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Look in your owner's manual for your motorcycle's gear ratios. If you don't have the owner's manual, contact the manufacturer. You will find a ratio for each gear, as well as a few other ratios: the primary reduction, sometimes a secondary reduction and the final reduction. The primary and secondary reduction are gears applied to the engine RPM before it reaches the transmission. The final reduction is another gear that's applied after the transmission.
Multiply the primary reduction, secondary reduction, gear ratio for the gear you want to calculate and the final reduction. The product is the total gear ratio. For example, say you want to calculate how fast you're moving in a 2009 Triumph Bonneville in third gear. The primary reduction is 1.741, there is no secondary reduction, the third gear ratio is 1.545 and the final reduction is 2.388. The total gear ratio is 6.423.
Divide the engine RPM by the total gear ratio. The result is approximately the RPM of the rear wheel. If you're driving your 2009 Bonneville in third gear at 4,000 RPM, the rear wheel RPM is 4,000 / 6.423, which comes out to 622.76 RPM.
Find the circumference of the rear wheel. Each revolution of the rear wheel moves you forward by the circumference of the wheel. You can calculate the
circumference from the size of your tire, assuming you're using the manufacturer's recommended air pressure.
The Bonneville has a type 130/80 R 17 rear tire. The width of the tire is 130 mm. The aspect ratio, the height of the sidewall as a percentage of the width, is 80. And 130 mm is 5.12 inches, so 80 percent of that is 4.1. The diameter of the wheel itself is 17 inches, so 17 plus twice the length of the sidewall is the diameter of the wheel and tire together. The result comes out to 27.24 inches.
The circumference of a circle is the diameter times pi, so the circumference of the rear wheel is 27.24 times 3.14159, or 85.577 inches.
Multiply the circumference of the rear wheel by the rear wheel RPM to get your speed in inches per minute. In your Bonneville, this is 622.76 times 85.577, or 53,293.93 inches per minute. Multiply this result by 60 to get your speed in inches per hour, which comes out to 3,197,635.8. There are 12 inches in a foot and 5,280 feet in a mile, so divide your inches per hour figure by 12 times 5,280, or 63,360, which comes out to about 50.5.
So, if you're driving a 2009 Triumph Bonneville in third gear at 4,000 RPM, you're going about 50.5 miles per hour.