Bubble wrap calculation

[Tusif Ahmad]

Hi,

I am looking for a custom function which should give me square meter area of bubble wrap if I give weight, length, width, hight. This is just to calculate how much bubble wrap will be required for any packet.

Thanks in advance for your help.

Regards,

TA

[comment]

How would you calculate this using pencil and paper?

[Tusif Ahmad]

Thanks for your reply.

I could be able to find following information on internet. Hope this will be helpful.

Calculus will only give you a rough answer because bubble wrap is compressible. Clearly if the roll were rolled more tightly or more loosely, you would have the same dimensions but differing amounts of bubble wrap.

Here's the easy way to get the correct answer: Unroll it and measure it. Obviously, that is impractical, so let's use some maths. What we are going to do is (theoretically) cut the bubble wrap into narrow strips and add up the areas of the strips. To get an accurate answer, we'll make the strips very narrow - so narrow that they are effectively zero inches wide. That's where the calculus comes in.

The area of the bubble wrap is its volume over its thickness, which is

[integral from D = a to D = b of (pi h D t) dD] / t = (skipping several steps) 0.5 pi h (b² - a² )

where:

t = thickness of the bubble wrap
a = diameter of the outside of the tube
b = diameter of the whole roll
h = height of the cylinder (what you have called width)

Based on your figures, that gives an area of 55270 square inches. That sounds a bit large to me, so I might have messed up somewhere along the line and no doubt others can point out any errors I might have made.

Note that this assumes that the thickness is uniform throughout the roll. In practice, it won't be because it will be compressed in the interior. It also assumes that the bubbles in each layer lie on top of the bubbles in the next layer, which is also untrue as they will tend to fit into the gaps in the next layer. Both of these considerations will mean my answer is too small.

Of course bubble wrap manufacturers don't do it this way - they know how much they have wound onto the roll. Contacting the manufacturer is the only sure way of getting an accurate answer.

tl;dr: You can't do this accurately without a lot more information and more complicated mathematics, but you can get a rough idea.

[comment]

I thought you wanted to calculate the amount of bubble wrap required to wrap a given package. I don't see the how the quoted passage is relevant to this problem.

[Tusif Ahmad]

Sorry to confuse you but I think this is the formula of integration which we need to build in custom function. 

[integral from D = a to D = b of (pi h D t) dD] / t = (skipping several steps) 0.5 pi h (b² - a² )

where:

t = thickness of the bubble wrap
a = diameter of the outside of the tube
b = diameter of the whole roll
h = height of the cylinder (what you have called width)

and I am not sure if there is any possibility to build derivative or integration in filemaker?

Edited January 24, 2017 by Tusif Ahmad

[comment]

If you want to steal the formula from here, they've already done the work for you:

t * Pi * h * ( b^2 - a^2 )

This is a simple calculation, no custom function is required.