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64 % of Prius Power gets to wheels during max acceleration?

Discussion in 'Gen 3 Prius Technical Discussion' started by briank101, Jun 3, 2013.

  1. briank101

    briank101 Member

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    So I was doing some physics calculations (reverse engineering wheel hp from 0 to 60 mph times) and considering the fact that the Prius has both a eCVT and electric motor, one would expect the 133 hp (~100 kW) of power with 3,197 lbs (1450 kg) should produce 0-60 mph times of 8 secs, taking into account a 15% transmission loss, and the fact the Prius does not put max power to the road until about 45 mph.
    But by my calculations a maximum 84 hp (63 kW) 64% of max. power is getting to the wheel above 45 mph, and only about 50% of max power is getting there at 25 mph and even then I'm assuming 12 hp (9 kW) to the wheel below 4 mph and a linear ramping up of power to 70 hp (~52 kW) by 25 mph. Note: at 60 mph only 12 hp is going to overcome aero and rolling resistance.

    A CVT should produce an over 20% acceleration advantage over more traditional stepped transmissions (auto or manual. Also an electric motor producing max torque and almost max hp at lower revs with fewer geared down ratios should produce less transmission losses also.

    Here's a spreadsheet of my calculations.
    Prius Gen III Acceleration vs Power

    Also attached Chart of Power/Speed vs time

    Any ideas or explanations welcome.
     

    Attached Files:

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  2. Indy John

    Indy John Member

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    The Prius isn't really a CVT (Continuously Variable [RATIO] Transmission) - they just didn't know what else to call it. The Power Split Device has only one "speed" (ratio). The ICE torque transmitted to the ground is approx. 74% of total, if memory serves, and has an effective ratio in the neighborhood of 3.7 - 3.9:1. The remaining ICE torque is available to spin MG1. The Prius ICE can't put enough torque on the ground to accelerate at an acceptable rate from a standing stop and requires assistance from the battery and MG2 to get up to speed. MG1 can send surplus electron's to the battery or to MG2 depending on how much of a hurry you're in. Your foot's "suggestion" helps the computer decide how much extra "oomph" is required, and it seamlessly orchestrates the magic going on behind the scenes.
     
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  3. fuzzy1

    fuzzy1 Senior Member

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    Does that take into account electrical losses too, not just mechanical? A jackrabbit start will put a much larger than normal power fraction through the electrical path, which has many more conversion losses than the mechanical path. Even if each electrical stage is reasonable efficient, the total losses through the whole chain really add up.
     
  4. David Beale

    David Beale Senior Member

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    A much larger loss is normally considered for the differential, typically in the 30% range. The Prius does have a differential. Consider the electrical parts (MG1 and MG2 as well as the inverter) to have in the area of 95% efficiency. So the DC comes out of the inverter as AC at 95% of input power, and is converted to torque at 95% of the input to MG2. I suspect the quoted power values are input not output torque.

    Yes, all that power being lost in a differential is converted to heat. We don't see this as a problem because the car can't produce that much power continuously. But if it could it would need a cooler, like a NASCAR racing car has.
     
  5. briank101

    briank101 Member

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    Still 36% of the mechanical power lost to heat after the flywheel (room for improvement ??). Before the flywheel about 70% of the power is lost to heat (estimating 30 % thermal efficiency in a rapid acceleration scenario). But it would be nice if the transmission losses were just 15% than sub 8 second 0-60 times would be possible. It would make those on the fence about Prius reconsider it. Maybe Prius Gen IV is working on this. It makes one think, no matter what car brand, how much wheel hp really is left for productive motion. Is there any movement to make manufacturers quote wheel hp throughout a 0 to 60 mph cycle? I think it would give more transparency on the power cars really have. Just for reference, if the full 133 hp could be constantly laid on the drive wheels to produce forward motion right from 0 to 60 mph (100% transmission efficiency), the Prius 0-60 time with a 220 lb driver and full tank, would be 5.25 seconds.
     
  6. JimboPalmer

    JimboPalmer Tsar of all the Rushers

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  7. Former Member 68813

    Former Member 68813 Senior Member

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    I don't think 0-60 time is a deal breaker on economy cars. My previous Corolla also had almost exactly 10 sec or so and sold in millions. I felt it was acceptable and I vividly remember European cars in 1970s/80s somewhere in 15 sec range, or closer to 20 if fuel efficient. BTW, the corolla's engine had 130 HP max power, and you cannot reasonably expect max power all the time during acceleration.
     
  8. briank101

    briank101 Member

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    It's not so much the 0-60 time that concerns me, it's the drive-train inefficiency, or put another way potential for improvement of said. I would be fine with the engine producing 100 hp with the same 0-60 time. I suspect the % drive-train efficiency at or near max acceleration is less (maybe quite a bit less) than that at moderate acceleration, which may explain why acceleration, at engine speeds a few hundred RPM slower than the RPM that produces best BSFC, is more efficient overall (drive-train efficiency declining while BFSC is still rising). Further I suspect the 2 areas that Prius engineers have the most potential for "eeking" out more overall fuel efficiency for the average driver, are the transmission/drive-train and re-gen (kinetic energy recovery) by means of large supercaps to capture more of the high current energy spikes that occur during faster deceleration, which can then be fed more gradually fed either into the subsequent acceleration event or more gradually at a more consistent optimum rate into the battery.
     
  9. FrankTiger

    FrankTiger Member

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    Hi briank101 [​IMG]

    You may enjoy taking a look at this thread Measuring GenIII Prius energy (power) flow with OBD | PriusChat

    Over there you may find the following diagram of energy flow while my 2010 Prius is going up a ramp of 4% with the HSD indicator still in the ECO but close to the POWER zone.

    [​IMG]

    In this case, 13228/19651 = 67% of the ICE mechanical power reach the road. The ratio is very close to the 64% you calculated

    Big hugs from Frank
     
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  10. xs650

    xs650 Senior Member

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    Power loss in an automotive differential is 5% or less, not 30%.
     
  11. usbseawolf2000

    usbseawolf2000 HSD PhD

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    Close but the maximum is actually 72%. That's how PSD is set up so that 72% of the torque goes out to the wheels. As ICE revs, so will the power peak at 72%. The remaining 28% goes to the generator (normally MG1) and the motor (MG2) will reroute the power back into the wheels.

    Therefore, 100% of the gas engine 84 hp will get to the wheels, minus the conversion loss through the electrical path.
     
  12. fuzzy1

    fuzzy1 Senior Member

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    Don't confuse power and torque. Revving the ICE per se does not increase the power through the mechanical PSD path to the wheels, if the wheel RPM and ICE torque remain the same. Instead, revving the ICE will also rev MG1, pushing all the increased power through the electrical path from MG1 to MG2.

    Depending on component RPMs, that 72-28 torque split can still produce just about any arbitrary power split.
     
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  13. usbseawolf2000

    usbseawolf2000 HSD PhD

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    You are right. Come to think of it, when Prius is at near top speed, all of ICE power would go out the wheels because MG1 rpm is near zero. 28% of the torque would be at MG1 but since it is barely spinning, no power would go out.

    Another example of this condition is at 60 mph with ICE at 2,500 rpm. I used to monitor MG1 rpm (with Torque app) when accelerating and I try to get it as close to zero as possible... because I knew at that point, there are no power going out the electric path, meaning the most efficient state to accelerate.
     
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  14. Former Member 68813

    Former Member 68813 Senior Member

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    I tried the same thing with torque app and couldn't find anything conclusive. As far I could determine, MG1 would always spin at various speeds and I tried MG1 torque readings too and could not catch the system at 0 MG1 torque.
     
  15. BruceInOKC

    BruceInOKC Member

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  16. usbseawolf2000

    usbseawolf2000 HSD PhD

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    -100 to +100 rpm is good enough for me. I couldn't get any conclusive result (MPG) as well.
     
  17. briank101

    briank101 Member

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    You mean 64% of 30% or in other words 19.2% of the fuel energy in the Prius is converted to motive power during a 10 second 0-60?
    The 30% figure is an estimate average ICE thermal efficiency throughout the 0-60 given that at the high RPM portion of the 0-60 run the BSFC is lower. ICE RPMs reach max hp after about mid-40s mph. The 64% figure is the one derived earlier in the OP.

    I think the only solution is an engine at optimum BSFC rpm turning a high kinetic energy flywheel and a high efficiency CVT with infinite "gear" ratio which could also recover the energy during braking. But they probably would have to use a PSD differential of some sort to achieve the infinite ratios, which means drivetrain losses Hmmmm.:cool:
     
  18. usbseawolf2000

    usbseawolf2000 HSD PhD

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    According to this, Prius ICE is 38% thermal efficient.
     
  19. xs650

    xs650 Senior Member

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    A problem with that is that high efficiency CVTs for automotive applications don't exist, and it's been over 100 years since the first CVT car (1908 Carter). Another problem is that the total range of ratios in a CVT is limited by materials science, lubricants and other ugly bits of reality. The present state of the art is stretched more than enough just generating the ratios that are needed to match an ICE engine to the road.

    Many people are under the mistaken impression that CVT transmission are efficient when the real overall automotive system efficiency gain is because they are able to keep the ICE engine at it's most efficient operating RPM for the power required at the moment. That's kind of like an overdrive gear ratio in a manual transmission is less efficient than the direct drive gear ration, but overall automotive efficiency is higher because overdrive puts the engine at a more efficient rpm for the load.
     
  20. briank101

    briank101 Member

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    Yes at optimum load/rpm.... Thanks for the very interesting article.