Ask A Scientist Mathematics Archive

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.
 charles c dorsey

Answer:
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.
 tee