# What is the optimum shape for a spacecraft?

I understand that these days a spacecraft design is very much centred on what can be lifted into space by current rockets, hence the modular, cylindrical shape of the ISS. So, with current manufacturing and design technologies and under the huge (unrealistic) assumption that there were no restrictions on lifting materials/components into space, what would be the most optimal shape for a spacecraft in terms of some of the following example factors (others are welcome)?

• Efficiency
• Construction practicality
• Internal navigation by crew
• Etc.

Would it be a sphere? cube? (I can smell the Borg...)

I should make clear that I'm not interested in a spacecraft that has to go near any atmosphere so there doesn't need to be any consideration for aerodynamics.

• "assumption that there were no restrictions on lifting materials/components into space" - this means we could build it any size/shape on the ground, then put it into orbit. So "construction practicality" is a bit difficult for me to to comment on. I think a sphere would be the most weight-efficient for internal pressure (atmosphere) by the way. – Andy Jan 13 '16 at 11:27
• Inflatable or otherwise expandable spacecrafts is a very practical way to make stuff larger in space than at launch. They should be pretty "solid", meaning that they don't have any holes unless desired. Spherical or cylindrical for habitats and flat for solar panels, radio dishes, solar sails. – LocalFluff Jan 13 '16 at 11:45
• Yeah exactly! The construction practicality aspect of this question was more in terms of which shape would be 'easier' to assemble within the same volume. I will remove this from the question if it's not necessary however. – Phizzy Jan 13 '16 at 11:48
• clearly suboptimal: i.stack.imgur.com/7xvoT.gif – uhoh Dec 3 '18 at 15:13

Spheres are best, but cylinders are easiest to manufacture

For the most internal volume compared to the surface area, and hence the smallest possible mass, a sphere is the ideal shape for a spacecraft. The orbital module of the Soyuz spacecraft is approximately a sphere:

Most construction techniques in use are based on metal plates. Therefore, spacecraft shaped like cubes or cylinders (a bent plate) are easy to manufacture. The sharp edges are however less optimal than the sphere to withstand internal pressure.

For long stays in space, it is beneficial to have some sort of artificial gravity induced by rotation. Cylinders and toruses are then good options. They are also rather easy to inflate. (that is a launch constraint, but an important one)

A spacecraft with artificial gravity must not necessary have to be of a curved shape, two spacecraft, or one spacecraft and a counterweight with a tether in between can basically do the same thing.

For some types of propulsion, most importantly nuclear-electric, solar sails, or solar-electric, huge areas of radiators, sails, or solar cells are necessary. That pretty much determines their shape. (huge but flat, with a long truss-segment in the middle)

Different parts of a spacecraft has different requirements, hence, you may use different shapes for them instead of an all-in-one trade off. Again, the Soyuz is an excellent example of geometry, using a sphere for the orbital module, an aerodynamically blunt body shape for the return capsule, and a cylinder for the equipment module.

Landers

One of the top priorities for a lander is to have a large base to prevent it from tipping when landing on the surface. Despite initial surveys from unmanned probes in orbit of for example the Moon, you can never be totally sure about the usefulness of a particular landing site. The Apollo 11 did for example change the target landing site in flight. Therefore, landers are typically very wide, so they do not fall over. The descent stage is often-shaped like a polygonal prism, with a symmetry depending on the number of landing legs. (three for a minimum configuration, four for a little more stability , or five or more for redundancy and extra stability).

The Apollo lunar module descent stage had an octagonal shape, corresponding to its four-fold symmetry:

• Why orthogonal, why did it have four legs to land on? Three would guarantee a plane while a "fourth wheel on the wagon", so to speak if you get the pun, might redundantly be hanging above ground, above a small depression. – LocalFluff Jan 13 '16 at 14:29
• @LocalFluff, yeah, it does not actually add a lot of redundancy either, to maintain stability, even if one of the legs broke, you need at least five – Hohmannfan Jan 13 '16 at 14:35

A large-enough donut or cylinder would allow for artificial gravity through rotation. Diameter would have to be several hundred m at least.

• For earth gravity, 100m dia is right on the limit. a=r*omega^2 . Substituting and rearranging: omega=sqrt(earth gravity 9.8m/s^2 / radius 50m) = 0.44 radians per second. each rotation takes 2*PI/0.44 =14 seconds. I reckon you'd get used to it. It's true that if you want to double the rotation period while maintaining the same acceleratiion, you have to quadruple the distance. For a given size ship, humans would probably be most comfortable with somewhat less than earth gravity in order to avoid the need for high rotational speeds. – Level River St Jan 14 '16 at 0:12

Due to gravitational forces and figuring out how they would affect the ship a sphere would be the most beneficial shape

• Welcome to space.stackexchange. This is an interesting point, but we would normally look for a more detailed argument in a stackexchange answer -- What gravitational forces are you thinking of, and why would "figuring them out" be both difficult and important. – Steve Linton Dec 1 '18 at 13:37
• The advantages of spheres are covered in the accepted answer. – Organic Marble Dec 1 '18 at 14:41

"current manufacturing and design technologies"

"no restrictions on lifting materials/components into space"

"I should make clear that I'm not interested in a spacecraft that has to go near any atmosphere so there doesn't need to be any consideration for aerodynamics."

Assuming these parameters, lifting something to low earth orbit requires this something to structurally withstand roughly 2-3g during launch. So there is no logic behind building one sturdy spacecraft on the ground, able to survive launch, and then carrying dead structural weight for the rest of its lifetime.

Instead, launch raw material and one huge building or printing factory in LEO first, then produce the spacecraft there, and build it the lightest (or best fuel/structural mass ratio) it can be along the constraints or accelerations it will face.

Since there's no launch weight restrictions from Earth, one of the best missions to achieve could be sending humans towards one neigbouring stellar system, using project Orion propulsion system, in a very very huge spacecraft, tuned to constant 1g acceleration along thrust vector. Hence this spaceship will be built in LEO so that it can withstand no more than 1g (+safety margin).

The best shape for maximum volume/surface ratio is the sphere (as mentioned in previous answer) so the shape of this massive thing could be a prolate spheroid aligned along 1g acceleration - or one eggly shaped nuke spitter human colony spacecraft -

I think that spaceships in the far future will be analogous to biology. They will constantly reassemble and reorganize themselves to repair damages from radiation and decay and to adapt to changing environments or desires. Or simply because one structure obtained reveals that another structure is more attractive to attain in an evolutionary fashion of discovery.

Life on "spacecraft Earth" has done this spontaneously. Fundamental logics of physics, geometry and economics set some constraints, but lifeforms still vary from tiny archean bacteria to huge reptiles and mammals to distributed ant and bee colonies as genetic unit. The wisdom of this billion year long evolution seems hard to beat. Lack of gravity and lack of interaction with atmosphere/hydrosphere removes important constraints to shape.

Tethers can be very useful. Microbiology seems to be full of microscopic "hairs" which guide transports and communication. In microgravity tethers are useful to simulate gravity by rotation, and maybe for launching or capturing smaller spacecrafts.

• Apologies if I have misinterpreted your answer but I'm not clear on how this address my question? Current technologies was specified. – Phizzy Jan 13 '16 at 12:27
• Don't apologize, I now see that you were more current than my wild speculations. I thought it was an open question which doesn't have an obvious answer like "42" :-) – LocalFluff Jan 13 '16 at 14:17
• LocalFluff thinks in good direction. Currently in labs are tested at least 2 key technology, suitable for that. Swarm logic and hardware implementations of working small robots. That is promising approach, and ppl try to figure how to implement it in better way in hardware and software. Cube is favorite form atm. So borg style why not. Second key technology - artificial actuators, based on carbon nanotubes. So we already try to invent stuff which should adapt to task and be more universal, or at least to help our tools to be more adaptive. Currently working examples are Mammoet SPMT. – MolbOrg Apr 11 '16 at 8:37