My Math Forum How to determine total angle of contact when a rope wraps around a curve!

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August 7th, 2017, 09:36 AM   #1
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From: Chaguanas

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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...

Any help would be greatly appreciated

Kind Regards,
David
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 Pic1.jpg (9.6 KB, 23 views)

 August 7th, 2017, 10:17 AM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 what length measurements are given?
 August 7th, 2017, 12:41 PM #3 Global Moderator   Joined: May 2007 Posts: 6,805 Thanks: 716 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
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From: Chaguanas

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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...

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?

Davi
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 August 10th, 2017, 01:35 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 The angle between the rope and the radius at the point of contact is 90°, so the diagram contains a right-angled 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.

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

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