What Is The Length Of The Ribbon?

SzauerAV

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A ribbon of thickness t, is wrapped around a tube of diameter d1. The outer diameter of the roll of ribbon is d2. What is the formula to calculate the length of the ribbon?
 
A ribbon of thickness t, is wrapped around a tube of diameter d1. The outer diameter of the roll of ribbon is d2. What is the formula to calculate the length of the ribbon?

Suppose there are n wraps.

Length of 1st wrap is π\displaystyle \pi * d1

Length of 2nd wrap is π\displaystyle \pi * (d1 + 2*t)...... total length for 2 wraps is π\displaystyle \pi * d1 * (2) + π\displaystyle \pi *2t = 2π\displaystyle 2 * \pi * (d1 + t)

Length of 3rd wrap is π\displaystyle \pi * (d1 + 4*t)...... total length for 3 wraps is π\displaystyle \pi * d1 * (3) + π\displaystyle \pi * 6t = 3π\displaystyle 3 * \pi * (d1 + 2t)

Now continue......
 
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