P&G or steady state driving?

Actually I've got some preliminary calibration data in the mph vs MPG chart:

I'm still calibrating my ZVW30 display so it is subject to change. But the preliminary data looks good.

Bob Wilson

 

Table 4. Summary of Results of 2004 Toyota Prius (added % improvement rjw)

	Column 1	Column 2	Column 3	Column 4	Column 5
0	Protocol	PnG MPG	Cruising MPG	%
1	. . . Lee	Nelson	Loshse-Busch . . .
2	30-40 mph	10 seconds of acceleration (NHW20)	151.5	81.0 @35	87%
3	30-40 mph	20 seconds of acceleration (NHW20)	99.9	80.9 @35	24%
4	. . . krousdb with a NHW20 . . .
5	30-40 mph	'n' seconds of acceleration (NHW20)	104	93.6 @35	11%
6	. . . bwilson4web with a NHW11 . . .
7	25-43 mph	15 seconds of acceleration** (NHW11)	87.8	79.0 @33	11%
8	25-43 mph	15 seconds of acceleration** (ZVW30)*	91.3	73.0 @35	25%

pp 6, SAE 2009-01-1322, "Vehicle Inertia Impact on Fuel Consumption of Conventional and Hybrid Electric Vehicles Using Acceleration and Coast Driving Strategy," Lee, Nelson and Loshse-Busch.

* Calibration corrected values.
** Using cruise control resume function.

NOTE: I found that bringing the traction battery SOC down before the runs leads to more consistent results. I just flip it into EV mode and circle a parking lot or nearby back road. Then I can pull on the test segment and get consistent results.

 

Wth? I give up... My gauge is currently below 40MPG, and I've NEVER seen above 50MPG...

Most of my driving is city. I should be getting 48MPG... very disappointed.

 

I think the PnG results are fairly understood.

Brick and I have some interesting findings on steady state. I have just about enough information to post something on it this week. Unfortunately it requires a few gauges that have only been decoded on the Gen II, but once the decodes come in I'm certain it will work on the Gen III. I do have some approximations for Gen III drivers though.

I'll link when my writeup is ready (gotta do resume first ).

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I know that bw sets up his tests with reproducibility in mind, but frankly I consider his methods invalidate his results. Cruise control is simply not a reasonable driver substitute in my opinion to mimic P&G.

 

Last night I woke up thinking about the Lee, Nelson, Lohse-Busch paper, SAE 2009-01-1322, and realized there was information hiding in plain sight in three of the figures:

	Column 1	Column 2	Column 3
0	Fig.	text
1	9	Fuel Rate (g/s) of 2004 Toyota Prius for PnG Drive Cycle: 20-30 mph	11 Seconds of Acceleration
2	10	Fuel Rate (g/s) of 2004 Toyota Prius for PnG Drive Cycle: 30-40 mph	10 Seconds of Acceleration
3	11	Fuel Rate (g/s) of 2004 Toyota Prius for PnG Drive Cycle: 30-40 mph	20 Seconds of Acceleration

.
Embedded in those three figures is the amount of fuel consumed to change the vehicle kinetic energy 10 mph. So I decided to go back and look more closely at the charts.

When looking at charts in a paper, I expand the view and take screen snapshots. I then put them into PowerPoint and use the embedded tools to stretch them until they have the same scales and horizontal and vertical lines to read the values (or close enough.)

Comparison of 10 and 20 Second Acceleration


The ballistics glide should be identical from 40 mph down to 30 mph. So I was surprised that the 'glide' part varied by 7 seconds out of ~51 seconds duration. This would be a 7/51 difference, nearly a 14% difference. This is why my testing involves multiple cycles so individual errors like these would average out. Two conflicting data points are not enough to tell which might be in error but shows an inconsistency that is significant.

As expected, the fuel rate times the power duration tells us the quantity of fuel burned to go from 30 mph to 40 mph. Notice that the engine didn't shutdown instantly but led to a lower rate for about 2.5 seconds (at 3:00 AM). This morning it looks to be closer to 5 seconds. Regardless, here is another fuel burn anomaly in the data. Potentially 1-2 grams out of 16, a 6.25-12.5% error in the fuel burn during the 20 second acceleration. It is easy to factor this out and for my purposes, I'm using the primary fuel burn of 16 grams for the 20 second acceleration. I'll come back to the chart in a minute.

BTW, the anomalies found in the figures from the Lee, Nelson and Lohse-Busch paper may or may not account for the exceptionally high mileage reported on the 10 second pulse and 40-30 mph glide. If the glide were actually of the 20 second pulse glide duration, the reported "151.5 MPG" (Table 4.) might be a little less.

Comparison of 20-30 PnG to 30-40 PnG


One good thing is you can see the curve in the coast down velocity from 40-30 that is nearly absent or difficult to see in the 30-20 coast down. This makes sense as aerodynamic drag is proportional to the square of the velocity. But what surprised me at 3:00 AM was the fuel burn to kinetic energy change.

As before, I calculated the fuel burn for 10 and 11 seconds and the 11.2 to 11.6 g were well within acceptable limits. But something bothered me about the change in kinetic energy. We know the familiar formula for kinetic energy (KE):

0.5 * m * (v*v)
​

If we calculate the change in kinetic energy as a change in velocity, the 10 mph change from 20-30 and 30-40 would appear to be the same. However, if we use earth as the reference, the power function of the velocity change is given by:

0.5 * m * (20*20)
0.5 * m * (30*30)
0.5 * m * (40*40)
​

You can see the mass and 0.5 constant can be taken out and the relative kinetic energy change is the difference of the squares:

_400
_900
1600
​

The reason these are the accurate indications of kinetic energy has to do with the speed of the vehicle when the acceleration is being applied. They would not appear if the "0 mph" velocity were taken from the position of the moving car as each pulse would be a 10 mph difference. They do appear when the absolute energy is calculated relative to the earth. The change in KE is the same force but over a longer distance because the velocity of the vehicle adds distance. So when we look at the change in kinetic energy per unit of fuel burned using an earth reference, we find acceleration is more efficient in the 30-40 mph range than in the 20-30 mph range. (There will be a brief paused while some heads explode.)

Engine Fuel Consumption

Returning to the first chart, I used the fuel burned during the 10 second pulse divided into the glide duration to come up with the ballistics glide, equivalent fuel burn rate. What this means is the amount of fuel that has to be burned to be able to glide from 40 mph to 30 mph.

I then used this rate of fuel burn to calculate the extra fuel needed to run the engine 10 seconds and found there was a 3.93 g unaccounted for. This is the fuel burned just to turn over the engine the extra 10 seconds minus what about what would have been needed to travel for that extra 10 seconds.

When the engine runs there is internal friction from the pistons, crankshaft, valves, and water pump that have to be turned. This internal overhead requires energy that has to come from somewhere and that would be the fuel burned. This is the first time I've had data that allows us to map this internal engine overhead.

Summary

In engineering there are different ways to look at a problem and energy flows happen to be one I'm fond of. Serendipity, the data derived from the Lee, Nelson and Lohse-Busch paper has shown that an energy based model of pulse and glide may account for more of the energy flows and losses and lead to a more accurate model.

Bob Wilson

ps. Facts and data is my approach to understanding how the natural world works.

 

GIGO. Explain the discrepancy between your CC P&G routine and the 110 mpg obtained by the Prius marathoners, or wake up and admit that your method is flawed.

How many more times are you going to post the same graphs to prove what is obvious: P&G by CC is a lousy way to P&G ?

 

I have found the cruise control (where possible) to be my best friend for great gas mileage

 

I think it does pretty well too -- for steady state speed driving over 41 mph on level routes.

 

My PnG experiments use:

• NHW11 - that is a 2003 model Prius (non-OEM tires, maximum sidewall, ~72F)
• ZVW30 - that is a 2010 model Prius (new tires, maximum sidewall, ~88F)
• NHW20 - was used by the Prius marathoners (different temperature, road surface and tire preparation)

Then addressing your second question:

Since you asked, as many times as it takes to get the last line of this table understood:

Table 4. Summary of Results of 2004 Toyota Prius (added % improvement rjw)

	Column 1	Column 2	Column 3	Column 4	Column 5
0	Protocol	PnG MPG	Cruising MPG	%
1	. . . Lee	Nelson	Loshse-Busch . . .
2	30-40 mph	10 seconds of acceleration (NHW20)	151.5	81.0 @35	87%
3	30-40 mph	20 seconds of acceleration (NHW20)	99.9	80.9 @35	24%
4	. . . krousdb with a NHW20 . . .
5	30-40 mph	'n' seconds of acceleration (NHW20)	104	93.6 @35	11%
6	. . . bwilson4web with a NHW11 . . .
7	25-43 mph	15 seconds of acceleration** (NHW11)	87.8	79.0 @33	11%
8	25-43 mph	15 seconds of acceleration** (ZVW30)*	91.3	73.0 @35	25%

pp 6, SAE 2009-01-1322, "Vehicle Inertia Impact on Fuel Consumption of Conventional and Hybrid Electric Vehicles Using Acceleration and Coast Driving Strategy," Lee, Nelson and Loshse-Busch.

* Calibration corrected values.
** Using cruise control, resume function.

You see the interesting thing is CC provides reproducible results and my 25% improvement with our ZVW30 is in close agreement with the Lee, Nelson and Loshse-Busch 24% using the NHW20. It is nice when folks can see their results hold true with independent experimenters using a different methodology. What this means anyone can repeat the test and possibly come up with different or nearly identical data. It is how science and engineering works. Fortunately, the acceleration rate using CC matches the rates reported by Lee, Nelson and Loshse-Bush in their paper, which is what reproducible methods means.

Now I chose to follow my earlier NHW11 protocol because I'm interested in the relative performance of our NHW11, my daily commuting car, and my wife's ZVW30. There was more than a doubling of PnG performance. My protocol is close to the Lee, Nelson and Loshse-Bush second results, the 20 second acceleration test, which seems to have mileage numbers that are easily reproduced.

Absent any other well defined protocol, CC pulse and glide agrees with the only Pulse and Glide paper involving the Prius, SAE 2009-01-1322. It really is a paper well worth the $15 SAE charges for a copy. The data is clear and unambigious, warts and all, and that is the hallmark of quality in a paper. A paper doesn't have to be perfect if it contains enough data that any anomalies can be understood.

The irony is when you look at the PnG performance improvement by Lee, Nelson and Loshe-Bush, 24%, and my ZVW30 improvement, 25%, my data supports a claim that the 2010 Prius does not provide a substantially improved platform for pulse and glide advocates. Weird but there it is.

Yet it is equally true from fleet mileage studies of the EPA user records, posting in PriusChat and even MyHybridCar show that the 2010 Prius is providing ~5 MPG overall fleet performance over the NHW20. That is ~40,000 ZVW30s are saving ~5 MPG each, nearly a 10% fleet performance improvement. That is simply astounding considering the ZVW30 is the 3d version of the Prius architecture, generation 0th was not sold in the USA.

Bob Wilson

 

For someone who loves data above reasoning, it's funny that you ignore the multiple reports of people that hyper inflating tyres from max sidewall to 60ish psi is good for another 1 - 2 mpg.

Anyway, at least update your table to make it clear that your P&G routine using CC is unlike what any real world driver would employ. Hopefully that is enough so that the discerning reader realizes the conclusions should be taken with a grain of salt.

 

Actually there is nothing in this thread to ignore. But over in the 2010 fuel economy area 'glider' recently completed an excellent write-up on tire pressure. Did you want to discuss tire pressure effects on rolling drag?

I have these charts from some papers I'd stumbled across:




But since you seem interested in tire pressure, my NHW11 is running Sumitomo tires with a maximum sidewall pressure of 52 psi. Since the current ones have about 20,000 miles on them, I don't want to void the warranty until they get closer to their rated 60,000 miles. The earlier ones were just approaching 50,000 miles when an unrepairable, side puncture took out one tire.

Discussing tires, I went from Sumitomo 175/65R14s to 175/70R14s last summer. On my trip to Hybridfest, I ran the smaller diameter tires on the way up. Then Sunday morning I skipped the technical discussions to swap the larger diameter tires for the return trip. I wanted to find out if the slower turning, larger diameter tires might improve mileage. So far, after one year:

• improved steering stability - the larger diameter tires seem to track better than the smaller diameter tires. On the way up, I had to watch what was going on all the time as steering stability in the NHW11 is neutral. But the larger diameter tires tracked much better. It was a subtle effect but pleasant surprise on the 750 mile trip back home.
• no change in MPG - none of my data shows a change in MPG. However, I have to adjust for the larger diameter when I put in my mileage records.
• 3% offset in indicated speed - this allows me to stay in the 'hybrid range' especially on 40 mph streets. My indicated 38-39 is really 39-40 mph. I'm better able to keep up with traffic yet still slip into EV mode when conditions merit.

Overall, the larger diameter tires appear to have no mileage impact, a slight improvement in steering stability and the ability to travel faster while retaining 'hybrid mode.' Hopefully, this answers your questions ... or do you have some data to share?

I stated the acceleration time just like Lee, Nelsen and Loshse-Bush, which is the only requirement in their paper. In fact their graphs (see earlier posting) shows a linear increase in speed in the 30-40 mph pulse which matches the linear increase speed in my charts:


Regardless, it does no harm to document the mechanism, the use of CC to resume, as well as the acceleration profile.

Are you volunteering another acceleration profile? I would be interested in seeing another profile versus the equivalent steady-state speed.

Interestingly enough, my review of the Lee, Nelson and Loshse-Bush paper has given me an idea of a new acceleration profile study. It might be fun to run a series of acceleration profiles to see what is the most efficient way to change from a slower to higher speed. I've got my BSFC chart handy:


First I want to work out the expected results and then go to the field and measure the effect. This would be the true test of model.

Certainly the posting styles and content vary. Folks are free to choose whatever insights one wants and everyone is happy.

Bob Wilson

 

Over in Cleanmpg I recently reported my last tank results from my NHW11 after a month of P&G - 985 miles on a tank of E10. The monitor showed 80.3 mpg (at 1003 miles, when I filled up, it was at 80.5) and actual mileage was 77.05. This included about 60 cold starts. 60*.03g/cold start=1.8 gallons just to warm up the car to 70 degrees so I can get into stealth. My data is not as detailed as what you have presented, Bob, but let me insert my best wisdom.

For a long time, I tried to accelerate quite rapidly, at between 2000 and 2100 rpm, hoping that my minimizing ICE time and maximizing glide time, I would gain efficiency. What I discovered is that there was a constant drain on the SOC to the point that after every 20 minutes or so, with the SOC at 55.5% it would go into a recharge mode, which would hurt mileage substantially during that 5 minute segment. At that rate of acceleration, the charge would fluctuate between using and draining the battery.

I discovered that by accelerating at close to 1650 rpm, I was able to keep the charge in positive territory, thus maintaining the battery at 58.0% almost indefinitely provided there was little wind. With the wind behind me, because of a lack of load on the ICE, and the shorter duration of acceleration, the SOC would eventually have to be restored. With the slower acceration rate of 1650, it was not too difficult for me to have four or 5 bars in a row showing between 95-100 mpg with my well-worn Tires Plus Touring (= Bridgestone Turanza) 175/65/14. When I had to replace two of my tires with some old Kumhos (175/70/14) I decided to try to use up (put on the back) it became much more difficult to get 90-100 mpg displays even with tire pressures at 51. But overall, I was very satisfied with the tank even though 15 more miles would have been nice.

My glides were between 34-35 - (the point at which the ICE would go into stealth mode) and 18-20 - the point at which riding a bicycle would probably be more advantageous.

Although I have no evidence to prove it, my gut tells me I do not believe I could have achieved these numbers with steady rate driving, even if at 25 mph. Common sense tells me that with the ICE cycling on and off at that speed, efficiencies would be lost.

Thanks to the many contributers for helping advance the state of knowledge of the P&G world. The data you have posted is simply amazing. And what you have derived from it is even more amazing. With answers now in hand, and ready to be proven emperically, this leads us closer and closer to resolving the age-old ontological question, "What does this mean?"

Dan

 

Thank you Dan,

Between you, VABeachPrius, and Tidewater, we're getting the type of facts and data that allows folks to understand what we're chatting about. The more we see of this kind of quality discussion, the faster we may all 'gain a clue.'

Your note also dove tails with some of the data from the Lee, Nelson and Loshse-Bush, SAE 2009-01-1322:

It is quite fine and really helps.

The SAE paper also showed a decrease in State of Charge, ~2%. Then when I was doing the high speed, PnG, with my wife's 2010, I was surprised to find the traction battery SOC had significantly fallen over the ~14 miles of each run. What this says is the "heartbeat" overhead, the term Ken@Japan coined, has to be incorporated into any realistic model _IF_ we are looking at single PnG cycles. But as you've noticed, the car automatically compensates for this by putting on a heavier charge during the "Pulses."

This makes sense and is why the SAE paper data for 20 second acceleration made more sense as well as seems more reproducible. The single 10 second acceleration test for the 30-40 cycle really looks like they may have been getting a traction battery boost in MPG. Not to beat a dead horse, this is why field testing with multiple cycles is so usefull ... to even out variables in single tests and identify trend information from secondary effects.

Excellent! This means you likely had an average speed of ~25-26 mph. I have some data in that speed range:

These NHW11 data and the "gray line" curve are indicated values.

My low speed PnG data suggests that at lower speeds, the PnG can consume more energy than steady speed due precisely the engine stop/start effect:



At these slow speeds, I have to account for all of the vehicle energy flows to measure the relative energy cost per meter:

	Column 1	Column 2	Column 3
0	Joules/m	avg mph	protocol
1	299	19.5	15-25Png
2	255	18.2	constant velocity

At these slow speeds, the aerodynamic drag effects should be much less than the 44 J/m seen in the data.

I appreciate the data point of indicated MPG error in the NHW11. Since we only have one MPG indicator, I've always used tank fill-ups for vehicle mileage and the indicated MPG for "A" "B" tests. That calibration point is useful data.

I suspect that using a PnG with a maximum of 43 mph and then coasting to an as yet undefined minimum will provide the maximum PnG mileage. As for the pulse acceleration rate, it has to needs to be high enough to keep the battery charging at a something less than a maximum rate. High charging rates reduce the battery charge-discharge energy loss but only on the charge side. But the engine "ON" time needs to be minimized to avoid engine operation losses.

If folks haven't guessed, there are a series of non-linear equations that need to be solved to come up with an optimum PnG cycle. This is really where the SAE paper was headed and what I'm interested in too ... but only to complete my understanding of the NHW11 systems.

If you get a chance someday, could you try warming up your Prius, 30 minutes of ordinary driving, and then driving to a closed loop where you can maintain 15 mph. Do at least one mile at 15 mph to normalize the battery (let EV bring it down to a steady state) and then drive for ~10 mles at 15 mph. This is what I got:

The models suggest the maximum range speed is 18 mph so I was trying to get a 'fall off' data point. I was surprised that after 10 miles it came in with an indicated 100 MPG and this was after a 1 mile loop to drain down the traction battery to a steady state value.

Bob Wilson

 

Wow! Terrific information. I would like to try that 15 mph steady state run to see what I get. A week from now, I will be in a new situation - with a 2 KWH (soon to be 4 KWH) Enginer pack. In other words, while I used to operate seeking to minimize traction battery use, I now want to maximize its benefits. At that point, the question becomes, "At what speed can I maximize the benefits of the electrical energy available, taking into consideration the 'heartbeat' losses, mostly the .62-.67 Amp constant discharge to keep the vehicle in ready state (the lower value from turning the display off), and secondly the ICE operation to maintain operating temperature. My guess is that in EV mode, P&G would not be beneficial for mileage - only for maximizing the distance the battery pack would be available for use.

There is one thing that is a bit confusing. About 5-10 minutes into my drive, I come to a point where it is very difficult to engage glide mode. No amount of feathering of the pedal seems to work. Engine temperature is not a factor because I have seen this anywhere between 75-85 C. SOC is not a factor because it is usually between 58 and 61.5 after a warmup. Topography sometimes appears to have a bearing -- this anomaly occurs often after a steady rate hill climb at slow speeds. Sometimes I simply drive in steady state for 15 seconds or so, then try again. Sometimes I speed up past 42, then decelerate; sometimes putting it in neutral and then re-engaging into drive will work. This happens only after a cold engine start - once I get past that block, I can P&G with no trouble at all. My theory is that it has to do with the ECU moving into a different control stage or perhaps it needs to analyze my current driving style. If I recall correctly, your advice to one individual was to come to a complete stop, then press the gas with the brake on. That was for the NWH20. Would this be true for NWH11 as well? I don't know if you have experienced this or not, or if this is common to NWH20 drivers.

Thanks again for your helpful information!
Dan

 

Borrowing from Hobbit's research, I think a constant rate of discharge in EV would be the best *for PHEV*. large current infux or outgo will be less efficient than a constant draw. At Highway speeds a WS-P&G will likely yield the best results. Less dramatic results would be to leverage SHM and heretical mode to cruise on the highway. Be warned though, almost any movement on the throttle (like CC) will kick you out of this "magic" part of this state and dump you back into a heretical cruise state.

It's your water pump. It comes on for 60 seconds once the engine warms up enough. You can still force EV with the EV button if your equipped.

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That is my thinking. PnG is based upon storing kinetic energy in the vehicle by operating the ICE at a peak efficiency region and then the glide draws on that stored energy. But if you are in EV mode, PnG's assumption about having an engine is gone. Just find a maximum range speed and hold it.

I can't help you there as I don't do PnG in my normal driving with one exception. After the initial 40-45 sec. catalytic converter 'light off,' I then maximize use of "N" until the engine reaches 70C. Let me explain what I mean:

• ~45 sec catalytic light-off - when the cold car or one that has been sitting for 2-3 hours, is first turned on, the O{2} sensors are still cold. During this time, light application of the accelerator does nothing to spin the engine and the car is running in EV mode. For example, I park near the exit to my work parking lot and watching the traffic from the parking place, don't start the car and pull out until I know I can do it within the 45 second window. On the street I accelerate to as much as 40 mph in EV mode, the engine is turning over but at an 'idle.' If I hit the light right, I'll have 40+ MPG on the display as I pass through the intersection.
• maximize use of "N" until 70C reached - from here on out, the engine will try to warm-up but the mass flow indicator shows it is really burning it up. But I found that if I'm in "N", either rolling or at a complete stop, the mass flow drops down from ~3.5 g/sec to ~2.5 g/sec. This is a significant fuel savings. You can see this if you are stopped at light while the car is still warming up. Watch the mileage click down while in "D" and then shift into "N" and you'll see in about 5 seconds that the rate decreases. It is "N" that I'm using to get the lowest fuel burn rate until the car can go into proper hybrid mode.

This has to do with four stages of warm-up. What I've found is that if you come to a stop and the car is not in S4, it can 'idle stop' as you come to a stop at the intersection. The last transition into S4 is to be stopped with the engine running and let the control computer stop the engine. So you just hold the brake, pulse the accelerator and the engine will spin. Depending up your state, it may take up to 20 seconds before it finally stops in S4 mode. However, I'll just shift into "N" while the engine is running and then after 20 seconds, shift into "D" and see if it stops.

This may may more sense if you convert it into a series of bullets ... I kinda got used to it.

It was something I'd picked up from some of the NHW20 drivers. I know it works on my 2003, NHW11.

No problem. In fact it is great to discuss things with folks who have a clue about what I'm posting. No, I'm not some geeked out, egg head, cyborg (although I do admire them) but just an ordinary practicing engineer sharing what little I've found over the years. There is so much more unknown and you've given me some ideas.

Bob Wilson

 

You're talking to a preacher here. I'd rather try not be heretical.

Could you explain what is meant by the terms I highlighted? I'm still learning.
Thanks!

 

Funny you should ask. Here's Graham's volumous research on the subject:
Power Split Device (read first to understand the next)
Introduction to Heretical Mode (very light introduction to it).
All Prius Energy Flows Explained (a much deeper dive).

So, in the Gen II (and probably I & III) there is special "balance" condition you can hit in heretical mode. Problem is you have to keep "input throttle" (ie gas pedal) UNMOVED for 7 seconds in order for it to trigger. Cruise Control unfortunately bounces throttle ALL OVER the palce and never holds it steady for 7 seconds to hit the state. Once "balanced" steady state MPG boosts by 10-20%.

I'm still working on some "pictures" to try to show it and may post a thread on it, but it's only "monitorable" in the Gen II. I don't know of anyone who has been able to measure "Gas Pedal Pressure" in the Gen I or Gen III yet, and this is what you hold to trigger "balance".

Reading Graham's Data it's real clear WHY this exists, and WHAT exactly is going on when your in it.

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