5000 Reel

5000 Reel
Calculation of length of steel sheet winded on a ring..?

Hello Everyone,
I would like to calculate the length of steel sheet (approx. 0.2 mm thick and 8 mm width) wound on a reel of 8 mm wide and 200 mm diameter. The outer diameter of the ring after the sheet being wound is 5000 mm. (Clarification: The sheet is wound over the previous winding everytime, as the width of the inner ring is equal to the width of the sheet, unlike a cable wound in a hub where the width of the hub is relatively many a times larger than the diameter of a cable and the cable being wound beside and over the previous winding).

Please propose a mathematical formula for the above problem.
Thank you very much,

Venkat
The calculation is quite simple, but i think it is 9.8 km and not 98 km… Is that right?

Consider the area of the pancake. It has a 200mm ID (d) and 5000mm OD (D). Since the area of a circle is pi*r^2 or 1/4* pi*d^2, taking the area of the whole thing a subtracting that of the reel, the area looking at it from the top is:

area = 1/4*pi*(D^2 – d^2) = 19,600,000 mm^2

dividing by 0.2mm strip thickness, length is:

length = 19.6e6mm / 0.2mm = 98 km

This is pretty long, are you sure the OD is 5000mm instead of 500mm?

Edit: I did the arithmetic 6 times; I still get 98km. Are you dividing by 0.2mm strip t, or 2.0mm strip t?

Sansui SD 5000 reel to reel