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!

Update on Sunday, July 12, 2009 at 11:22PM by Bill Wood

This post caused a fair amount of discussion here, at PriusChat, and at CleanMPG.  I've made a followup post to recap some of the discussion.

Comments

[a priori]

Bill,

This is an interesting approach, but it doesn't represent the reality of pulse and glide.

In your example, you talk about one pulse and one glide, but you miss the whole point -- it continues. At the end of the glide, the driver is not back down to zero mph, so there is residual energy, meaning the next pulse will not take as much energy as the first. This is repeated, again and again.

The distance coverd in any pulse is a fraction of the distance covered in the corresponding glide, and your example of equal time/equal distance is not a description of reality.

If your example suggests the driver already was driving at 35 mph and then accelerated for 30 seconds at 20MPGs, what speed do you believe the driver would reach before going into glide? Whatever that speed is (unless it is above 60 mph), the glide for equal time will result in an end speed higher than the speed at the onset of that glide. If this is repeated, either the driver will exceed the speed limit, of the driver will require less and less energy to sustain a decent speed.

[Bill Wood]

Well, as I said, "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." So I think I do "get it".

You're correct that a good glide will be longer in distance than the pulse, and I wasn't disputing that. The interesting thing is the easy misconception that the average MPG is higher than it really is. To get 60 mpg in my example of a 20 mpg pulse and 100 mpg glide, your glide needs to be 5 times the length of the pulse, which is often not possible.

[Jon]

The FFH doesn't actually have a neutral. You can't disengage the ICE and MG1/MG2 from the drive wheels. The N position on the (simulated) gear shift just tells the computer to interpret the throttle differently (not quite ignoring it as you will still get engine braking which I find odd). You can actually get a better glide with just the right throttle position than you can with the gear shifter.

J

[C]

Given the ECU programming, going to neutral would be bad in most modern cars? Isnt the injector cycle almost nothing using the energy of motion to keep the engine lit? Therefore slipping into Neutral uses more fuel.

And given a hybrid, I would have to assume that "coasting" to a certain extent would be helpful in charging?

[Bill Wood]

When you shift the FFH to "neutral" you can feel the reduction in engine braking. Jon, I believe you are saying there is still some engine braking going on which may be the "back EMF" that Wayne Gerdes talks about? He says, "___You can glide the FFH in N or by applying a small amount of accelerator to remove assist and regen (the second being harder) but the problem lyes with the way the fields are still being generated even while in N from higher and higher speeds Ford did not drop the MG1/2’s fields out in N like the Toyota’s do. You can see a the pack pull via the Power mimic while in a Glide from 47 down to about 40 mph where it disappears from the mimic but it is still there. Theories about HSD during a Glide in N include a back EMF build which you can remove in N under 41. The Ffh unfortunately was not constructed in such a manner and a glide no matter if in N or D with the pedal is drawing current " - so he's saying that even in drive with careful throttle control you get current draw. Going to neutral is just easier sometimes even if not better.

C, as Jon says, there is no real "neutral" in the FFH, its just a difference in the way the software controls the ICE and electric motors. In neutral on the FFH, there is no regen available. Only in drive do you get regen.

[donee]

Hi Bill,

Argonne National Labs, and Virginia Tech might disagree with your conclusion. Their recent SAE paper shows very good mileage improvements for the P&G method. They tested cars simulated on a computer using the software used to design hybrid cars, and also tested actual cars doing P&G cycles on a dynamometer. My own experience doing a 40/35 mph P&G indicates about a 75 mpg , versus about 50 mpg for steady speed. And that even in a Atkinso engine Prius, which has very good partial load engine efficiency. If conditions would permit, coasting down to 25 mph would be even better. And of course, the 125 mpg tank average acheived by Wayne Gerdes et al in a secluded area in a Prius several years ago is testament to how good P&G can be when executed carefully.

[Bill Wood]

Hi donee, I'm not dissing P&G here, just pointing out that the math is unintuitive. For a 20 mpg pulse and a 100 mpg glide, the glide must be 5 times longer than the pulse to get 60 mpg total.

BTW, Bob Wilson tried to replicate those SAE numbers and only got 11% improvement using P&G in controlled tests on a real road (not on a dynamometer). See:
http://www.myhybridcar.com/forums/gasoline-fuel-economy/385-sae-paper-pulse-glide.html

[Larry]

I still don't think you completely understand P&G. For me, the pulse lasts for 5-10 seconds but, the glide lasts for 20-30 seconds and even more. Just yesterday on the way home from my mother's, I achieved 160 mpg in a 4.6 mile trip in my '07 Prius. My pulse would last 1/8th mile or less however, the glide would last 1/2 mile or more; with one glide lasting over 1 mile. Also, the day before, I achieved 114 mpg over a trip of 18.0 miles You also are not taking into account that someone who has a good grip on the concept of P&G will use the terrain to their advantage. There are certain cases where my short 1/8th mile pulse will result in a glide of 1 mile or more. At the risk of this sounding like bragging, the above 160 mpg segment wasn't a record as I have achieved just over 170 mpg for that same trip.

[Joel]

Before I learned P&G in my Scion xB, my best tank was around 40 mpg.
When another xB owner gave me some P&G deltas to try, my first tank went to 48 mpg!
It may not be intuitive, but it made a huge difference for me.

[Crajig]

Like many others, I am trying to help educate - the focus of your article should be different.
The point should be that a properly applied P&G will deliver VERY SIGNIFICANT fuel economy benefits. As an example, I am averaging approximately 60 MPG in my car by using P&G (a Ford Contour SVT that nearly qualifies for the cash for clunkers bill). I've actually had serious debates about whether or not I should try to go below the 1/8th mark on this tank because I am very close to 1000 miles on this tank (~850 miles).

[Bill Wood]

Larry, I've made this response in my followup post:

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.

[Bill Wood]

Joel and Crajig, see my followup post at:
http://ffh.squarespace.com/blog/2009/7/12/the-myth-of-pulse-and-glide-revisited.html

[Taliesin]

The math behind P&G may not be intuitive, but I just let the computers take care of that.

All I know is that in my Ranger (note that this is not a hybrid, so SOC does not apply) it works very well. Due to the hills on my commute there are few places where I can use it, but since I have started I have gone from 33 mpg on a tank to my current 40 mpg tank.

[Lepentene]

I highly enjoyed reading your post, keep up creating such exciting articles.