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Transmission Effectiveness Factor - A New car performance metric

Discussion in 'Gen 3 Prius Technical Discussion' started by donee, Jan 9, 2011.

  1. donee

    donee New Member

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    Hi All,

    I am proposing that car testing organisations give us a new test metric - the Transmission Effectiveness Factor.

    This metric will be a measure of how effectively the transmission matches the engine to the vehicle dynamics in the zero-to-60 mph test.

    Car manufacturers claim a certain horse power rating for the drive train (power to the wheels). But, as we Prius drivers know, there is a disconnect between the zero to 60 times an actual car achieves and this power between vehicles with more effective transmission systems.

    Here is the Math:

    Transmission Effectiveness Factor =

    0 to 60 time if engine/hybrid drive train was at claimed full horsepower over entire time of the accelleration / measured 0 to 60 time.

    The idea being, that the transmission wastes time by shifting, and by not having the engine at max power, and of course there is HP loss in the transmission as well.


    One can calculate the numerator in the following manner.

    First, convert the engine HP to KW - KW = .7456 HP.

    Next, convert the mass of the car into KiloGrams - KG = Pounds / 2.205 .

    Next convert 60 mph to Speed in Meters/Second - S = MPH * .44704 , or 26.82 m/s



    http://answers.yahoo.com/question/index?qid=20100410140842AAhDEZ5

    Gives the Average Power (in watts) to be Mass * V^2 / 2T

    Average Power (KW) = Mass (in KG) * 26.82 * 26.82 / (2000* Time)

    So, we want Time for the numerator:

    Time = Mass * 719.31 / 2000 * Average Power
    = Mass * .359655 / Average Power

    The Transmission Effectiveness Factor would then be

    TEF = Vehicle Mass (in KG) * .359655 / ( 0 to 60 Time * Claimed HP * .7456 )

    = Vehicle Mass (pounds) / (0-60 T * Claimed HP * 2.0731 *2.205)


    For a 3rd Gen Prius, Car and Driver claims 9.8 seconds for the 0 to 60 time,

    TEF 3rd Gen Prius = 3242 (includes 200 pound driver)/( 9.8 * 134 hp * 4.5712)
    = .540

    For the 2nd Gen Prius (2004) Car and Driver claims 11.3 seconds for the 0 to 60 time,

    TEF 2nd Gen Prius = 3187 (includes 200 pound driver) / (11.3 * 110 HP * 4.5712 )
    = .561


    Cross checking with : http://www.engineeringtoolbox.com/car-acceleration-d_1309.html

    The calculated average HP for the Gen 3 is 72.8 in a 9.8 second 0-60 acceleration to 96.8 km/hr (60 mph) of a 1473.6 km vehicle. And 72.8 / 134 is .543 .

    After doing all this, I am supprised these numbers are not closer to 1. And also that the Gen III is not bigger than the Gen II. Some reports are the Gen 2 has a 0 to 60 time closer to 10.5 seconds, which would give a TEF of .603.

    Comparing to a Pontiac G6 GT (V6) http://www.caranddriver.com/var/ezf...lication/c48aaa7893a1a503df01e2373df58c32.pdf

    with the traditional 4 speed automatic transmission gives a TEF of .517 . Which is worse than either the Gen 2 or 3 Prius, but not dramatically so...

    I imagine there are some comfounding factors, like inacurate 0 to 60 times from car to car, and rated HP being smaller than the maximum horsepower.

    This link gives some other cars results: http://www.caranddriver.com/var/ezf...lication/2b9b90ffff3f7097761045f403ee0866.pdf

    Honda Accord EX- .471
    Hyundai Sonata SE - .496
    Suburu Legaci 2.5i - .535
     
  2. qbee42

    qbee42 My other car is a boat

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    As an example, in a slightly different mode of transportation, our sailboat has a slow turning 10 hp diesel engine with a very efficient transmission and propeller. Most production boats the size of ours would come with a high speed 20 or 25 hp engine and a less efficient drive system. Testing has demonstrated that our 10 hp system develops the same propulsion as most 23 hp systems.

    As the OP points out, horsepower is only half of the equation.

    Tom
     
  3. F8L

    F8L Protecting Habitat & AG Lands

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    The only problem I see here is using peak power ratings and ignoring power under the curve. Meaning some cars make peak HP at a specific RPM but that peak is preceded by very low numbers. Some cars such as those that are supercharged often have very broad HP curves where average Hp is nearly the same as peak. I think a better way to calculate would use average hp numbers. I admit those numbers are harder to find. There is also the factor of torque converters to consider. Two identical cars will differ in 0-60mph if one the cars has a torque converter designed for max acceleration. Kinda like the trans in the Prius is designed for max efficiency. :)
     
  4. donee

    donee New Member

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    Hi F8L,

    The idea is the transmission should match that peak HP load and torque to the instanteous wheels load thru-out the 0-60 HP accelleration run, without any losses to get a 1.0 TEF.

    BTW, the Suburu is a CVT car, which is why its close to the Prius....

    I guess maybe there should be a TEF max power, and TEF max efficiency?
     
  5. F8L

    F8L Protecting Habitat & AG Lands

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    I agree. I had just woke up and had not read your first post clearly. :)
     
  6. xs650

    xs650 Senior Member

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    I see more problems. The article admits that aerodynamic drag and friction losses aren't considered, so they make the calculated TEF artificially low. A couple of other things not mentioned are tire traction limitations which would unfavorably skew the results. It also ignores the losses due to power train inertia which are considerable at lower (higher numerical) gear ratios.

    As an example of traction limitations:

    If the idealized 100% TEF power of 134 hp were available at the drive wheels.

    134hp*(550 ft-lb/sec)/hp = 74250 ft-lb/sec power available at 100% TEF

    Gen 3 Vehicle weight = 3240 lb

    Assume tractive effort is limited to 0.5 x 3240 = 1620 lb
    0.5 is a SWAG based on about 60-65% of the static vehicle weight on the front wheels, some weight transfer from acceleration and a bit less than 1.00 coefficient of friction for the tires.

    power = force * velocity so
    velocity = power/force

    74250/1620 = 45.8 ft/sec = 31 mile/hr

    The rate of acceleration implicitly claimed for 100% TEF couldn't occur for a Gen 3 Prius until the car had reached 31 mph.

    The numbers don't suprise me, I calculated the same thing for several cars when I was taking physics in the 1960 (my gearhead oriented responses to physics exercises used to drive the physics instructor nuts). The numbers were even lower because horsepower ratings were more inflated and most cars were limited to 3 speed manual or automatic transmissions.

    TEF is an interesting concept, but unless it is adjusted for externalizes such as traction rolling resistance and aero-drag it doesn't tell you as much about transmission efficiency as it should. It should also be adjusted for engine inertia is it is to truly be a TEF. Although, engine inertia could be ignored if you considered the engine to be part of the power transmission system. That would lead to the situation where you could significantly improve the lower speed TEF on a car by lightening the flywheel.:D

    PS: I'm not as negative towards the concept as the above sounds. I am admiring the problem of turning it into a meaningful rating.:rockon:
     
  7. Former Member 68813

    Former Member 68813 Senior Member

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    Very interesting concept. I'm shocked that Prius is not way above the conventional cars especially since the issues sx650 mentioned should work in Prius' advantage?

    I have a sneaky suspicion that the hybrid power system humpers acceleration at the low speeds ("too tall low gear") and possibly at high speeds too (we know Prius has poor fuel efficiency at very high speeds).
     
  8. xs650

    xs650 Senior Member

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    You suspicion about low speeds correct. The Prius transmission doesn't allow the engine to get up to peak hp rpm until the car is moving pretty fast. Playing with one online model it looked like 50+ mph. It's done to limit electric motor rpm and current and possibly to limit torque to the limits of the mechanical part of the drive train.

    If MG1 and MG2 were unlimited in their capability and the mechanical drive train were strong enough, a Prius could have infinite gear reduction at standstill. It's a clever system.

    In other news, if Pigs had wings they could fly:D

    I agree that the hybrid drive is less efficient that a manual transmission at very high car speeds, but from what I have seen, fuel economy at high speeds is very good compared to other cars. Mostly because of the low Cd of the Prius.
     
  9. F8L

    F8L Protecting Habitat & AG Lands

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    That jives with my experience at the drag strip. The Prius regularly threw up 2.6 to 2.8 0-60ft times which is quite horrible considering the car was not suffering from traction problems. Once moving though, the car scooted along just fine and the 79mph trap speeds were not bad for a high 17sec 1/4 mile.

    Maybe it is my drag racing roots coloring my opinion but the Prius has poor low speed acceleration considering the torque available.
     
  10. JimboPalmer

    JimboPalmer Tsar of all the Rushers

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  11. SageBrush

    SageBrush Senior Member

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    Well ...
    Since I could not care less about 0-60 or max power ratings, I cannot really support an effort to force manufacturers to report a variant -- even if an attempt to internalize efficiency into the metric is included.

    Not to take away from this as an interesting exercise.
     
  12. FL_Prius_Driver

    FL_Prius_Driver Senior Member

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    What would be the purpose? My concern is not with the math, but with the utility. Specifically, parameters like this can certainly be improved and optimized....but usually at a cost to other parameters, like fuel efficiency. Do we want to go there?

    I'm not being critical of what you have worked out, but what is the next step and why should I pay specific attention to it (especially for a Prius).
     
  13. twittel

    twittel Senior Member

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    Putting aside the technical aspects, doesn't this discussion prove that Prius' effectiveness is in "idled traffic" rather than 50+mph transmission effectiveness?

    Happy Motoring,

    Tom
     
  14. donee

    donee New Member

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    Hi Xs...,

    I think you got that wrong. The Prius transmission wide ratio range allows full hp (actually max HP RPM) at a much shower speed than other cars.

    But, from a standing start, with the engine off, the delayed engine on time makes its seem the reverse is true.

    This can be evaluated with a running start, shifting into neutral while approaching the start at a 45 plus mph, then braking to 10 mph, then shifting to D and going from there. The shift to neutral keeps the engine on, so that when you shift to D at 10 mph the engine is already running. Somebody interested in doing that test ?

    I used to have this situation merging with traffic from a cross-highway ramp. I would be doing 40 mph (gen II) on the ramp, have to slow to around 10 mph to match traffic, and then shoot forward to grab the gap before the ornery drivers would close it up. Worked everytime. And the ornery drivers were just there with the jaws on the dashboard.

    Yes, I also see some dificulty making it a meaningful metric....
     
  15. donee

    donee New Member

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    Nope. I am not going to put aside the technical aspects. This is the "Gen III 2010 Prius Technical Discussion" page. And If I cannot talk Technical here, where can I?

    The idea of TEF, is the higher the TEF, the smaller the engine can be for the same acceleration. Which is very much a fuel economy issue. I think Toyota went with the bigger engine in the Gen III because of the basic ignorance of this issue in the general customer space. And we now have to get poorer slow-and-go Prius mileage because they felt that the public felt the 1.5 was too small, when its just not, because of the TEF of the Prius....
     
  16. donee

    donee New Member

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    Thinking about this, I believe the engine turn-on time, which is very smooth, but probably about a second, is the root of the issue, from a standing stop.

    The power button should probably turn on the engine, when pressed if the car is at rest.....

    The exercise I illustrated in the reply to xs650 in a Gen II Prius is really quite amazing. The car really takes off , when the engine is already running...
     
  17. xs650

    xs650 Senior Member

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    The online models show that you have to be up speeds on the order of 50-60 mph to hit peak hp rpm. If you put a tachometer in your car you will see it.

    Here's fun toy. It lets you find out what engine rpm is available at different speeds. It's for a Gen II but still gives you an idea what to expect in a Gen III.
    Toyota Prius - Power Split Device

    Economy cars tend to hit peak hp rpm at around 30 mph.

    The Prius transmission has an advantage because it doesn't need to shift'
     
  18. FL_Prius_Driver

    FL_Prius_Driver Senior Member

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    Good Logic. That is a worthwhile point to explore. I certainly see the likelyhood of a smaller engine having better FE and could be designed for a better TEF. What I'm not sure of is that some other constraint might force the engine to be big. Let's say a minimum performance (e.g. speed) up the rockies or area with long steep grades. I also do not know if there is an emissions breakpoint that might be in play.

    Why do you think the TEF is not higher than it is for the present design? Any idea what would be the most likely limitation?
     
  19. xs650

    xs650 Senior Member

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    Money, limiting the transmission to one planetary gearset, rpm limitations on the electric motors, current/power limitation on the motors and mixes of those. A higher TEF would only help below about 50 mph and the car performs decently their so it's not worth much money to improve that,

    At higher speeds though, the Gen III is about the lowest level of automotive performance I will accept and is one reason I didn't get a Gen II. I think most of the motoring public also doesn't want a more sluggish car.

    The Gen III transmission is as good as any transmission at highway speeds so you aren't giving up freeway mountain road performance compared to a more idealized transmission. Where you are giving up some grade performance is below highway speeds. not much for most drivers though because the average driver is afraid to use the full capabilities of their car.
     
  20. donee

    donee New Member

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    Hi xs650,

    The online models show a great range of engine RPM for any road speed, before MG1 or MG2 are overspeeded.

    In the early days of the Gen II Prius we would have old guys come on here and ask us if we thought their Prius transmission was slipping, because the engine reved so high at low speeds.

    This model puts red limits on the MG1 that are not realistic for the Gen II Prius. 6500 RPM is the failure limit of the Gen 1 MG1. For the Gen II, this limit is 10K RPM, and the operational limit is 6500.

    At 30 mph, the engine RPM limit is then 3098, which gives about 3098*76 / 4500 is approximately 52 ICE HP (assuming flat torque). The Battery then contributes 30 HP, for 82 HP total, or about 75 % of total system power.

    At this speed, my impression is most 2.0 liter or smaller automatic transmission cars are limiting their engines below this power level. But, I guess I got no way to prove it right now. A manual transmission car, can be operated to get full power at this speed, by staying in first gear.