what's the formula to calculate gear ratio's?

[Celica RZ]

let's say we start with I want 5th gear to be a 1:1 ratio. I want the quickest accelaeration so I need the numerically highest final drive. I want though for 6th gear to be about 3500-4000 rpm cruising around 75mph. What's the formula I need to calculate all this?

[GTS LAID]

well to figure out your final drive ratio needed just take your speed and figure out what it comes out to in RPM of the axle...

to do that ... let say 75 mi/h * 1/60 h/min * 5280 ft/mi * 12 in/ft.

that gives you 79,200 inches per min.

now you have to figure out the circum. of your wheel.. our wheels and tires are 24 inches from side to side... so the rad. is 12 inches... easy...

circum = 2 * pi * rad = 2 * 3 *12 = 72 inches per cycle

so to figure out cycles per min... take 79,200 in/min * 1/72 cycles/in and you get 1100 cycles /min or rev per min...

now if you want to be at 3500 in 6th then you need to have an engine to final drive ratio of 3500/1100 = 3.2:1

our differential has a drive ratio of 4.529:1 so it looks like if you need to go 75 mph at 3500 rpm then your 6th gear ratio has to be 3.2 / 4.529 which is 0.71:1

as of right now the GTS 6th gear is at 0.725 so we're not far off.

by the way if you take a look at the ratios you'll find that they're very similar to what you're looking for and that they're quite well optomized

6-SPEED MANUAL


Ratios 1st 3.166
2nd 2.050
3rd 1.481
4TH 1.166
5TH 0.916
6TH 0.725
Reverse 3.250
Differential Ratio 4.529