Category: Transportation

Anything related to transportation, including cars, traffic, other modes of transport, and so on.

Post #1705: When is electricity the cheaper motor fuel?

In prior posts, I noted that my “break-even” price of electricity for my wife’s Prius Prime is currently around 24 cents per kilowatt-hour.   That’s the point where running the car on electricity costs as much as running it on gas, with gas at $3.24 a gallon

I can say that with precision because the Prius Prime can use either fuel.  As long as I know the EPA ratings for miles-per-gallon and miles-per-kilowatt-hour, it’s trivial to figure out the break-even rate, for that one car.

Breakeven electricity price = Gas price x (miles-per-KWH/miles-per-gallon)

In other words, if one KWH takes you 7% as far as one gallon of gas, then the break-even price for that KWH is 7% of the price of a gallon of gas.

Call that term at the end —  (miles-per-KWH/miles-per-gallon) — the “break-even ratio”.

Here’s something that I find interesting.  All PHEVs have roughly the same break-even ratio.  To show that, I downloaded the EPA 2022 model year vehicle mileage database.  Using the MPG (gas) and MPGe (electric) figures, and the constant that one mile per KWH is 33.705 MPGe, I was able to calculate this break-even ratio for every PHEV offered in the U.S. in 2022.

Roughly 70% of all the PHEVs offered in 2022 currently have a break-even electricity price between 23 cents and 25 cents per KWH.  That’s using today’s current U.S. average gas price of $3.36 per gallon of gas (per the Federal Reserve Bank of St. Louis).

Note that each one of those ratios is a straight-up apples-to-apples comparison, because it’s literally the same vehicle being driven either as a gas hybrid or as an electric vehicle.

By contrast, for a lot of pure electric vehicles, there is no obvious way to do that apples-to-apples comparison.  Most famously, there is no such thing as a gas-powered Tesla.  Less obviously, even if a vehicle manufacturer offers the same vehicle in gas and electric versions, the versions won’t be identical because factors such as interior volume will change between the models.

An important caveat for the table above is that all of these PHEVs are hybrids, when they are burning gasoline.  That’s going to translate to above-average gasoline fuel economy.  And, because the efficiency of the electrical side of the vehicle does not change much across manufacturers, that’s going to lead to a low break-even price.

But what about those cars where the gas “twin” uses a conventional gas engine?  What would the theoretical “break even” price be, for those nearly apples-to-apples comparisons?   You’d expect that without the hybrid efficiency in the gas “twin”, the break-even price of electricity ought to be higher.

It’s much hard to do this electric/gas “twins” analysis from the EPA data, for a couple of reasons.  First, there aren’t many examples of conventional gas/EV twins.  Second, you have to find them by searching the EPA database for instances of the same model, but different propulsion system.  I also have to rely on manufacturers using the same base model name for both gas and electric models.

I only found four plausible “twins”, and two of them have so many power trains listed for both electric and gas that I’m not sure I’ve made an apples-to-apples comparison.  That said, the two at the bottom appear to be fairly unambiguous twins.  They both suggest a break-even gas price (say) 34 cents per gallon.   Which makes sense, as standard (non-hybrid) gas engines are inefficient relative to the hybrid engines of the prior table.

The outlier is the Mustang, and there’s good reason to believe that’s not a coincidence.  Performance cars have notoriously fuel-inefficient engines.  Likely, the more you move toward the performance end of the gas-car spectrum, the higher your break-even electricity rate is.  And the higher your fuel cost savings would be in switching to a performance electric vehicle instead of gas vehicle.

So, if your only two options were a pair of seemingly-similar cars — one using a standard gas engine, the other using electricity — and you would not consider a car with a hybrid gas engine — and you’re not looking for a performance vehicle — then, plausibly, you could start counting you fuel cost savings at 34 cents per KWH.  Because your gas-vehicle comparison is so inefficient.

Obviously, YMMV.  For any two cars that you consider to be close substitutes — one gas, one electric — you can simply look them up on fueleconomy.gov and do the math.

For example, the Tesla and BMW above have nearly identical interior volume, and are similar in price.  Doing the math, the 132 MPGe equates to (132/33.705 =) 3.92 miles per KWH.  The break-even price of electricity for this pair of cars, at $3.36 per gallon of gas, is $3.36*(3.92/30) = $0.44 per KWH.  Presumably that’s due to the fuel-inefficient engine in the gas BMW, for performance driving.

In summary:  If you’re the sort of person who is considering buying either a hybrid or an EV, at today’s gas prices, your break-even electrical rate is going to be somewhere around 24 cents per KWH.  If you insist that your only realistic choice is either a standard gas vehicle or an EV, your insistence on using the less-efficient gas technology means that your break-even electrical rate is going to be plausibly somewhere around 34 cents per KWH.  But if you insist that your comparison is between gas and electric performance cars, you can plausibly boost that break-even electrical rate to around 45 cents per KWH, or so.  YMMV.

What’s the policy point?

Almost all discussion of electric vehicles either explicitly or explicitly assumes that electricity is a much cheaper fuel than gasoline.  The standard reasoning is that sure, EVs may be more expensive up front, but they’ll pay you back in fuel savings.

By inference, then, there’s an assumption that sooner-or-later, EVs will be the economically preferred choice, owing to their lower fuel costs.

My point is, that’s only true sometimes.

The only true apples-to-apples comparison of gas versus electric fuel costs comes from PHEVs. In that case, the exact same car can use either fuel.  There, the break-even price of electricity is centered around 24 cents per KWH currently, with gasoline at $3.36 per gallon.  Anything cheaper than that, and electricity is the cheaper fuel.

There’s a caveat.  The gas engines in those cars are all hybrids, so that benchmark really only applies to individuals who are considering a purchase of either a hybrid or an EV.  My guess is, that’s most of the EV market.  For those folks, that current 24-cent break-even price is appropriate.  But as you move up the scale of inefficiency, from hybrid to standard gas engine to gasoline performance car, your savings from electricity grow, and your benchmark break-even electrical price rises.

That said, for anyone driving a PHEV now, or anyone considering buying either an EV or a hybrid, that’s the correct current benchmark rate at which gasoline and electricity are equally costly fuels (with gas at $3.36/gallon).

As long as we are talking about PHEVs, or electric versus hybrids, large portions of the U.S. population face electrical costs for vehicle charging as high or higher than that break-even rate.  At current electrical and gas prices, there are no fuel savings from going electric.

First, in New England, recent spikes natural gas prices have resulted in unprecedented electrical rates.  Prices seem to be easing a bit in most states, but only a bit.

Source:  US EIA.

A PHEV user in New England will get little-to-no cost savings from driving on electricity rather than gasoline, assuming they pay somewhere near the U.S. average price for a gallon of gasoline.  Which appears to be true, per the American Automobile Association.  By inference, a New Englander choosing between similar hybrid and EV models probably could not count on significant fuel cost savings from going EV.  At today’s gas and electric prices in that area, a hybrid and an EV would have roughly equal fuel cost per mile.

Source:  AAA, accessed 2/7/2023

 But a far more important population is individuals who cannot charge at home, and must use public charging stations.  This probably includes most of the roughly 30% of the U.S. population that does not live in single-family dwellings.  For these individuals, charging is expensive enough to eliminate any material fuel savings from electricity, compared to driving a gas hybrid.

My experience is that for most public charging stations, it’s just about impossible to figure out the cost.  But I think the following ad is representative of the best rates you are likely to find.

Source:  EVgo.

Ignoring the weasel-wording (“as low as”, “TOU pricing applies”), and paying attention to the monthly fees, none of these options offers any material fuel savings for the PHEV owner or for the individual considering electrical versus gas-hybrid transport.

Bottom line is that at current prices, EVs are going to be a hard, hard sell for people who have to rely on expensive public charging stations.  At least at current gas prices.

Rather than turn a blind eye to that, public policy needs to acknowledge it.

I’m a big believer in electrical transport.  Right now, it doesn’t make good economic sense to a large portion of the population, looking narrowly at purchase price.  And for a pretty big chunk of the population, there will be no material fuel cost savings to offset that higher purchase price.

Maybe that will change, somewhere down the road. Some combination of higher gas prices and lower electrical prices might result in universal fuel savings from EVs compared to hybrids.  But right now, you really shouldn’t based policy on the assumption that everyone will see fuel cost savings from EVs.

Post #1657: The World Turned Upside-Down, Part 2

 

Background:  <=24¢/KWH

Yesterday I calculated the cost of running a Prius Prime on electricity versus gasoline.  At the current U.S. average of $3.24 for a gallon of gas, electricity is the cheaper fuel for a Prius Prime if and only if it costs 24 cents per kilowatt-hour or less.

That calculation was prompted by the claim that in much of New England, it’s now cheaper to run a Prime on gas, rather than electricity.  As it turns out, that’s true.  As of September 2022, most of New England faced electricity prices that exceeded that threshold.  (As did the average price in California.)  I’m guessing that New England rates have gone up further since September, owing to a recent spike in the price of natural gas.

Source:  US EIA.

In a previous rant (Post #1548), I had already noted how expensive public charging stations were.  Not only did I find the one I tried to use to be both baffling and unreliable, you can pay anywhere from $0.50 to $1.25 per KWH for the privilege of using one.  Even last summer, when gas was expensive, it was cheaper to buy gas for the Prius Prime than to charge the battery at the commercial charging station I visited.

I’ll note in passing that there didn’t seem to be anything unique about the Prius Prime in this gas-versus-electricity calculation. I did the same calculation for a PHEV Volvo getting gas mileage about half that of the Prius, and came out with just about the same break-even price for electricity compared to gasoline.  The Volvo simply uses more of either gas or electricity per mile.

The upshot is that, at current gas and electric prices, some fairly large segments of the public will not see fuel cost savings from electric transport.  At the moment, that’s pretty much the entire population of New England and California.  (Though I did not factor in generally higher gas prices in California.)  And, likely indefinitely, that includes people who can’t charge at home and so must use a commercial charging station.

How large?  California and New England together account for about 14% of the U.S. population.  More importantly, near as I can tell, about a third of U.S. residents live in something other than owner-occupied or single-family housing.  Assuming those folks typically have no option other than commercial charging stations, that means at current gas and electric rates, something close to half of Americans will see electricity as a more expensive motor fuel than gasoline. 

I’m a big believer in electric transport.  But I wasn’t quite fully aware of the large fraction of the population for which there are no fuel cost savings in switching to electricity.  Sure, eventually apartment buildings might all come with chargers.  And sure, gas and electricity prices will vary over time.  But right here, right now, electricity is the cheaper motor fuel for only about half the population.

Tesla?  No thanks.

Which got me to thinking about a name that’s been in the news these days:  Tesla.

When we were shopping for our last car, and eventually settled on the Prius Prime, we considered going fully electric.  But I can’t recall giving even a moment’s thought to getting a Tesla.  And offhand, I couldn’t quite remember why.

So I took a look.

Oh, yeah, it’s because I’m cheap.  And because we buy our cars purely to be practical transport.

In any case, here’s the head-to-head comparison between the Prius Prime and the cheapest Tesla, the Model 3 rear-wheel-drive, courtesy of fueleconomy.gov

To boil it down, the cars are equally efficient as electric vehicles, and are the same size (same total interior volume).  But the Tesla costs almost $20K more, and has less than half the range.

The Tesla is faster, for sure.  But in Northern Virginia traffic, that’s more-or-less completely irrelevant.  My zero-to-sixty time isn’t set by my car, it’s set by whatever pace the inevitable traffic dictates.

I’m sure there are some bells and whistles on the Tesla that you don’t get on a Prius Prime. But, to tell you the truth, I don’t much like the ones we got on the Prius.  The very first thing I switched off, from the factory settings, was the automatic-steering function in cruise control.  I guess if I’m driving my car, I want to be driving my car.  Not having the car second-guessing where I want to be on the roadway.

And, to be fair, the Prius lacks snob appeal. It’s a pedestrian workaday vehicle, suitable for middle-class people who have some sense of concern for the environment.  It’s also exceptionally cheap in terms of lifetime cost-of-ownership.  Or so said Consumer Reports, at some point.

But with a Tesla, you can user their network of superchargers.  And if you have to pay for that, you’ll pay an average of $0.28 per KWH.  (That, per a 2021 article in Motorbiscuit.)  And, duly noted, $0.28 > $0.24.  So even with that dedicated network of branded charging stations, at today’s prices, you’ll pay more to fuel your car with electricity than with gasoline.

But the environment …

In America, we burn an average of 600 gallons of gasoline, annually, per licensed driver.  (Calculated from this reference and this reference).  Driving a Prius Prime, I’m guessing that my wife and I are down to maybe 25 gallons each, per year.  (I have to guess, because we go so long between tanks that neither of us could remember when we last bought gasoline.)  That’s the result of driving mostly on electricity, and otherwise driving an extremely efficient hybrid.

In theory, sure, we could reduce that 25 gallons down to zero by going fully electric.  But, honestly, in the context of my fellow Americans, I can only feel but so bad about the 25 gallons.  And that annual quarter-ton of C02 emissions from driving is probably not the worst environmental sin I commit.

But, as importantly, right now, one of the biggest constraints to electrifying the U.S. fleet is the lack of battery manufacturing capacity.  All the majors are now going full-out to build more battery factories.  There just are not enough traction batteries available to electrify the entire U.S. fleet, and there won’t be for years to come.

So the other way to think of the Prius Prime is that it makes efficient use of a scarce resource:  EV batteries.  The same amount of batteries that will build one EV Tesla Model 3 will build about eight PHEV Prius Primes.  Those eight Primes, displacing standard gas cars, will have a far larger environmental benefit than that single Tesla.

Moreover, that big battery, in the Tesla, is mostly wasted, in the sense that the driver will rarely use the entire capacity of the battery.  By contrast, the PHEV Prius Prime has a much smaller battery, that is fully discharged far more frequently.

From that standpoint, EVs are … wasteful.  As long as lack of battery capacity is a hard constraint on electrifying U.S. transport, we’d get a lot more environmental bang-for-the-buck out of PHEVs than EVs.  For the simple reason that a PHEV has a small battery, and uses it hard.  While an EV has a big battery that is hardly used.

Bottom line:  I just don’t see the fundamental value proposition in a Tesla.  Which means, to me, that people by-and-large were not choosing it based on a simple dollars-and-cents calculation.  And if image was a big factor in the choice, well, based on what I’ve been reading in the newspapers of late, Tesla may face some challenges moving forward.

Post #1656: The World Turned Upside-Down

 

Today my wife came across a thread on PriusChat in which a New Englander claimed that it now cost more to run his Prius Prime on electricity than on gasoline.

After I got done scoffing, I decided to look up the data.  Actually check the facts.  Just as a last resort.

And, in fact, that’s plausible.  With the recent declines in the price of gasoline, and sharp spikes in electricity prices in New England, it’s entirely possible that running a Prius Prime on gas is now cheaper than running it on electricity in that area.

Let me just chuck out a few numbers here, all based on the current EPA ratings of 4 miles per KWH and 54 miles per gallon for a Prius Prime.

First, it’s just math to figure out the break-even price of electricity, for any given cost of gasoline.  That is, the price at which it would cost you the same to power the car with electricity as with gasoline.  Because a gallon gets you 54 miles, and a KWH gets you 4 miles (per the U.S. EPA), just multiply the price of gas by (4/54 =~) 0.074.  So running the Prius Prime on $4/gallon gas costs the same as running it on electricity costing ($4 x 0.074  =) 30 cents per KWH.

Like so.  The “break-even” price of electricity just shadows the actual price of gas:

Source:  Gas price data from the St. Louis Fed FRED system.

Historically, at least in my area, that gasoline-equivalent cost was well above the actual price of electricity.  Hence, the fuel cost for electric-powered miles was well below the cost for gas-powered miles.

But now?  In, say, Boston?  Not so.  Take the red line off the prior graph — that’s your gasoline-break-even cost of electricity — and compare it to the actual cost of electricity in Boston and in the Washington DC area.

Source:  Electric rates via the St. Louis FRED system, e.g., DC electric rates.

And, sure enough, of late, the precipitous drop in gasoline prices, combined with the spike in New England electricity rates, has made it noticeably more expensive to run a Prius Prime on electricity, than on gasoline, in that area.  Although, as you can see from the very bottom line, it’s still cheaper to fill up on electricity than gasoline in the DC area.

Discussion

Apparently the spike in New England electric rates is due to a spike in U.S. natural gas prices, which, in turn, seems to be blamed on the war in Ukraine and the resulting spike in European gas prices.  The general idea being that the New England area is heavily dependent on natural gas for electricity production.

Either way, prices in the natural gas market now seem to be easing.

On the one hand, this raises an interesting advantage of having a true dual-fuel vehicle like the Prius Prime.  Within the limits of your battery capacity, your fuel cost can always be the lesser of the gas or electric per-mile rate.  You are protected from price spikes in either the gas or electric markets.

The question is, is the Prius Prime something of a special case, owing to its overall high efficiency? Or, does this have any strong implications for the per-mile cost advantages of electric vehicles in general?  I think the answer is, I think, the latter.

So, let me do the same calculation on a more typical U.S. vehicle.  Offhand, let me choose a PHEV Volvo, getting a pitiful 2 miles per KWH or equally pitiful 26 miles per gallon of gas.

Source:  2022 Volvo from Fueleconomy.gov

But the key here is “equally pitiful”.  The conversion factor from gas price per gallon, to the equivalent cost in electricity, is calculated just as it was for the Prius.  In this case, with 26 MPG and 2 miles per KWH, the conversion is (2 /26 = ) 0.077, virtually identical to what it was for the Prius.  And that’s because the Volvo uses just about twice as much gas, and twice as much electricity, as the Prius does.

Equally pitiful mileage on either gas or electric.  Which means that, as with Prius Prime drivers in New England, Volvo drivers in New England will also now find it cheaper to run on gas instead of electricity.  Sure, they’re paying twice as much per mile as Prius Prime drivers.  But that’s true whether they are burning gas or electricity.

I should probably do another one or two, to make sure that wasn’t an accidental cherry-pick.  But I’m guessing that what that sharp-eyed New Englander calculated for his Prius Prime applies to much of the dual-fuel gas-electric fleet.  With gas as cheap as it is now, there are spots in the U.S. where the fuel cost of gas is lower than the fuel cost of electricity.

In prior posts, I already showed that recharging your car at typical commercial-charger rates already costs more than running it on gasoline.  So if you don’t have a home-recharge option, or can’t recharge for free, there are no fuel savings from converting to electricity.  This means a significant fraction of the U.S. market may have little financial incentive to go electric.  This latest analysis just shows that unless those electrical rates come down, entire geographic areas of the U.S. will be in the same fossil-fuel-powered boat.

Post #1649: Capital Bikeshare at Tysons: 170 slots, 14 locations, 6 round trips a day.

 

This final bit of analysis of Capital Bikeshare is here just in case anybody in Vienna actually believes the cheerleader-style reporting you may read regarding  Capital Bikeshare.

Here’s the actual use of the Bikeshare racks around Tysons, for the past 12 months. To understand this, realize that the underlying unit of data is a “trip leg”.  It’s a transport of a bicycle from one rack to another, or, in the case of a round trip, from one rack back to that same rack.  E.g.  if you rode one of these bikes from the Metro station to work in the morning, and then back in the evening, that would be two trip-legs.

To get a better estimate of the actual number of users, I divide trip-legs by two to get “trips”.  (Except for round-trips, for which each one counts as a trip).  I’m betting that in most cases, this is a far better estimate of the number of unique users on any given day.

Then, I divided these 12-month totals by 365 to get them on a per-day basis.

The upshot is that, on a typical day, the entire Capital Bikeshare investment in the Tyson’s Metro area — 14 racks, total of 170 bike slots, and an unknown number of bikes — typically benefits six people.

Let me point out that this is a mostly-mature system at this point.  Most of those racks have been there for years now.  And let me further point out that it looked just like that the last time I analyzed the data for Tysons Metro in isolation.  And it looks like this out in the far Maryland ‘burbs as well. And in Reston.

If you can look at that, and say, oh, boy, let’s spend a quarter-mil to install those in my Town  — then let’s pay Lyft (the owner of the company that operates Capital Bikeshare) whatever annual maintenance they charge, on top of that.

If you can say that, then I think you and I live in alternative realities.

I don’t even care if it’s somebody else’s tax dollars paying for it. Building more of these, when we already know what the outcome looks like out here in the exurbs, is just the worst kind of government.

In case anybody wants to check my work — nobody ever does — the underlying data are here:  https://ride.capitalbikeshare.com/system-data.

Finally, let me reiterate that in the central urban core of the DC area, Capital Bikeshare is a fine idea and it works well.  (I’ve said that in almost all of my prior posts on this topic, and repeat it here to be sure that you understand I am not anti-bike or anti-Capital-Bikeshare.)  The heavy use of the bikes in that area contributes to a reasonable cost-per-ride.  But in those areas, a) there are lots of nearby places to go from and to, where racks can be sited, and b) as I recall, a typical bike rack slot turns over an average of six times a day.

In other words, there are maybe two-orders-of-magnitude more riders per bike slot in the dense urban core than in the far-flung suburbs.  Bikeshare provides value in that urban core.  It does not out here.

Realistic transportation policy needs to recognize that and be shaped accordingly.  Early on, local governments could be forgiven for taking a chance on a technology that, in hindsight, just doesn’t work out here.  Now, by contrast, with all the accumulated evidence, there’s no longer any excuse.  We know it doesn’t work, in the sense of having an outrageous average cost per mile of transportation, due to negligible use rates.  Why are we still expanding it?

Post #1624: 80 MPG?

 

Not quite.  But I think I’m finally figuring out how to drive my wife’s Prius Prime.

Above is the gas mileage on my wife’s Prius Prime, after a round trip from Vienna VA to Harper’s Ferry WV.  This is all after resetting the odometer once the battery was depleted.  So it’s straight-up gas mileage.

This trip contained a short section of high-speed driving, but was mostly hilly primary and secondary roads in western Virginia and West Virginia.  And I think I finally understand how I’m getting such great mileage.

The Prius Prime loves hilly roads.  It is an excellent car for a particular style of pulse-and-glide driving.

Continue reading Post #1624: 80 MPG?

Post 1621: Look ma, no battery!

 

Or, “why I truly don’t give a 💩 about high gasoline prices in the U.S.”, the sequel.

Back in June of this year, in Post #1454, I explained why I didn’t give a 💩 about the price of gas.  In a nutshell, I don’t use much.  I drive my wife’s Prius Prime.  The 30-mile battery range covers essentially all our local travel.  One we’ve run through that, the gas mileage is outstanding.

The genesis of the prior post was our annual trip to Ocean City, Maryland, where the car got 72 MPG on the highway.

I figured it was a fluke.  There were no hills to speak of.  We probably caught a tailwind.  Unlikely to be repeated.

Today we went leaf-peeping, driving from Vienna VA to Sperryville, VA and back.  There is just something about the autumn scenery in central Virginia that my wife and I both love.

(Best sign seen on the trip:  “God Allows U-Turns”.  This, at the exit of the parking lot of a little church in Sperryville where we were — yeah — making a U-turn.)

The trip was a combination of interstate highways, then primary and secondary highways traversing hilly terrain. It was a nice drive — once we got off the interstate.  I reset the odometer after the battery was depleted so that I could check the gas mileage.

Lo and behold, in round numbers, 72 MPG.  Straight-up gasoline-powered transport, no battery.  Completely different terrain, time of year, and driving conditions compared to last time.

So, no fluke.  I’m not drafting trucks. I’m not doing 35 in the right-hand lane.  I’m  just keeping up with traffic, and paying a bit of attention to instrumentation on the dashboard that offers guidance for best fuel economy.  (And it didn’t hurt that we didn’t need AC or heat for this trip.)

It’s odd how your expectations change.  These days, if I come in under 65 MPG for the gas portion of a trip, I’m disappointed.

This is not as clean as a pure EV of the same size.  At least, not as clean, at Virginia’s current electrical generating mix.  But it’s not bad for the latest refinement of a gasoline-based technology that Toyota put on the road more than two decades ago.  And the same drive train that gets us 72 on the highway allows us an effortless transition to electrical transport for all our around-town driving.

For us, this plug-in hybrid electric vehicle (PHEV) is absolutely the sweet spot in the spectrum of what’s on the market today.  After a year of driving this car, we have no regrets about buying it.

Post #1618: There ain’t no disputin’ Sir Isaac Newton: Efficient driving in an EV.



Driving an electric vehicle (EV) efficiently is forcing me to learn some new driving habits.  And, in particular, I have to un-learn some cherished techniques used for driving a gas-powered car efficiently.


When I look for advice on driving an EV efficiently, all I get is a rehash of standard advice for driving a gas car.  But the more I ponder it, and the more I pay attention to the instrumentation on my wife’s Prius Prime, the more I’m convinced that’s basically wrong.


An electric motor is fundamentally different from a gas engine.  With an electric motor, you want to avoid turning your electricity into heat, rather than motion.  That boils down to avoiding “ohmic heating”, also known as I-squared-R losses.


To minimize those heating losses, you want to accomplish any given task using or generating constant power.  That task might be getting up to speed after stopping at a red light, or coming to a stop for a red light, in some given length of roadway.


Here’s the weird thing.  Assuming I have that right — assuming that an efficient EV driving style focuses on providing or generating constant power over the course of an acceleration or deceleration — that implies a completely different driving style, compared to what is recommended for efficient driving of a gas-powered vehicle.


In particular, the standard advice for gas cars boils down to accelerating and decelerating with constant force.  When you take off from a stop light, aim for a constant moderate rate of acceleration.  When you are coming to a stop, aim for a steady rate of deceleration.  Constant acceleration or deceleration boils down to constant force on the wheels, courtesy of Sir Isaac Newton’s F = MA (force is mass times acceleration).


But power is not force.  As I show briefly, in the next section.  In a car, power depends on speed.  Constant force on the brake pedal (and so, on the brake rotors in a traditional car) generates far more power at high speed than at low speed.  Similarly, a constant rate of acceleration consumes more power at high speed than at low speed.


And so, there seems to be a fundamental conflict between the way I was taught to drive a gas car efficiently, and what seems to be the right way to drive an EV efficiently.


In a nutshell, to drive an EV efficiently, you should be more of a lead-footed driver at low speeds.  And taper off as the car speeds up.   Conversely, hit the brakes lightly at high speed.  And press the brakes harder as the car slows.


That’s the driving style that aims for production and consumption of power at a constant rate, over the length of each acceleration or deceleration. And that’s completely contrary to the way I was taught to drive a gas vehicle.


Think of it this way.  Suppose you apply a certain level of force to the brake pedal of a traditional car.  The resulting friction between brake pads and rotors will generate heat.  That rate of heat production is, by definition, power, as physicists define it.  You’re going to generate a lot more heat per second at 80 MPH than you are at 4 MPH.  (In fact, 20 times as much.)  Restated, for a given level of force, you are bleeding a lot more power off the car’s momentum at 80 MPH than at 4 MPH.  And those big differences in power, over the course of an acceleration or deceleration, are exactly what you want to avoid in an EV with regenerative braking, in order to avoid I-squared-R losses.


 




Force and power:  A brief bit of physics and algebra




1:  Two definitions or laws of physics


Work = Force x Distance


Power = Work/Time


2:  A bit of algebra


Substitute for the definition of work:


Power = (Force x Distance) / Time.


Re-arrange the terms:


Power = Force x (Distance/Time)


Distance/time = speed (definition)


Power = Force x speed.


For a constant level of force applied to or removed from the wheels, the rate of power consumption (or production) is proportional to the speed.


Upshot:  To accelerate or decelerate at constant power, the slower you are going, the heavier your foot should be.  The faster your are going, the lighter your foot should be.  For the gas pedal and the brake pedal.




Ohmic heating:  Why a long, hard acceleration trashes your battery reserve.




Anyone who drives a PHEV — with a relatively small battery — will eventually notice that one long, hard acceleration will consume a big chunk of your battery capacity.  On a drive where you might lose one percent of battery charge every few minutes, you can knock several percent off in ten seconds if you floor it.


Another way to say that is that getting from A to B by flooring it, then coasting, consumes much more electricity than just gradually getting the car up to speed.


I’m not exactly sure why that is.  But I am sure that it is universally attributed to I-squared-R or ohmic heating losses in the motors, batteries, and cables.


Any time you pass electric current through a wire or other substance, it heats it up.  From the standpoint of moving your car, that heating is a loss of efficiency.  The more current you pass, the more it heats up the wire.  And that heating is non-linear.  Watts of heat loss are proportional to I-squared-R, in the argot.  They go up with the square of the current that you pass through that wire.


Again, I’m not completely sure here, but my takeaway is that your heating losses, at very high power, are hugely disproportionate to your losses at low power.  At constant voltage, I believe those losses increase with the square of the power being produced by the electric motors.  In other words, ten times the power produced to move the car creates 100 times the ohmic heating losses.


And that’s how ten seconds of pedal-to-the-metal can use up as much electricity as 10 minutes of moderate driving.


That said, I have to admit that I’m relying on “what everybody says” for this.  For sure, hard acceleration seems to trash your battery capacity far in excess of the distance that you travel at that rate of acceleration.   Whether the root cause for that is I-squared-R losses, or something else about the car, I couldn’t say.


Either way, my takeaway is that if losses are proportional to the square of power consumed or generated, then to accomplish any given task (any fixed acceleration or deceleration episode), your aim should be to do that at constant power.  Because that’s what will minimize the overall energy loss from that acceleration or deceleration episode.




Drive like you are pressing on an egg — that was a real thing.  EV drivers should chuck the egg.




Source:  Duke University Libraries, via Internet Archive.


Those of us who grew up during the 1970s Energy Crisis will probably recall public service announcements that asked you to drive as if there were a raw egg between your foot and the gas pedal.  I managed to find a Texaco ad of roughly that era, laying out that egg-on-gas-pedal meme.  The picture above is from that video.


As kids, that was pretty much beaten into us.  Responsible driving means no jackrabbit starts, no tire-smoking stops.  Easy does it.  We’re in the middle of a prolonged gasoline shortage, after all.


So now I come to the part that is absolute heresy for someone of my generation.  If you’ve absorbed the prior two sections, you realize that this advice probably isn’t correct for an EV.  Why?  To consume power at a constant rate over the course of an acceleration, you should start off with a brisk rate of acceleration, then diminish that as the car speeds up.


In other words, if you drive an EV, drive with a lead foot.  Not all the time.  But at the start of every acceleration.  And the end of every deceleration.


If you drive an EV, chuck the egg.




The Prius Prime Eco display




Source:  Underlying picture is from Priuschat.


With that understanding in hand, I’m finally starting to make some sense of the “eco” display on my wife’s Prius Prime.


In theory, this little gauge is giving you guidance on how to drive the car most efficiently.  In practice, I could never make head or tail out of it, except that it seemed to be telling me to drive with a lead foot.


Which, I now understand, it was.


On this display, if you put your foot on the gas, it will show you your actual throttle (gas pedal) position, and the gas pedal position that will, in theory, give you greatest efficiency.


By contrast, when you put your foot on the brake, it doesn’t show you the brake pedal position.  Near as I can tell, it shows you the amount of power than you are generating.  That is, a constant brake pedal position will lead to a shrinking bar, as the car slows down and less energy is generated.


Watch what happens if I try to accelerate gently:




It’s possible that all the meter is actually telling me is that a very lightly-loaded electric motor will operate inefficiently.  I don’t think the Prius eco monitor is actually trying to get me to drive at constant power.


Edit 3/11/2024:  After driving around with a ScanGauge III, my conclusion is that accelerating at constant power is exactly what the eco-meter is trying to get you to do.  It wants you to start off with a heavy foot, and then, as you accelerate, it wants you to back off.  Near as I can tell, that bar is set up to keep you at around 23 HP of power output, or 50 amps of discharge current, or a “2 C” rate of discharge, for this battery.


In particular, my diagram above is labeled wrong. The two red arrows should be labeled “desired power output” and “actual power output”.  You will notice that if you don’t move the gas pedal, the “actual power output” line will creep up as you speed up.  The only way to keep that line in the same place is to back off the gas as your speed increases.  So that line isn’t the throttle position, it’s the power output (power = force x speed).


But no matter how I arrive at it — from theory, or from finally paying full attention to the Prius eco meter — the whole drive-like-there’s-an-egg-between-foot-and-gas-pedal is clearly obsolete.  Gentle acceleration may get you your best mileage in a gas-powered vehicle.  But it’s not the correct way to drive an EV.



	


	
	






	
	

		
Post #1613:  How the Prius does its thing.
	


	

		
 


Introduction:  The U.S. market for gas-powered cars in 2005.




Source:  Analysis of US EPA gas mileage and vehicle specification data, 2005 model year.


Back in 2005, my wife needed a car.  And by that I mean, we were interested in a gasoline-powered passenger car.  Not a truck, crossover, van, SUV or the like.   And not a diesel.   We’d done that, and didn’t much like the drawbacks of the diesels of that era. A passenger sedan, in the parlance of the era.  Fueled by gasoline.


I was interested in buying something that was efficient.  But the raw MPG numbers were a jumble, driven largely by the size of the vehicle.  I didn’t really want to try to squeeze into some tiny econobox just because it got better mileage than a bigger car.  I was interested in identifying something that was efficient at converting gasoline into movement of passengers and luggage.  Not just the tiniest car I could fit into.


I took data from the EPA and calculated fuel efficiency in a way that put large and small cars on more-or-less equal footing.  Instead of looking at miles per gallon, I calculated cubic-foot-miles per gallon.  Where “cubic foot” is combined interior passenger and luggage room, measured in cubic feet.  Under this approach, a car that was twice as big, but got half the gas mileage, would count the same as a car that was half as big, but got twice the gas mileage.  They both used the same amount of gas to move a given volume of passengers and luggage.


My “cubic-foot-miles per gallon” for passenger cars is similar to the concept of ton-miles per gallon for freight vehicles.  For the simple reason that miles-per-gallon doesn’t tell you how much you were able to haul.  Trains, after all, burn a lot of diesel fuel per mile.  But they also move a lot of tonnage with that fuel.  In some sense, what matters isn’t the amount of fuel burned, it’s the usable carrying capacity that the fuel consumption provides.


The idea was to make this a two-step process.  First, I would separate out the vehicles that were efficient, regardless of size.  Then, from the lineup of vehicles that rose to the top of that listing, we could try to make an informed choice about what size of car we wanted to buy.  Given the choice of efficient vehicles on the market at that time.


Things did not quite turn out as planned.  I figured I’d get a “spectrum” of efficiencies, with a few dozen cars to choose from at the high end of the spectrum.


When I did that calculation– and so removed the variation that was driven merely by the size of the car — the data resolved into the amazingly simple picture, shown above.  For gasoline passenger cars, the 2005 American market consisted of three pieces:


    

  • The Prius
    • 

  • The Honda Civic Hybrid
    • 

  • Everything else.
    • 



The real eye-opener, to me, was the extent to which “everything else” was just that.   Basically, all non-hybrid cars were roughly equally inefficient.(!)  Sure, you had some muscle cars come in at the bottom of the heap.  But the point is that there wasn’t some nice, smooth distribution of cars in terms of their efficiency.  There was crowded mass of vehicles with little to distinguish one from another.  There was the Honda Civic Hybrid, poking up above that mass.  And there was the Prius, running about three times as efficiently as the average.  


The upshot is that if you wanted an efficient gas car in 2005, the decision was a no-brainer.   You bought a Prius.  The only other gas car that came close to it was the Honda Civic Hybrid, and that was just a bit too small for me.


The best way I know of to illustrate how different the Prius was from other offerings at the time is to ask this simple question:  In the 2005 car market, what was the most efficient gas-powered vehicle capable of moving six people?  The answer?  Two Priuses.  Every six-passenger sedan, van, or SUV got less than half the gas mileage of the Prius.  It was that far ahead of its time.


(As a footnote, I never put pickups, vans, or other special purpose vehicles (SUVs, etc.) on this graph because I couldn’t get the interior volume information.  The EPA showed the MPG for those vehicles, but in 2005, the EPA only tracked interior volumes of passenger cars.  And, as it turns out, that’s still the case.  They only note the interior volume of traditional passenger cars.)




Redo:  The U.S. market for gas-powered cars in 2022.


Now fast-forward to the 2022 model year, and ask the same question.  If you were interested in buying an efficient gas-powered car, what would your options be?  (I use 2022, not 2023, because the 2023 model year data from the U.S. EPA are not yet complete).


First, you have to acknowledge how much the market has changed.


In 2005, there were no electric vehicles (EVs) or plug-in hybrid electric vehicles (PHEVs).  For passenger cars, 99% of the offerings were straight-up gas vehicles.  There were a couple of hybrids, and a couple of diesels.  Roughly speaking, 99% of the models offered were standard gas cars.


In 2022, here’s how the U.S. passenger car market shaped up.  (Recall, this is just cars, not pickups, vans, SUVs, and the like.)  In 2022, three-quarters of the offerings are still standard gas vehicles.  But more than one-quarter are  alternatives — hybrids, plug-in hybrids, or EVs.




Now let me ask the gas-car-efficiency question, for 2022.  I’m ignoring EVs, and for the PHEVs, I’m using just their gas-only mileage.  How do gas-powered cars shape up, in terms of my efficiency measure (cubic-foot-miles per gallon)?




 Source:  Analysis of US EPA gas mileage and vehicle specification data, 2022 model year.


Unlike 2005, the Prius now has quite a bit of company.  The 2022 Prius is slightly more efficient than the 2005 model, but now there are a couple of gas-powered cars that top it, and many that are nearly as efficient.


Unsurprisingly, everything at the top of the efficiency charts, for gas-powered cars, is a hybrid of some sort.  The entire cluster of gas sedans at the top consists of hybrids and PHEVs (where only the gas portion of the PHEV mileage has been counted.)


For the record, the two Prius-beaters on that graph are the Hyundai Ioniq and Ioniq Blue.  For reasons that must make sense to Hyundai, those are no longer being made as gas hybrid versions.   Hyundai discontinued those cars as of June 2022 (reference).


So, by the time we get to the 2024 model year, the Prius will be back at the top of the heap.  As it should be.  But now, at least, it has some close company.


Finally, I have to emphasize that this was for gas-powered vehicles.  On paper at least, there are many fully-electric (EV) and partially-electric (PHEV) cars that get MPG-equivalents in excess of the 54 MPG for the Prius Eco (highlighted in the chart above).  But here, I wanted to look at gas-powered cars, for comparison to my 2005 analysis. And I don’t want to get into what those MPGe numbers actually mean.  It’s not straightfoward.




How does the Prius achieve such efficiency?


You see a lot of bad information about how the Prius achieves its high efficiency, for a gas-powered car.  Some is just plain confused, some gets the orders-of-magnitude wrong.  Some explanations appear to violate basic physics, such as the law of conservation of energy.


To be clear, Toyota did optimize many aspects of the operation of that car.  If you look at a list of where energy gets dissipated in a typical car, the Prius addresses every area.




Source:  Energy.gov


Take wind resistance, for example.  Once you actually manage to get energy to the wheels of the car (Power to wheels line, above), about half of that energy gets dissipated as wind resistance.  If you want decent mileage, you need to keep that to a minimum.  The Prius has a “coefficient of drag” of 0.24, among the best ever measured for a mainstream U.S. passenger car (see the extensive list in Wikipedia.) By contrast, your basic brick-on-wheels design  — a Jeep Wrangler — has a coefficient of drag of about 0.45.  What people perceived in 2005 as the somewhat odd shape of the Prius was all about providing interior volume while minimizing air resistance.


There are other minor contributors.  The Prius comes with low-rolling-resistance tires.  It minimizes losses from braking by using regenerative (electrical) braking where possible.  It reduced the parasitic losses from (e.g.) air conditioning by employing a more efficient compressor design.  And so on.


But as you can see from the chart above, most of the energy wasted by a standard gas car is wasted by the engine.  As I understand it, the single largest driver of Prius efficiency — and the reason it had to be made as a hybrid in the first place — is that it uses a different type of gasoline engine.  It’s an Atkinson-cycle (or maybe Miller-cycle) engine, instead of a standard car Otto-cycle engine.




Why do I think the use of an Atkinson engine is key?  Well, here’s a list of the top 20 most-efficient gas cars offered in the U.S. in 2022, listing their specs and the type of engine they use.


Notice anything?




What was unique to the Prius in 2005 is now the standard way to achieve good fuel efficiency in a gas-powered car.  But, as explained below, in most cases, you have to add some secondary propulsion (electric motors) to get adequate on-road acceleration.


Here’s the explanation in brief.


The chemistry of gasoline dictates that you need a fairly “rich” gas-air mixture in an internal combustion engine.  If you make the mix too lean — too little gasoline relative to the air — the spark plug can’t ignite it and/or it burns poorly and/or it generates a lot of nitrous oxides.  To get reliable ignition and a clean burn, you more-or-less need to mix gas and oxygen in the ratio needed for complete combustion of the gas.  Too little gas in the mix and the engine stumbles and dies, or runs dirty.


But if you fill the engine cylinder with that relatively rich gas mix, you end up with more chemical energy in that cylinder than you can use.  Sure, you can compress it and ignite it.  But there’s so much energy that you’ve still got quite a bit of usable gas pressure left when the piston gets to the bottom of the cylinder.  (The number I see cited most often is that, under load, the gas pressure in the cylinder is still at five atmospheres when the piston hits the bottom of its range of motion.)  At that point — once the piston bottoms out — all you can do is open the exhaust valves and let all that potentially usable energy — that still-usable gas pressure — escape out the exhaust.


And that’s exactly what a standard Otto-cycle car engine does.  The intake stroke and power stroke are the same length, the valves open and close within a few degrees of the piston being at bottom dead center/top dead center.  At the end of each power stroke, there’s plenty of pressure left in the gas inside the cylinder.  And with each cycle, that energy gets tossed out the exhaust port.


This has been known for decades, i.e., that gas engines would run more efficiently if you could put a much leaner mixture into the cylinder.  The problem was getting that leaner mix to ignite and burn well.  Back in the 1970s, Honda tried to address this with its stratified-charge engine (reference).  That used two carburetors — one rich, one lean — and two intake valves.  It filled the top of the cylinder with a richer mixture that the spark plug could ignite.  And the rest of the cylinder with a leaner mixture that would itself be ignited by the rich mix at the top.  It was moderately successful, and I recall that the Honda CVCC with that engine was among the most fuel-efficient cars of its generation.


A better way to put less gasoline into the cylinder, and yet have it burn well, is to fill only part of the cylinder on the intake stroke.  Where I need to define “the cylinder” as the full length of the resulting power stroke.  That way, the air-to-fuel mix is correct for consistent ignition and clean burn.  You simply have less total fuel in the cylinder before you ignite it.


And that’s exactly what the modern Atkinson (or Miller) cycle engine does.  And it does that by closing the intake valve well after the piston hits bottom dead center.  This allows the piston to push out maybe 30% of the total air-fuel mix, then compress and explode what’s left.  As a result, you get both the right chemistry (the right air-to-fuel ratio) and the right amount of fuel to allow the resulting energy to be used efficiently.


In the Prius engine, more-or-less, the intake valve closes when the piston is 30% of the way up the bore.  (The engine has variable valve timing, so, well, that varies).  That works out to be, in effect, about a 10.5:1 compression ratio, and a 13.5:1 expansion (power stroke) ratio.


And so, while the standard Otto-cycle engine has nearly-identical compression and expansion (power stroke) ratios, the Atkinson-cycle engine has a much lower compression ratio, compared to its expansion (power stroke) ratio.  The whole point of which is to allow you to put the right fuel-air mix into the cylinder, just less of it.


But this comes at a cost.  With less fuel, and a longer expansion stroke, there’s less power with each power stroke.  And part of that power stroke now occurs at pressures much lower than you would get in an Otto-cycle engine.


As a result, the Atkinson engine is efficient, but it has a relatively poor power-to-weight ratio.  In the case of the Prius, the older 1.6 liter engine might have produced maybe 140 horsepower configured as run as a standard Otto-cycle engine.  But as an Atkinson-cycle engine, I think it barely broke 90 horsepower.


The result would have been a car with unacceptable on-road performance.  (Yeah, even for Prius drivers.)  So, the engineers at Toyota (and Ford) added electric motors, a big battery to run the motors, and so on.  And the hybrid was born.


To be clear, the electrical side of the modern hybrid is more-or-less a necessary evil.  It was something tacked on after the fact, to allow the engineers to replace the inefficient Otto-cycle engine with a more efficient, but less powerful, Atkinson-cycle engine.


So, now you know the primary source of Prius efficiency.  And you know why the 20 most efficient gas-powered cars offered in the U.S. all use Atkinson-cycle engines.




 

	


	
	






	
	

		
Post #1589:  Correction to Post 1586
	


	

		
 


A local who has the Tea Party plates on his car took exception to my blanket statement that those plates mark environmentally insensitive individuals.  My claim that I’d never seen cars with (e.g.) greater than 30 MPG EPA rating, with Tea Party plates, is now wrong, courtesy of three outliers that he photographed and emailed to me.  I haven’t bothered to check the EPA ratings, but these at least aren’t low MPG trucks.


The gist of that prior posting still stands.  But as a matter of fact, there are some vehicles with Virginia Tea Party plates that do, probably, get over 30 MPG.  Contrary to what I said in that posting.  I don’t think that’s the norm, but mea culpa.


Still seeking a photo of that rarest of beasts, the Tea Party Prius.


As to why I call them the Tea Party plates, well, that’s what they are.


https://vatp.org/2010/11/13/va-tea-party-plates/


Three photos courtesy of an email correspondent:


   


Just to be clear — because I didn’t blur the plates or anything — it’s legal to photograph anything you can see from a public right-of-way.  At least here in Virginia.  Commercial use of such an image may fall under some different set of statutes.   But posting such an image with no claim to copyright and no intent to harass is fair use here in the Commonwealth.