# Optimal aspect ratio of a cylinder under internal pressure

I was trying to imagine an ideal cylindrical vessel under internal pressure. Assuming it is a thin walled pressure vessel.

I.e. For storing a given Volume of contained fluid ( ie volume of cylinder) at a known pressure what would be the optimal aspect ratio that minimizes the amount of steel ( or any other material that the cylinder is built from)

If I use the usual formulae for thickness of a vessel under internal pressure that's proportional to both P and diameter. If I do the math then the volume of steel comes out as independent of the aspect ratio entirely.

In that case why are pressure vessels mostly long and narrow diameter? Of course the thickness is indeed proportional to dia but the d^2 term also appears in the Volume contained equation.

• That would be a sphere: greatest volume cf external surface area. Feb 19 at 8:02
• The primary structural issues are the deflection and stress risers in the are where the end caps join. There are three typical end cap designs, and those have been studied to death by NASA and others. There are some closed form solutions and a lot of heuristics for local reinforcements at the connection of the ends. Feb 19 at 12:14
• Yep, for given internal pressure and material stress limit, you'll get thickness/diam ratio independent of length. The ratio of sidewall_volume / internal_volume will also be a function of this t/d ratio, and again independent of length. That leaves the endcaps as Phil says , and they should get lighter with smaller d. Feb 19 at 14:26
• @SolarMike but the required thickness is a function of curvature. The only reason a pressure cylinder would weigh more than a pressure sphere is that the axial stress in the cylinder shell is less than the hoop stress, so the sphere ends up being a bit more efficient, at least as far thin-wall approximations are concerned. Feb 20 at 0:14