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Speed versus RPM Calculator
 

Speed versus RPM Calculator

Engine Speed   RPM
Transmission Gear Ratio :1
Differential Gear Ratio :1
Loaded Tire Radius   inches

Vehicle Speed   MPH

 Copyright 2007-2012,  Richard Shelquist


Tire Expansion:

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.

Calculator Equations:

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 to create an equation for the vehicle speed...

First, let's define the meaning of the gear ratios:

Transmission Gear Ratio (R1): denotes how many engine revolutions there are for each driveshaft revolution.

 Differential Gear Ratio (R2): denotes how many driveshaft revolutions there are for each axle revolution.

Now, we'll derive the equation:

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

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

and the rear axle speed is the driveshaft speed divided by rear-end ratio R2 = ( 6000 / (R1*R2) ) revolutions per minute.

(Note: the symbol * 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.

Rewriting that all into a tidy form:

(0.00595) * (RPM * r) / (R1 * R2) = vehicle speed in miles/hour

    where:
           RPM = engine speed, in revolutions/minute
           r = loaded tire radius (wheel center to pavement), in inches
           R1 = transmission gear ratio
           R2 = rear axle ratio
 

Example:

SCCA Ford Spec Racer -

   RPM = 6000
   transmission gear ratio R1 = 0.73 in high gear
   rear end ratio R2 = 3.62
   loaded tire radius r = 10.9 inches
  
The car's speed at 6000 RPM in high gear will be:

(0.00595) *  ( 6000 * 10.9) / (0.73 * 3.62)  = 147 miles/hour

 


Enjoy!

 

Last Updated: 3-Apr-2012

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----- Shelquist Engineering -- Richard Shelquist -- Longmont, Colorado -----