Length of Wire Around Circle of Cylinders.

[cemcem]

Alright guys, wouldn't have wanted this to be my first post, but here it goes;

I'm trying to find out the length of a loop which is enclosing 'n' number of cylinders.
I've found the length of the loop touching the cylinders, and now need to find the rest of the length of the loop (which is not touching the cylinders).

The formula I obtained for the length of the loop touching the cylinders is as follows;
L (of loop touching cylinders) = 4[2pi(r)(3pi/n)]
given that a pentagon has an internal angle some of 540 degrees.
I need clarification that this part of the formula is correct and need the remainder of the formula which I've stated above.

Here is the question straight from the assignment:
http://s5.tinypic.com/116oysj.jpg

Here is a top view of the diagram I've drawn, indicating the sections I've found the formula for:
http://i44.tinypic.com/mk95sn.jpg

Here is a question similar to mine, previously asked on physics forums (with 4 cylinders), which did not resolve with an answer;
https://www.physicsforums.com/attachment.php?attachmentid=14794&d=1216796703

Your help is greatly appreciated.

 

[cemcem]

The diagram in the similar question asked previously is better labelled.

 

[cemcem]

Alright guys, I've finalised my complete formula.
I found it to be;

L (total) = 3(2πr + Rcosπ)/n

Did anyone else get this formula, can I please get a confirmation?

 

[cemcem]

π = pi

just in case you can't tell because it doesn't look like the pi symbol.

 

[Dick]

Alright guys, I've finalised my complete formula.
I found it to be;

L (total) = 3(2πr + Rcosπ)/n

Did anyone else get this formula, can I please get a confirmation?

That's not what I get. The part that depends on 'r' is the part touching the cylinders. I get that that is just 2*pi*r. How do you get that it's multiplied by 3/n?

 

[cemcem]

Thread can be closed. I found the solution. I'll upload it later on for the use of it by others.

Your help was greatly appreciated, Dick.