[Math] Roll Weight calculation

geometry

I have for some time tried to create a formula to guess or find the weight of a roll of aluminum foil wound onto a core. Since my I have not been able to solve this issue I want to ask this question here and hopefully be able to solve it this time.

The initial data I have is the following:

Core Diameter = 76,2 mm
Material Thickness = 108 microns
Roll Length = 751 m
Width = 486 mm

I use a formula to find the outer diameter (converted to cm for this example)

R = \sqrt{L×t/π + r2}
R = \sqrt{75100*0,0108/π + (7,62/2)^2}
R (Outer radius) = 33,0267 cm

Am I using the correct values and if I have these values, can I calculate the weight of a given roll?

EDITED

After reading the question again i noticed that i forgot to mention a few things in my question. Sorry about that.

The roll is made out of aluminum oxide foil wound onto a core of PVC material which is hollow in the middle. Outer diameter of the core is 91mm but inner diameter (hollow part) is 76.2mm. Weight of the core is 1.64 KG.

John's answer pointed my in the right direction (sadly math is not my strongest area) and found the way to calculate the weight. However i feel like i'm not doing it correctly, partly because i have to remove the core so that the calculation is correct.

Known limitations to the calculation:

  • Thickness is not always correct. Depending on foil type it's from 110µm to 115µm and on a few 85µm (i have a table for that depending on material).
  • Roll can be tightly wound or in rare cases less well wound. This may affect the weight.

I hope that by calculating the weight i can predict with a small margin of error if the roll length or roll width is incorrect (basically catch larger discrepancies)

So my revised question is: Am i trying to solve an impossible scenario? If not, am i on the right track with this or am i missing something in my calculations? Is there some other way of doing this?

The following image is a screenshot of the calculation i made in excel. The data is from an actual roll that has been worked. Length might be a few meters less or more but i know for sure that the weight is correct.

My Calculation

Best Answer

I don't think the roll matters.

The mass will be $m = \rho V = \rho l w t$, where $\rho$ is the density of the aluminum foil. ($V$ is volume, $l$ length, $w$ width, and $t$ thickness.)

You have the length, width, and thickness already.

To get the appropriate density, you may need to take an appropriate sampling of the foil and measure the mass. If there's variability in there -- thickness, porosity, roughness, etc. -- then you'll need to take enough samples of sufficient size, from appropriately differently places from the large roll, to bring the measurement error down to something you can live with.

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