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Let's try to make sense of all the numbers we have

Discussion in 'Model S: Driving Dynamics' started by sillydriver, Oct 31, 2015.

  1. sillydriver

    sillydriver Member

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    #1 sillydriver, Oct 31, 2015
    Last edited: Nov 1, 2015
    I will never again make a post as long as this one, I promise.


    I thought it would be interesting to take all the data we now have and see what can be made of it. That includes what’s in the newest MS owners manual and elsewhere.


    In the manual (p 161) it says overall final drive ratio is 9.73:1, apparently for both motors (and I thought the front was geared differently). Tires are 245/35R21 on my non-staggered P85D. That’s 727 revolutions per mile (calculated and checked against tire manuf data). So 727*9.73 = 7074 motor revolutions/mile = 7074 motor RPM @ 1 mile/minute (60 MPH), so divide by 60 to get 118 motor RPM/MPH.


    Max combined motor torque is 713 lb-ft from Tesla website, presumably from 0 RPM up. P85D battery-limited horsepower is 463. RPM = 5250*HP/Torque. Output hits 463HP at 5250*463/713 = 3409 RPM: that’s at 3409/(118 motor RPM/MPH) = 29 MPH, so max acceleration is limited by rated torque up to ~30MPH, as we know by experience. How much acceleration? Tire radius = 1.16 feet (calculated from tire specs). Combined axle torque = 713*9.73 final drive ratio = 6937 lb-ft. Torque = force*radius, so force = torque/radius. So force = 6937/1.16 = 5980 pounds of force. The manual says curb weight (weight ex-driver) = 4963 lbs. Adding 160 lb driver gives 5123. Acceleration (in G-forces in these units) = force/mass = 5980/5123 = 1.17 Gs. So 1.17Gs maximum acceleration from 0 to 29MPH, Vbox measurements yield 1.10Gs from 0 to 30MPH, where I assume the difference is traction, very small air resistance and surprisingly small frictional losses – apparently much smaller than in ICE car drivelines, which is one reason Teslas go so fast on less HP than we thought. Note that max torque and thus max acceleration is apparently the same for P85D and P90DL (or so the website implies) so the difference between them is their torque in the battery-power-limited region over 29MPH (33 MPH for the P90DL), where the P90DL has 532/463 = 15% more.


    What's the significance? In the dispute over the horsepower of the P85D, the most accurate statement is that BOTH the 762 motor HP and the 463 battery-limited HP are significant, and subjectively I think they are about equally significant. From 0 - 30 MPH the car performs like a 762 HP car because its limiting factor is rated engine torque. That's why it has hypercar acceleration off the line. Above 30 it behaves like a 463 HP car, and from 30 - 60 like a 463 HP car with short gearing and multiple gears that keep it right at the peak of its power band. Then at high speeds it falls out of its power band and performs like a less-than-463 HP car. Subjectively, I think we P85D owners have experienced hypercar enjoyment off the line and a bit of frustration at more typical passing power in about equal measure. But I think it's as misleading to say it is only a 463 HP car as it is to say it's a 762 HP car.


    In this way, when Elon said the P85D has 1 1/2 times the power of the 85D, that is true below 30MPH where power at a given MPH is proportional to speed and max torque, so 713 lb-ft (P85D & P90DL) /485 lb-ft (85D) = 1.47.


    Also interesting is that the manual says max rear motor RPM is 16000, and max front motor is 18000. If the final drive for both is 9.73:1 (as the manual implies) and with non-staggered tires, then 16000RPM/(118 RPM/MPH) = 136MPH, while 18000RPM gives 153MPH. From which I conclude 1) power for you autobahn-driving Europeans is entirely out of the front motor, the rear must be deadheading unpowered above its max RPMs, and 2) the reason Tesla has taken a while to raise the MS from a 135MPH max speed to a 155MPH max speed is because they have to overspeed the rear motor in this way.


    Next, the manual says the max ‘net power’ for the ‘performance’ rear motor is 350Kw @ 5950RPM (divide by .7457 to get 469HP), and the front ‘performance’ motor is 193Kw @ 6100RPM (259HP). This disagrees with the 503HP for the rear now on the website, but DOES agree with the 259HP for the front. Discrepancy unexplained. Note that the ~6000RPM for peak powers in each = 51MPH. It sounds like the MS, with its single gear, begins to fall out of its power band over 51MPH, but how this interacts with max battery power is unclear.


    Finally, Dragtimes has the P85D running 11.6 @ 116MPH. Motor Trend has the P90DL running 10.9 @ 122.7MPH. If you put these and 5123 lbs into Dragtimes’ HP calculator you get 634 and 760 HP respectively. Obviously the calculator is designed for the characteristics of ICE car engines and transmissions, but the the ratio might be meaningful: 760/634 = 20% more. This is more than the 15% difference in battery-limited power between the two. What I infer from this is that software in the Motor Trend car controls the motors in an improved way, so the motors fall our of their power band more slowly and are able to apply max battery power across a greater range of RPM. Hopefully this will work for the ludicrous-upgraded P85D too.
     
  2. mobe

    mobe Member

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    Interesting. Thanks for posting this.
     
  3. Oil4AsphaultOnly

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    I appreciate the OP's efforts in crunching the numbers, but I think there's a flaw in the logic. From 0-30mph, the acceleration is traction limited, not battery power limited. The traction control prevents any further power to be applied to the wheels, to prevent wheelspin. That's why the 0-30 times of both insane mode and ludicrous mode are identical. So 30-60mph is where its battery-power limited. Note that the battery power is now used to both maintain the current speed as well as accelerate the vehicle.

    If you had both the 30-40mph time and the 50-60mph time, then you can calculate the slope and extrapolate back what the peak power at 0 rpm would've been if there were enough tire grip. Do you know of anyone putting drag slicks on their P85D and see what their times were?
     
  4. sillydriver

    sillydriver Member

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    Actually, the point I was trying to make is just what you said: 30-60mph (and up) is where it's battery-power limited. I think you are also right that under most circumstances it IS barely traction limited below 30, but the car is engineered so the difference between being traction limited and motor torque limited (which is what I said it was under 29mph) is cut very fine. Calculating from the data, the motor torque with perfect traction, no driveline losses, no rolling resistance, no inertia spinning-up the tires, and no air drag, should accelerate the car at 1.17 Gs. Vboxes say it actually accelerates below 30 at about 1.10 Gs. If we assume only a very very small 5% driveline, etc., losses, that 1.17 torque-limited Gs becomes 1.12. So there is almost no additional is loss from lack of traction (0.02 Gs). Or to put it another way, drag slicks should make almost no difference. Also, I think the insane mode and ludicrous mode acceleration below 30 would be the same even with drag slicks because the max motor torque is the same in both modes, so that max motor torque with small driveline losses would produce 1.12 G acceleration for both. The greater battery power in ludicrous comes into play by allowing 15% higher torque significantly over 30 mph where both modes are battery-limited, as I think you pretty much said.
     
  5. FlatSix911

    FlatSix911 918 Hybrid

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  6. tstafford

    tstafford Member

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    OP: Based on your analysis (and the tiny bit of info we have from Tesla) what do you surmise regarding the upcoming P85D Ludicrous upgrade? It sounds like increasing the max current should result in some improvements but that the real benefit will come if and when there is a related software upgrade. Also what do you infer from the statements that the upgrade doesn't match the P90DL spec?

    Finally - you are right on when you say that the frustration as a P85D owner is being spoiled by the 0-30 and underwhelmed by the passing power. Do you believe the upgrade has a reasonable shot at closing this gap?

    Thanks for the thoughtful analysis.
     
  7. sillydriver

    sillydriver Member

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    #7 sillydriver, Nov 2, 2015
    Last edited: Nov 2, 2015
    So that is not a question that an outsider like me can answer by crunching some numbers in a high school physics exercise. The only way I can answer is to look at history and politics, so take this with more than one grain of salt.

    First the history part. I think Elon was not trying to be deceptive when he originally said or implied a while ago that more P85D performance would come in a software upgrade. So that looked possible in principle, but they ran into issues putting it into practice. I also recall he originally said that the 90 v. 85 pack issue was orthogonal to the ludicrous v. insane issue, the first being energy density and the second power density. But then they discovered the 90 does have better power density (lower impedance?) and both packs need hardware debottlenecking, which you and I will pay $5k for.

    They shipped the P90DL, but as @P85DEE pointed out recently in another thread, in 32 passes at 3 different drag strips, the P90DL runs a very repeatable 11.4 to 11.5s – so repeatable that performance is surely software-regulated – the problem being that 10.9 was promised. P85Ds run about 11.6 (Dragtimes) to 11.8.

    In the mean while they offered the P85D hardware upgrade for $7500 and then, in just one spot on their website, they cut the specs to just 0.2s better than the downregulated P85D. Then they cut the upgrade price to $5000.

    Finally, Motor Trend tested a P90DL that is not only faster, but delivers 10.9, exactly what was promised originally.

    Now the politics part. It would be insane (or ludicrous) for Tesla to send MT a 10.9 car – 10.9 being a special number because it is what was originally promised – unless the downregulation was going to be taken off P90DLs soon. The MT article must be a signal that 10.9 for existing P90DL owners is just about ready. And if P90DL owners were only going to get, say, 11.1, then Tesla would not have given MT a car that matched the original promise exactly.

    I think the conspiracy theory that this performance improvement has been delayed just to sucker P85D owners into paying for an expensive upgrade is also insane (or ludicrous): particularly since the recent cut from $7500 to $5000 drains profit for Tesla. Also, with all the company has on its plate, I cannot believe Tesla would set up the whole infrastructure to do the upgrade for monetary gain: it has to be because they want to do right by their P85D customers, and if they deliver 11.7s – 0.2s = 11.5s performance for P85DLs, while P90DL owners are given 10.9, then the upgrade would make P85DL owners less happy than if it had never been offered, so I conclude it will produce better performance in the end, once the downregulation is removed from both cars. I believe the hedged 0.2s improvement statement was given by lawyers in the context of the existing downregulation for both. I expect P85DL owners will ultimately receive a few tenths less than the MT car because of the power density of the 90 batteries, so 11.2 is my prediction, which is a guess.

    On passing power, the MT car produced 2.6 to 60 and ‘less than 7’ to 100, so 6.9 – 2.6 = 4.3s from 60 to 100. That fixes the problem since the RS7 and similar cars do 60 to 100 in 4.5. The P85D now does it in roughly 5.0. My hope is that the upgraded P85DL with downregulation off will deliver 4.5, right there with the Germans. That is also just my guess.
     
  8. llavalle

    llavalle Member

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    Thanks for all this info OP. Never thought of the traction / torque limited implication at low speed.

    I knew that saying "electric motor make 100% of their rated horsepower on all the powerband" is not really true and since HP is a matter of torque and RPM that makes a lot of sense. Never thought of it that way.
     
  9. thimel

    thimel Member

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    OP, thank you for such clear and well thought out posts.
     
  10. EarlyAdopter

    EarlyAdopter Active Member

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    Agreed.

    But I keep running into this problem:

    "You must spread some Reputation around before giving it to sillydriver again."
     
  11. tstafford

    tstafford Member

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    Same here. Need a software upgrade.
     

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