Trying to solve a problem (math)

I have an air tight vinyl fabric I am working with. I am trying to find a specification for how many PSI pressure it can stand. The only spec I can find is tear strength. Here is what I did and if possible tell me if I did this correctly. I will be forming a bag from this fabric that is roughly 11" diameter by 16" long. That correlates to about 100 sq inches and 1600 cubic inches when inflated. I have a circumference of about 35". The bag needs to withstand 2# PSI. The 2 PSI would be developed by applying 200# fore against one end of the bag while the other end was stationary. Can I correlate the PSI to the tear strength by assigning 2 PSI to each cubic inch and then diving that by the diameter? If so my fabric is about 20% too light. The tear strength is roughly 70# per inch I think but I am not absolute at how the 70# is applied.

I just did a break test on the fabric and I am getting 70# for a 1/4" wide strip. So I don’t know what their 70# represents.

I posted too quick. But the break test is closer to what you need to calculate. A tear test is usually done on a pre cut piece. It seems that 70 pound break test means it is sufficient to withstand 2 PSI. You should try and heat seal the fabric edges for the break test to lessen the chance of an easy tear.

That’s a good point, thank you

I’m not 100% on the situation you’re describing, but you probably want to do:

pressure * area < (circumference * tensile strength per width) / factor of safety.

Can you describe your break test? It’s possible the number they cite already includes the factor of safety.

[quote=“Snarky_Kong, post:5, topic:1013113”]
I’m not 100% on the situation you’re describing, but you probably want to do:
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I cut a strip of fabric 1/4" wide and about 24" long. I wrapped on end around a dowel and the other end around my luggage scale. It broke clean about 4" from the dowel. It actually broke at 68#. The specs they give on tearing are 65# in one direction and 73# in the other direction. I only tested one direction. I might just make a small bag and pressurize it to see where it breaks, it would be nice to know it’s capacity.

What you want is a “hoop stress” calculation. They are readily available but you may not have the material properties the calculator requires.

I have done a lot of testing with strings. I notice the factory specs almost always give a rating that is double what I get. When I use the hoop test our numbers match. I make a hoop from the string and just pull it apart. Is this what you are reffering to ?. Maybe I will run that test.

Unless your finished bag is a seamless sphere the materials properties are just one input into how much PSI your bag can withstand. The seams are potential weak points. If the shape is other than spherical the stress from inflation pressure will be concentrated at various spots where the shape is conducive to that. e.g. a closed cylinder made from 2 circular end caps and one rectangular sidewall formed into an open cylinder will have massive stress concentrations at the seams.

Said another way, the bulk material strength is probably a very weak upper bound on how much inflation load your finished envelope can contain.

As with most backyard engineering, there’s a lot less that can be usefully calculated than it might at first appear. Over-building is the solution to being forced to under-engineer. In the modern sense of “engineer” which means devise an optimally weak solution that doesn’t waste materials.

the seams seem to be as strong as the material. if I do them right. I am actually trying to figure out how far over my current specs I could go. Here is where I am having a hard time grasping the problem. If I push up with 200# force I am developing 2# PSI internally. Does stored energy have any significance here at all. Does it even exist? I am compressing the air less than 15% but at a 500# push I would be compressing it over 33% does that play any part in anything or is it just peak pressures I need to deal with.

For a PSI test without actual air pressure setup. Wouldn’t it be better to clamp a section of material at both ends. Then add a weight with no sharp edges upon the middle? Even better if the weight had a 1 inch square area. Maybe a lead ball or such thing.

Seems a regular party balloon will pop at just over 1 psi. If that is any help.

This was actually the first thing I looked up, my source said just under 1 psi.

Ok , I just did this per your suggestion. I did it slightly different . I placed a dowel facing straight up from the floor and secured a andle on each end of some fabric. I was able to read the contact area as I pushed by looking at the mark showing through the fabric. It looks like I had about 20% of a square inch. I applied 80# pressure to it and it did not break through. This tells me with some certainty that the end caps are by far my weak point.

What are the end caps to be made of?

Ideally they will look just like the end caps off of a 12-in PVC pipe. Right now I am actually using a special kind of 5 gallon bucket lid it has a screw on top it’s pretty strong. But I know there’s a weak point where the mounting bolts are attached I imagine that will wear out pretty quickly with flexing.

Wonder if a ring of PVC pipe inside this, with the fabric trapped between could be airtight? Maybe too flexible / soft for purpose.

I have exactly that in 6-in. You wouldn’t believe the price for 12-in if you don’t buy in large quantities $159. If I buy in large quantities I can get that number down to 12.95 and if I buy a minimum of two dozen I can get them for about $25. I need something under $10… they have to be rigid because they have bolts going through them on both sides one side is mounted stationary and the other side is pushed and pulled. To set up I’m using now works okay but I don’t think it’ll last long I could probably get by pretty good by using four bolts and large flat washers. With a rigid PVC cap it would be bulletproof

Maybe a cheap 12 inch aluminum or steel cake pan? Might still be too flexible though.
How to make an air tight seal as well. Silicone coating and a hose clamp?

Oh. Maybe nested pie plates. Double thickness and trap the fabric between.

Right now I use a hose clamp and a stri if 1`/4" X 1" self adhesive dense closed cell foam like weather stripping, that seems to work well. the existing top I think is ok for up to about 125# it can take well over 200 but it does flex a lot at that point and I assume it is weakening when it flexes.