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August 7th, 2017, 09:36 AM  #1 
Newbie Joined: Aug 2017 From: Chaguanas Posts: 2 Thanks: 0  How to determine total angle of contact when a rope wraps around a curve!
Hello guys, Quick question. I'm trying to figure out a way to determine what the angle of contact would be if I was to suspend a cylinder with a rope in a sort of basket setting... Please see the image attached... Any help would be greatly appreciated Kind Regards, David 
August 7th, 2017, 10:17 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319  what length measurements are given? 
August 7th, 2017, 12:41 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,342 Thanks: 534 
Not enough information. It will depend on the angle where the two parts of the rope cross as well as the outer radius of the cylinder.

August 8th, 2017, 04:24 AM  #4 
Newbie Joined: Aug 2017 From: Chaguanas Posts: 2 Thanks: 0 
Thanks for the response guys... Ok, so the total length of the rope is 30 feet and the diameter of the cylinder is 56 inches... Here's the scenario...Let's say someone says that they have a pipe that is 56" in diameter and they want to suspend it with a rope that is 30 feet long...so it will look like the setup in the attached image.. I'm trying to determine the angle of contact between the rope and the pipe so I can accurately draw it... I'm trying to use the parametric constraints in AutoCAD to set it up automatically but no luck... hope this additional info helps... In the attached image the total length of the rope is about 26 feet...but I want the total length to be 30 feet... Does anyone know what math or trigonometric calculations I would need to do this? Thanks in advance... Davi 
August 10th, 2017, 01:35 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,050 Thanks: 1395 
The angle between the rope and the radius at the point of contact is 90°, so the diagram contains a rightangled triangle whose other angles are related (by the usual trigonometric definitions) to the proportions of the triangle. Given the length of the hypotenuse of the triangle and the length of one leg, the remaining leg can be calculated by the use of Pythagoras.


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angle, contact, curve, determine, rope, total, wraps 
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