The physics of pulse and glide
 

Acceleration on a level road is the same energy-wise (in energy consumed per mile of travel) as climbing a hill at constant speed if the acceleration in g's is equal to the slope of the hill, for example an acceleration of 0.02g is equivalent to climbing a 2% grade. Similarly, decelerating on a level road is the same as coasting down a hill at constant speed. Coasting at constant speed of course will only happen if the downslope is just right; too steep and you will accelerate, too shallow and you will slow. In the glide phase of P&G the time taken to fall from say 44 to 22mph defines the deceleration rate: it would be 1.0g if the time was one second, and .02g if the time taken was 50sec. My HCH takes about 60 seconds on a level road to drop from 44 to 22, so I should be able to coast downhill at constant speed on a downslope of 1/60 or .0167. The problem I have is there are very few level roads around here, especially ones that I can use to dink around at 22mph. So I don't have a strong feeling for the accuracy of that 60 seconds. I do have some pieces of road that I have determined from GPS data have a slope of about .017 and indeed I can coast at nearly constant speed on them.

So where is all this leading? Well, I have used my Trip A meter to measure fuel consumption while climbing long hills of various slope and I've found that my fuel consumption is something like

FC = B(1+C*S) gallons per mile

where B and C are constants and S is the slope (.02 for a 2% grade). B is the fuel consumption you get at constant speed on the level, and C is a number somewhere between 30 and 50. Now let's imagine a P&G session where on a level road we pulse from 22 to 44mph in P seconds and then glide from 44 to 22mph in G seconds. The slope (S) in the equation can be replaced by acceleration (1/P), so the fuel consumed in pulse is B(1+C/P) multiplied by the distance traveled in pulse. The average speed is 33mph, so the distance traveled is 33P/3600. Fuel consumed in glide is zero and the distance traveled is 33G/3600. Taking total fuel used divided by total distance traveled we get

FC = B(P+C)/(P+G) gpm

You can play with this result but as long as C is numerically less than G you'll get lower FC with very small values of P - meaning hard acceleration is better. You have no choice with G - you get whatever your tire pressure dictates. Finding C is a little tricky because some of the hill climbs I made were assisted by the battery pack. If I started with low SOC I got values of C near the high end of the 30-50 range mentioned above.

I would dearly love to hear what others get for G - the number of seconds to glide from 44 to 22mph, and how it depends on tire pressure. You should go both directions to average out wind and slope (if there is any).

Dave (your friendly geezer physicist):)

Re: The physics of pulse and glide
 

That jives with the results of the Pulse & Glide marathon in the Prius. The best laps worked out as higher average FE with the engine on (harder acceleration) but more time with the engine off.

Re: The physics of pulse and glide
 

Define 'hard' acceleration. To the marathon men, it meant an instantaneous MPG of 20 - 30 at 30 MPH. Most people would call that gentle to moderate.

The OP's equations do not take into account varying engine efficiencies at different power demands.

Re: The physics of pulse and glide
 

"hard" acceleration means something less than 50 sec to get from 22 to 44mph (that would be a=.02g), but the equation says that you'd get even better performance to do it in 2 sec (which would get you from 0 to 60 in about 5 seconds). I can't imagine smoothly going to a glide after that kind of neck-jerking, tho. Just letting the engine idle down before you kill it would probably take a few seconds.

I think the varying engine efficiency is accounted for in my hill-climbing experiments which led to the equation involving C, the number which lies between 30 and 50 for a HCH.

Re: The physics of pulse and glide
 

Decelerating from 44 to 22 MPH depends no how fast I was going and the slope of the hill if any. Drafting behind larger vehicles will result in longer glides as well.

Re: The physics of pulse and glide
 

I've been wondering about the pulse and glide.If the gasoline motor didn't have any internal friction then pulse and glide wouldn't work any better than just keeping a constant very slow speed that would be equivalent to the average speed of the pulse and glide run.I'm just thinking out loud,and just thinking in terms of using it with a gasoline only engine.The same situation applies to the hybrids,but it is easier for me to see it with just a gas motor.
I'm guessing it works because keeping a constant 40 mph-say 2000 rpms with an auto trans Corolla costs more in internal friction losses than accelerating to 60 mph from 20 mph-shutting down the gasoline motor and gliding down to 20 mph..Yes,a rev at 60 mpg-3000 rpms-cost more internal friction than a rev at 40 mph-a 2000rpms rev because the piston-rings are moving faster,and the higher pressure in the CC should press the rings into the cyl walls a bit harder.Still,I think the frictional loses from a gasoline motor would be less with pulse and glide.It would probably work-some-not shutting the motor off since auto trans do tend to let the motor drop waaay down when you let off the gas.There probably isn't any practical way to do an actual shut down of the motor with a modern vehicle.Part of the advantage of hybrids is that they actually shut the gasoline motor off when you let off the gas(well-the toyotas will at some speeds-te Hondas will at least let the RPMS drop waaay down-I think).
I might have this backwards,so I'm open to correction.Thanks.Charlie

Re: The physics of pulse and glide
 

Dave,

As a Prius marathon man and an HCH hypermiler with some 38,000 miles in my HCH, I can attest that a harder acceleration is better for FE in the P&G mode in the HCH. As to the rest of your post, I barely passed 9th grade algebra, and never took Alg II, and I don't even know what Trig or Calc are.:confused:

The problem I have with a hard acceleration pulse mode, is that the IMA is in assist mode draining the battery pack. In glide mode, the battery is not getting recharged. It does not take long before the battery pack is empty. :cry:

Further, it seems to me (a history major, not a physicist), that much of the increased ICE efficiency would come from using the energy stored in the battery pack without replacing it.:embarass:

In my mind, the only sustainable P&G in the HCH is to ensure that during pulse you are also charging the battery pack. This means a very gradual acceleration with a whole lot of gas pedal control, watching the IMA display to make sure you have green lights, not none or blue.;) I have found P&G in this manner in my HCH is good for FE of 113 mpg over a closed course and the battery back pack stays charged. That's good enough for me.

Bob:shade:

Re: The physics of pulse and glide
 

P&G has always seemed rather intuitive to me once I heard about it -- so maybe I have it all wrong :)

Pulse: Use the ICE at it's most optimal power output range
Glide: Engine off, so no idle waste, no partial power drag

Ever wonder about theoretical maximum MPG ? For the Prius:
According to Wayne Brown, on level ground with no wind at 35 MPH, steady state energy demands are 3.5 - 4 kW. One gallon of summer gasoline has 36.3 kWh of energy, and the Prius atkinson ICE at it's best turns about 38% into mechanical energy, or 13.8 kWh. Five to 10% is lost in the transmission, leaving 12.4 - 13.1 kWh.

Computing the two extremes of the range:

12.4 kWh/Gallon / 4kW * 35 mph = 108 mpg.
13.1 kWh/Gallon / 3.5kW * 35 mph = 131 mpg.

The best leg of the marathon was about 120 mpg

Re: The physics of pulse and glide
 

And our average was just 110 mpg. My leg was just 108.5 mpg if I remember correctly.:embarass:

It only goes to show that we left room for others to improve on our efforts.;)

Re: The physics of pulse and glide
 

[QUOTE=EricGo]According to Wayne Brown, on level ground with no wind at 35 MPH, steady state energy consumption is 3.5 - 4 kW.

This energy consumption should define the B factor, before you start pulse and glide. Doing P&G will improve mileage further:omg: possibly getting you to 150mpg, depending on the other factors.

RJB: I hear your complaint about depleting the pack, but didn't Xcel & Tbaleno find that it stops depleting when it gets low enough? My problem with P&G in HCH is you never get into lean burn.

Dave (wish I could figure out how to show quotes:( )

Re: The physics of pulse and glide
 

Dave,

When the pack gets low enough it stops depleting? No, that is when it is too low!! :omg: Below 2 bars of battery pack charge, auto stop no longer works, and you no longer get assist, but the battery pack still depletes, especially in forced auto stop mode. I have often depleted it until there are no, zero, battery charge bars showing, nada. :embarass: And in glide mode with the engine off, the 12 volt is on its own running the radio, fan, instruments, and at night, the lights, and it is not being supported by the pack. When the 12 volt gets too low it does not have even enough power to engage the IMA and battery pack, let alone start the ICE. At that point all you can do is get out the jumper cables. :angry: I know, I have been there many times, testing the limits of the HCH.

As far as lean burn is concerned, despite all of my experiences in the HCH, I don't really know when the HCH goes into lean burn mode. I do think, however, that I am in lean burn above 30mph, accelerating in 4th gear until 42mph, then 5th gear (manual transmission) when I have green battery charge bars showing. But maybe I don't know what I am talking about.:confused:

In any event, whether it is in lean burn or not, P&G in the HCH gets better mpg than in cruise control at any speed. In cruise control mode, I prefer 44mph (55mph on an interstate) for a good balance of mpg, flow of traffic and going fast enough and with enough rpms to deal with the hills. I don't even know if 44mph gets me into lean burn mode, but the FE is better there than any faster.;)

Bob:shade:

Re: The physics of pulse and glide
 

This is pretty interesting.I still think that the reason that P&G works is because you pay the internal friction penality of the ICE motor with as few RPMs as possible,which would probably mean that it will cost less ICE friction loss accelerating to a speed and shutting the ICE off-or dropping the RPMS a lot like the Hinda does.This would explain why rjbarlows hard acceleration "works".Normally hard acceleration would be a killer,but not in this case.For example-a gasoline motor only car
Accelerate to 60 mph with a 4 cyl-take 12 seconds at constant accel.You will probably average 4000 rpms over the 12 seconds.It will cost 800 rpms,you will travel maybe .1 mile.A crude guess is that you could glide at least another .9 mile,and the total one mile trip would average ~30 mph-2 minutes-.
Now start the trip at 30 mph-your Toyota Corolla will be turning about 1500 rpms to do 30 mph.It will take 2 minutes to go 1 mile.It will take 3000 revs of the motor to go 2 miles.
PG takes 800 revolutions-to go 2 miles in 2 minutes
Steady speed-3000 mph- takes 3000 revolutions to go 2 miles.
Granted those 800 REVs will be higher friction revs-higher piston speed,and more pressure on rings from increased cc pressure.
I can't see any reason for the P&G to work otherwise.Pay the internal friction and general inefficiency penality of the ICE motor with as few Revolutions as possible ,and in the range where the ICE motor is efficient-close to full throttle near the torque peak where you are getting good volumetric efficiency.Of course you don't want to go way above the torque peak to near the hp peak-too inefficient.
The numbers used here are rank guesses to to help my thinking out loud.I didn't really do the arithmetic to show that 800(hard revs) revs cost less friction than 3000-soft- revs-I'm not up to chasing down the formulas for that.
In short get up to speed using revs near the torque peak with fairly heavy throttle pressure(doesn't the Prius CVT motor do essentially that?),and then do whatever it takes to get the ICE to go off,or to drop the revs waay down.
The aerodynamic forces seem to be against P&G-takes 1.33 squared times the power to overcome aero forces at 40 mph vs 30 mph-this is 1.7 times the power.The other forces are generally just proportional to speed-not the square of the speed.The payoff has to be the decreased revs.If 1 hp is the power it takes to overcome areo forces at 30 mph-it takes 1.77 hp at 40 mph and .44 hp at 20 mph.
I think the decreased revolutions have to be where the payoff is on P&G.Now,I could be wrong-not 1st time.Thanks.Charlie

Re: The physics of pulse and glide
 

[QUOTE=solecondad]I've found true lean burn over extended periods of time, i.e. maybe 3+ miles of 40-50 MPH roads w/o heavy traffic and w/o any stops has come very close to equalling P&G over the same period. Then again, my tests are slighted as I only enter P&G or execute FASs on those same roads when traffic conditions do not allow for a steady optimal lean burn pace, i.e. they're worse conditions but yield equal results. If I've got all the space in the world and want to get from X to Y in decent time, I'm totally content with lean burn. Either method makes the same argument for hard acceleration, as it takes you into lean burn quicker and allows for longer tenure there.

I myself enjoy making use of both strategies depending on traffic. I know FASs shouldn't be recommended for the noob in heavy traffic conditions, but that's where I believe there are able to make the highest relative gains over other techniques. If traffic is light and speeds are right, I rarely reboot.

Re: The physics of pulse and glide
 

Hi All:

___Some generic discussion of the P&G model can be found at the following: Lakedude takes the Gloves off …

___Good Luck

___Wayne R. Gerdes
___Waynegerdes@earthlink.net

Re: The physics of pulse and glide
 

This discussion seems to be about full-hybrids (e.g. HCH).

Any idea if the same technique would help the mild hybrids (e.g. HAH) where the ICE never switches off (except when coming to a stop) so the savings in ICE friction won't apply.

My commute was 40 mile round trip, mostly freeway but I will be doing a 2000 mile road-trip over Thanksgiving. I willdo the first oil/filter change before I go ( a little early @6500 miles) but wonder if a P&G technique will also be worth trying (up till now I've been a gentle as I can bear on up-hill climbs, and have needed the AC on most of the time here in the humid NC summer)

Re: The physics of pulse and glide
 

We cannot P&G easily in the HAH because we cannot shut off the ICE and restart it without getting locked out of overdrive (4th and 5th) unless you restart at or below the 1st gear range. So you get stuck in 1-3, with the check engine light on.

(The HCH guys have to manually shut off and restart the engine too, but the CVT and MT don't have the interlocks our AT does)

The best we can do is go into neutral and coast that way, then reengage and pulse back up, coast again, etc.

It is very hard to pulse on 3 cylinders at the lower speeds P&G is often used at. The HAH will almost refuse to go into eco mode, depending on gear selected, at these lower speeds (or at least its tricky to keep it in eco mode). The cost of pulsing, usually on all 6 cylinders, outweighs the benefit of the short coast. You're talking 6-10 cycles per mile- that is a lot of work for the driver, too.

However we have the eco mode trick up our sleeves that nobody else has. I keep it in eco mode at almost all costs and then glide in neutral on any downslope I find. That gets me 41-43mpg, 45 if I'm lucky.

Re: The physics of pulse and glide
 

Hi All:

___I have been racking my brain for quite some time on this and I have no idea what I am doing anymore … I was comparing the non-hybrid Accord in a high speed P&G to the Prius II in a low speed P&G and the numbers just do not add up when taking the Prius II up to the higher speed P&G of the Accord?

___The Accord is a 3,300 # mid-sized sedan can achieve > 70 mpg in a high speed P&G with an average speed of ~ 55 mph (45 on the low and 65 to 70 mph on the high)? Besides terrain balancing, D-FAS and FAS to achieve the P&G, I am also amongst traffic side drafts to aid that much more … The road, tires(s), bearing(s), ICE rotational parts, and aero-drag effects with the pulses up to 65 - 70 mph have to be horrendous however … The Accord’s instantaneous hangs in the 30 mpg range during the high speed pulse and I estimate ICE-Off vs. ICE-On at ~ 2:1. It just shouldn’t receive that high of FE at those speeds compared to the much cleaner Prius II.

___In the Prius II “Marathon Attempt”, the instantaneous during a “hard pulse” would hang in the 17 - 50 mpg range with a max ICE-Off Time vs. ICE-On of a bit > 3 to 5:1 for 110 + mpg. The speed range was much lower with an 30 mph average w/ the stops and slows for lights.

___A quick study in order to calculate Wh used to sustain 110 mpg from a Prius II in a P&G.

Prius II’s thermal efficiency at 2,500 RPM for example is ~ 35%.

1 gallon of gasoline contains ~ 114,500 Btu’s.

Conversion: 3,413 BTU’s/kWh

1 gallon of gasoline = ~ 33.5 kWh

@ 35% efficiency we have 11.7 kWh via 1 gallon of gasoline.

11,700 Wh/110 mpg = 106 Wh/mile traveled.

___When I plug in the speeds for 55 mph in the Prius II using MPH vs. Wh/mile, the Prius II’s appears to fall far short of what the Accord can do at these much higher P&G speeds?

55 mph = 213 Wh/mile

@ 35% efficiency we have 11.7 kWh per 1 gallon of gasoline.

(11,700Wh/gallon)/(213 Wh/mile) = 54.92 miles/gallon

___How can an Accord achieve higher FE in a high speed P&G vs. the Prius II at a steady state …

___Ahhh, never mind, I see A/C was on in the Prius II calc’s …

___Anyway, maybe someone can use the following to model what the hell is going on inside of a P&G? It has something to do with climbing hills with the inefficient ICE and gliding for longer periods down them with ICE-Off but I do not know what the answer is? My Series or parallel hybrid scenario’s I have been pushing as of late may be all messed up with the above as well???

___RJ, at ~ 6 bars SoC, the HCH-I will stop assisting and will only force charge on the pulse which is exactly what it should do for sustainability.

___I am beginning to ramble like an idiot given the time I was trying to figure out the key to P&G over the past 2 or 3 hours. I think I need a break ;)

___Good Luck

___Wayne R. Gerdes

Re: The physics of pulse and glide
 

Hi Wayne,

Using Wayne Brown's (WB) simulator, the Prius II is expected to acheive a maximum MPG of about 80 MPG in the 30 - 35 mph range. As you know, the Prius does better than that. I have always thought that the discrepancy lay in the fact the WB obtained his data at steady speeds, in which two additional energy expenditures occur as compared to P&G: 1, More of the ICE->wheels mechanics are creating friction a larger fraction of the time; and 2, the Prius II ICE in the power output range required for steady 35 mph driving of around 4 kW is inefficient.

This last point is a bone of major contention, actually; and as AFAIK, has not been resoved to everybody's content amony the Prius intelligentsia: how good are the Prius brains at lower power output demands. Clearly, the algorithm allows the ICE to produce more power than is demanded by the driver, and shunt the excess to the battery for later consumption, but the efficiency is I think uncertain. And of course the shunting on energy to and from the battery has it's cost.

Bottom line: to the extent that steady rate driving is below the sweet spot of the Prius ICE, P&G will show benefit.

--
Two nitpicks with your analysis to consider:
I have seen estimates of max Prius ICE efficiency of 38%, although there is interplay between rpm and torque, so pinning down exactly where it is has eluded me.

I have to believe you are constitutionaly incapable of NOT drafting :P, so your accord MPG data may require a fudge factor.

Cheers -- Eric

Re: The physics of pulse and glide
 

Hi EricGo:

___The only thing I have accomplished with the above post is give myself a headache ;) A Glide should be just that, a powerless coast down but it is not in the Prius II. I included full 213 Wh/mile even in the glide although you won’t use 213 Wh/mile unless you maintain a steady speed and the ICE will be on at that speed of course. There is a lot more current flowing in the Glide below 41 mph that I cannot account for and I have the feeling it is MGSet synch current? In the Accord, a FAS is close to a powerless free coast as possible although again, it is in the coast down only … Add in a D-FAS after every third of fourth pulse and she does allow some incredibly long Glides at way over the limit speeds.

___In the Insight it was a powerless glide in a FAS as well but I never received anything but a traffic side draft which gave her a few more mpg’s. I held onto lean-burn so hard I would not let it go. Lean-burn was that good but was only maximized at much slower speeds. Boy do I wish I had my Insight for a few weeks to see what she would be worth knowing what I do today ;)

___I have to think about this some more because my serial or parallel hybrid calc’s are falling apart with a P&G’ed ICE behind a steady speed EV. I just do not know what the answer is right now although I do know the Prius II’s 1.5 L ICE is way oversized for the envelope I would drive her in if I owned one :(

___Good Luck

___Wayne R. Gerdes

Re: The physics of pulse and glide
 

Wayne, if the glide in the Prius is wasting power, how do you explain your fantastic marathon results ? If I remember correctly, your instrumentation told you what fraction of the drive was in glide. If you accelerated at a steady MPG, some quick calcs should lay this question to rest.

Re: The physics of pulse and glide
 

Hi EricGo:

___The FE was outrageous but something was holding back the Glides vs. a pure coast in other automobiles. There were slopes on the course where the Accord would actually accelerate in Neutral (ICE-Off) and the Prius was barely holding a steady speed. In some cases, her speed was actually falling! There was a nice ¾ + mile down slope heading towards the hotel we were staying at right on the course and I’ll be ****ed if I could never just coast her in with a full blown Glide. A pulse was always needed somewhere along that lengthy slight decline … In the Accord, I was on the brakes to make the turn into the hotel on that same lengthy down slope. Dan’s Prius II was setup perfectly so there was nothing in the way of tire/wheel/aero or any other kind of drag other then something in the HSD holding her back ever so slightly … There was also an unexplainable few .1 of a volt drop in pack voltage after a lengthy glide that could not be accounted for by the displays alone. 200W over ~ 2 minutes shouldn’t drag the Prius II’s pack down .1 V but it was pulled down a bit more then that in the Glide phase IIRC? I would not have a clue as to what it was other then possibly the MGSet’s were using quite a bit of current to remain in synch as a WAG???

___Good Luck

___Wayne R. Gerdes

Re: The physics of pulse and glide
 

Can you solve Barlow's Quandary?
Go to https://www.greenhybrid.com/discuss/...2033#post32033

Re: The physics of pulse and glide
 

Hi RJBarlow:

___Done …

___Good Luck

___Wayne R. Gerdes