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1$\begingroup$ There's a big problem here. The skin thickness must scale with radius for a given pressure and material stress. $\endgroup$– Abdullah is not an AmalekiteCommented Aug 20, 2021 at 12:42
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$\begingroup$ You are correct. If we assume we need twice the skin thickness for twice the radius, we would get 21,56 kg per m³ wich would be worse. Maybe we can use secure.outokumpu.com/steelfinder/Storage-Tank/Default.aspx to calculate the needed thickness? $\endgroup$– Georg PatscheiderCommented Aug 20, 2021 at 13:26
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$\begingroup$ Also, my toy model assumed uniform wall thickness. In reality, the walls at the bottom of the tank will be thicker, because they need to support more load. $\endgroup$– Georg PatscheiderCommented Aug 20, 2021 at 13:27
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$\begingroup$ One important point is that the top and bottom surfaces of the tank do not experience more pressure if we increase the radius, as long as we keep the height of the cylinder the same (the weight of the column of propellant over a unit area of steel at the bottom stays the same). I do not know how to calculate the pressure increase on the side walls. $\endgroup$– Georg PatscheiderCommented Aug 20, 2021 at 13:47
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$\begingroup$ Rocket tanks are not pure pressure vessels, they are also columns directly providing mechanical support to stages above, anchoring components of the rocket, withstanding aerodynamic forces while flying at non-zero angles of attack, etc. They also can carry insulation or protective coatings that scale more or less directly with surface area. So it's not a straightforward application of square-cube scaling, but larger tanks are more structurally efficient. $\endgroup$– Christopher James HuffCommented Aug 20, 2021 at 14:55
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