# Vehicle transmission ratios

• mahoutekiyo

#### mahoutekiyo

I think I have devised a formula to depict the correlation between engine speed and tire speed. Can anyone confirm or correct this?

[ 1 mile / ( diameter of rim + profile thickness of tire ) * pi ] * ( x / 60 ) * ( gear ratio ) * ( final gear )

I used this in a function to graph the 5 gears for a 240sx. The results seem reasonable but I have yet to actually test this data.

Welcome to PF, Mahoutekiyo.
I know nothing from math, but I see an unnecessary step in your equation. There is absolutely no need to incorporate the rim size. It is only the diameter/circumference of the tire that's relevant.

I knew this, however, I thought it would be easier to calculate it this way because people can get those number right off the tire rather than have to measure the tire, which would be less accurate because the tire is curved unless you had a T-square.

I thought it would be better using tire numbers because you can get specs like that for any car with physically having to be there to measure it. For example:

a tire that says 206/60 R15 would be:
(206mm)(.6) + 15in = diameter

Unfortunately, I just discovered this is inaccurate. ='\

a tire that says 206/60 R15 would be:
(206mm)(.6) + 15in = diameter
Try ((206mm)(.6)x2) + 15 inch = diameter.

Try:

(rpm * diameter) / (drive ratio * 336) = MPH

There's a constant in there of approximately 336 to convert from tire diameter to mph, which is basically:

(12*5280) / (60 * pi).

In my case, my drive ratio is determined by 4.11:1 differentials, a 4:1 transfer case, and a 4.46:1 1st gear, so I have a 73:1 drive ratio and 31" tires.

In first gear in 4Lo at 2000 rpm, I'm cruising along at about 2.5 mph. In the scary parts, I drop my rpm down to about 1000 rpm or even a little lower.

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