I’m talking physics, and what would be the optimal angle for getting a coaster to it’s highest point [at the start of the ride] (as per the traditional chain-driven lift hill (though, if the same physics are comparatively applicable for LSM lift hills, then the question applies there as well)).

I know there are not only armchair physicists here, but also actual, physics-degree-holding thoosies (btw, I love that term lol, but anyway) that frequent this sub.

Basically, as one of those armchair physicists, I’m aware that, while a lower angle of attack [for the lift hill] would require less force, it would of course also take longer for the train to crest the hill and thus require more building materials (raising the cost of an already multi-million dollar project) to accommodate. However, make that hill too steep, and the energy required to make the train crest the hill would become “too” great/inefficient.*

Therefore, there surely must exist an optimal angle of attack for a lift hill that would provide the greatest [angle of] lift for the lowest cost, physics-wise.

So, what would that optimal angle of attack be? Would it be 45 degrees? Would it be greater or lower? Why?

I fawn over physics, and this question is a slight splinter in my mind right now.

Thanks in advance to all for any and all help in answering this question.

Bonus question: What is the coaster with a lift hill of the lowest angle of attack, both historically and presently existent?

*Yes, vertical chain/LSM lifts are a thing, but [I’m led to believe] they’re more of a gimmick/GP draw than an optimization of the physics of the situation (I’m open to being proven wrong; though, I’m not sure that such cases are actually physically optimal).

Edit: u/binarystrigoi gave pretty much the perfect answer to my question. Thank you to everyone who contributed! To me, this question has been sufficiently answered.