# In a theoretical car does gear not affect mileage?

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?

• Commented Apr 13, 2017 at 18:28
• That question deals with highway vs. roads, and focuses on wind and acceleration more than purely gear differential Commented Apr 13, 2017 at 18:36