When towing with an EV (especially something large like an RV) it is well understood that the #1 greatest drain on available range is wind resistance. Driving more slowly helps to mitigate this. This is of course true even when not towing, but the effect is much more pronounced when you have a giant sail of a trailer behind you.
Then there is the energy lost due to gravity when climbing hills. You can of course get a fair amount of that back on the backside of the hill through regen, but regen is not 100% efficient.
It requires a certain amount of energy just to counteract gravity when your vehicle is on a hill. Imagine that you are on a hill and hold the car still just by feathering the accelerator. You’re getting zero mi/kWh. You’ll drain the entire battery after some time (probably a few hours) without moving an inch. That energy doesn’t just disappear once you start moving. It’s there the whole time you’re on a hill, a parasitic load on your battery that grows linearly with the amount of time you spend on the hill.
So based on that, there is clearly some advantage to completing the ascent of a hill faster, so as to spend less time on the hill (and thus spend less of that parasitic drain). However, this has to be balanced by the wind resistance. It doesn’t make sense to go 70mph towing an RV up a grade, as the additional losses due to wind resistance would likely exceed the gains from spending less time on the hill. Conversely, driving 20mph up the hill would also not make sense, as the parasitic drain from gravity would almost certainly exceed the gains from less wind resistance.
There’s two curves here and they surely intersect at some optimal speed to climb a hill. So given your vehicle’s frontal area, Cd, angle of the grade, length of the grade, and probably a few other parameters, it must be possible to determine the optimal speed to ascend a hill. It’s surely also possible to factor in the descent, assuming something like an 70% efficient return of energy on the backside through regen.
Does anybody know if anybody has worked out such a formula? Maybe the wizards at ABRP?
TL;DR drive at the speed that is save and comfortable. Take the shortest route, even if it’s steep. If this is I-70 up to Eisenhower tunnel, just go at “speed limit”, even pulling 11,000 lbs (or even with an 82,000 lbs Semi)
With a high-school physics level, the amount of energy used for elevation on a given hill and trailer is pretty much proportional to the elevation gain. It matters not (at first order) how fast you go up, the work done is the same and thus the energy used is the same.
But speed still matters, driving at 70mph will be double the air drag than 50mph. Air drag matters much less at lower speed, so 25mph vs 35mph will make less of a difference
In theory, it also matters not which road you take up, but in practice regen is not 100%, so a road that only goes up will be better than one that goes up and down and up. Also, a longer road will lead to more losses due to friction (both pavement and air). You also have more “parasitic” load (heating, etc.) if you drive the long way around - but that parasitic load is immaterial if you are moving heavy loads up and down.
Regen is pretty good in modern EVs, maybe 80%+ You only have losses in the vehicle, 90% on the way to the wheel, and 90% on the way back to the battery.
Note that if it takes you 30kWh to climb Eisenhower pass, you don’t get 0.8*30kWh=24kWh back when you drive back down. Some of the energy used to go up went into friction (road, air), and you still pay that penalty on the way down.
For a walk through of high-school level physics for this problem, check out
https://kilowatt.page/tesla-semi-vs-eisenhower-pass/
it has links to a Google calculator that you can use to play with numbers.
This is one of the underappreciated advantages of an electric Semi. No more slow, painful crawl up Eisenhower, Donner, the Grapevine or any of the other passes. An EV Semi goes at speed limit, both up and down (down speed limit is limited for Semis, though, but an EV Semi will not have any brake issues, regen is enough to keep it at any speed desired)
Speed also matters because going up a 25 mile long grade at 45mph takes 33 minutes, but taking that same grade at 60mph takes just 25 minutes. You’re fighting gravity for an extra 8 minutes at slower speed.
I understand what you are saying about how the work required to climb the hill is the same regardless of how fast you climb it. But that looks at the problem in a “spherical cow on a frictionless plain” kind of way. If it really was true that it’s all the same no matter how fast you go, then it should be possible to climb a grade at some ridiculously slow speed – say 1mph, and it would use the same amount of energy as climbing it at 50mph?! No…that’s not right. That super slow 1mph climb may consume the same amount of power to climb the elevation required ast the 50 mph climb, but the overall energy consumption of the entire system is going to be a lot higher for the 1mph climb.
That’s the crux of my question. And the article you linked about the Tesla Semi (and EV trucks in general) is more about “can they drive steep grades at the speed limit”, not “what is the optimal speed to climb a grade”. The computations done in the blog post are all assuming driving at the speed limit, not comparing the different consumption amounts for climbing at different speeds. It also completely hand-waves away the effects of wind resistance, which is the crux of what I’m asking.