# Two-pipe Circumference Problem

• November 18th 2009, 02:18 AM
bbeckett
Two-pipe Circumference Problem

I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!
• November 18th 2009, 10:20 AM
aidan
Quote:

Originally Posted by bbeckett

I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!

Take a look here:http://www.mathhelpforum.com/math-he...perimeter.html
There needs to be a slight adjustment since the circumferences are separated by (C-R-r).

Let R be the radius of the larger pipe (includes pipe wall)
Let r be the radius of the smaller pipe.
Let s be the distance separating the two pipes.
theta is the angle at the intersection of the tangents to the pipe (theta in radians):

$\theta = 2*arcsin \left( \dfrac{R-r}{R+s+r}\right)$

TotalStrapLength = $R(\pi+\theta) + r(\pi -\theta) + 2\sqrt{ (R+r+s)^2 - (R-r)^2}$

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• November 19th 2009, 02:48 AM
bbeckett
Thanks very much. It looks so simple now that I can see the answer!