Interesting. I would expect that both air pressure and the tensile strength of your enclosure would scale directly in proportion with the area of the enclosure.
But some thought experiments about enormous pools - ponds, really - make me think that you're correct.
Indeed, looking it up, in a sphere, the stress (in units of pressure) is equal to (pressure x radius) / (2 X thickness). In a cylinder, it's worse - axial stress is the same as a sphere, but hoop stress is (pressure x radius) / (thickness)! You also have to think about increased stretching in the hoop direction compared to the ends of a flat-plate cylinder, which should probably be a sphere or complicated ellipsoidal shape to best deal with the stress.
Applying these equations, an ideal steel (assume an alloy with tensile strength 700 MPa) sphere with 1cm thick walls would have a maximum radius of 138.2m. A cylinder would have half the radius. Using Kevlar (tensile strength 3620 MPa) increases the radius by 3.62.
Doubling the thickness doubles the allowable radius but also increases the mass of our sphere from an already staggering 136 metric tons (3 Falcon Heavy payoloads) to an astonishing 546 metric tons, or more than 10 Falcons Heavy.
Kevlar is, of course, lighter than steel by about 5 times, but that many tons of Kevlar will not be cheap. That's about 0.5% of the total world annual production of the stuff!
We won't be going up to inflatable planets anytime soon.
But some thought experiments about enormous pools - ponds, really - make me think that you're correct.
Indeed, looking it up, in a sphere, the stress (in units of pressure) is equal to (pressure x radius) / (2 X thickness). In a cylinder, it's worse - axial stress is the same as a sphere, but hoop stress is (pressure x radius) / (thickness)! You also have to think about increased stretching in the hoop direction compared to the ends of a flat-plate cylinder, which should probably be a sphere or complicated ellipsoidal shape to best deal with the stress.
Applying these equations, an ideal steel (assume an alloy with tensile strength 700 MPa) sphere with 1cm thick walls would have a maximum radius of 138.2m. A cylinder would have half the radius. Using Kevlar (tensile strength 3620 MPa) increases the radius by 3.62.
Doubling the thickness doubles the allowable radius but also increases the mass of our sphere from an already staggering 136 metric tons (3 Falcon Heavy payoloads) to an astonishing 546 metric tons, or more than 10 Falcons Heavy.
Kevlar is, of course, lighter than steel by about 5 times, but that many tons of Kevlar will not be cheap. That's about 0.5% of the total world annual production of the stuff!
We won't be going up to inflatable planets anytime soon.