How do I calculate the RPM needed to power my system?

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To design a lure course system for dogs, a 12v car starter motor is commonly used, but it is not ideal for continuous use due to solenoid limitations. Alternatives like an 18v drill or battery-powered drills are suggested for better performance and compatibility with a car battery. To achieve a string speed of 30 mph, the relationship between linear and angular velocity must be utilized, focusing on the drive pulley's radius to calculate the necessary motor rotation speed. It's emphasized that a drill offers more moderate torque suitable for prolonged operation compared to a car starter. Overall, careful consideration of motor choice and calculations is crucial for effective system design.
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I want to design a lure course system for my dogs to chase after.
The systems I have seen use a 12v car starter motor, solenoid and car battery. It is a closed loop system with nylon type string around the drive pulley of the motor and then the string stretches out over 700+' along the ground. When you turn it on, the string moves a plastic bag along the ground and the dogs chase it.

Could I use something other then a car starter system? A lot of those systems have issues because the solenoid of those starters are not designed for that type of continuous use (on for 10 mins+ at a time) Maybe something like an 18v drill? or an electric drill (but I don't always have access to 120v)

How do I calculate how fast I need to power the pulley to make the string travel upwards of 30 mph? Would it be based on the size of the drive pulley only?

Any help would be appreciated.
 
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You can use the relation between linear and angular velocity:

linear velocity = radius of pully X angular velocity

Solve for angular velocity (which will be your motor rotation speed). Watch your units.
 
Car starter is definitely the worst choice, I am afraid. It is designed to provide very high torque for a short period of time. You need rather moderate torque for long time. You must check (or estimate) the torque you need, but at the first guess the drill seems to be better choice. There are battery powered drills - their internal battery is also 12V, so you may connect it to car battery if you want to operate it in place where normal AC is not available.
 
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