Unraveling the Prius throttle-control mysteries

Ever since buying my Prius, I've tried a number of techniques to maximize
its fuel efficiency when running the engine.  While "pulse and glide" is now
a well-understood technique of using the engine efficiently or not at all
for high MPG at low speeds, many drivers experience a significant drop in
fuel economy when they have to travel above 41 MPH.  This is partly because
the drivetrain wants to have the engine turning when the car is at 42 MPH
or above, and partly due to the ease with which the system can fall into
inefficent, low-demand modes in which the engine is still burning fuel for
relatively little motive power produced.  But it doesn't have to be like
that, because the Prius actually can be a very efficient system over *all* of
its operating speeds.  Sometimes it just takes a little encouragement from
the driver.  This article offers some improved guidelines for best engine
utilization at highway speeds and in the mysterious "mid-speed" ranges.  It
also presents supporting rationale for a conceptual "sweet-spot" indicator,
to give a driver immediate visual feedback on whether the engine is being
used under solid torque load or not.

The shortest possible "executive summary", which doesn't tell the entire
story and may still not even be entirely right, is this:

	We're ignoring the hybrid battery in this discussion.

	Recommendations when burning fuel at highway speeds [~60 MPH] are:

	   keep instantaneous MPG between 35 and 75 MPG, and/or

	   keep RPM between 1400 and 2200, and/or

	   stay in the "good" region of a "sweet-spot meter".

	Competent "warp stealth" holding ability and other subtle
	aspects of HSD operation is assumed.

Making best use of this information requires some knowledge of what is
going on overall in the drivetrain, so the reader will want to make some
time to digest this and the subsidiary information carefully and get some
on-road practice.  For a good review of the driveline, particularly of
"heretical mode" and complete with cool animations, see Graham Davies'
seminal writeup.  Adding appropriate instrumentation to the car also helps.

  It's a concept ...
There is a strong personal-choice caveat to this, too: strictly utilized,
the sweet-spot range and methodology as presented can leave the car with
the acceleration and climbing power-to-weight ratio of a loaded semi, so a
self-imposed limit on the high end of that range may not be for everyone.
You are free to push harder than that when needed, at the expense of a few
MPG.  We will readily note that once those loaded semis do get up to speed,
they fly right along!  It is assumed that a hybrid driver interested in fuel
economy is satisified with maximum speeds between 60 and 65 MPH, beyond
which the effects of air resistance rapidly climb.  But for most terrain,
staying within these suggested ranges of performance works well and returns
surprisingly good fuel economy compared to typical Prius drivers' results.
In these higher speed ranges, pulse-n-glide becomes more like "run under load
and warp-stealth glide when appropriate", with more of a tendency toward
steady-state running as speeds increase.

So, what does "under load" mean?  This is really the central principle, and
most of this discussion is about the throttle control necessary to achieve
it.  In general it means running the engine close to its maximum *torque*
output across a broad range of RPM.  It is well-known to the "hypermilers"
that running through the gears quickly and driving in the highest one that
still allows the engine to run correctly at lowest RPM without dangerously
"lugging" gives the most efficient transfer of the engine's output to the
road -- versus letting it "float" at high RPM with relatively little shaft
load.  In general engines are more efficient when loaded, and everything
beyond that, for any engine, is a matter of optimal RPM and how that relates
to cylinder geometry, intake/exhaust design, etc.  The torque and efficiency
curves for the Prius in particular are very broad and forgiving, as shown
in this pair of diagrams.

And before we get too far along in this and risk misleading the
reader somewhat, take note:

Update:   Subsequent studies indicate that the low end of this range, below 5.8 milliseconds or so, also falls off the peak efficiency curve somewhat at true highway speeds. See this later article for more details on power output and how to really optimize highway fuel economy, and for what is said below here apply the caveat that it may be too delicate an approach in many cases.


The Prius has no step gears, of course -- its output ratio comes from an
computer-defined torque balance between the two electric motors across
the planetary gearset, and the computer meanwhile gets to handle the
throttle opening as it pleases.  It presents a different way of thinking
about engine control, and can be problematic for drivers to get used to.
In my own experience, it seemed as though I was stuck running in higher
RPM ranges at highway speeds at the expense of good MPG, and couldn't quite
figure out optimum strategies -- if it's better to try and pulse the engine
hard and then "warp stealth" to glide, or just try to bring everything to
a steady state and hold it there.  I already knew the cruise-control is
*way* too aggressive about holding an exact speed, and that while some
owners are perfectly happy to just let the cruise-control do its thing on
highways and deliver mid-fifties MPG at best, there had to be a better way.

Interestingly, it has often been through talking with Honda Insight owners
that I've learned the best ideas about high-mileage driving technique.
With the Insight's traditional throttle linkage and transmission, drivers
get much more manual control of their gearing and throttle settings, which
when properly played can easily return 100 MPG for them.  They also have the
advantage of lean-burn, which does require a lighter load on the engine.
But then trying to plow those ideas back into how the Prius operates has been
a bit of a struggle since it seemed like I had much less control over the
throttle and powertrain output ratio.  It seemed impossible to duplicate the
high-torque, low-RPM "almost lugging" methodology of running through the
gears quickly while accelerating and get into the highest gear as soon as
possible.  It always seemed like if I wanted to go a reasonable speed on
the highways, RPM would automatically climb into areas of more fuel
consumption.  So the big question became, "how do I get the Prius into
the equivalent of high gear earlier in the game?"

I started occasional discussions about this in the Prius technical forums,
which were somewhat inconclusive but allowed me to bring my own observations
forward to see if anyone else had ideas or followups.  Shortly after getting
aboard the "hypermiler" hangout at cleanmpg.com I posed the questions again
and some of the condensed observations and thinking to date, but even the
discussion there was still rather inconclusive.  There were several half-
formed theories about the Prius, but nobody seemed to have the answer yet.
That exchange is still worth reading, because at that point in time I didn't
know but was SO CLOSE to finally getting it:

The answer had been sitting right there in front of my face the entire time.

The very first instrument I ever played with in this car, in fact, was my
old vacuum gauge left over from previous projects, and after driving around a
little with it I was *completely* mystified as to what the Prius throttle was
doing.  A vacuum gauge is a good "how hard is the engine working" indicator,
since a larger throttle opening resists engine suction less and lets it pull
more air/fuel mixture through the cylinders.  Traditionally, a vacuum gauge
tracks the inverse of the accelerator pedal position fairly linearly, dropping
to zero at or near full throttle opening.  But with the Prius, the throttle
is controlled electronically and completely decoupled from the pedal.  While
I didn't always understand exactly what it was showing me about the Prius,
the vacuum gauge has been part of my extra-instrumentation panel since
the very beginning and has been useful when trying out yet another theory
about efficient highway travel.  At a minimum, I knew that when the vacuum
began to rise away from 5 inches of mercury, that the engine was likely to
be "loafing" -- still burning gas, but inefficiently and not providing any
appreciable power, just heat.  But with new factors like the Atkinson-cycle
engine and computer-controlled throttle, I couldn't be sure about the
possible causes of what I was seeing in the gauge.

Before the trip out to Hybridfest 2006 in Wisconsin and back, I had also begun
playing with monitoring fuel injector pulse time and duty-cycle percentage.
This started with simply watching it on an oscilloscope and eyeballing some
timing, and then once I understood what that was doing I started playing
around with some circuits to integrate pulse times and display proportions
as a voltage.  Through a bit of dumb luck with some components stuck into a
prototype circuit, I seemed to have given myself a meter that would start
reading just as low vacuum was reached, and crest at 10 volts as vacuum
headed a little lower yet above 2300 RPM or so on the highway.  A conceptual
0 - 100% display of what I believed would be an efficient range, in fact.
With all this sitting on the dash as the typical breadboard bristling with
parts, I set off for another 2500-mile learning experience.  And the running
MPG during that trip was respectable -- north of 60 the whole way, at speeds
between 60 and 65 MPH.  "Sixty-three at sixty-three", I started calling it.
Nicely above the EPA numbers, especially the highway rating for the Prius --
and I began believing that it was due to letting a little needle waving back
and forth govern what my foot was doing.  Maybe it wasn't perfect, and there
were still other techniques I could be doing to get even better, but this
lashup was doing more for my running MPG than anything prior.

But on the way back from Hybridfest, the real epiphany came to me.

It was an observation that lasted only about a quarter-second, but which
completely confirmed all of this new thinking.  I was on some secondary
highways in Pennsylvania, and had just come down a fairly large hill that
had run the battery up to its displayed "full" at 80% SOC.  In that state,
the hybrid system often tends to get a little confused and try to do things
to bleed off some of the charge -- such as by starting and stopping the
engine a few times, and various other thrashing that is a bit less smooth
than the usual control scenario.  After the downhill, I was coming up a
gentle rise toward a red light, and trying to use the injection meter and
vacuum gauge to stay just barely "under load" while still letting my speed
gradually fall.  During the next run/stop transition, I suddenly heard a very
brief but aggressive "rev-up" from the engine -- like you would hear upon
stabbing the clutch pedal on a manual transmission while cranking uphill in
high gear.  The motors, just for an instant, had evidently "let go" of the
engine's output, and then just as quickly recovered and rebalanced the
torque.  But that blip ran the engine RPM up so fast that I realized that
my vacuum gauge had never lied to me -- when it read low, the engine was
indeed running in a high-torque mode, even if I couldn't really feel it
pushing the car.  I thought about it a little more, and realized that even
though the engine was running barely above idle -- 1100 RPM or so -- the
throttle was significantly open, shaft torque was high, and RPM was being
kept down by the "heretical mode" electrically-routed overdrive feeding
straight into the road load.  *There* was my "high gear" answer.  It was
already happening -- I didn't have to do anthing except make sure I kept the
system demand down near the low end of my "sweet spot", but not let it drop
down past there.  Toyota's throttle-control strategy took care of the rest.

It's bloody brilliant.

As I played around with this concept more on secondary highways and surface
streets, I found that carefully holding the low-RPM "high gear" scenario
without yielding to the temptation to push harder can indeed get the car
going respectably fast, it just takes longer -- as one would expect from
doing a similar thing with a manual gearbox.  It requires a little patience,
or that MPG-eating RPM starts sneaking up again.  If a lower road speed is
required, the driver must alternate this mode with some engine-off periods
by going to electric-only or warp-stealth state -- which only serves to
deliver even better MPG!.  This switching can usually be matched to upcoming
terrain with a little forethought.  While Toyota's control strategy does
in general try to hop over the "efficiency pit" near the low end, it often
enough manages to fall in, requiring driver intervention.  As I worked my way
homeward, the MPG average kept climbing higher than I'd ever seen it go during
*highway* travel, and after I got home I wrote up a preliminary report.

So, to review: as non-intuitive as it seems, more right foot is equivalent
to downshifting.  "High gear" in a Prius is achieved simply by applying
*less* right foot, within certain limits.  The next question is how to
determine those limits.

Conceivably, it can be done very easily if such a "sweet spot meter" makes
it past prototype stage and becomes an easy add-on kit for the Prius and
possibly some other cars too.  But exactly where that range [or ranges!]
exists and how to display it is still under discussion and research.

It can be done in a minimally instrumented Prius by watching a tach --
keeping RPM between 1400 and 2300 at highway speeds.  If you have a vacuum
gauge, the observed range generally starts as vacuum drops to 5 in-Hg or
lower as demand increases, and tops out before it sinks lower to 2 or 3
while crossing 2300 RPM.  Torque is also kept high at lower RPM at lower
speeds, but it appears that efficiency starts to fall off below 1400 RPM
regardless as the engine isn't producing as much net *power*.

To some extent, it can be approximated in an uninstrumented Prius at nominal
highway speed above 55 MPH or so, by keeping the instantaneous MPG bargraph
between 35 and 75 MPG.  The downside to this is that the entire scale of
what's optimal shifts confusingly at lower vehicle speeds, leaving a certain
amount of guesswork.  This is why a simple add-on meter unit would be cool.

However, using any such sweet-spot range is merely one technique out of an
entire suite of high-MPG tools.  It is definitely necessary to understand
the other major running modes such as
warp stealth too, to avoid
burning any fuel during the times you aren't applying meaningful power to
the wheels.  That is possibly the most important one to learn about since it
gives the equivalent of electric-only "glide" in the higher speed ranges.
The bottom line is that efficient running can happen equally well above or
below the magic 42 MPH, subject to the other factors that creep in such as
air resistance and outside temperature.  One thing to note is that between
42 and about 55, such as on secondary highways, even a minimal-power efficient
running mode can get the car going too fast for local conditions, requiring
backing off into a zero-consumption mode like warp stealth until power is
needed again.  And secondary highways tend to have more extreme hills and
speed changes and traffic lights, bringing all the high-MPG driver's skills
and gauge-watching into wild manic-depressive play one after the other.
Nonetheless, proper use, overall smoothness, and attention to state changes
*does* solve that puzzling mid-speed problem, returning 70 or 80 MPG segments
on surface roads in many cases.  On the interstates, it's generally a lot
easier but one must still try to track hills to some extent and decide just
how much "rollercoaster" constant-load driving can be allowed.

So, let's do a little analysis of what's going on here, using my own
instrumentation as a guide.  First, here's the key to what's what on
this panel:
and in this case the "multifunction voltmeter" is connected to the prototype
circuit sitting in front of it, displaying a theoretical "sweet spot" from
0 to 100% at 10V or higher.  [Meter goes to 15V]

On a slight downhill, we're in warp stealth:
As the state was entered, the manifold vacuum backed off from over 20 in-Hg
down to 15 or less, indicating that the VVTi valve timing had been fully
retarded.  With a throttle setting of very slightly above idle level, net
airflow through the engine is almost zero and minimal "engine drag" pumping
loss is presented.  No injection is happening at the LED indicator.  About
ten amps are drawn from the battery to keep the engine turning and very
slightly pushing the car.  The tach erroneously reads 0 RPM, but that's
simply because its input comes from the IGF spark feedback line -- which
isn't sparking since there's nothing to burn.  Over on the screen you can't
see, instantaneous MPG is reading "infinite".

Once back on the flat, we need to bring on some engine power to
maintain speed:
50% or less sweet-spot range [SSR] is often enough to carry us along.  If
a downhill is immediately followed by an appreciable uphill, then it is
likely that 100% SSR is needed immediately to keep the most momentum up while
attacking the climb.  Vacuum has dropped to its normal highway 5 in-Hg,
injector pulse time is running about 6 ms, battery current is back to
essentially zero.  At this point sweet-spot range is entirely affected by
engine RPM, from 10% around 1400 RPM up to 90 or 100% at 2200 RPM.  This is
accompanied by injector pulse length between 5.5 and 6.5 ms -- since the
throttle remains pretty much at the same setting through that entire range
with only a slight increase to allow for higher airflow, injector timing
doesn't vary a lot either.  Screen probably reads about 50 - 60 MPG at this
point.  I had the circuit tweaked so it was pretty close to reading 50 MPG
at 50% SSR, but that varies a bit with vehicle speed.  The important thing
to note here is that over a large range of right-foot demand, injection and
vacuum and throttle all vary VERY LITTLE, while the HSD simply controls engine
RPM by sliding the electronic "ratio" between MG1 and MG2 up and down.  Too
low, and we get into the "loafing" scenario which is death on MPG; too high,
and we get into more of a "power" regime which also guzzles fuel.

Here's what happens if we push harder than 100% sweet-spot on a rise:
Note that the vacuum has dropped a little *lower*, to 2 or 3 in-Hg.  There
is a very definite high-side cutoff point, in fact, which I still don't
entirely understand -- nearest theory at this time is that in the described
sweet-spot range, the valve timing runs fully *advanced* for best compression
and volumetric efficiency, i.e. range 4 in the valve diagrams below, and
begins retarding into range 5 as RPM crosses up over 2300 or so.  As that
happens, there's a rise in RPM vs. power output that other people have also
observed, which appears to lead to somewhat lower *road* efficiency.  Injector
time can widen out to as much as 7 or 8 ms along with the other changes.

	UPDATE: the above theory about valve timing has been debunked.
	It's simply done with throttle control.

If we push RPM well up over 3000, something completely different happens that
I've referred to as "WFO mode", a common play on "WOT" or wide open throttle.
Under serious high-power demand, it's pretty clear that the engine goes into
either an open-loop or enrichment-driven mode to deliver that.  Evidence of
this is LOUD intake noise, larger throttle openings, vacuum at *zero*, and
scooting briskly down the road with MPG completely in the toilet.  What's more
interesting is that if demand is brought down very slowly, it can *stay* in
that mode while returning down to 2000 RPM or below, with vacuum still at
zero and injector timing hunting all over the place but remaining fairly
long.  This is a completely useless state for high mileage, but one should
be aware of its existence simply because if the WFO mode is entered, the
way out of it is to back completely off the accelerator and gently reapply.
The aggressive must-hold-speed behavior of the cruise control can easily enter
WFO mode up a hill and then fail to get back into a more efficient mode for
a while thereafter, thus killing MPG for no reason.  Not that someone driving
for efficiency optimization would be using the CC in the first place...

Valve timing charts, from Toyota:

These two diagrams are from the same section of the New Car Features
documents, and point out some very interesting relationships.  For vehicle
speed ranges between 30 and about 60 MPH, the slight rise and plateau of the
vacuum [or lower MAP, if you think of it that way] appears to be a result
of intake valve advancement, running in range 4 -- fairly high load, low RPM.
Put another way, a higher compression ratio returns better thermal efficiency,
but we've still got the Atkinson-cycle difference between compression and
expansion which helps optimize that even more.  It's a balance.

Pushing harder brings vacuum slightly lower around a very specific engine
RPM whose value depends on vehicle speed, and it turns out that over most of
the useful speed range that point is about where MG1's backward rotation [in
heretical mode, being driven by electricity from MG2] comes to zero and
begins rotating forward as a generator again.  In general, MG1's response
to varying driver demand is to drift freely back and forth between backward
and forward rotation -- it never locks, and we rarely if ever actually feel
the reversals.  But we need more engine RPM to compensate for getting through
the zero point and entering the forward-spinning scenario, so we see engine
demand change fairly quickly right where that zero-crossing is.  This begins
to become less true at higher vehicle speeds, where higher demand is likely
to drift out of the "overdrive" scenario -- say, to sustain speeds much over
70 mph.  The whole "sweet spot" thing probably falls apart at the high end
in those operating ranges.  More research is needed into this and what the
valve timing is really doing.  It is clear that Toyota's engineers had a bunch
of interesting high-efficiency thinking going on when designing the control
strategies, but it apparently remains up to us, the consumers, to ferret out
how to really utilize it.

Some time later I went out and tested the high-side scenario in a reasonably
well-controlled A/B/A/B set of 55-mile loops with an MFD reset between each.
The variable was either staying strictly within the higher-vacuum range or
allowing slight [but not extreme] excursions above the high-side RPM limit
on uphills.  Ambient temps were a fairly brutal 85 - 93 F, but I stuck it
out for the four or so hours this took, kept my speeds about the same over
each run to eliminate wind-resistance as best as possible, and logged the
average MPG over my runs:

	63.4	constrained
	62.3	allow 2400+
	64.6	constrained
	63.7	allow 2400+

While the differences seem minor, it seems that entering range 5 too often --
if that's what I was doing in the first place -- is a bit of a mileage hit.
Other prior observations about higher RPM ranges seem to support this, well
enough that I don't believe it's just due to some incremental delta in air

If it develops that a particular operational range that best optimizes fuel
economy in highway travel can be "metered", it must still only serve as a
guideline.  So far the working theory appears to return good results for most
terrain and at speeds that are most recommended for improved highway mileage.
The major human acceptance problem here is that not allowing excursions into
the above-noted higher-power mode delivers about a maximum speed of 73 MPH on
the flat, and you'll be joining the trucks in the "slow vehicle" lane up the
mountains.  So it's an area that requires best judgement and tradeoff from
the driver.  If such a meter were to become sufficiently researched and
packaged to become an add-on product for the car, I could still see some
people installing one, thinking it might magically gain better miles per
gallon numbers, and then completely ignoring what it tells them, sort of
like those "upshift" idiot lights that suggest economical use.  There's no
magic here.  The light bulb, as always, has to *want* to change.

_H* 060808, 070506