Most efficient speed for best MPG?

[bwilson4web]

<div class='quotetop'>QUOTE(ken1784 @ Mar 24 2007, 07:41 AM) [snapback]411445[/snapback]</div>

I believe the marathon was done using Pulse&Glide, a lot of speed changes, and we can't compare the data with Wayne's constant speed graph. [/b]

Actually, I think we can but my performance models are not ready for inspection. Still, let me share the logic:

• power = drag * speed
• drag = F(rolling_force,aerodynamic_force)
• ICE_power = F(rpm, torque, fuel)

We often simplify vehicle drag into a fixed rolling drag and an aerodynamic constant times the velocity squared. This sets the power required and the amount of energy needed to move the vehicle EVEN IF the velocity changes.

Changing the velocity over any given route will always require more energy than maintaining a steady state speed. The non-linear aerodynamic effects at speeds above the steady state speed increase the drag, power and energy requirement much faster than the reduction in drag, power and energy at a speeds below the steady state. Using calculus, we can calculate the power and the energy required to move any given distance and this is where I have to dust-off my college texts to 'do the math.' (NOTE: I remember having to do this calculation in one of my engineering classes, thermodynamics I think.)

The "pulse" part works for ordinary cars because traditional gas engines are terribly inefficient at partial throttle settings (See Figure 15, "Development of New-Generation Hybrid System THS II - Drastic Improvement of Power Performance and Fuel Economy", K Muta, M. Yamazaki, J. Tokieda, SAE 2004-01-0064.) By putting an ordinary ICE into a higher power mode, it will generate power at a more efficient specific fuel consumption than partial throttle but the excess of power causes the vehicle to accelerate. The "pulse" is a by-product of trying to operate a traditional ICE at high power settings but our Prius is different.

"Pulse and glide" is critical to Honda and gas-only vehicle mileage but the Prius has not only an unusually flat, specific fuel consumption but also the ability to auto-start/stop the ICE. If the Prius ICE is kept within the 1,600-2,600 rpm range (based on current data,) it will be in the most efficient power mode. But there is an energy loss associated with starting and stopping the ICE and this is an area under investigation. To properly model Prius efficiency, the ICE start and stop energy has to be part of the model.

There may be a Prius "Pulse and Glide" profile that delivers better performance than a steady state speed. If so, it is likely to come from using the battery to extend the glide and optimum acceleration in the high-efficiency speed range as a way to minimize ICE start/stop energy loss. But the battery recharge has to happen during the ICE operation time and if done badly, it won't be recharged enough to sustain the next glide. Also, the minimum speed needs to be balanced against the 'overhead' power requirement. But this performance model with real data doesn't exist in an open source, yet.

I'm sorry if this seems long and somewhat confusing. I didn't take enough time to write it shorter. But as I refine my data and models, eventually, I'll share AND THEN TEST the results.

Bob Wilson

[ken1784]

Hi Bob,

It is hard to understand your post what's the point is.

Agin, the 1400 mile marathon was based on Pule&Glide, pulse up to about 40 mph the glide down to 30 mph.
I believe the bast shift (#10) by Wayne Gerdes was slower than that, pulse up to 35 mph and glide down to 20 mph, average 24.3 mph.
The FE on pulse part was 9.84 km/L (23.1 mpg) and engine on % distance was 19%, so the rest 81% is just gliding from 35 mph to 20 mph.

I still believe we can't compare the 1400 mile marathon data to Wayne's constant speed graph.

Ken@Japan

[bwilson4web]

<div class='quotetop'>QUOTE(ken1784 @ Mar 25 2007, 02:56 AM) [snapback]411820[/snapback]</div>

Hi Bob,

It is hard to understand your post what's the point is.
. . .
I still believe we can't compare the 1400 mile marathon data to Wayne's constant speed graph.

[/b]

Hi Ken,

I'll see if I can't get the math model worked out this week but I'll have to review some of my old engineering texts (if I still have them.) If I don't have much luck, excel can model a successive series of approximations. But for now, I would suggest looking at the MPG vs MPH plot with the marathon data (you may need to refresh the browser to get the latest copy



The NHW20 Prius marathon used high pressure, well-worn tires, a more efficient transaxle, warmer than standard temperatures, a lower coefficient of drag and more efficient transaxle system. Still the Prius endurance test is within engineering measurement error of the NHW11 theoretical line. Furthermore, the slope of the Prius endurance data points suggests a curve that has a higher peak MPG value that Wayne has nailed that at 20 mph, backed up by testing.

The speed log for the Insight test shows an average of 18 mph and over the last days, closer to 15 mph. Now an Insight's IMA system would respond especially well to any pulse and glide protocol that uses ICE off, neutral" for the glide. But the Prius systems are different with a built-in, automatic cycling between ICE-on and ICE-off operation at speeds below 42 mph.

It is possible that the energy lost in starting and stopping the Prius ICE is significant at the peak MPG, constant speed. It is possible that acceleration at an ICE speed between 1,600-1,900 rpm followed by a glide that ends at a speed that permits recharge on the subsequent 'pulse' may be the most efficient protocol.



Understand that I prefer to start with a good model, followed by data and testing to answer this question and develop a reproducible protocol for Prius marathon driving. The ultimate answer is an automated Prius that drives the marathon under computer control with a mannequin or crash-dummy for the driver.

Bob Wilson

[shanelabs]

No matter what, if you're going to fast you're going to get horrible gas mileage. There's calculator at MpgForSpeed.com - Fuel Efficiency Vs. Speed that shows you the effects of your speed on your mileage.

[ewxlt66]

Can we bring this back in to the real world where people have to drive at least the speed limit....and don't have an excel spreadsheet and DNA analyzer always with them?

If I'm taking a 250 mile road trip that will be 80% high way...driving the speed limit will produce better mpg than driving 15mph higher.

THERE! Solved.

[Danny Hamilton]

Originally Posted by ewxlt66

Can we bring this back in to the real world where people have to drive at least the speed limit....and don't have an excel spreadsheet and DNA analyzer always with them?

If I'm taking a 250 mile road trip that will be 80% high way...driving the speed limit will produce better mpg than driving 15mph higher.

THERE! Solved.

True, however, keep in mind that most U.S. Interstates have a posted MINIMUM speed limit of 45 MPH. Therefore driving 45 MPH will produce better mpg than driving the posted MAXIMUM speed limit.

Then, if you get off the Interstate onto the country roads, and get yourself behind an International Harvester chugging along, you might be lucky enough to exceed 100 mpg. You can certainly improve your mpg by driving these non-Interstate roads and keeping your speed below 45 MPH. It all depends on how much of a hurry you are in to get to your destination.

[Danny Hamilton]

Originally Posted by bwilson4web

. . . .The NHW20 Prius marathon used high pressure, well-worn tires, a more efficient transaxle, warmer than standard temperatures, a lower coefficient of drag and more efficient transaxle system. . . .

Wow, a more efficient transaxle and a more efficient transaxle system?

Originally Posted by bwilson4web

. . . .
It is possible that the energy lost in starting and stopping the Prius ICE is significant at the peak MPG, constant speed. It is possible that acceleration at an ICE speed between 1,600-1,900 rpm followed by a glide that ends at a speed that permits recharge on the subsequent 'pulse' may be the most efficient protocol. . . .

All kidding aside, I just wanted to point out that while shutting down and restarting the ICE may require some amount of energy loss, the entire time the ICE is off, you eliminate the energy loss of internal friction of the various moving parts (and fluids?). Furthermore, as the ICE cools a bit while off, you reduce the rate of heat transfer out of the ICE (heat transfers faster with a higher delta, right?). It would be interesting to know just how much energy is used in starting and stopping the ICE, as well as how much energy (per unit of time) is lost during steady state to internal friction and how much extra energy is lost in heat transfer to the atmosphere. Then it'd be a pretty simple calculation to know how long a "glide" needs to be to gain advantage over steady state.

[rsforkner]

Originally Posted by Danny Hamilton

True, however, keep in mind that most U.S. Interstates have a posted MINIMUM speed limit of 45 MPH. Therefore driving 45 MPH will produce better mpg than driving the posted MAXIMUM speed limit.

Now that would scare me to death. Doing 45 (legal or not) out on a highway where 90% of the traffic is doing 70-80. I know you're not really suggesting that we do it, (At least I hope you're not) but just thinking about it... shudder.

And think about how much road rage that would instill in other drivers...

I'll stick close to the posted limit, just for safety's sake.

Bob

[Fraser]

Originally Posted by ewxlt66

Can we bring this back in to the real world where people have to drive at least the speed limit....and don't have an excel spreadsheet and DNA analyzer always with them?

If I'm taking a 250 mile road trip that will be 80% high way...driving the speed limit will produce better mpg than driving 15mph higher.

THERE! Solved.

I appreciate your real-world position. I also appreciate the amazing (to me, a math-deficient writer) amount of laboratory effort of Pri-fans to get the best out of their cars.

That said, can there be real-world test reports based on actual use, speed, P&G, on normally traveled roads -- nothing too high-falutin', just "we drove this fast at this temperature with a head wind on this terrain for this many miles and got this MPG", all without inciting road rage or keeping us from getting where we want to go expeditiously. Multiple tests should give a good idea of what we can expect day-to-day.

Perhaps moderators can set up a forum for that? I'm willing to contribute results of our first trip, some 460 miles after we pick up Black No. 2 in a couple of weeks.

[bwilson4web]

Originally Posted by Danny Hamilton

Wow, a more efficient transaxle and a more efficient transaxle system?

See if you can get a copy of "SAE 2004-01-0064", "Development of New-Generation Hybrid System THS II - Drastic Improvement of Power Performance and Fuel Economy" by Koichiro Muta, Makoto Yamazaki and Junji Tokieda.

Originally Posted by Danny Hamilton

All kidding aside, I just wanted to point out that while shutting down and restarting the ICE may require some amount of energy loss, the entire time the ICE is off, you eliminate the energy loss of internal friction of the various moving parts (and fluids?).

You realize the Prius does this automatically, right?

Originally Posted by Danny Hamilton

Furthermore, as the ICE cools a bit while off, you reduce the rate of heat transfer out of the ICE (heat transfers faster with a higher delta, right?). It would be interesting to know just how much energy is used in starting and stopping the ICE, as well as how much energy (per unit of time) is lost during steady state to internal friction and how much extra energy is lost in heat transfer to the atmosphere. Then it'd be a pretty simple calculation to know how long a "glide" needs to be to gain advantage over steady state.

This is a little confusing:

• Heat loss when the engine is off depends upon ambient air and air flow. The coolant temperature drop is very modest for short periods, measured in unit minutes. Any period less than 5 minutes is insignificant at temperatures of 70F or greater and low winds.
• ICE start/stop energy is observable but accurate measurement is difficult because it typically happens in about 0.250 second and the current scanners are too slow to measure the exact value without gathering a large number of samples.
• Energy loss during engine operation comes out of the engine efficiency, directly. No energy is generated without the engine working.
• I look forward to reading your 'simple calculation'

So I took a simpler approach and benchmarked P&G versus stead-state speeds. Use the search function and you can find the postings including the data. The conclusions:

• 18 mph - steady speed with the Prius handling the systems is more efficient than P&G with the same average speed
• 34 mph - P&G is more efficient than steady speed, 34 mph provided the P&G speed range is 25-43 mph.

Of course these are direct measurements, no modeling required. Even you could go out and replicate these tests and report the results. Remember, the key is to compare the equivalent steady-state speed for your P&G profile and read out the MPG for both. I look forward to a little reality training.

Bob Wilson