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The myth of pulse and glide revisited

My post on the myth of pulse and glide generated a number of comments here, over on PriusChat, and at CleanMPG.  I thought I'd respond and clear up a few misconceptions with a followup post here.

A number of people thought I was saying that pulse and glide (P&G) doesn't work.  Nothing could be further from the truth.  I continue to learn about this important technique for getting good gas mileage.  The "myth" I was referring to is the common intuition that if you pulse at, say, 20 mpg and glide the same distance at, say, 100 mpg, then you will average out to 60 mpg total. You actually get 33 mpg in that case and don't get 60 mpg until the glide is 5 times longer than the pulse.  If you assume infinite mpg for the glide, you get 60 mpg when the glide is twice as long as the pulse, which is also not particularly intuitive.

Others noted correctly that the glide is usually longer than the pulse, whereas my example stipulated the pulse and glide as being the same length.  The intuition I spoke about above usually arises when people are thinking of equal length pulses and glides, which is why I used equal length pulses and glides in my example. Here is a chart showing the Total MPG for various glide MPGs where the glide is 1, 2, 3, 4, and 5 times as long as the pulse.

Several people made posts or commented on the blog saying that they had gotten great gas mileage (one poster got just over 170 mpg!) while using P&G. That's great! A couple of things to look at in those results, if you really want to understand the long term sustainability of P&G:

  1. Was the battery state of charge (SOC) at the same level before and after the P&G session. If the battery SOC was lower, the P&G is not sustainable over time with that same great gas mileage as the engine will eventually fire up to charge the battery and shorten your glide.
  2. Was it a round trip? Wind and/or downhill slope can make a glide last longer than it would otherwise. By going both directions, those factors are eliminated.

Some posters were concerned about my use of 100 mpg as an estimate of gas mileage for the glide portion. I picked that number because my first P&G experience was with my old 1998 Audi A6 whose engine does not automatically shut off during the glide. These same posters pointed out that in a hybrid like the Ford Fusion Hybrid or Prius, the glide gets infinite mpg. This is where things started to get hot!  This discussion is not bottomed out yet.  For the mathematical model of P&G that I am using, it makes sense to not think of the glide as having infinite mpg.  During the glide there will be battery discharge - from A/C, or lights, or feathering the throttle to extend the glide a little.  Even without these electrical draws, the electric motors still draw some current. You can account for any battery discharge during the glide by reducing the glide's equivalent MPG. Equivalent MPG is a way to think about the true cost of a given transport mode. When discussing all-electric cars, equivalent mpg is used to determine the true cost of moving the car, even though the car is getting infinite mpg in the sense that its not using any fuel at the time its in motion.  Looking at the big picture though, the car has a cost to operate, when its charged at a later time from the electrical grid. So you'll read about the Tesla having an equivalent MPG of 120 or so.   When you glide in a hybrid car but are using the battery, its the same situation. The battery has to be recharged eventually somehow, and this always involves the car's internal combustion engine (brake regeneration can't restore the whole charge on a round trip due to conversion losses).  To keep the mathematical model simple you can select an equivalent mpg for the glide to account for this battery charge loss, which, if you keep doing the P&G for long enough, will eventually cause the engine to run to recharge the battery.  Here is the simple mathematical model I used for my original blog post:

Distance = Glide Distance + Pulse Distance
Glide Gal = Glide Distance/Glide MPG
Pulse Gal = Pulse Distance/Pulse MPG
Total MPG = Distance/(Glide Gal + Pulse Gal)

If you don't like assigning an equivalent MPG to the glide, then set Glide Gal equal to 0.

Thanks to all the posters and commenters for helping me to refine my understanding of P&G, and helping me to develop the pulse equivalent mpg idea.


The myth of pulse and glide

The math behind "pulse and glide" seems intuitive enough.  At least that's what I thought.  Until I started calculating my total MPG for trips to and from work.  On the way to work I have gotten 60 MPG; on the way back I have gotten close to 40 MPG - that's 50 MPG total, right?  I did the math, and my MPG to and from work is only 48 in that case.

How does this apply to pulse and glide? Pulse and glide is a technique where you accelerate moderately to an upper target speed such as 45 MPH, then lay off the accelerator and glide down to a target speed such as 35 MPH, possibly putting the car in neutral during the glide to minimze fuel use.  Then you repeat.  The idea is that the pulse MPG and glide MPG should average out to some pretty good gas mileage.

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, it seems natural to assume you'll be getting 60 MPG total - after all, 1/2 of the way between 20 MPG and 100 MPG is 60 MPG. This is the myth of pulse and glide. Please bear with me for a little math of pulse and glide ;-)

Here's a chart showing total MPG for a pulse at 20 MPG and a range of glide MPGs from 20 to 150.  At 100 MPG for the glide, the total MPG for the pulse and glide is only 33 MPG, not 60 as we intuited.  At 150 MPG for the glide, the total MPG for the pulse and glide is still only 35! 

The maximum possible total MPG, even if you use no gas at all during the glide, is only 40 MPG.  Why?  During the pulse you get 20 MPG, using G amount of gas and travelling D distance.  Your mileage for the pulse is D/G MPG.  During the glide you use no gas and travel D distance also.  Your total gas usage is G.  Your total distance is 2*D.  Your total mileage is 2*D/G MPG, or twice the pulse MPG.

So, in our example of a 20 MPG pulse and 100 MPG glide, how far must you travel during the glide to get 60 MPG total?  Five times the pulse distance!