## Tuesday, February 14, 2012

### The relationship between RPM, Transmission, Wheel, Speed

This article will discuss about the relationship between engine speed, transmission ratio, wheel size, and speed of the vehicle.

For more details about the function of RPM gauge on a vehicle can be read in the article What is Tachometer Function on Vehicle?

Transmission function is to adjust torque generated by engine to vehicle speed and vehicle load on a particular condition. Examples of transmission ratio:

 Gear Ratio 1 3.307 2 1.750 3 1.171 4 0.923 5 0.767 Final Reduction 4.625

Final reduction is the ratio between input and output rotation of differential, before rotational power is given to wheel. Final round of reduction will decrease and increase torque. On a motorcycle, the final reduction ratio is big chain sprocket on the rear wheel, divided by a small sprocket on the transmission output. Some vehicles are designed with more ratios, such as the ratio of primary and secondary, low, high, and others. If those transmission ratios are working at a certain speed, then those ratios should also be included in the calculation for that certain speed.

You need to check your vehicle specification for gear ratio and final reduction to get accurate calculation result.

Wheel size will affect the speed of the vehicle. Because wheel and tire are often modified, then the measurement of vehicle speed with the speedometer will be less accurate. To calculate the speed based on the engine RPM, then tyre circumference data is needed. Measurement of tire circumference is done by center of axle height from the ground and it is called tire rolling radius. Keep in mind that the height of center of axle from the ground will be slightly smaller than the radius of the tire, it is because of the flexible part of the tire and vehicle weight due to the height a little lower. Please see tire picture below, red arrow is tire rolling radius.

If you drive a vehicle with the engine speed 3000 RPM and use the 5th gear with a ratio as on the table above, and tire rolling radius is 270 mm. So, speed of the vehicle is:

Wheel rotation = engine rotation / transmission ratio / final reduction
Wheel rotation = 3000 RPM / 0.767 / 4.625 = 846 RPM

Tire circumference = 270 mm x 2 x 22/7 = 1697 mm

Vehicle speed = wheel rotation x tire circumference x 60 / 1,000,000
Vehicle speed ​​= 846 x 1697 x 60 / 1,000,000 = 86 kmh

If the vehicle speed is known by speedometer, but no RPM gauge available. Then the engine speed can be determined by inverse of above calculation.

For example: you are changing 1st gear to 2nd gear at a speed of 30 kmh, and need to make sure the engine speed of 30 kmh on 1st and 2nd gear. Using the example table above for the gear ratio, and example tire rolling radius is 270 mm, then:

Circumference of the tire = 270 mm x 2 x 22/7 = 1697 mm

Wheel rotation = velocity x 1,000,000 / 60 / circumference of the tire
Wheel rotation = 30 x 1,000,000 / 60/1697 = 295 RPM

Engine speed on 1st gear = wheel rotation x lst gear ratio x final reduction
Engine speed on 1st gear = 295 x 3.307 x 4.625 = 4512 RPM

Engine speed on 2nd gear= 295 x 1.750 x 4.625 = 2388 RPM

If the modification is only done on the vehicle wheels and tires, no modification to transmission ratio, speedometer measurement can be corrected by ratio of tire rolling radius of modification divided by tire rolling radius original. Example: standard tire rolling radius by manufacturer is 270 mm, then wheels and tires are modified and tire rolling radius become 300 mm, if the speedometer reading is 100 kmh, then the actual vehicle speed is:

Actual speed = speedometer x tire rolling radius modification / tire rolling radius standard
Actual speed = 100 kmh x 300 / 270 = 111 kmh