PreDetermining Master Roll Diameters
It sometimes becomes necessary to print or slit rolls to diameters smaller than the original, or master, rolls. Knowing beforehand what diameter master rolls should have can reduce the number of splices, down time, and scrap.
One way of determining the correct master roll diameter is to assume that the total side area of the rolls rewound from a master roll is equal to the side area of that master roll. It then follows that, if we determine the total side area of the rewound rolls, we can calculate the master roll diameter.
For example, let's say that we expect to rewind about four 18" diameter rolls on 4" O.D. cores from a master roll whose core O.D. is 7". Using the following formula:
A_{t}= n(pi)[r_{r}^{2} r_{c}^{2}] Where: A_{t} = Total side area We get: A_{t}= n(pi)[r_{r}^{2} r_{c}^{2}] A_{t}= 4(3.1416)[(9in)^{2} (2in)^{2}] A_{t}= 4(3.1416)[81in^{2} 4in^{2}] A_{t}= 967.613in^{2}= 968in^{2} This is the total side area of the rewound rolls. We can then "plug" this figure into another formula to get the master roll diameter. Using the formula: r_{mr}= [ (A_{t}/pi)+ r_{mc}^{2}]^{1/2} Where: r_{mr} = Master roll radius We get: r_{mr} = [ (A_{t}/pi)+ r_{mc}^{2}]^{1/2} This is the radius of the master roll. It's diameter is twice that, or 36 inches. If you'd like a larger or smaller diameter use a larger or smaller value for "n".
This method should work regardless of core diameters. However, variables such as tension, substrate compressibility, etc. may affect it's accuracy. I hope that this information proves useful to you. If you have any questions, please contact me at: frankb@flexoexchange.com ©1997 Content of this article is original and may not be copied or reproduced without the express written consent of Frank Burgos. 
