### Gearing & Speed - The Final Solution by: Ken Saunders from: Fortification - March 1996

Fortification is the Club Magazine of the GT40 Enthusiasts Club

#### GEARING & SPEED - THE FINAL SOLUTION

The gearing/speed equation that we all use from lime to time always causes a lot or scratching of heads and stirring of the grey matter. I repeat below the calculations that are required to achieve the solution. I have also listed a short program in the BASIC programming language that could be used in your computer or programable calculator to automate the calculations. As many members are changing tyres these days due to the non availability of the original tyres or to increase traction, it is well to remember that not only will these changes have effect on the road holding performance but if the rolling diameter of the wheel has been changed, it will also effect the acceleration and the speedometer reading will be incorrect.

You can use these formula or the BASIC program to see just how much effect these changes have.

BASIC PROGRAM

10 CLS
20 INPUT "INPUT WHEEL DIAMETER IN INCHES ";WD
30 INPUT "INPUT GEAR RATIO (e.g. 0.82) ";GR
40 INPUT "INPUT DIFFERENTIAL RATIO (e.g. 3.44) ";DR
50 AN = 1000 / (GR*DR) * (26*PI / 36) * 60 / 1760
60 PRINT AN;"MPH PER 1000RPM"
70 END

GEARING CALCULATIONS

1000 / (Gear ratio x Differential ratio) = Number of revolutions of rear wheels per 1,000 RPM

Wheel diameter(in yards) x TT(3.142) = Movement of car per revolution of rear wheel.

(Number of revolutions of rear wheels per 1,000 RPM x Movement per revolution of rear wheel) / 1760 (number of yards per mile) = Movement of car per 1,000 RPM (= Movement per minute)

Movement of car per 1,000 RPM x 60 (To convert to MPH) = MPH per 1,OOORPM

EXAMPLE

If we assume a rear wheel diameter of 26 inches and are using the Renault 21 turbo gearbox which has a 0.82 fifth gear and 3.44:1 differential ratio we get the following:

1000 / (0.82 (Fifth gear ratio) x 3.44 (Differential ratio)) = 354 (Wheel revolutions per 1,000 RPM).

26 (Diameter of wheel in inches) / 36 (convert diameter to yards) x TT (3.142) = 2.27 (Yards per revolution of wheel)

(354 (Wheel revolutions per 1,000 RPM) x 2.27 (Yards per revolution of rear wheel)) / 1,760 (Yards per mile) = 0.453 (Miles Per Minute per 1,000 RPM)

0.453 (Miles Per Minute per l,000 RPM) x 60 = 27.4 MPH per 1,000 RPM.

At 6,000 RPM this gives a theoretical maximum speed of 165 MPH.

#### Email to Robin Sundt:

email to sundt@pncl.co.uk