Holy Wind Batman

[Zetopan]

High school physics? Really? My three years in high school (1968-1971) had no such class as part of the curriculum.

Well, in a relatively small podunk community high school in Oregon over 50 years ago we had a couple of relatively competent science teachers who were eventually replaced with an idiotic and totally worthless creationist "science" teacher who was actively trying to convince the students that science was a complete waste of time. One of the previous science teachers taught biology very well, and the other taught and chemistry and physics. We also did not have a computer in the school at that time, but now those are commonplace and even calculus is now being taught at the high school math level.

Calculus was mentioned as a college/university topic when I attended high school but nothing else was provided at that time. I would have jumped at the chance to learn calculus at that age, since I was one of only two students who were reading ahead in the geometry and trigonometry book to learn trig before the rest of the class. My wife told me that the other students didn't like the fact that two students were way ahead of the rest of the class. Resentment from other students for being so interested in math and science topics was a thought that had never even occurred to me at that time. And our high school term was 4 years long.

 

[jsmay311]

But the induction motor efficiency does not actually reach zero with your stated test conditions, it is a much larger number than that (infinitely larger in fact). As long at the motor is moving the power efficiency is definitely non-zero.

I do not have any specific performance data for the Tesla induction motors so I cannot indicate what the efficiency for those would be under your assumed testing conditions. Driving at 81 MPH is legal in some states in the US, but finding a location with a constant 80 MPH wind is rather problematic. I also do not have any access to a sufficiently long, or dyno equipped, wind tunnel to drive at 1 MPH in an 80 MPH wind (which is all really quite sad, but true).

However, the modern internet makes numerous technical resources readily available so that I can easily provide a link to a technical paper that evaluated induction motor efficiencies over a range of speeds provided by a VFD. An IGBT Variable Frequency Drive (VFD) is what is Tesla uses to control the motor power and RPM. The bottom line is that the loss in efficiency at lower speeds is actually relatively low, at least with the motors and inverters and the testing conditions they used.

However, they only evaluated these motors and inverters over a 40% to 100% relative speed range. Fortunately with the wonders of modern computers we can trivially plot their data and even extrapolate it back to essentially zero RPM (1 MPH out of 155 MPH is close to zero, but not zero). I have attached a screenshot of the resulting plot, and as you can see the efficiency under load at near zero RPM with the motors and inverters that they used (which are obviously not optimized for the wider speed range that Tesla requires) still comes in at about 73% efficient. I would not be at all surprised if Tesla does significantly better than that the tested motors and inverters over your assumed speed range.

The Tesla induction motors are actually built in-house and they are *very* efficient since they use higher conductivity copper rotors, while common industrial induction motors use lower conductivity aluminum rotors for a lower materials cost. Copper has about 66% to 71% higher conductivity than aluminum, while the best room temperature conductor (silver) is only about 5% better than the best copper. The Tesla inverters are also surely optimized for the extremely wide speed range their vehicle requires, rather than what is usually required for most industrial induction motors.

And since we are now talking about induction motor efficiency at very low RPM, we have also entered the realm where viscous and other related losses also become vanishingly small, etc. At low speeds but with significant torque loads many frictional losses become insignificant relative to the torque being produced.

http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1004&context=bae_fac

View attachment 224590

I know the efficiency of a motor is not 0% when the motor is moving and didn't suggest otherwise. But it IS 0% at 0 RPM, is it not? Without any motion, it's not doing any work, so the numerator in the efficiency calculation will be zero. But to provide a force, the energy consumed will be non-zero, right?

In other words, I don't think you can linearly extrapolate the efficiency curve of a motor down to 0 RPM -- or even near 0 RPM -- like you've done in that plot. Although exactly what shape that curve would take at slightly above 0 RPM, I don't know.

 

[Zetopan]

Sorry to take so long to respond to the above, I was busy and I see that this thread is now buried on the third page. Of course you are correct that the power efficiency has to drop to zero at zero RPM, since no work is being done then. The linear extrapolation merely shows that over the range of measurements that were employed, the efficiency was so close to linear than it would be a bit silly to argue otherwise. At some point the power efficiency has to decrease to zero at zero RPM, but we do not currently have that data available.

The load on the motor *usually* decreases with reducing RPM for most loads. For example: pumping water, operating a generator (MG sets), moving a Tesla on a level road with no wind, etc. In these cases the efficiency tends to drop faster than the RPM because the torque loading also drops with decreasing RPM. At some point the tire rolling resistance, gearbox viscous and gear friction, bearing friction, and rotor grounding friction etc. can start to become significant parts of the motor loading. In your assumed test case the torque loading on the motor remains at the same level in both cases due to the aerodynamic drag. At low speeds the induction motor is approaching a torque motor operation in operation (e.g. platform leveling motors and similar). Hence you never really approach the bearing and other low level frictional losses because the required motor torque remains relatively high for both of your test cases since the aerodynamic drag is still the dominate force.

The back EMF that the rotor generates in the stator winding also approaches zero as the RPM drops. Since the battery voltage is generally between 300 and 400 volts, there is a *lot* of extra voltage available from the motivation battery when using a VFD. Remember that the same VFD can run the motor at about 18,000 RPM. The VFD is essentially a 3 phase switching regulator, and since the back EMF is approaching a very low value at low RPMs, so it takes very little average current from that battery to maintain a *much* higher current in the stator windings to generate the required torque. As the motor torque loading remains constant, both the input power to the motor and the output power of the motor will drop nearly together instead of separating like they normally would due to inherent lower level losses that cannot be eliminated because the required output power got so low.

Since I have not yet instrumented my Tesla I cannot provide actual numbers for how much power is required to operate at a very low speed on a level highway without any wind loading. By measuring the battery power with the vehicle stopped and not using the brakes, but still operating, a baseline power level could be established. Any additional battery power to move at 1 MPH or similar slow speed can then be determined by the difference between being stopped and moving slowly. Moving very slowly represents nearly parasitic losses since only the rolling resistance, gearbox friction, VFD inherent voltage drops, etc. need to be overcome with essentially no loading on the motor. If the motor and VFD are efficient then this parasitic loss will remain far smaller than the power required to overcome your 80 MPH headwind.

Without the headwind loading the efficiency would drop much faster because the required motor output power more quickly approaches the parasitic losses. Since I do not have any data for the required battery power to overcome the drag at any given speed I currently cannot model the Tesla motor / VFD system power efficiency. This status should greatly improve over time as I permanently install the required instrumentation (I prefer a permanent installation to temporary ones where pulling part of the car apart each time would be required). Hence the linear extrapolation down to low speeds (but not zero) is the best that I can do for a first order approximation due to the current lack of relevant data.

However, we can still make some interesting observations based on what little data about this exists from Tesla. In a previously referenced graph provided by Tesla (which is quite dated by now) showing the range vs speed for a Model S85 (not P and not D) we can see that the range peaks at near 20 MPH and then drops below that speed. While this is not a power efficiency plot that we would like to have, it still shows that at 10 MPH that older model Tesla has nearly 2X the range as it does at 80 MPH. We can also see from that same plot that with a continually reducing load at lower speeds, the same range as 80 MPH can likely be achieved at 5 MPH or slower. This is not a power efficiency plot, but it still does provide some useful trends. The current P85D has a much better WH / mile rating (at or below 300) that the one shown in this dated plot (about 400 WH / mile, as per the lower text at the link).