[Appletank]

(searching about hill climbing on google again)

Hey Redpoint, I think I agree with you that a spherical car hill climbing in a vacuum would ideally be using maximum power to go up an infinite hill to minimize the effects of gravity. And vice versa, engine off on an infinite downhill because gravity can do all the work for you.

I believe the conflicts with IRL are: assuming you never have to go downhill, assuming you're starting off stationary, and other inefficiencies from the engine working too hard and going too fast.

If you have a decent speed before you hit the hill, and the hill isn't too high, then you functionally don't have to change throttle as momentum alone can bring you over the hill. Losing speed/DWL is thus ok because fuel/kinetic energy is being converted into potential energy, you reduce air drag, and the energy is repaid on the downhill gravity assist. Thus, you end up getting back to your initial speed, even without additional gas if you have the space. Using too much power puts the engine into too inefficient an operating zone to come out ahead of minimizing gravity's effects, such as running at 5K RPM instead of 3K.

I think your scenario is most applicable if one finds themself at a stop sign at the bottom of a hill. Going over a mountain, for example. Cars are all inefficient in the first couple of gears; you want to spend as little time possible stuck in them, even more so if you're having to fight gravity on top of it. Accelerate up until: aero drag starts becoming dominant, which leads to the engine power required being too inefficient to balance out the effect of fighting gravity, air, and friction to keep accelerating, or a downhill coming up.

In which case, you try to lock the throttle into its efficient operating zone, aka DWL, until you reach the crest of the hill. Here you can let momentum take you the rest of the way over, after which gravity takes over.

TLDR: I think High power up a hill is mostly applicable from the speeds 0 - 30 mph, depending on % grade, in which case DWL/steady state/gliding may be more appropriate.