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Is it the transmission that converts the high rpm of the engine into the lower rpm of the wheels rotation? Let's say that an engine was running at 500 rpm (this refers to the rpm of the crankshaft, right?) but the wheels obviously aren't running at 500 rpm, so what mechanism lowers the rpm?

I'm also confused by the sizes of the gears in the transmissions that I've seen cross sections of. If the rpm of the engine was 400 rpm but the wheels were only turning at 10 rpm wouldn't the gear ratio have to be huge? It would be 40:1 , but when I see the gears of the transmission the gear ratios don't look anywhere near that big.

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The short answer is "yes, the gear ratio is larger than you think."

The longer answer is that you're getting confused and thinking that only one number applies. Let's think about some of the major components used to turn engine speed into road speed:

  1. Engine revs (you can see this on the tachometer).
  2. Transmission gearing (the gear ratios that you've seen cited).
  3. Final drive (this is a base multiplier that you don't normally hear about).
  4. Circumference of the wheel + tire combination (used to turn rotations into forward motion - not part of your question but important if you want to think rpm => mph).

Let's use your example:

  1. Engine speed = 400 rpm (idling along).
  2. Transmission gearing = 3.454 (first gear in my car)
  3. Final drive = 3.9 (again, from my car)

That gives us a combined ratio of 3.454 * 3.9 = 13.5 (approximately). So, for every 13.5 rotations of the engine, I can expect one rotation of the driven wheels. At 400 rpm on the tachometer, this amounts to about 30 rotations of the wheels during one minute.

If I were a crazy person, I might opt to swap out the final drive in my car in an effort to create an acceleration monster. For instance, with a 4.444 final drive, I would be looking at a combined ratio of 4.444 * 3.9 = 17.33. At 400 engine rpm, this would translate to about 23 wheel rotations over that minute.

I used the Rallispec site for my numerical reference. I openly lust for their gearsets.

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