The myth of pulse and glide

I get around 50 MPG in city I use pulse and glide on a hilly road I get about 78MPG in that area.. it just works...

 

That's not quite right either. Even in no-arrows glide mode with the Prius there is some electrical consumption for traction (not to mention overhead of the electrical system which will occur even in neutral.) Traction draw is minimized, but still present and increasing with speed if I remember the charts right.

P&G is about running the engine most efficiently...and that means leaving it off whenever possible without going into EV pulse mode. It's already understood that this doesn't mean running with the engine, then exhausting the traction battery. Yes, electrical conversion losses factor in, but you are drifting into an EV pulse with your glide extension claim, rather than P&G.

As to whether one is better off extending the glide or not with some yellow arrrows EV it depends on the situation. It makes little sense to let the ICE cycle on when it is going to be shutting down in a few seconds, so it is more efficient to use a short EV pulse in some situations. Examples would be on some short hills in town where I roller coaster with only ICE input for the higher/longer climbs, for the roll through the neighborhood into the garage, in some heavy traffic situations where I know I will be stopping shortly, and in parking lots where I again know that the ICE will no sooner start running (and in a very inefficient light throttle/low speed mode) than it will need to be shutdown.

The battery controller is going to begin adding energy back to the battery during some of the pulses anyway or forcing the engine to be on at times if the SOC reaches some threshhold, so when considering a no arrows glide, it makes sense to treat it as infinite mpg. The mpg impact will be reflected in the duration of the pulses at a given mpg anyway.

 

Adding to the wonderful Shawn's comment, I still can't understand what you're saying.
The heavy use of A/C consumes more fuel at following pulse stage, therefore the pulse 20 MPG becomes pulse 10 MPG.
It does not mean 20 MPG glide.

Thank you!

Ken@Japan

 

This is a case of making the statistics or nunbers say what you want them to say. Anyone with any experience hypermiling a Prius knows that P&G will give sustantially improved results.

 

Actually you've overcomplicated it by inserting an artificial value when no gasoline is consumed. You end up double counting on the glide side, because the pulse includes the glide energy. (This is assuming that we are doing enough P&G's back-to-back that the state of charge is essentially unchanged from the 1st to the last.)

Now for a single P&G you could account for this by showing the SOC change and converting that to kwh and therefore mpg for the distance covered. Unfortunately you need some conversion assumptions there as well for the kwh consumption. Since folks regularly exceed 100 mpg doing P&G in ideal conditions, the actual factor is probably more like 200 mpg. However, this is a function of the speed profile of the P&G.

If I do a 20 mpg pulse it is a 20 mpg pulse...whether the battery is charging, the AC is on, lights are on, wipers are on, etc. Those things will make the pulse longer since less power will go to acceleration. The electrical consumption is being accounted for then, assuming the P&G is measured over a long enough distance that the beginning and finishing SOC are roughly the same. The glide is infinite mpg with respect to gasoline, but not energy consumption.

The energy required to move the vehicle is not fixed during the glide either. It is speed dependent among other things so this is even more complicated if you try to account for the glide.

At really low speeds (perhaps 20 mph and below) the overhead of running the electrical system and other things actually exceeds aero losses.

 

Without getting lost in the semantics, this is the goal of efficient driving but two pieces of information are needed:

• Brake Specific Fuel Consumption(BSFC) - this is the amount of fuel burned to produce a given amount of mechanical or shaft energy
• drag reduction - this is the sum of the rolling, aerodynamic and what Ken@Japan calls, 'heart beat' power ... the energy that is consumed by the electronics with the car regardless of what it is doing

If you plot the drag force product with the velocity, you get an energy curve, the least amount of energy needed to sustain any given speed:

This is data for the 1.6L, NHW11 (2001-03) Prius:

• red line - the amount of power needed to move the vehicle at different speeds based upon rolling and aerodynamic drag.
• blue line - the amount of fuel consumed if a fixed efficiency engine is used to generate this power
• gray line - the blue line plus the vehicle overhead power that powers the brake pump, coolant pump, day-light running lights and control computers.

Now you'll notice in some cases, the plotted performance exceeds the theory. This isn't "cold fusion" but upon closer inspection we find:

1. tires fully inflated - in the first Prius marathon, one report claimed 50% over maximum side wall pressure and nearly bald tires.
2. warm temperatures - generally above 80F. So far, no one has reported attempting a maximum, density altitude test, say Wyoming or Colorado during the hottest days.
3. aerodynamic modifications - starting with bumper air inlet blocks and proceeding to wheel well covers and stripping off all external objects or if on public roads, putting them in a least drag position.
4. minimum weight - take out everything that can be removed.
5. lubricants - using a lower viscosity engine and transmission oil to minimize mixing losses and other properties that reduce thin film friction without leading to wear that shortens the vehicle life.

But we also know the engine efficiency, the BSFC, is not fixed but varies over the power band. This is data from a 1.6L Prius engine:

These data combine engine torque, engine rpm, and fuel flow:

• large dark blue dots - the least efficient BSFC observations
• smaller light blue dots - more efficient BSFC observations
• smaller yellow dots - even more efficient BSFC observations
• smaller still, orange dots - improving BSFC observations
• smallest red dots - the peak BSFC observations

Notice there is curious 'dead band' of red dots in the 1700-1800 rpm range. But at rpm ranges lower and above up around 2,600 rpm, we have a good cluster of high efficiency, red dots. These are the regions I like to operate my NHW11 (2003) Prius. Although in the last year, I'm mapping out the equivalent bands in mass air flow, an easier value to 'drive to.'

Sometimes you need more power for the road conditions. For a slow acceleration, up to 2,800 rpm seems to work well. Still, sometimes, you need even more power such as climbing a hill on an interstate. But there is one region I avoid, anything over 3,800 (other data see lower chart.) Above 3,800 rpm the engine is producing the maximum power but burning fuel at a terrible rate:


But this detailed analysis presumes many things not available as standard instruments in the Prius. So to simplify what is going on, the "Pulse and Glide" terminology is used as at best, a 1st approximation of what is needed:

The key to efficient driving is maximum engine efficiency combined with minimum drag and vehicle overhead. Sad to say but the ordinary instrumentation we have in our vehicles could be better.

The challenge is to generate similar performance metrics for the 2010, ZVW30, Prius.

Bob Wilson

 

To do this analytically you need non-linear differential equations. Anything less is a gross approximation, unless we look at the entire system as a black box.

Tom

 

Yes there is. I explained why, but you dismissed it. Not much else I can do.

Your way is not increasing the MPG of the pulse to account for power consumed in charging the battery...that power is being consumed in the glide, but not gasoline. That is what you would have to do for equivalency.

actual distance travelled/actual gallons consumed

No gasoline is consumed during the glide. By your method one will have phantom gasoline added to the denominator and will get the wrong result.

You are mixing your bases so many different ways that what you described on paper calc does not match what you are saying in the way of driving in the article:

"Let's say you decide to pulse for 30 seconds, then glide for 30 seconds. If you get 20 MPG during the pulse, and 100 MPG during the glide"

Gallons consumed during the glide are zero. If you are going to treat the glides as consuming X gallons, then you must subtract X gallons from each pulse where the electricity for the glide is generated...assuming that one is returning to about the same SOC at the end of a series of pulses.

 

Hi Bill,

Do a new chart where Glide Gal = 0, and we might start agreeing with you. People have given you reasons why this is so.

 

I've been having my math fix on this one, and I haven't resorted to DiffyQ (Diff-E-Q?). We never had spreadsheets (much less computers) for solving the difficult equations when I was in college, but I've sure enjoyed using them the past 25 years or so to work the simpler stuff much faster.

Glide consumption really isn't much of an issue here. What we're looking at is whether P&G generates a benefit in terms of MPGs. Those of us who've been driving the Prius for a little while "know" the answer because we've experienced it. Now we are faced with a mathematical quiz and we get all in a tangle over it.

Perhaps we can just get a couple of people to gather some empirical data on a single question: If you are driving on a level surface at 35mph and you pulse up to 50mph, measure the time and distance for the pulse and for the glide. The assumption is that you return to 35mph. The other, somewhat critical, part is the SOC on the HV. Let's suggest that you pulse at a rate that doesn't discharge the HV so that at the end of your glide your SOC is the same as at the start. This may not be the best way to P&G, but it is the easiest way to measure. The other action is to go back to the same starting point, get to 35mph and keep it there. You measure the time and distance from the point the pulse started in the first try to the point where the glide ended in the first try. The result? Compare the total MPGs of try one to try two.

Anyone game?

Oh -- the math! I ran some pretty simple spreadsheets and found that distance traveled in glide vs. pulse is the critical measure. An example: A 20MPG pulse followed by a no energy (10,000MPG) glide. I assumed a quarter mile pulse followed by a three-quarter mile glide (3x multiplier for distance), and found the end total FE would be 80MPG. If the glide were only twice the distance of the pulse, the FE would be 60MPG. If the glide were five times the pulse, the FE would be 120MPG.

I chose 10,000MPG for the glide for two reasons. The first is that people with ScanGauge report up to the max readings of 9,999 MPG in glides. The second is that there is no statistical difference between 10,000 and infinity when measuring on the left side of the decimel point (when the distance multiplier is 3). The point where higher MPGs are required in order to estimate infinity increases steadily with the increase in a multiplier of glide distance to pulse distance. (Example: If glide distance is 5 times pulse distance, then the "infinity" equivalence is found at 24,000MPG where the total FE for the P&G becomes 140MPG.)

 

I've already explained it. If you want to create an artificial gasoline usage where there is none for the glide, then you need to subtract that value for the pulse.

Your model will not agree with empirical results because of your phantom gasoline use. Let's say I drove a whole tank doing 20 mpg pulses with various distances for the glides and pulses (to hold some preset speed targets.) Whether I use AC or not doesn't really matter if I know the total distances covered in each stage. For grins lets say I drove 200 miles total at 20 mpg pulse, and 800 miles total in glides with no gasoline use. The car will use a total of 200/20 = 10 gallons to travel 200 + 800 miles. That will be the empirical result as well as my calculated result.

But by your method some mpg (say 100 mpg) is applied to the glide, but NOT subtracted from the pulse. So you would calculate 200/20= 10 gallons for the pulse, and 800/100 = 8 gallons for the glide.

Nobody is disputing that there is energy use and conversions occurring in the glide. We all understand that, but where you are having trouble is in your accounting method.

 

Shawn,

I may be missing something in this conversation. If Bill did make the assumption the glide would produce 100mpg, then wouldn't his result be correctly calculated at 1,000 miles/18 gallons or 56MPG? Similarly, if the glide were to be calculated at 10,000MPG, then it would produce 800/10,000 or 0.08 gallons, so the final FE would be 1,000/10.08 gallons or 99MPG. This compares to 1,000 miles per 10 gallons in your description (or an FE of 100MPG).

What I'm missing is why something would have to be subtracted from the pulse side if the glide side is not assumed to have an infinity reading for the fuel economy. If the assumption you bring to the table is that at the end of the 1,000 mile journey the SOC is exactly the same as at the beginning, then I see your point: The pulse events recoup any electrical usage lost during the gas-less glides. Otherwise, we do need to account for the delta in the SOC.

I understand that most of us would disagree about assigning 100MPG for the glide's FE. That's why I put in 10,000MPG. Even if we used 1,000MPG, the final result of your 1,000 mile P&G odyssey would be an FE of 93MPG. Not bad considering the maximum feasible is 100MPG under the scenario you've drawn. That would be using just three-quarters of a gallon of gasoline more (per 1,000 miles) than in the infinity assumption. It is still more than enough to cover the difference between an 80% SOC and a 20% SOC, so it is unlikely that there would be such low mileage during true glides.

If my description covers the "subtraction from the pulse side" please let me know.