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Why Prius can get 50 mpg even at constant highway speed?

Discussion in 'Gen 3 Prius Technical Discussion' started by AllenZ, Jun 23, 2012.

  1. AllenZ

    AllenZ Active Member

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    Assuming the road perfectly flat, and you can keep a constant speed, with all engine powers goes to wheel, no battery charge/discharge. Now compare it to another Prius, modified to have same engine and a mechanical CVT. Assuming same weight too. Shouldn't those two cars get same mpg?
     
  2. Adam H

    Adam H Junior Member

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    At constant speed the only thing the Prius has going for it is the aerodynamic shape, small engine, and optimal rpm with the cvt.
     
  3. JimboPalmer

    JimboPalmer Tsar of all the Rushers

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    Assuming you pushed the Mechanical CVT car to highway speed, yes. The Atkinson cycle engine is way more efficient than a normal Otto cycle engine, but produces much less power. Perhaps 3/4 of the peak power of the same engine as an Otto cycle.
    Toyota ZR engine - Wikipedia, the free encyclopedia
    98 HP versus 134 HP

    You don't see Atkinson cycle engines in cars without some other power plant.
     
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  4. bwilson4web

    bwilson4web BMW i3 and Model 3

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    I'm not sure but this reads as if you are asking about transmission/transaxle efficiency?

    I am aware of these transmission architectures: manual, hydro-mechanical automatic, belt-CVT, and electro-CVT. As a general rule of thumb, I use the following efficiency numbers:
    • ~98% - the energy loss of one pair of gears
    • ~95% - estimated belt/cone mechanical CVT
    • ~90% - torque converter loss
    • ~85% - the energy loss of a generator-to-motor (92%*92%)
    Engine Shaft to Wheel Efficiency

    To determine the end-to-end gear efficiency, multiply the efficiency of each stage:
    • 3 reduction gears :: 98%*98%*98% -> 94%
    • 4 reduction gears :: 98%*98%*98%*98% -> 92%
    One of the Prius c efficiency improvements eliminated one gear reduction stage.

    The Prius transmission moves 28% of the power through the generator-to-motor path and 72% through the mechanical, power split device (PSD) planetary gear assembly. These are combined after the power split device when either MG2 or MG1 adds them together:
    • electrical path :: 28%*85% -> 24%
    • mechanical path :: 72%*98% -> 71%
    • total efficiency this stage :: 24%+71% -> 95%
    Again, this is back of the envelope as efficiency varies based upon factors we are leaving out for now:
    • manual transmission, 4 gear reduction :: 92%
    • ordinary Prius transmission, 4 gear reduction :: 95%*92% -> 87%
    • ordinary torque converter transmission, 4 gear :: 90%*92% -> 83%
    WARNING

    Total vehicle efficiency includes the engine and tire efficiency. The Prius Atkinson engine has exceptional efficiency if kept in the peak efficiency range which the electrical CVT transmission provides across the power range. In contrast, Otto engines have poor, partial power efficiency yet must have enough excess power to handle acceleration to the constant speed. Once at the constant speed, Otto engine efficiency falls off.

    The Prius typically has low-rolling resistance tires, a 1-2% efficiency gain. Non-Prius cars tend to have less efficient, performance oriented tires.

    The brilliance of Toyota engineering is they will sacrifice efficiency in one part to improve total vehicle efficiency. Sad to say this is not a common practice in many other vehicle design shops.

    Bob Wilson
     
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  5. walter Lee

    walter Lee Hypermiling Padawan

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    Supposing - there was a Fuel Efficiency Marathlon/Rally Race - among different Prii and you wanted to level the playing field to prevent any one driver from having a mechanical or chemical advantage...That is you wanted to test driver skills - the parameters that you would want to control are as follows to get all the vehicles to start off the same...


    IF
    (1) the two Prii are exactly the same AND
    (2) driven on the same road at exactly the same time(same weather/traffic conditions) AND
    (3) burning the same type of gas(e.g. 10% ethanol 87 oct gas) AND
    (4) started off with same battery state of charge AND
    (5) both Prii have the same tire make/model (if tires are not considered part of the car) AND
    (6) both Prii have the same tire pressure AND
    (7) both are warmed up the same way AND
    (8) driven exactly the same way (*)
    THEN
    the mpg should be the same.

    (*) When vehicles are not driven the same way - mileage can increase or decrease. When driven inefficiently it is very difficult to get the Prius to reach its EPA rating. When driven efficiently - a Prius can beat the EPA ratings on a consistent basis...

    hope this helps
    Walter Lee
    aka "HyperDrive 1" on cleanmpg.com
    2010 Toyota Prius III, Blue Ribbon/Dk gray. oem floor mats
    Yokohama Avid S33D (44 psi front/42 psi rear)
    2 scangauges
    no grill blocking
    Odometer =+24750 miles, overall 60 mpg
    best tank/mpg = 10.25 gallons/ 727 miles/70.9 mpg... 50/48 psi, going at 25-35 mph most of the time...
    worst tank/mpg = 09.31 gallons/415 miles/44.6 mpg... 38/36 psi, cruise control set at 80 mph most of the time...
     
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  6. AllenZ

    AllenZ Active Member

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    Bob,

    Glad to get your response and I like your quantitative analysis.
    I am not sure I understand correctly, but from your analysis, the transmission efficiency difference between PSD and a mechanical CVT is 8% (95% vs. 83%). The rest of the difference is on Otto vs. Atkinson.

    My guess is, if you put an Otto engine and a mechanical CVT into Prius body, it should get 35 mpg at 60 mph (comparing to similar size none hybrid cars). If real Prius can get 50 mpg, with 8% transmission efficiency difference, an Atkinson + CVT Prius will get 46 mpg. So the efficiency difference between Atkinson and Otto engine will be (46-35)/46 = 25% ?
     
  7. bwilson4web

    bwilson4web BMW i3 and Model 3

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    Only 28% of the ICE power takes the 83% efficient path. The rest, 72%, takes the mechanical, 98%, efficient path. Together the efficiency through both paths is 95%.

    I might not have been clear:
    • Atkinson - high efficiency over a broad power range.
    • Otto - high efficiency in a narrow power range with significant drop off at partial power.
    The Atkinson engine does not have the high, peak power density of the Otto engine but it can 'borrow' energy from the traction battery to accelerate briskly. It is also fairly efficient over a broad power range. In contrast, the Otto has to provide acceleration power but once cruise speed is reached, the power demand falls off and its thermodynamic efficiency drops.
    The Prius c and Yaris are pretty close to that experiment. Identical 1.5L engine block and body style:
    Column 1
    0 [th]model[/th][th]City[/th][th]Hwy[/th][tr][td]Yaris Auto[/td][td]30[/td][td]35[/td][/tr][tr][td]Prius c[/td][td]53[/td][td]46[/td][/tr][tr][td]Yaris Manual[/td][td]30[/td][td]38[/td]
    Source: Fuel Economy
    • Yaris Manual vs Yaris Auto Highway - automatic transmissions are less efficient, 35 MPG, than a manual transmission, 38 MPG.
    • Yaris M/A vs Prius Highway - here the Atkinson cycle efficiency puts the Otto to shame. At cruise speed, the Otto looses thermodynamic efficiency ... 38 MPG vs 46 MPG.
    In the City, the hybrid shuts down gas and diesel pretenders.

    Bob Wilson
     
  8. walter Lee

    walter Lee Hypermiling Padawan

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    I have read that the Prius ICE is basically an Otto engine electronically re-timed to be an Atkinson engine.
    In otherwords, my readings suggest that the Prius Atkinson cycle gasoline engine is physically them same as an Otto cycle engine in all but the electronic ignition/fuel injection programming. If this is so - why isn't the Prius programmed to (automatically or by driver selection) dynamically switched back and forth between Otto cycle and Atkinson cycle?

    Walter Lee
     
  9. JimboPalmer

    JimboPalmer Tsar of all the Rushers

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    The intake valves close when the piston is about 1/3 of the way up the cylinder, this gives it a much larger expansion ratio than compression ratio. If you adjusted the intake valve to close nearer to bottom dead center, the compression ratio would be too high for regular gas.
    Atkinson cycle - Wikipedia, the free encyclopedia
    Compression ratio - Wikipedia, the free encyclopedia

    In theory, Toyota could use knock sensors to select an ideal compression ratio or some form of supercharging to increase the quantity of air trapped in the cylinder. In practice, Toyota is meeting the mileage/emissions goals it set for itself.
     
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  10. bwilson4web

    bwilson4web BMW i3 and Model 3

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    Another way to look at it:
    • 8-to-1 compression stroke - the delayed intake valve closing means only a partial charge is compressed. This reduces the octane requirement and compression stroke energy required.
    • 13.2-to-1 expansion stroke (Prius c) - the full expansion stroke, this is diesel range and well in excess of ordinary, gasoline octane.
    There are more advanced, valve timing mechanisms that would put in more charge including turbo-charging but the problem with compression ignition remains. Stuffing in more charge and the knock will destroy the engine unless a higher octane is used ... needed ONLY for peak power. But the traction battery power comes without the engine knock.

    Bob Wilson
     
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  11. walter Lee

    walter Lee Hypermiling Padawan

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    I understand that one of the reasons for an Atkinson cycle engine is to lower the emission levels so that the Prius comforms/adheres to the objectives set by the Kyoto Protocol. Is the position of the valves and pistons during the compression cycle mechanically different between the Atkinson and the Otto cycle such that the engine designs are mechanically different? If not then if the valve-cam-piston design ratios are the same could not the Prius (atleast in theory) be re programmed to allow the compression ratio/valve timing to be dynamically switched between either the Otto or Atkinson cycle without destroying the engine?
     
  12. JimboPalmer

    JimboPalmer Tsar of all the Rushers

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    There are wildly impractical ways to alter the compression ratio on the fly.
    Saab Variable Compression engine - Wikipedia, the free encyclopedia
    The Prius can change it's with valve timing, but the 13.2 expansion ratio is too high to be a compression ratio on 87 Octane gas. Some form of supercharging would be more practical to stuff more air in the engine when needed.
    Miller cycle - Wikipedia, the free encyclopedia

    And yes, the Otto cycle version of the Prius engine would be 'easy' to swap into your (suddenly 30 MPG) Prius to get 25% more HP.
     
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  13. bwilson4web

    bwilson4web BMW i3 and Model 3

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    Yes, the intake camshaft and the swept volume of the piston in the cylinder. It would take extensive mechanical changes: (1) variable duration and angle intake valves, and (2) variable displacement cylinders. These are not trivial changes.

    Bob Wilson
     
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  14. fuzzy1

    fuzzy1 Senior Member

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    Prius' valve adjustment mechanism does not have range to reach the Otto cycle.

    Electric solenoid valves would abolish the camshaft and its friction, and allow changing between Otto cycle and various degrees of Atkinson cycle. But I haven't heard any recent updates on progress towards a reliable and affordable implementation.
     
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  15. austingreen

    austingreen Senior Member

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    There are two things different in the prius engine than its otto version. First is the compression ratio is higher, since the idea behind an Atkinson is to reduce pumping losses, it doesn't let a full charge of air in, so it does not detonate. Since the expansion stroke is longer it captures more of the energy of combustion. The second is the valves don't have variable lift to allow the full range they would need to do both modes.

    Mazda in skyactiv does exactly what you are talking about but they use electronically controlled input valves, direct injection, and different shaped pistons to be able to run at the same expansion ratio without knocking. This is a more expensive and complicated engine, but has been done with regular gasoline and the same 13:1 expansion stroke. So yes for more money the prius could do exactly what you are suggesting. It may add part or all of it with the next generation, or may make the expansion stroke even longer.
     
  16. austingreen

    austingreen Senior Member

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    Bob I found your answer after searching from another hsd question. I have two questions. First is doesn't the psd split torque, so that we would need to know rpm of mg1 and mg2 to know the power split percentage?

    The second is where are the 4 universal gears. Are there 3 mechanically after the psd to go from it to the transaxle?

    Thanks
     
  17. bwilson4web

    bwilson4web BMW i3 and Model 3

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    Thanks to the second law, no. The torque split is the ICE torque and it comes in via a single, engine shaft. Only ICE rpm counts for the power split along with the inverse of the counter torque provided by the MG1 and MG2.

    Hobbit once called what MG1/MG2 do a 'wild dance' and he is absolutely right with MG1 being 10 times madder than MG2. MG2 is mechanically tied to the final gears and has a fixed ratio relative to vehicle velocity so it does not change 'that much.' In contrast, MG1 has significant inertial changes and this makes any calculations using MG1 rpm and torque all but nonsense. I know, I tried with the Graham miniscanner data it did not make a lick of sense. But the second law saved me from trying to calculate energy flows of MG1/MG2 that has to include the rotor moment of inertia.
    Correct!

    The NHW11 and NHW20 have one extra gear stage after the power split device. The rule of thumb I follow is each gear stage has ~2% loss and that seems to be fairly consistent. One of the improvements in the 'Prius c' transmission was removal of a reduction gear stage . . . remarkable! However, they did add MG1 and MG2 reduction gears so they could spin faster.

    The MG1/MG2 are the 28% power path so the 2% penalty is 'less bad' because it is not the combined, mechanical path. It also means MG1 and MG2 can spin faster which reduces the current needed saving wire diameter, reducing internal (I**2)*R overhead, and stator mass.

    Bob Wilson
     
  18. austingreen

    austingreen Senior Member

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    Bob to convince yourself otherwise, do a thought experiment. In heretical mode power flows into mg1, and this combines with ICE power so that the output shaft equals mg1 power plus ice power. The power split is .28 Ice Torque x mg1 rpm. To get the full split torque falls out. Power percentage is simply (.28 x rpm1)/(.72 x rpm2 + .28 x rpm1) when mg1 is acting as a generator. Where rpm2 is the rpm of the output shaft of the psd, which IIRC is 1/2 of the rpm of mg2. If on average rpm1 = rpm2, then we will send 28% of the power down the electrical path, but I have no idea what this is in real life. When we are going slow, much of the power needs to go through the electrical path, which is much more efficient than a conventional transmission/ice since mg2 is much more efficient high torque low rpm than an ice.

    OK what is the second law? Yes you should be able to calculate the power split percent just from ice rpm and vehicle speed. While mg1 is doing that wild dance the efficiency of the transmission is changing:) Even at constant speed, hills will cause higher loads and higher ice rpm which means changes mg1 and power percent constant. Do you know the average ice rpm at say at 60 mph and 70 mph? There are ofcourse extra losses.


    Yes, the hsd is about motor as well as ice efficiency. I understand part of it but am still misunderstanding a little. The psd gear ratio can be optimized for ice and one motor, so they stuck a gear reduction between mg2 and the psd output shaft in the gen III prius. Are you saying they stuck a gear between the mg1 output shaft and the psd, in the prius c? I would think you could simply change the gear teeth in the psd to make it work out.
     
  19. bwilson4web

    bwilson4web BMW i3 and Model 3

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    You are correct and I should have accounted for this mode. But a proper analysis entails a series:
    1. 28% flows from MG2->MG1
    2. 100% takes the mechanical path towards MG2
    3. repeat #1 so 28% of 28% takes a second pass through the MG2->MG1 path
    4. repeat through #3 until vanishingly small loss of the ~80% loss path
    The second law simply means we can reverse the sign of MG1 toque and that is what the ICE rpm generates. It makes calculation of the ICE power simple.

    As for average ice rpm at 60 and 70 mph, I found that difficult to record and report. So instead I use the drag formula to calculate the power required and using my BSFC chart, identify the likely rpm values. In real life, things happen too rapidly and roads aren't that level.
    The final step down gears are all after the PSD. There is a great SAE paper I have on the home computer that covers the 'prius c.' If you'll search for "bwilson4web" and "SAE" you should find my posting about the specific paper. I also discussed it in Prius Technical Stuff.

    Bob Wilson
     
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  20. austingreen

    austingreen Senior Member

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    Thanks for all the good information.

    I brought up the mode, hoping it would get you to realize that the 28% is torque not power. Let me try one more time, or find out I am wrong.

    Think of the situation where no electricity flows to/from mg1 or mg2. Ignoring losses mg1 at 0 rpm will make all the ice power flow out the output shaft. Mg2 will free wheel with speed neither generating or consuming electricity.

    Now say more torque is required at the wheels at the same speed, and this does not get supplied by the battery. The ice will increase rpm to provide more power, and mg1 will act as a generator to provide electricity to mg2 to generate that torque. In the psd, now a percentage of power is flowing to the electrical path. We can't know the percentage of power flowing without knowing two of the three rpms.