A roll of film - Math Central

HOME

Math Central

Quandaries & Queries

Question from John:

Hi there,

I need to know how to calculate the build up on a roll of film is calculated.
Example: I start with a 6" diameter core, and I start winding .005" thick film on the core, so I am adding a total of .010" to the diameter each wrap.
If I continue to do this for a total length of film of 3000 feet, what will the roll diameter be?
So what I need is the formula to perform this type of calculation.
Can you help me? I want to be able to plug the formula in a spread sheet and to be able to input a core diameter, a film thickness and a total length and get a roll diameter.

Thanks

John

Hi John,

We had a similar question a while ago about a roll of paper. Have a look at my response to this question. The radius of the roll is

R = √(L ×t/π + r²)

In your example L = 3000 × 12 = 36000 inches, t = 0.005 inches and r = 6/2 = 3 inches. Thus

R = √(36000 × 0.005/π + 3²) = √(57.30 + 9) = 8.14 inches.

Thus the diameter of the roll is 2 × 8.14 = 16.28 inches.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.