|
Gearbox - Formulae for FD/tyre size/car speed
and gear ratio calculation. |
24
October 2000 |
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 -
|
60000 |
= |
60000 |
= |
18.25 mph
per 1000 rpm. |
|
3.105 x 1059.06 |
|
3288.38 |
|
|
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 |