Speed versus RPM calculator

Speed versus RPM Calculator

There is a potential for error in these calculations with bias-belted tires due to centrifugal force expansion of the tire at high speeds, but that effect is generally negligible for radial-ply tires due to the circumferential belts used in their construction. To get accurate results, racers using bias-ply tires should check with their tire supplier to determine how much the tire radius will change at various speeds.

For those who are curious about the calculations, here are the gory details of the speed versus engine RPM calculations:

Each revolution of the engine is reduced by the transmission gear ratio.. each revolution of the output shaft of the transmission is reduced by the rear-end ratio... and each revolution of the tire makes the car move a distance equal to the circumference of the tire. Pretty simple really.

Let's go thru the calculations step by step:

If the engine speed (for this example) = 6000 revolutions/minute

then the driveshaft speed = engine speed divided by tranny gear ratio R1 = ( 6000 / R1) revolutions/minute

and the rear axle speed = driveshaft speed divided by rear-end ratio R2 = ( 6000 / (R1*R2) ) revolutions per minute (where * indicates multiplication, and / indicates division)

So, the rear tire will be making 6000 / (R1*R2) revolutions each minute, causing the car to move forward (2*pi*r) * ( 6000 / (R1*R2) ) inches/minute (where r is the loaded tire radius in inches, and 2*pi = 6.28).

That is, the car will be moving ( 6000 * 6.28 * r) / (R1*R2) inches per minute.

Since 1 mile = 5280 feet = 63,360 inches, and 1 hour = 60 minutes, then the conversion from inches per minute to miles per hour is ( 60 / 63,360 ).

So, if the engine is turning 6000 rev/min then the car must be going (60 / 63,360) * ( ( 6000 * 6.28 * r) / (R1*R2) miles/hour.

Now, let's plug in the numbers... for my car, the transmission gear ratio R1 = 0.73 in high gear, the rear end ratio R2 = 3.62, and the loaded tire radius r = 10.9 inches, so the car's speed at 6000 RPM will be:

(60 / 63,360) * ( ( 6000 * 6.28 * 10.9) / (0.73*3.62) ) = 147 miles/hour

where:
           RPM = engine speed, in revolutions/minute
           r = tire radius, in inches
           R1 = transmission gear ratio
           R2 = rear axle ratio