tomsax
Member
Kudos to both Smorgasbord and Bud for making progress on this calculation, and my apologies for not acknowledging their fine work before launching into my take on it. I agree, the analysis is quite tricky, and I fell victim to a brain cramp. It's good to know I haven't lost all credibility as a result. :smile:
I also agree that Smorgasbord had a great idea for collecting data. Smorgasbord's calculation gives the energy penalty for climbing a given hill at a given speed.
Bud's method calculates one-way regen efficiency correctly, whereas my "correction" to his method does not. I've edited my post to call out this error. To be clear, Bud's method computes the wheel-to-battery drivetrain efficiency during regen, estimated at 80% in the Tesla blog, not the roundtrip number given as 64%.
There are three issues with this that are affecting the accuracy of this calculation.
First: the assumption that driving one mile on level ground uses one ideal mile depends on the speed travelled. The data we have from the two Roadster distance records suggest that in the range of 25 to 35 mph, we would expect to drive between 1.28 and 1.42 miles per ideal mile.
If we adjust for this by assuming 1.35 miles per ideal, Bud's result changes from 68% to 49%.
In general, this can be improved by driving at the same speed and equivalent driving conditions and computing the energy use per mile. But, before we do that...
Second: the ideal miles number is rounded to the nearest integer. 11 represents some number between 10.5 and 11.5, so doing 11 - 7.7 = 3.3 is misleading and overstates the accuracy of the measurement. Likewise for the 3 ideal miles gain going downhill.
If I take the best and worst cases for the ranges of these two numbers, I get a range between 38% and 62%. That's a huge range!
See this spreadsheet for the calculation details.
There's a reason why ideal miles are rounded to the nearest mile: they are a rough approximation. Further, they don't tell us how much energy we've used, but rather how much energy is left in the battery pack. The amount of energy you get out of the pack depends on how you drive (the harder you push the go pedal, the more the pack voltage sags, yielding less energy per amp-hour). Therefore starting energy minus energy used is not always equal to energy left. (We know this is tricky to get right and that the IM reading often changes after the 10-minute settling period following any drive or charge session.)
Smorgasbord proposed a better method that solves this whole issue: use the trip meter energy reading. That reading tells you net energy out of the battery pack in much higher resolution than the IM reading. It goes up when you're using energy and goes down when you are regenerating energy. That's really the number we want. It's also the number we need for the equivalent level drive energy.
Third: Knowing the extra energy used to climb the hill doesn't tell us the potential energy we gained. Because the drivetrain isn't 100% efficient, we'll be spending more energy than the potential energy we gain.
The good news is that we can calculate this number directly from the mass of the car and the change in elevation: mass * height * gravity = potential energy.
So, clearly we can do this. We just need a hill big enough that rounding effects won't play a significant role in the calculations, and with driving conditions that can be replicated on a flat road. I have accumulated a ridiculous amount of data from our Roadster. I'll poke around at what I have to see if I've got a data set that will work well for this problem.
