Expert: Sherry Wallin - 6/8/2010

Question
I need to calculate the length of bobbin. A paper of thickness 0.038mm is winded over a core of diameter 375mm until the outer diameter of the bobbin reaches 435mm.please let me know how to calculate.

Answer
Kaleem~
    If I understand you correctly you just want to know the length of the material that is being wrapped around the bobbin which is just adding up the change in each circumference.
The initial circumference (C) is 375*pi and the ending C is 435*pi since C = pi* D, where D is the diameter. Each time you wrap around the circumference you are adding double the thickness, so ask yourself how many 2(.038) = .076 are in the difference in the diameters?
So 435mm - 375mm = 60mm is the change in diameter. Next ask yourself how many .076 are in 60 (change)? 60/.076 = 789.47. This means that you will wrap around the bobbin 789 times and almost another half turn. Each time you do this you will add pi*.076 to the length of the material on the bobbin. So that means that the length is at least pi*.076*789 ~= 188.38mm. You still need to add that .47 of a turn which is .47*(.076)*pi ~= .11 so add this to your previous answer 188.38 + .11 = 188.49mm. This is the length of the material on the bobbin.

Another way to do this is to take the initial C_0 as 375*pi and add .076 to the diameter and call this the next circumference C_1 = (375 + .076)*pi. The change in circumference is
C_1 - C_0 = 375.076*pi - 375*pi = .076*pi. This is the same change that will occur for each winding on the bobbin. Add these changes up until you reach a circumference of 435*pi.

Math Prof