Understanding gear ratios

[AkumaNoZeta]

I'm asking this because it just jumped in my head while thinking about cars. First I was thinking about matching the diff's gear to the ratios of the transmission's gears. I was trying to think of it mathmatically at first starting by saying "since 4th gear is a 1:1 ratio and if the diff was a 3.50 (random number) then that would make the final ratio 3.50 so tran's gear X diff gear = final ratio. So if 1st was a 3.73 (random again) that would make the final ratio of 13.05" Which just sounds too high to me. Is there a real mathmatical way of looking at it? If so, am I even close to it? A different way I was thinking of it was time. Let's say you were going WFO (wide f***ing open, as in full throttle) in your car and you spent 2 seconds in first, then 3 seconds in second, 5 seconds in third, and 8 seconds in fourth. When you put a smaller gear in the differential would it just change the time spent in first, changing it to 1s in 1st, 3s in 2nd, 5s in 3rd, and 8s in 4th or would it change all of them making it like 1s in 1st, 2s in 2nd, 3.5s in 3rd, and 6s in 4th?

 

Sorry for the length and if it's ununderstandable, but I'm just curious and have a yearning for the learning.

[JMortensen]

You have it correct as far as multiplying the trans gear and the diff gear to get the actual torque multiplication effect. In terms of changing the diff, it will affect all of the gears, because as you said, it's the gear ratio in the trans x the gear ratio in the diff. Although this site is more about speeds in each gear, if you think about it in terms of torque multiplication = getting to the next gear faster, you can play with the ratios and see it in action here:

http://www.geocities.com/z_design_studio/

[AkumaNoZeta]

The time thing was just to help me understand it a little better, sorry about that. Here's something else I've been thinking of. A smaller final drive in my high torque, low RPM Mustang performs better while a bigger gear in the low torque, high RPM Z (thinking 9000 RPM SR20) works better. From the factory the 5500RPM 5.0 Mustang comes with a 3.08 gear and I've heard that the 9000RPM S2000 comes with a 4.11 gear, that's been making me thinking final drive ratios has a lot to do with RPM. Is that right? I know rear tire size is another factor, but what other things are the big factors of rear gear ratio selection?

[JMortensen]

That's pretty much it. Tire size, gear ratio, diff ratio, and engine power range. There have been some threads on here as to how to choose a diff ratio previously. I think the general idea is that if your engine makes peak power at say 5000 rpm, you'll want to change gears a bit above that, say 6000 rpm. Then if the trans is geared right you'll be driving over the hp crest of a dyno plot in each gear without falling too far down the hill when you jump to the next gear. Diff ratio is then about getting the right top speed or trap speed based on the rpm range, tire size, and trans ratios as described above.