Length of Material on a Cylindrical RollDate: 6/21/96 at 21:56:30 From: Anonymous Subject: Length of Material on a Cylindrical Roll Is there a formula for calculating the length of material on a roll knowing the roll diameter, the core diameter, and the material thickness? I recently tried using a formula I saw in a newsletter, but it was not even close when I tried a real life example. The formula was something like (64.54*(D*D)-(C*C))/T*1000 where D is the roll diameter, C is the core diamter, and T is the thickness, all in inches. The answer was supposedly in feet. Thanks. Date: 6/22/96 at 11:37:6 From: Doctor Anthony Subject: Re: calculating material length on roll The area of cross-section of the roll can be expressed in two ways. When stretched out in a straight line it is a rectangle of area L*T where L is the length in inches, and T the thickness viewed edge on. When rolled on the drum, this same cross-section will be pi*R^2 - pi* r^2 where R = outer radius =(D/2), and r = inner radius (=C/2) So we have L*T = pi{D^2/4 - C^2/4} L = pi/(4T){D^2 - C^2} inches Length = pi/(48T){D^2 - C^2} feet = (0.06545/T){D^2 - C^2) feet (T,D and C in inches) Try this in real life. It will be sensitive to the value of T you use, so measure that carefully. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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