## 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:

- 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.
- 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.

## Reader Comments (4)

"If you assume infinite mpg for the glide, you get 60 mpg when the pulse is twice as long as the glide, which is also not particularly intuitive."

Don't you mean: when the glide is twice as long as the pulse ?

That would seem pretty intuitive to me.

But then maybe I don't belong to your target audience, considering the supermarket tabloid style title of the original post.

The actual subject of your original post was the general mathematical problem of averaging mpg. This mathematical problem is not specific to pulse and glide as implied in the title. In fact, it is not even any more of a problem for pulse and glide than for any other time when one calculates average mpg.

Question: Does your car charge the battery while pulsing?

Thanks for catching that! I corrected it.

In my first article on P&G, I described how averaging my MPG to and from work led me to think about averaging MPG for pulse and glide. Because of that post and discussions stemming from it, I've learned a lot and will soon post some ideas I have on measuring equivalent glide MPG over at PriusChat.

Yes, the FFH will charge the battery while pulsing. Why?

Because if it didn't charge during pulsing, that would be a clear justification for adding equivalent fuel consumption only to the glide phase in the mpg calculation.

I confess; I am also sceptical of adding an mpg equivalent to the glide value without also subtracting it from the Pulse value. (conservation of energy)

If you were calculating tens or hundreds of consecutive pulse and glide cycles, would you at some point start also subtracting the eqivalent mpg from the pulse value? Or drop the equivalent mpg (set to zero)?

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

I think you meant: set glide Gal equal to 0.

Thanks for catching yet another one!

I would not subtract MPG from the pulse because the driver can target 20 mpg using the instantaneous gauge. Charging during the pulse reduces the overall MPG because you must pulse longer to reach the target speed.