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Theoretical best 0-60mph times & the Tesla P100D

Discussion in 'Electric Vehicles' started by garsh, Feb 12, 2017.

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  1. garsh

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    This is a great video. If you remember your Newtonian physics from high school (or you at least remember that you knew it once upon a time), you should be able to follow along. It first shows that the P100D now accelerates at what is believed to be the theoretical optimum rate with street-legal tires. I love the logic of the whole process.

    Then, it seeks to answer the following: If the P100D drivetrain were placed into a much lighter Roadster, would it be faster due to less weight, or slower due to having less grip due to being lighter.


    Next, I'd like to point out this video, which once again uses Newtonian physics to determine what the fastest theoretical 0-60mph time is for any vehicle using street-legal tires.


    After viewing both of those videos, I'd like to draw your attention to @TrevP 's post here, where he talks about a rumored Tesla Model 3 (which is possibly a future Roadster mule in Model 3 clothing) that can reportedly accelerate from 0-60mph in 2 seconds.

    Fun times. :cool:
     
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  2. MelindaV

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    I posted this over in a thread on TMC to an immediate disagree (without rebuttal), so maybe someone here has an answer:
    I get the 'want' for the lowest 0-60 time, but practically speaking, the 'need' for anything quicker than 4-5 seconds (outside of a true track car) someone may need to explain to me a situation where that is 'needed' in a street car.
     
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  3. garsh

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  4. garsh

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  5. Michael Russo

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    @garsh , you are correct... though I would expect that with a 0-60 time of ~4 seconds you can already get out of dodge pretty darn fast, if you're attentive enough... ;)
     
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  6. Twiglett

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    I love that physics lesson, starting from the best braking time.
    I also remember this older video from 2013 about a little Datsun doing sub 2 second 0-60 runs which must weigh quite a lot less, but I'm also guessing he doesn't use street tires, but pretty impressive none the less!
     
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  7. garsh

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    Looks like street-legal drag radials. Legal for the street, but you wouldn't want to drive it in the rain.
     
  8. Badback

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    A common mistake when talking about cars is to equate HP with acceleration. Acceleration is a product of TORQUE. Top speed is a product of HP.
     
  9. Mad Hungarian

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    Actually both are a result of HP. HP is a function of torque multiplied by RPM, and it's the HP that ultimately decides how much work gets done in a certain time period, whether that be acceleration or top speed. To illustrate let's compare two versions of the same car, one with more torque and one with more horsepower, both with manual transmissions (taken from Car and Driver magazine):

    1. 2015 VW Golf TDI - 150 hp / 236 ft-lbs torque - 0-60 8.3 secs. - 1/4 mile 16.6 secs

    2. 2015 VW Golf 1.8T - 170 hp / 200 ft-lbs torque - 0-60 6.8 secs. - 1/4 mile 15.4 secs

    No contest.
    Torque will give you that nice immediate response, which is why the TDI is so quick in cut-and-thrust traffic. But all other things being equal, HP always wins in the end.
     
  10. Badback

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    #10 Badback, Feb 13, 2017
    Last edited: Feb 13, 2017
    You are comparing apples and oranges. Neither figure describes the shape of, or peak of the torque curve. Electric motors can produce constant torque regardless of the speed. This is actually more a function of the inverter. More than full torque is possible at very low, or even zero speed. Torque being a function of current is somewhat speed limited my motor impedance, but voltage forcing can somewhat compensate for this loss.

    If you examine the images below you will see that the torque curve of the gasoline engine is much broader than the diesel.

    [​IMG]
    [​IMG]
     
  11. Mad Hungarian

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    #11 Mad Hungarian, Feb 13, 2017
    Last edited: Feb 13, 2017
    "You are comparing apples and oranges. Neither figure describes the shape of, or peak of the torque curve."

    You're right, and that's exactly my point. Torque alone as a value is useless, it's torque x RPM gives us the torque curve, and that relationship between torque and RPM in turn translates into HP. The reason the TDI accelerates more slowly is because it can only produce its superior torque over a shorter RPM range, resulting in less horsepower.

    "Electric motors can produce constant torque regardless of speed"

    In theory yes, but I've yet to see this in practice for EVs. Here's a dyno chart for a P85D, most others I've seen from various Tesla runs are similar:
    [​IMG]
    If another P85D were modified somehow to maintain that peak torque figure to a higher RPM, it would accelerate more quickly. But wouldn't be producing any more torque. It would be producing more HP. I therefore respectfully maintain my assertion that HP wins races, not torque

    EDIT: Sorry for the typed-in quotes, I botched the original snips :(
     
  12. garsh

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    The torque curve of an electric motor really depends on the design of the motor. It just so happens that it's *possible* to design an electric motor with lots of low-end torque (all the way down to 0 RPM), which is really, really nice for cars.
    [​IMG]
    (typical torque curve for a DC motor)
    It's also possible to design an electric motor with a really flat torque curve (all the way down to 0 RPM), which is also really, really nice for cars.
    [​IMG]
    (From Understanding Induction Motor Nameplate Information, showing various possible torque curves for AC induction motors)
     
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  13. Mad Hungarian

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    Good examples.
    Bottom line, we must know both the torque value AND the RPM at which it is available at to determine the amount of work - in this case acceleration - a given motor can perform. By definition, that's HP (or kW if you prefer).
     
  14. Badback

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    a=F/m acceleration equals force divided by mass. Force is torque times the radius of the tire. HP does not appear in this equation anywhere. HP is derived from torque and speed. Acceleration is derived from torque and mass. Acceleration is not derived from HP.
     
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  15. Mad Hungarian

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    #15 Mad Hungarian, Feb 13, 2017
    Last edited: Feb 14, 2017
    These formulas are correct, but your simplification of an automotive drivetrain doesn't take into account the fact that a higher HP motor can be geared to produce more torque. You're also assuming that a constant torque is available to the rear wheels no matter how high the rotational speed climbs. We can't look at rear wheel rotational force in a vacuum, we need to consider where it comes from to understand which motor measurement really predicts acceleration capabilities.
    Let's try this another way.

    Motor 1 produces 100 ft-lbs of torque from 0 to 4000 rpm.
    Motor 2 produces 100 ft-lbs of torque from 0 to 8000 rpm.
    Although both motors produce identical shaft torque, if we put a 2-1 reduction gearbox on the output of Motor 2 it will deliver twice the torque to the wheels as compared to Motor 1 while still being able to reach the same top speed. But it will now clearly clean Motor 1's clock in a drag race.
    This is because Motor 2 has more HP.
    Torque in the absence of rpm data does not tell us anything about a motor's quantitative ability to perform work in a given time period. Only once we know at what RPM that torque is produced can we determine that. And that combination of torque and rpm is measured as HP.
     
  16. Badback

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    We were talking about Teslas, they do not have transmissions. And, an induction motor can produce constant torque for the duration of the 0-60MPH run.

    My only point from the start is that they guy in the video should have said: as long as the car can produce sufficient TORQUE, and should not have said HP.
     
  17. Mad Hungarian

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    Although Teslas don't have a conventional transmission with multiple gear ratios as we're used to seeing in ICE vehicles, they do use the same type of reduction gear for torque multiplication in the final drive unit. In the Model S RWD most seem to be a 9.27:1 ratio. So there is definitely gearing at work there to achieve the desired blend of efficiency, reliability, acceleration and top speed. Saleen actually offers a shorter 11.39:1 ratio for those that want to improve acceleration at the potential expense of those others factors. And dual motor models use higher ratios on the front motors to achieve better efficiency when cruising.
    As for the induction motor being able to provide constant torque all the way to 60 mph, the Tesla dyno runs performed to date show that for whatever reason they appear to be limiting it to less than that, most seem to taper off significantly after about 40 mph. Of course it's probably the controllers limiting it for whatever reasons they decided were best. There's a good discussion about torque properties of Tesla motors here: http://electronics.stackexchange.co...a-car-maximum-torque-at-0-rpm-is-this-correct
    However even when unleashed to the extend that's so far been possible, the torque definitely dies off with rpm. On that subject, here's an interesting article on Jason Hughes' (better known to you who frequent TMC as wk057) impressive work on tuning his P85, with dyno graphs: http://insideevs.com/dyno-testing-tuned-tesla-model-s-p90-video/
    In this case the "unleashed" P85 actually makes more torque as the revs climb to a peak around 4500 rpm, and then begins to drop.

    My bad if I missed something and didn't get that part. Here I agree with you in that the most technically correct way to state it in reference to the car accelerating on the limit of the tire's grip would indeed have been for the narrator to say "as long as the car can maintain production of this level of torque at the wheels". However when you said broadly "A common mistake when talking about cars is to equate HP with acceleration. Acceleration is a product of TORQUE. Top speed is a product of HP." I felt that needed to be cleared up, as many people do have trouble understanding the full roles these two measurements play in determining performance. I hope on the broader point we can agree after this friendly and intriguing debate that when looking at a car's rated torque and HP as it pertains to the motor, it's the HP that will tell us what its ultimate accelerative capabilities are.
     
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  18. Badback

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    We might be close to speaking from the same page, although I'm not sure that it is the same book.;););)
     
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  19. Mad Hungarian

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    Cheers to that :cool:. My problem may well be that I'm a product of 35 years of studying / tuning / preaching from the book of ICE. Strangely the (usually) much simpler ways and behaviors of the EV having me puzzling and questioning a looooottt of stuff!
     
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