 # Gearbox - Formulae for FD/tyre size/car speed and gear ratio calculation

Terminology -
FD - Final Drive (diff ratio)

Calculation for establishing vehicle speed for different final drives.
Formula : 60,000
FD (Final drive/diff ratio) x wheel rev per mile.

Wheel/tyre combinations - revolutions per mile:
145/70/10 1176.78
165/70/10 1078.47
145/70/12 1059.06
155/70/12 1030.71
165/60/12 1047.27
175/50/13 1058.82
These are for common tyre types, and accurate enough for assessment - a combination of using industry standard for theoretical calculation, actually measured assortment of wheels/tyres, and calculated averages! Applying the formula to a modern Mini with 12” wheels gives the following -

60,000 = 60,000 = 18.25 mph per 1,000 rpm.
3.105 x 1059.06 3,288.38
So 70 mph is achieved at a whisker over 3,800rpm. (I just know a bunch of you are going to check this out next time you’re driving around! But remember the speedos are grossly inaccurate, whereas the rev counters are fairly good).

Calculation for gear ratios and transmitted engine rpm
Basic rule to remember is ratio is established by dividing tooth count on driven gear by the tooth count on its driver. To work out overall gearbox ratios you also have to establish the constant ratio.

Constant ratio = tooth count on laygear input gear
tooth count on input shaft

This is NOT the fourth gear ratio assumed by many. Fourth gear doesn’t actually exist, as once in top gear the first motion shaft directly engages the mainshaft. Consequently it’s always a 1 to 1 ratio.

Gear ratio = tooth count on driven mainshaft gear X constant ratio
tooth count on driver on laygear

Example: 1st gear of A+ standard gearbox
Constant ratio = 30 = 1.765
17
Gear ratio = 31 x 1.765 = 2.066 x 1.765 = 3 .647
15

Calculation for transmitted engine rpm at output shaft
Input gear speed in rpm = engine rpm
transfer (drop) gear ratio

Pinion speed in rpm = input gear speed (rpm)
actual gear ratio

Out put shaft speed in rpm = pinion speed (rpm)
final drive ratio