Quote:
Originally Posted by kubark42
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Exercise for the reader: you are the driver of a car on a road that is horizontally straight, but that has exactly the shape of a sine curve in the vertical dimension. (Imagine a roller coaster) The car starts of on the righthand side of one of the waves, pointing uphill. You have one single gear, and an ideal clutch. Your engine efficiency curve looks like a bell curve (i.e. there’s a certain speed toward the middle of the curve at which you have maximum efficiency). Whenever you disengage the clutch, the engine turns off. You have no air or rolling losses whatsoever. (In fact, no losses at all aside from those dictated by the efficiency curve.)
Your goal is to get to the top of the hill three hills to the right, all while using the least energy possible. What is your optimal strategy?
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All you have to do is to generate the energy needed to get to the top of the first hill in the most efficient way possible.
Engage the clutch, start the engine, set engine speed (and load obviously) at max efficiency while climbing till you have just enough kinetic energy to make it over the top of the hill at which point you disengage the clutch while you're still climbing, shutting the engine off automatically, you'll just barely make it over the top and you then coast this way going up and down hill for a while with the engine off and just brake (or barely engage the clutch, the resistance of the engine should stop the car) when you want to stop at the very top of the third hill.