  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 2007-2015,  Richard Shelquist

A Couple of Possible Sources of Error:

1) Tire Expansion:

There is a potential source of error in these calculations due to centrifugal force expansion of the tire at high speeds. While that effect may often be negligible for radial-ply tires due to the circumferential belts used in their construction, to get the most accurate results (especially using bias-ply tires) users should check with their tire manufacturer to determine how much the tire radius (or revolutions per mile) will change at various speeds.

2) RPM delivered to the Transmission:

Another potential error source in these calculations is when the engine RPM is not identical to the RPM of the transmission input gears.

For example, using this calculator for a vehicle having a torque converter (such as an automatic transmission), or using this calculator for a vehicle with a slipping clutch may produce incorrect results. In such cases, the engine RPM may be significantly higher than the RPM delivered to the transmission gears, and the calculated vehicle speed will then be significantly higher than the actual speed.

On the other hand, if the torque converted is fully locked, or if the clutch is not slipping, these calculations should be reliable.

Determining Loaded Tire Radius from Revolutions per Mile:

When it is not convenient to measure the actual loaded tire radius on the vehicle (such as when evaluating a variety of alternate tire sizes), it may be acceptable to use the tire manufacturer's "Revolutions per Mile" (rev/mi) specifications to determine the loaded tire radius "r" which is needed in this calculator.

Simply use this equation to determine the radius to enter in the calculator:

r = (10084) / N

where: r = loaded tire radius, in inches
N = revolutions per mile

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: 20-Sep-2018

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----- Shelquist Engineering -- Richard Shelquist -- Colorado, USA -----