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## Current Model S motor limitations

## Current Model S motor limitations

Submitted by jonerickson1 on 17. Juli 2013

From what I understand, the motor in the Model S is limited by the size of the battery and the inverter. The 85kwh cars have a constant torque of 443 ft-lbs. If you assume the torque stays at that level up to the 16,000 rpm limit, the maximum power of the motor is 1350 hp. If they upgraded the battery and inverter, could the current motor reach this limit? Here are some rough calculations with a lot assumptions.

Calculations:

Motor:

Torque = 443 ft-lbs

Max RPM = 16,000

Hp = T * RPM/5252

Peak Hp = 1350

Battery:

Kw = Hp*.746

Kw = 1006

Kwh = kw/C-rate

Kwh = 1006/5

Kwh = 201

Range:

Kwh = 200

$/kwh = $240

Increased cost = (200-85)*240 = $27,600

EPA Range = 265/85*200 = 624 miles

Another question is would you select this option?

jonerickson1| 17. Juli 2013Would you rather have this or a Model X with a 170Kwh battery and two P85 motors? AWD 832 hp would be pretty awesome.

Docrob| 17. Juli 2013Would be awesome to see what a stripped down model S could do with a super capacitor instead of a battery pack with an upturned inverter in a drag race. Will be really interesting to see whether modding electric cars for drag racing will become as common as modding ICE cars, so far we have seen stock model S's holding their own or even beating some drag vehicles, would be great to see what the model S is capable with some performance modifications.

Docrob| 17. Juli 2013Uptuned*

jbunn| 17. Juli 2013Geeze, I don't follow the math. Couple thoughts - I think you're taking peak torque, and top RPM and multiplying. The motor does not have peak torque at top RPM. Torque starts to drop off at higher RPM. Don't know if you've considered that. I'm wondering if some of those early assumptions drain through the rest of the numbers.

Brian H| 17. Juli 2013You don't get double the hp with two motors. That's determined by battery size and power. The same power is divided more efficiently between front and rear by the Stability and Traction Control computers.

jbunn| 17. Juli 2013Why are you posting this article twice. You have another one with different title and same exact text.

jonerickson1| 17. Juli 2013@Brian H I was saying use implying using twice the battery capacity to supply enough power.

@jbunn I know it drops off but usually you assume "flat" torque throughout the rpm range. Like i said there are a lot of assumptions. Withou having a map of the performance thats the best guess i could make. Do you know if there is a common percentage of torque loss vs rpm?

jbunn| 17. Juli 2013At one point there were graphs showing the torque vs RPM curves. I Volkerized and can find the threads, and the links to the graphs, but when clicking the links, Tesla just redirects to their home page. Even tried an archive site, with no luck.

Oh well. No graphs, I guess it didn't happen.... : (

jonerickson1| 17. Juli 2013I still agree that the torque will drop off but with Tesla stating that Peak Torque is 443 @ 0-5,100 rpm, they are making the same assumption I am. Would you agreee that the real world number would be above 1,000 hp even with this decline?

Brian H| 17. Juli 2013No. Would require double the batteries.

negarholger| 17. Juli 2013cfOH| 17. Juli 2013To make the quickest car (not the fastest), it seems like you'd need a bigger motor, a tiny (e.g., 10kWh) battery pack (to lighten it up), a performance inverter, and a 2- or 3-gear transmission to keep the motor in peak torque range over the 1/4 mile.

It's basically the EV equivalent of a dedicated drag car.... definitely a specialty vehicle for racing only.

Duplicating all that kit to make an AWD drag car seems unnecessary.

jonerickson1| 18. Juli 2013@Kleist

Doesnt this show that the only reason torque drops is because the amount of power available from the battery/inverter? If the Battery was doubled, wouldnt the torque curve continue to be relatively flat until 12k rpm?

GeekEV| 18. Juli 2013@cfOH - The roadster was originally supposed to have a 2-speed transmission but they scrapped that idea because the instantaneous savage torque kept blowing them up.

Zelaza| 18. Juli 2013Doesnt this show that the only reason torque drops is because the amount of power available from the battery/inverter? If the Battery was doubled, wouldnt the torque curve continue to be relatively flat until 12k rpm?

NO!

The torque produced by this motor is proportional to the current into the motor as determined by a motor parameter called the Torque Constant, usually in NewtonMeters per Amp, or FtLb/Amp. To get the necessary current, the Battery, working through the Inverter, provides the voltage necessary to shoves the current through the motor. But when the motor is turning there is also generated a counter voltage, or Back EMF, in the motor windings that opposes the applied voltage and works to limit the current. The back EMF is also defined by a constant called the BackEMF constant and expressed in Volts per Rotation Rate ( V/RPM, or more naturally, Volts per radian per second.) As it happen, the two constants are actually one and the same; but that's another story.

In any case, the break point in the torque-speed curve occurs when the back EMF is just enough to subtract from the applied EMF so that the necessary current (for that max torque) is generated. As the motor turns faster, and the battery voltage is maxed out, the net voltage driving the current is less and less and, as a result, the current is less and, therefore, the torque is less. At the top motor speed, the Back EMF generated just about equals the applied EMF, the current goes to zero, and there is no more torque. To accommodate mechanical losses, the system naturally adjusts its speed so that there is just enough current to balance the necessary torque.

What determines the maximum speed of the motor is the supply voltage. The energy capacity determines how long the speed and torque can be maintained and how hard the battery has to work to maintain these quantities: and not self destruct.

Based on the previously available data, I estimate that the Tesla Motor torque constant is about 0.25Nm/Amp and to attain the stated maximum torque of about 400 NM (about 300 ft lbs) a current of about 1600 amps is needed. The back EMF constant is, then, 0.25 Volts/radians/sec which comes to about 0.025 Volts/rpm (@ 15000 rpm the back EMF is 375 volts, the battery supply voltage.)

At low speeds, with little back EMF, way more current (and resulting torque) could be provided. However, to keep things from melting, and other bad stuff, the inverter probably limits motor current to under 2000 amps.