Speed versus RPM Calculator
Speed versus RPM Calculator |
Copyright 2006, Richard Shelquist |
Link to this web site
http://wahiduddin.net/toc.htm
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 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
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 = tire radius, in
inches
R1 = transmission
gear ratio
R2 = rear axle
ratio
Enjoy!
Richard Shelquist
Longmont, Colorado