cylinder with convex endcaps?

There is another reason that convex endcaps can make sense.

Any spinning object whose greatest moment of intertia is not around the spin
axis is rotationally unstable. A wheel or thin disk is stable; a long
cylinder is not (and technically, a simple sphere is not, although if a
sufficiently large fraction of its mass is along the equator it can be).

Try to spin a long cylinder about its axis and any imperfections will -
unless dynamically countered - eventually induce a wobble which will
ultimately result in spinning end-over-end, probably not the spin it was
designed for!

Al Globus, in the paper "Kalpana One Revised", showed calculations that
suggest the largest width for a rotationally stable spinning cylinder is 1.3
times the radius.

But what counts, of course, is the mass distribution, and a cylinder with
convex endcaps has a greater fraction of its mass further from the center of
mass around the equator where you need it for stability, thus a larger
aspect ratio is possible.

The discussion of excessive stresses at the joint may be misguided. To a
first approximation, the total mass of the shell of any pressure vessel is
the total applied stress (enclosed volume times pressure) divided by the
tensile strength of the shell material (tensile strength per unit area)
times the density of the material. There are engineering formulas which are
more accurate, especially when the mass of the shell is large enough to
significantly contribute to the stress for a spinning structure.

But that implies that, to a first approximation, the stress is less for the
convex endcaps, thus less shell mass is required.

Also, the magnitude of the stress at the seam is identical to the stress at
the same (meaning every) point in a sphere - it is not greater at the seam,
although there is a transition from compressive to tensile stress which
means it is a shear stress.

And while we are on the topic of shell strength, I note that having 10
tonnes per square meter of shielding along the outer shell and inside of the
pressure vessel is exactly equivalent to having a second 1 atmosphere of
pressure. Thus instead of designing for 1 atmosphere (100 kpa), design for 2
atmospheres (plus a contingency, of course). It's not really that bad to
rotate yuur shield mass.

Stephen Covey

Director of Research & Development

Deep Space Industries

There is another reason that convex endcaps can make sense.

Any spinning object whose greatest moment of intertia is not around the spin axis is rotationally unstable. A wheel or thin disk is stable; a long cylinder is not (and technically, a simple sphere is not, although if a sufficiently large fraction of its mass is along the equator it can be).

Try to spin a long cylinder about its axis and any imperfections will - unless dynamically countered - eventually induce a wobble which will ultimately result in spinning end-over-end, probably not the spin it was designed for!

Al Globus, in the paper "Kalpana One Revised", showed calculations that suggest the largest width for a rotationally stable spinning cylinder is 1.3 times the radius.

But what counts, of course, is the mass distribution, and a cylinder with convex endcaps has a greater fraction of its mass further from the center of mass around the equator where you need it for stability, thus a larger aspect ratio is possible.

The discussion of excessive stresses at the joint may be misguided. To a first approximation, the total mass of the shell of any pressure vessel is the total applied stress (enclosed volume times pressure) divided by the tensile strength of the shell material (tensile strength per unit area) times the density of the material. There are engineering formulas which are more accurate, especially when the mass of the shell is large enough to significantly contribute to the stress for a spinning structure.

But that implies that, to a first approximation, the stress is less for the convex endcaps, thus less shell mass is required.

Also, the magnitude of the stress at the seam is identical to the stress at the same (meaning every) point in a sphere - it is not greater at the seam, although there is a transition from compressive to tensile stress which means it is a shear stress.

And while we are on the topic of shell strength, I note that having 10 tonnes per square meter of shielding along the outer shell and inside of the pressure vessel is exactly equivalent to having a second 1 atmosphere of pressure. Thus instead of designing for 1 atmosphere (100 kpa), design for 2 atmospheres (plus a contingency, of course). It's not really that bad to rotate yuur shield mass.

Stephen Covey
Director of Research & Development
Deep Space Industries