had the energy density of gasoline, it would have a 3168 MWH battery good for about 9600 miles on a charge. Even the most anxious would probably have no range anxiety then! Anyway, many people here probably already know this, but I figured I'd put it out there in case anyone was wondering like I was...

Nice looking graphs, thanks for putting these together. Notice the difference on the Model S between 60 mph and 80 mph. This just shows that on days where you are really pushing the limits of the car distance wise, the first thing to do is slow down.

In the first season of Fomula E racing all 10 teams used the same cars to keep startup costs down. For season 2 (which started in October) the teams are allowed to develop their own motors, transmission, and control electronics. Two teams stuck with the first season cars, the others reduced the number of gears in the gearbox, even down to 1 gear like a Tesla. Will be interesting to see when the season is done in July if there is any statistical significant difference.

This is going to sound odd at first, but the reason it looks like the EV has a much narrower range of efficiency is because the EV powertrain is much more efficient for a broader range of speeds. You're trying to look at the top level efficiency, energy consumed per mile travelled at a given speed. That's composed of the efficiency of the drivetrain in converting the stored energy into useful energy and the energy required to cover a mile. The energy required to cover a mile is composed of a bunch of design/operating factors, but they all follow one of three behaviors: First, there are fixed per unit time type loads (heating the cabin, for instance - if it takes 4 kW of heat to keep the driver happy, that 4 kW stays the same whether the car is stopped or driving 100 mph - which means that the energy required per mile for these loads becomes infinite at 0 speed and rapidly drops as you accelerate, reaching 0 at infinite speeds. Second, you have constant loads - rolling resistance in the tires, transmission losses (for a given gear). These loads are a first order function of velocity, and so require the same amount of energy per mile to overcome at various speeds. Finally, you have aerodynamic loading. Wind drag is a function of velocity squared, so it starts as a minor factor that costs almost no energy, but rapidly increases to become the biggest piece of the energy requirement by the time you reach freeway speeds. So if you have a perfect conversion from stored energy into motion (and HVAC) displayed in the form you're using, it'd start with 0 range at 0 mph, and rapidly build to a peak then fall progressively as aerodynamics becomes more of an issue. The location of that peak would be a function of the relative size of the fixed and aerodynamic loads - for a modern car in good weather, it'd probably be in the 20 mph range, possibly a little lower (higher when the weather is bad and you need more HVAC usage - but a substantially worse peak number.) I won't really get into the efficiency of the electric motor/inverter here. The systems used in EVs now are mostly over 85% efficient in the peak range, and over 70% in the worst operating range - meaning that it only puts a ~20% change into the load based curve. That's why the EV range charts look like they do - at low speeds, the fixed loads dominate, and at high speeds the aerodynamic loads dominate, leaving a narrow range in the middle where the two are about equal - the EV's efficiency changes are small enough that you see the whole load curve only slightly distorted. (Aircraft efficiencies actually look pretty similar as they are playing off a "fixed" load in the form of induced drag and a "squared" load in the form of parasitic drag, which is basically the same drag you're looking at in the car. This is where being "behind the power curve" comes from, if you've come across that phrase.) So how come all the graphs don't look like the EV ones? Well, the ICE cars aren't very efficient at getting power down, especially at low power levels. Not only does it take more fuel per unit energy when you produce less power in a given engine, but it can actually take twice as much fuel to produce the same power, depending on the rpm and throttle setting! Here's a wikipedia article on Brake Specific Fuel Consumption - in SI, grams of fuel per kWh of energy produced by the engine, or pounds per horsepower-hour in english system. Ecomodder has a whole bunch of these charts for various engines in a wiki, too. You'll note that on any of these charts (except the lean burn Honda and HCCI engines) the best efficiency comes at nearly wide open throttle and fairly low RPMs. Unfortunately, no one drives anywhere close to there, except for hybrids (The Prius curve is higher and more arched partly because it has lower loads (less weight, better aero,) partly because it converts gas better (Atkinson cycle,) but mostly because it runs the engine closer to optimal bsfcs. Also, all of the engines we put in cars are massively oversized to the speeds we normally drive them at because people like high accelerations. That's why there's the recent trend toward smaller engines with high pressure turbocharging - it gets the basic engine up closer to the operating range on normal road loads, while retaining the acceleration through use of boost. Does it make sense now? The short version is that the EV is showing you the whole load curve while the ICE is so inefficient at low load levels that you can't see the benefits of the low levels - giving it the appearance of a broader range of high efficiency because they never get very efficient. (I haven't tried to do the math, but if you scaled the loads off of the 70 to 85 mph range and used that to graph them all against the EVs, you'd see what you aren't getting from the ICEs - you should really put the whole range over that as the "most efficient" EV part - some of it is just a lot more efficient. ) Walter

I felt that intuitively, but couldn't put it into words. The best analogy I had was it being like test scores. If you're averaging 90%, a 50% on a test will tank your grade, but if you're averaging 30%, 50% will raise your average. The ICE cars can average 30 MPG over a relatively wide range by being a little less inefficient in some areas when drag is beginning to become a factor. ICE engines are at their most efficient when running at constant speed, which you can usually do on a highway, but not in city driving. An electric motor is so efficient to begin with, anything that is going to have an impact on efficiency is going to show up and there is nothing you can trade off for it. Your explanation is better than what I could come up with though.

TL;DR Internal combustion engines are terrible. (Well, there's one crucial advantage: the ability to use energy dense fuel. Really, they're marvels of engineering.)

Thanks for sharing this information. It looks like maximum range for the Model S can be achieved at approximately 25mph.

FWIW, there are also ICE's that have similar efficiency curves. http://avt.inel.gov/pdf/phev/fact2013toyotapriusphev.pdf Those curves are more a function of auto design than anything else (EV versus ICE efficiency).

I really like this thread, and really have nothing to add. But just commenting because I don't want this thread to disappear! :biggrin: Really helped answer some questions I had about ICE vs. EVs. Thanks!