# How do I model the friction on a rolling pulley wheel, which holds weight, on a horizontal cable?

I am currently designing a motorized zipline trolley that will carry a person on a horizontal cable, so I am trying to calculate the friction on the wheels to determine what kind of motors I need. I initially approached the problem using a static friction model using the coefficient of static friction between two steels. However, my professor told me to replace my model with a rolling friction model, so I took the coefficient of rolling friction between two steels. This greatly reduced the calculated value of friction; however, I feel like there should be more friction because the weight of the person will cause deflection in the cable, so a portion of the wheels' circumference will be in contact with the cable. I want to assume no slipping for the wheels, so I don't know how to account for the static friction while keeping the rolling friction model. How can I calculate the additional frictional force that I am not modeling?

• Can you draw a diagram of what you're trying to do? I'm imagining something like a ski lift system, where the cable is driven by the pulley. In that case, there is no (or should be no) relative motion between the cable and pulley. For an idler pulley in the same system, again there shouldn't be any relative motion between the cable and pulley (or else the pulley isn't doing its job!). I think you're confused by the same thing that I am - how do you have a rolling friction model between two objects that are moving in unison? Rolling implies relative motion, but there isn't any. Again: diagrams. Sep 23, 2016 at 14:01
• I can draw you a diagram when I have chance but for now, literally think of a zipline. The wheels DO have a relative velocity to the cable because the wheels roll on the cable. The only difference is that this device is propelled by a motor across a horizontal cable, as opposed to the potential energy due to the elevation difference. Sep 23, 2016 at 15:16
• when a wheel rolls on a surface, or in this case a cable, there is no relative velocity at the contact point. Rolling friction is what you use. Note there is no chance your cable will be perfectly straight. The force required to climb uphill due to slight cable sag is quite likely larger than the friction you are worrying about. Sep 28, 2016 at 0:50