Author: chogan@directresearch.com

Why pulse-and-glide saves gas.

Gasoline engines run most efficiently when under a fairly heavy load.  Load them too lightly, or too heavily, and their efficiency drops.

Below is the “efficiency contour” of a hypothetical 2 liter Atkinson cycle engine. Engine RPM is on the X-axis.  Engine load (output) is on the Y-axis.  The labels on contour lines are percents, and show the fraction of the energy in the gasoline that is converted into motion by the engine.  Those contour lines define a sort of hill, with the peak of the hill — maximum efficiency — occurring when this engine is running around 2500 RPM, putting out about 100 horsepower. And converts just shy of 39% of the energy in the gas into usable power.

Source:  Kargul, John & Stuhldreher, Mark & Barba, Daniel & Schenk, Charles & Bohac, Stanislav & McDonald, Joseph & Dekraker, Paul & Alden, Josh. (2019). Benchmarking a 2018 Toyota Camry 2.5-Liter Atkinson Cycle Engine with Cooled-EGR. SAE International journal of advances and current practices in mobility. 1. 10.4271/2019-01-0249. Accessible though this link.

The engine modeled above is a 2.0 liter Atkinson-cycle engine.  That’s just a bit bigger than the 1.8 liter engine that’s actually in the Prius Prime.  But it’s close enough.

Below, there’s the crux of the problem.  Much of the time, the engine is inefficiently lightly loaded.  I’ve marked the power required to cruise on level ground at a steady 55 MPH in a Prius.  The car only needs about 12 HP.  (I infer this from the ~12 KW of power drawn to keep the car at that speed in electric (EV) mode.   That power, less about a 20% loss in the electric motors, is the energy required at the wheels to keep the car moving forward at that speed.

And so, if you cruise along at a steady 55 MPH on the gas engine, even though the car won’t be burning a huge amount of gas, what little it burns will be burned inefficiently.

Instead of running that engine steadily at 12 HP output, you could alternatively run it hard — run it briefly at 100 HP — then shut it off.  And repeat as necessary.  That’s pulse-and-glide.

And that’s why pulse-and-glide saves gas.  You extract energy from gasoline as efficiently as possible, by running the engine under heavy load.  And then you match the engine output, to the average power required by the car, by cycling the engine on and off as needed.

Traditional pulse-and-glide makes you a rolling hazard.

With traditional (or kinetic-energy) pulse and glide, you first run the gas engine and speed up.  Then switch it off, coast, and slow down.  And repeat.

Practically speaking, this is of almost no value on the public highways, because this makes you a nuisance to other drivers.  It makes you into a rolling traffic hazard.

Potential energy pulse-and-glide requires the right terrain.

Speeding up, however, is not the only way to store the output of the car’s engine.  Going up a hill works just as well.  You store that excess output in the form of potential energy (height) instead of kinetic energy (speed).  Apply gas on the uphills, coast with engine off on the downhills.

I can attest that this most definitely works.  This is how I achieved my last two 80-MPG all-gasoline (no energy from the grid) road trips.

Needless to say, this only works where you have significant hills.  Ideally, hills large enough that the car will maintain the posted speed limit on the downhill with no or minimal energy input from the drive train.

A new/old concept:  State-of-charge pulse-and-glide.

Both methods described above can be done by a standard gas car.  No electric motors are required.  In fact, in a Prius, you achieve maximum efficiency under either method if you never use your electric motors.  (Using the gas engine to charge the battery, then run the motors, wastes about 30% of the power produced.)  Champion Prius hypermilers actually shift the car into neutral on the “coast” phase, specifically to avoid moving electric current into or out of the battery via the motor/generators.

But a plug-in hybrid electric vehicle (PHEV) like the Prius Prime has yet a third option, which I’m going to call state-of-charge pulse and glide.

To be clear, what I’m about to describe is something that the car does, on its own, anyway.  The only question is whether you can modify your driving behavior to take exceptional advantage of it.

If you use the gas engine to charge the battery, then run the electric motors, that wastes about 30% of the energy produced by the gas engine.  So, at first blush, it seems like you’d want to avoid using those electric motors.

But, if you charge that battery at the peak of the gas-engine efficiency curve, that means the electric motors are using up your gas with somewhere around (0.7*38% = ) 27% efficiency.

This leads to the section that I’ve labeled “EV carve out” above.  Roughly speaking, if the driving situation requires less than about 25 KW of power, it’s more efficient to run in EV (electric-only) mode, as long as you can later recharge the battery at relatively high engine load.  (So that the recharge happens near peak gas engine efficiency.)

In the Prius Prime, assuming this engine chart is a reasonable proxy for the actual Prime 1.8 L engine, that has the following practical implication for running the car in hybrid-vehicle (no-grid-power-used) mode.  If you can, you should run on electricity-only up to a current draw of about 90 amps.  That’s the point at which the electric motors, less their inherent 20% loss, are producing about 25 KW of power. That’s the point where switching to gas propulsion is more efficient.

But the closer you get to that 90 amp limit, the less advantage electricity has over gas, and the less gas you are saving.  So, from a battery wear-and-tear perspective, it’s probably best not to push it that far.  You will likely get the bulk of your savings with a more conservative limit of (say) 50 amps, or roughly a “2 C” discharge rate.  (The rate at which the entire EV battery would be dead in half an hour.)  Assuming the car will let you do that, in hybrid mode.

So, a conservative rule-of-thumb is that a power output of somewhere around 17.5 KW (25 HP) is where you should try to flip the car from gas to electric and back.

To be clear, the car does something like this on its own.  At low power demands, it shuts off the gas engine and used the electric motors.

What I have noticed, however, is that there’s considerable hysteresis in the car’s decision.  In particular, once the gas engine is on, it tends to stay on until power demand gets quite low.

So I believe that driver intervention can improve mileage, using (e.g.) terrain anticipation.  If you’re coming to a stretch of road with likely low power demands — cresting a hill, starting a slow deceleration, or just coming up to a level stretch — you may be able to beat the Prius’ internal algorithms.  Conversely, when you see a high-power-demand situation coming up — a hill, say — you can flip the car into gas mode before it begins to bog down in electric mode.

My simple initial rule-of-thumb will be a 50-amp cutoff.  When in hybrid mode, drive the car on the electric motors up to 50 amps current or low state-of-charge cutoff, whichever comes first.  Anything over 50 amps, nudge the accelerator to kick the car into gas mode.

Edit:  I decided to do a little acid test of the concept.  As every driver knows, the worst trips for a gas engine are short, around-town jaunts.  I decided to do a little run to a couple of stores, in hybrid vehicle mode, total trip of about 8 miles, divide into three legs with stops in-between.  After the mandatory gas-engine warm-up period, whenever the gas engine came on/power was needed, I loaded the gas engine heavily.  I gave it enough throttle to bring it immediately to the “power” zone on the dashboard.  But, once up to speed, I let off the accelerator to shut the gas engine off, and drove for as long as feasible on electricity only, respecting a maximum draw of 50 amps.

Results:  71 MPG.  And it was clear that if I’d had a longer distance between stops, that would have increased. 

One short trip does not prove the concept.  And the Prius chastised me soundly for those hard accelerations, basically giving me a flunking score on the eco-meter.  Nevertheless, I consider this first test to be encouraging.

By the book, and by the dashboard readouts, I was doing everything wrong. And yet, it’s hard to argue with the MPG.

Edit 2, 2/19/2023.  Not so fast.  Building on the above, I went to a local disused office building and circled the parking lot.  Roughly a 1.3 mile circuit, 25 hour speed limit, three full stops per loop.  On one set of loops, I tried this hypermiling approach.  On another set, I drove gently, then used the “charge” function to bring the battery state-of-charge back to its original level. 

Results:  In both cases, I got about 75 MPG.  Which, in hindsight, may simply be what the Prius Prime gets, driven in hybrid (gas-using) mode, around 25 MPH.

I think the moral of the story is that I’ve done so little around-town driving in hybrid (gas-using) mode that I’m not sure sure what sort of gas mileage I should expect as a baseline.

Conclusion

Anyone who has ever used the Prius cruise control in hilly country knows that it’s quite “reactive”.  It doesn’t anticipate the hills, but instead holds speed steady, then pushes the car far out onto the power curve in an attempt to maintain speed on the uphill.  For that reason alone, I don’t use the cruise control on hilly roads, as I feel that I can drive the car more efficiently in manual mode, making some modest adjustments in speed on the downhills and uphills.

Similarly, I’m betting I can squeeze a little extra mileage out of the car, in hybrid mode, by manually selecting the point of switch-over between gas and electric propulsion, and pushing the gas engine at high load to maximize efficient use of gasoline.  Then, once at speed, or over the crest of a hill, lifting my foot off the gas briefly to shut the gas engine down, and continuing in electric-only mode as feasible.

You need an extra bit of instrumentation to be able to do that well.  I’m using a Scangauge 3, which will show me quantities such as battery current, engine RPM, and engine output.

What makes this work, as a form of pulse-and-glide, is, of course, the traction battery.  That’s where the excess power production of the gas engine is stored if not needed.  So the right way to view this is state-of-charge pulse-and-glide.  Instead of letting the speed vary (kinetic energy), or the height vary (potential energy), you let the battery state-of-charge vary (electrical energy).

Same concept either way, you just choose a different place to store the excess power output of well-loaded gas engine.  With different implications for how usable pulse-and-glide is, in actual highway traffic, for a given terrain.

Finally, I note that there have been recent patents issued for systems that would automatically pulse-and-glide large trucks, based on a system that anticipates changes in terrain.  They seem to be characterized as a more fuel-efficient form of cruise control.  With everything in modern cars being controlled by a computer, it doesn’t seem too far-fetched to think that some form of automated pulse-and-glide — a fuel-saving cruise-control mode — might eventually become a standard option on vehicles capable of doing it.

With that point of view, driving a gas engine at a constant, low engine load is something of a relic of the past.  It dates to the era when there was literally a metal cable connecting your gas pedal to the throttle body on the carburetor.  With everything computer-controlled these days — and carburetors a thing of the far distant past, for cars — it doesn’t seem like a stretch to ask your computer to do your energy-saving pulse-and-glide for you. As long as you have some safe way to store that excess gas-engine output.

My wife bought her first Prius in 2005.  We tend to forget, but there was a lot of hatred expressed toward that car, at that time.  Which sounds hilarious now, but is true.  There was also disinformation spread about that car, similar to the disinformation you’ll hear these days regarding electric vehicles.  E.g., that the Prius had single-handedly ruined Sudbury, Ontario due to the need for nickel for the battery.

There was also a lot of just-plain-ordinary denial.  That car got an EPA-rated 46 MPG, which, for the time, and the size of the car, was absolutely outstanding.  This was a time when you could not find a traditional gas car with similar interior volume that broke 30 MPG.

It was, as I have noted before, alone in its level of efficiency.  That’s expressed below by an index combining gas mileage and interior volume.  (This is my calculation, from EPA mileage data.)

At that time, if you were willing to drive a small car, and required that it get at least a whopping 35 MPG overall, your choices were:

• Honda Insight (basically, a tiny 2-seater).
• Honda Civic Hybrid (as shown on the chart above).
• Three small VW models with 35 MPG turbo-diesels.

This per the federal website fueleconomy.gov.

And yet, I used to joke that my wife’s Prius single-handedly improved the gas mileage of the U.S. automobile fleet.  Because, every time we mentioned 46 MPG, the universal response was, “Big deal, I get almost that good of a mileage in my fill-in-the-blank.”  That Prius was the best thing that ever happened to the gas mileage of all of our friends’ cars.

The first year we owned that car, we heard about all kinds of mythical non-hybrid vehicles that easily got over 40 MPG.  Easily.  All the time.  Without all that fancy hybrid nonsense.

In reality, none of these folks had a clue what they were talking about.  None had actually carefully tracked mileage.  Most had some impression of some road trip they once took where they think they got great mileage.  Nobody was talking about city mileage.  And so on.

But they all knew that hybrids were just so much hype.

As I continue to learn how to drive my wife’s 2021 Prius Prime for greatest fuel economy, I keep setting new personal bests.  Most recently, we drove out to a local scenic byway (the Snickersville Turnpike) and back.  Door-to-door, using “hybrid mode” (no energy from the grid), we managed to get 82.4 MPG over the course of the 80-mile round trip.

That was a mix of 55+ MPH urban arterial highways, country roads, and then small-town streets.  So, no high-speed interstate driving.

Back in the day, people could fool themselves into thinking that their non-hybrid vehicle was just about as efficient as a Prius.  Even though the U.S. EPA clearly said otherwise.

But this most recent generation of Prius, when driven with an eye toward best mileage (Post #1624), gets such eye-popping numbers that I don’t think you can kid yourself any more.  This is now my second trip where I’ve ended around 80 MPG, driving the car in hybrid mode (i.e., not using energy from the grid.)  Even our interstate trips now routinely yield high-60’s MPGs (admittedly, without the extreme speed limits present on Western interstates.)

And, separately, more than 70% of our miles are run purely on electricity from the grid.  Which means the 65-to-80 MPG observed in hybrid mode is our version of gas-guzzling.  In “EV mode”, using the battery and not the gas engine, we manage somewhere around what the EPA would term 150 MPGe.

This isn’t by way of bragging.  It’s by way of setting the record straight about what’s routinely and reliably available these days.  For not much money, as new car prices go.

I continue to read articles about how hard it is to move to electric transport, what a huge expense it entails, and so on.  And, yeah, you can make it hard, and you can make it expensive, and inconvenient.

But none of that has to be true.  Buy a quality plug-in hybrid electric vehicle (PHEV).  If you’re like us, you’ll get most of the benefits of electrical transport and none of the drawbacks.  Sure, you have to have some faith in the technology.  You need to learn the do’s and don’t of taking care of that big battery.  In a few areas,  electricity is currently a more expensive fuel than gas, by a modest amount.  But as far as I can tell, hybrids started out pretty good, and they just keep getting better.

I’m no longer satisfied when I only get 80 MPG, driving my wife’s hybrid.  And I find that absolutely mind-blowing.