Alright, so I kind of asked this question yesterday, but did some more thinking on the topic. Here's my new question. Changing the rear end gears to a higher ratio will bring more acceleration but a lower top speed - this I know. My question, however, is how. Let's take this into consideration; I'll use easy ratios to help me out: the driveshaft is spinning at 1000 rpms. If the ratio is 2:1, then the axle would be turning at 500 rpms, whereas if the ratio is 4:1 then the axle would be turning at 250 rpms. This explains why the higher gear ratio would have a lower top speed, however it does not explain to me why it would have a faster acceleration. The driveshaft is having to spin 4 times to turn the axle once in the 4:1 ratio, but wouldn't it be receiving the same resistance no matter the ratio? So the engine would have to work as hard to turn the axle half the speed as the 2:1 ratio? Any help understanding this would be greatly appreciated. Thanks!

 

Get a 10 speed bike and try starting out in tenth gear.

 

You awnsered your own question. 4:1 will require less force to complete one rotation that 2:1. I don't remember physics all that well (its been a LONG time) but quite simply its twice a easy to complete one revolution - it will just take twice as many.. The bike analogy is perfect

 

The gear ratio is a "torque multiplier". Assuming your tranny is in direct drive (1:1, 3rd on an A4, 4th in an M6), the output torque on the driveshaft will be = to engine torque. Let's say your engine makes 300 ft-lb. That 300 ft-lb makes it all the way to the pinion shaft, and then the gear ratio MULTIPLIES the torque. With a 3.42 rear axle ratio, the 300 ft-lb input to the pinion will show up as 1,026 ft-lb at the rear wheels. Assuming you had a 24" diameter tire, that means you will have 1,026# of force pushing your car forward.

Change those 3.42 gears to 4.11's, and the 300 ft-lb at the pinion shaft becomes 1,233# pushing your car forward. Since....

Accleration = force / mass

.....your car accelerates faster. But is reaches its upper limit in each gear at a point 20% of the MPH lower.

The above ignores things like drive train losses, torque convertor multiplication, etc.... but illustrates the point. Increase your rear axle ratio by 20% (3.42->4.11) and you have 20% more force accellerating your car.