How to Calculate when A Roll Back Would Occur on a Ski Lift

[Chairliftop]

Hello!

First off, here is a video of what a roll back is:

Here's my question:

How could I determine how much of a load the lift is carrying for there to be a loss of friction between the haul rope (the cable) and the bull wheel (the main wheel at both the top and bottom terminals), causing the lift to run backwards?

Here's my attempt:

I know I am going to have to find the friction coefficient between the rubber lining of the bull wheel and the haul rope.

The chairlift I am talking about has the following:

- 169 Chairs (82 are loaded at one time)
- Each chair has a 6 person capacity
- Assuming the average person weights 137 pounds

Besides that, I need help figuring out when a roll back would occur due to a loss of friction between the rope and the bull Wheel! Help!

Note: I have never taken physics before, so an explanation in basic terms would be great!

Thanks!

 

[haruspex]

The maximum frictional torque available should be proportional to the tension in the cable. That increases as the payload increases. So it is not apparent that merely overloading the chairs should lead to such a failure. More likely, it would lead to snapping the cable or toppling a support.
The frictional torque needed is proportional to the difference between the tensions in the cable on the two sides of the bull wheel.
The tension added to the cable when the load on a chair increases depends on the angle between the cable on the uphill side and the cable on the downhill side of the chair. If the cable is initially too slack, the chair hangs low and the weight on the chair doesn't add so much tension. That is how I can imagine getting a rollback in normal operation.
In the video, I did not understand the details, but it sounds like the rollback occurred because the wrong brake was applied, not because the frictional contact with the bull wheel failed.