Vacuum collapse — the same wall holds far more pressure in than out

One tank, three metres across, with a full vacuum inside it. The only thing you are changing is how thick the wall is. Drag upward for thicker plate, down for thinner; the arrow keys do the same. End is thirty millimetres; Home is three. Watch how far apart the two markers stay. Sound is off until you turn it on.

What you are looking at

Push from the inside and the wall goes into tension. Every part of it pulls against every other part, the shell holds its shape, and the question is simply whether the material is strong enough. Double the thickness and you can hold twice as much. It is the most forgiving kind of structural problem there is.

Push from the outside and the wall goes into compression, and compression in a thin shell is a different animal. Long before the steel is anywhere near its strength, the shell finds it cheaper to stop being round: a slight flat spot gets flatter, the flatter it gets the less it resists, and the whole section folds in on itself. Nothing yielded. The tank was not overloaded. It simply stopped being a circle, and a shape that is not a circle cannot carry pressure from outside at all.

Because that is a stiffness problem rather than a strength one, the capacity goes as the cube of the wall thickness — which sounds enormously favourable until you notice it is a cube of a number that starts hundreds of times lower. Doubling the wall multiplies what it holds in by two, and what it takes from outside by eight, and the outside figure still loses.

The last part is the part that kills tanks: the whole available vacuum is one atmosphere. You cannot pull harder than that, which is precisely why nobody treats it as a load. A vent that frosts over, a blinded nozzle nobody took off, a tank of hot liquid that cools overnight, a drum being emptied by a pump — each of them is capable of the entire load, and it is free.

The two things worth taking away

A pressure rating tells you nothing about vacuum. The plate that holds several atmospheres in is not thick enough to take a fraction of one atmosphere out, and no amount of reading the nameplate will reveal it, because the nameplate is answering a different question. If a vessel can ever see a vacuum, it needs to have been designed for one.

Thickness is the expensive answer and usually the wrong one. Getting this tank to survive a full vacuum on plate alone takes something like six times the wall it needs to hold pressure. Stiffening rings do the same job for a fraction of the steel, because they attack the stiffness the shell is short of rather than the strength it already has. And a vacuum breaker — a valve that lets air in — costs almost nothing and removes the load entirely.

What is not verified

Stated plainly, because a piece whose value is trustworthiness should not overclaim. The first list is the part that would change how you read the result. The second is scope — true, worth saying, and not load-bearing.

• No engineer has reviewed this. If you are one and would check it, REVIEW.md says what would actually help and is meant to cost about fifteen minutes. The relations are the standard membrane-stress and long-cylinder collapse expressions, and the built-in checks confirm the arithmetic — but that check is the author's own, not a pressure-vessel engineer's.
• The collapse figure drawn here is the OPTIMISTIC one, which is the dangerous direction. The elastic formula assumes a perfectly round shell. Real vessels are not round, and a small initial out-of-roundness knocks the collapse pressure down hard — which is why the codes apply a substantial design factor rather than using the elastic value. Both are drawn, and the gap between them is not a safety margin so much as an admission of what the formula does not know.
• A long cylinder, with no help from anything. No stiffening rings, no end closures near enough to matter, no attached pipework. Ends and rings raise the collapse pressure substantially, and designing for external pressure is largely the business of arranging them.
• Elastic collapse only. On thicker walls the shell can yield before it buckles, and the governing expression changes. This piece stays in the range where the elastic one governs, but does not draw the boundary.

Scope, for completeness. True of the model, and none of it changes the answer above.

• The section drawing is indicative, not to scale. The two-lobe mode is the right one for a long cylinder, but the depth it folds to is chosen to be visible rather than calculated, and the wall is drawn about nine times thicker than it really is — at true scale the thickest plate here would be one per cent of the radius and you could not see the control working. Nothing the piece claims depends on either: the numbers are all in the panel on the right.
• One diameter, one material, one allowable stress. Diameter matters enormously — the collapse pressure goes as the cube of thickness over diameter, so a tank twice as wide is eight times weaker against vacuum at the same wall.

Commissions

The subject changes; the method does not. If you have a failure mode, a mechanism, or a process that people keep getting wrong because the diagram cannot move, that is the shape of problem this suits. You get one file, the checks that hold it honest, and the notes explaining every decision including the ones that were reversed. Commissions start at £4,000 and take three to four weeks from an agreed brief. yinxueshi1017@gmail.com

Not commissioning anything? Still worth an email. If your version of this failed differently — other geometry, other numbers, a mechanism this piece leaves out — tell me in one line. Corrections are the main thing that decides what gets built next.