# Re: OT:Linear length of material on a roll

From: EdGrenda@aol.com
Date: Fri May 19 2000 - 17:51:45 EEST

In a message dated 00-05-19 05:01:08 EDT, SHogarth@pactiv.com writes:

<< Subj: OT:Linear length of material on a roll
Date: 00-05-19 05:01:08 EDT
From: SHogarth@pactiv.com
Sender: owner-rp-ml@ltk.hut.fi
To: rp-ml@ltk.hut.fi

I need to know the linear length of material I have on a roll. I know the
ID and OD and the thickness of the material, can someone supply the
formula I need.

Stuart Hogarth

Pactiv (UK) Ltd
>>

Hi:

I couldn't recall the formula, but we used it a lot years ago when I was
working on tape equipment. A quick perusal of the net turned up "Ask Dr.
Math's Site":

Here's the answer to someone's similar question:

------
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://forum.swarthmore.edu/dr.math/
------

I checked the last equation for the heck of it against an 1800 ft roll of
tape here and it came out exactly, showing that the roll is a little longer
than the indicated length and by about the right amount. Also keep in mind
that tension can cause a material to stretch and the cross section to
decrease enough to affect the results.

Have fun!

Ed Grenda
Castle Island Co.