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Hello:
I am using a 3 inch stainless steel pulley to power a 24 foot cable around two bike rims. The motor is a 3/4hp garage door opener motor.
The unit is a moving target assembly, the targets being paper only for pistol and rifle practice. The cable is 1/8th inch, stainless steel braided.

I want to increase the speed of the targets from point A to Point B, approximately 9 feet. (The target will then reverse direction.)

Is there a formula to use to increase the speed of the cable turning?

I have a video I can send to show you the current speed, if you would like to see it.

Thanks.

Assuming that the rotational speed of your motor remains the same the speed cable will double if you double the diameter of your drive pulley.

In this case you would increase the diameter of the pulley from three to six inches.

Niel Leon
engineering.com