Determining Length of Material Remaining on a Roll
Date: 11/24/2003 at 11:40:51 From: Laura Subject: Need formula for determining linear length of material Many apologies if this is not what you do, but I'm at a loss for where to find this answer. I need to know the mathematical formula to determine the length of material as it is on a roll. Specifically; my company supplies rubber and tape, both in rolls on a core. Without unrolling the roll, we'd like to determine the length of the material with the following information: Outside diameter of the core, outside diameter of the whole roll and thickness of the material (determined by a micrometer). Do you have any such formula? Laura
Date: 11/24/2003 at 15:51:25 From: Doctor Peterson Subject: Re: Need formula for determining linear length of material Hi, Laura. We get this question a lot; here are some of the explanations in our archive: Length of Material on a Cylindrical Roll http://mathforum.org/library/drmath/view/51723.html How Much Carpet is Left? http://mathforum.org/library/drmath/view/56481.html Fabric Left on a Roll http://mathforum.org/library/drmath/view/54357.html Briefly, the length of the material will be the product of the number of layers and the average length of one layer in the roll. Both are easy to find: Number of layers = (Do-Di)/(2t) [total thickness/one layer] Average layer = pi(Do+Di)/2 [circumference at average diameter] where Do and Di are the outer and inner diameters, and t is the thickness of the material. So the length is L = pi(Do+Di)(Do-Di)/(4t) = pi/4 (Do^2 - Di^2)/t A small error in the thickness measurement can make a big difference; I would recommend measuring it not with a micrometer, but by measuring the outside diameter of a roll of known length and calculating t from this formula in reverse. That will ensure that the number you use reflects the way the material lies on the roll. But try both measurements to see how they compare. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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