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

From: Coe Nigel EEV/Hebburn (Nigel.Coe@vatechuk.com)
Date: Mon May 22 2000 - 12:36:44 EEST

Try this as a simpler version...

pi * ((OD+ID)/2) * ((OD-ID)/2T)

i.e. pi*mean diameter*number of turns

>| -----Original Message-----
>| From: EdGrenda@aol.com [mailto:EdGrenda@aol.com]
>| Sent: Friday, May 19, 2000 3:52 PM
>| To: SHogarth@pactiv.com; rp-ml@bart.lpt.fi
>| Subject: Re: OT:Linear length of material on a roll
>|
>|
>| 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:
>| 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
>| Math's Site":
>|
>| http://www.forum.swarthmore.edu/dr.math/problems/d14now.6.
>| 21.96.html
>|
>| 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.
>| Arlington, MA 02474 USA
>| 781-646-6280 (voice or fax)
>| EdGrenda@aol.com (email)
>| http://home.att.net/~castleisland/
>|
>|
>|