Being at big pedantic, but power at 0 rpm isn't zero, useful power yes, but battery power is equal I²R losses, which are quite high at full torque
But I think Tesla quotes mechanical motor power, since Plaid does well above 1020 hp from the pack, if they don't, we need to consider the losses
And I guess I'll play pedantic right back at you.
Power is Not Energy. The simplistic view is that P = dE/dt, where E (as correctly pointed out, above) is E = (1/2)*mass_of_car*d(v(t)/dt)), and d(v(t))/dt = a(t). After doing all the substituting, we got P(t) = 1/2*mass_of_car*a(t)
But, as you correctly point out, there are losses that are vaguely related to i(t), and the power losses in the car are something like i(t)^2/R, where R is the resistance in the battery, wires in and outside of the motor, and in transistors everywhere
.
So, we finally get P(t) = 1/2*mass_of_car*a(t) + i(t)^2/R. Whee. And we don't know i(t), we don't know R, we don't know the power at t = 0 (but it's not zero, since a(0) isn't zero), and so on.
Likewise, for an electric motor, the equations of state for a rotating object are torque = I*d^2(w(t))/dt^2. (There're no Greek letters around here.. but that's angular acceleration in rads, that stuff there. But the energy in a stopped shaft might be zero; but the Power present that
accelerates that shaft is
not zero.
So, when I wandered in here, and
@Artful Dodger was making a valiant attempt at the math: We don't have a clue about the instantaneous acceleration, energy, and power on a Tesla under acceleration; nor do we know the dynamic (rolling) resistance and all that jazz. All we can make an attempt at is the
average power, which, after a couple of false steps, appears to be around 590 HP.
Now, the specs on the Beast Mode, from Tesla, says that the motor is capable of 845 HP. Wonderful. But I'll bet a quarter.. no, make it $50, that power level is only achieved with the car on a dynamo at a
particular, fixed speed. Nothing wrong with that: ICE guys rate their motors the same way.
So, it might be that max power is achieved at 30 mph; or 90 mph; or some other $RANDOM number. All we're saying, here, is that if we had 590 HP, constant, starting at t=0 to 2.6 seconds (ha!) we'd get the same time in a quarter mile.
Back when I used to inhabit a Prius forum, far away, there was a poster who actually owned a recording accelerometer. He used to amuse people by measuring the acceleration in a straight line and going around curves. And there was a point to his madness: What with the always-on hybrid in that car with the dual motor-generators and a planetary gear set, the rpm of the gasoline engine could be set arbitrarily with respect to the wheel rpm; that is, there was a infinitely-variable transmission built into the car. Given that was the case, when one floored the gas pedal, the ICE didn't go to max revs - it went to the revs
where it could deliver maximum power. At the same time, in the same architecture, the maximum power available from the battery was
also applied to the motor generators, giving this relatively lethargic car more acceleration than one would think.
Now, there's no "transmission", per se, in a Tesla. And I'm sure the miracle workers at Tesla in the motive power division have a riot making more power out of an electric motor than people might think would be possible. But, no question: The power out of that motor is
not going to be a constant.
Might be fun if somebody with a recording accelerometer took some Tesla on a 0-to-60 "drag" race to see what a(t) actually
is. From that, and the mass of the car, we could probably get a closer approximation to P(t).
Fun.
