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Newb to thinking about mileage, and largely a newb to newtonian mechanics!

Theoretical car: Combustion force is in exact direct proportion to amount of air/fuel. No minimum amount of fuel/air needed in cylinder to cause a single combustion, and no cap on amount of fuel/air that will fit into cylinder and combust properly without flooding system.

Not sure how a transmission actually works, whether it’s the “upstream” or “downstream” gear that changes size when you shift, but we’ll say it’s the upstream.

My thinking is that for a fixed downstream gear, to accelerate a fixed amount across a fixed time, the same amount of work is done:

1) In low gear (smaller upstream gear), with a LARGER cumulative downward distance travelled by the piston over many cycles due to the gear ratio, but with each cycle requiring LESS force behind it due to leverage

or

2) In high gear (larger upstream gear), with a SMALLER cumulative downward distance travelled by the piston over less cycles due to the gear ratio, but with each cycle requiring MORE force behind it due to less leverage

I think the Work (Fxd) is the same in both cases – we always say the work done on either side of a lever is the same due to one side exerting more force but the other moving further. I think this is simply a case of that idea. Or is my thinking incorrect?

Maybe fuel use is not actually in direct proportion to work done...

If I’m right, does the real-life need to switch gears at “ideal” ranges have more to do with each combustion requiring a minimum amount of fuel, which would add to the consumption when in low gear?

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The big reason for having a transmission in a real world internal combustion engine is that IC engines have a fairly limited range of revolution rates at which they work. At revolution rates above their favored speed range friction forces get worse (friction is usually a v squared thing) and at high rates the downstroke doesn't last long enough for combustion to finish, so there is a loss of power. At the low end, the combustion strokes aren't often enough to keep the engine spinning. So you need a way to start the vehicle from zero speed and get up to highway speed (or more) with the IC engine staying in its happy speed range. Hence the multi-gear transmission.

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