Wrap angle and Length

[nashbaker]

Could use some help with the following problem, I keep drawing it in autocad 2d so I can figure this out each time, but was hoping to understand the equation so I could have an excel document do it for me.

Rope is ran over a roll and fixed to a recoiler of a known ID. As the rope accumulates the OD grows. I am trying to get an equation to show how wrap angle and length changes as the OD grows.

So ID and OD are inputs, wrap angle and length are outputs

Please see attached.

Thanks!

 

[tkhunny]

You'll have to try harder to explain exactly what it is you are doing.

Don't you need the cord thickness, too? It's not a continuous function.

 

[nashbaker]

You'll have to try harder to explain exactly what it is you are doing.

Don't you need the cord thickness, too? It's not a continuous function.

Rope is coiling around the pulley on the left. It has a known center to center distance to the right hand upper pulley of 9 feet. I want an equation that will show that as the material increases on the left hand roll, that the wrap angle and tangent to tangent length of the material will change.