Math for Calculating the Length of Edgebanding on a Roll

Try these complicated formulas, or the slightly simplified versions ... or maybe just weigh the material. July 7, 2011

Question
Can anyone tell me what the formula is for calculating how many feet of edge band remains on a used roll?

Forum Responses
(Veneer Forum)
From contributor D:
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)"

If that doesn't do it - here's another:
"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."

From the original questioner:
As I read your response I began to think logically and kind of bastardized your second option with a simplified version that actually worked pretty well. (I selected a small roll from our edgeband cabinet so I'd be able to check my answer). I was within 6" of actual. I simply determined a average circumference by adding the outside and the inside (D*Pi) and then divided by 2. Then I multiplied this average circumference dimension by the number of layers. To determine this, the difference between the outside radius and the inside radius, divided by the thicknes of 1 layer.

Like I said I was 6" of the actual, on a roll containing 30' (+/-). Now undoubtedly this error would compound itself with longer rolls but as I found out later by running the numbers on your actual second option, as well as your first (after enlisting the help of our engineer) none of the answers were spot on. In fact out of all of them, mine was the closest. Anyway, regardless of the means, I have my answer and I appreciate your help.

From contributor U:
Being one of somewhat less technical background than other responders (English Literature), I simply weigh a 12 inch piece of subject edgebanding and weigh it. I weigh the roll of banding and divide that weight by the weight of the 12" piece. This provides amount of feet left on the roll within 1/2 to 3/4 of a foot. The process requires a good scale, but we've purchased a couple of them to use in the inventory of fasteners, edgebanding, t-molding, etc.