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Question:
I have a problem where I need to calculate the length a roll of tape without unwinding the tape. I know the diameter and thickness of the tape. The tape is wound on a core. I know the diameter of the core. Given that information, how do I calculate the length of the tape? I need a formula that I could plug into an Excel or Lotus spreadsheet. Thank you.



Replies:
A reasonably simple formula is L = pi*N*(D+d)/2 where N = (D-d)/(2*t) is the number of wraps of tape of thickness t on a roll of diameter D (when full) around a core of diameter d. The formula represents the average of two estimates using the sum of circumferences of concentric circles (inside vs. outside diameters based on t). The summation formula 1+2+3+...+N = N*(N+1)/2 is needed to develop each estimate.

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