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What is the optimum shape for a spacecraft?

So I've already read this link, and a few other similar ones, and the main issues I am already aware of... but yet it still seems like a large majority of the designs for rotating (for 'gravity') ships and stations use a torus, or perhaps a cylinder.

Why is this?

The main issue I have, is the radiation shielding. It seems that if you're using water (for example), you would need 2 tonnes of water for every square meter of surface area. So if you use a torus, that's a huge amount of extra weight. A sphere is (by a fair margin) a shape with a better volume/surface area ratio. And saving those 2 tonnes per square meter would make your fuel consumption significantly better.

Is there something I'm missing? I suspect there is. In my head a torus just seemed like a much more 'streamlined' shape (not aerodynamically, just much less waste of volume). But it seems like the sphere gives you much more volume for much less mass, mostly due to the shielding requirements?

nirurin
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A spherical spinning station faces a number of problems. First, different latitudes will have different amounts of centrifugal "gravity" (due to different radii to the central axis), which is fine under some scenarios but not at all helpful if you only care about the parts that are at your target acceleration and maybe a bit at free-fall in the middle (which is how most spinning stations seem to be designed). In other words, a cylinder or toroid trades away a lot of total interior volume : mass ratio to maximize the interior volume at desired radius : mass ratio. Additionally, a spherical spinning station is going to try to become an oblate spheroid (as the earth itself is) due to the same centrifugal force pushing outward hardest along the equator, which poses some design difficulties and requires more mass to compensate (the earth's solution - fill the middle with solid or molten rock and metal to keep the bulge under control - is obviously not viable here).

Finally, you're talking about "a large majority of the designs" without mentioning if you're considering any other filter, which - for anything that has never yet been built and would be very expensive to build - means you're implicitly getting a filter for the minimum viable product (MVP). The MVP for a spinning station isn't trying to maximize the interior volume : mass ratio, it's trying to get something that has any usable amount of interior volume at the desired acceleration, for the minimum cost. To use some made-up numbers, a station with 20x the interior volume for merely 2x the cost just might not be worth it, if you don't need that much volume.

CBHacking
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  • "To use some made-up numbers, a station with 20x the interior volume for merely 2x the cost just might not be worth it, if you don't need that much volume."

    I agree with this, and this was essentially the logic I was using when I was originally considering a torus-style design. However that only worked up to the point where I realised the torus needs a huuuuge tonnage of radiation shielding because of the increased surface area. In theory, some of that tonnage could be used to turn the station into a sphere instead, ending up with essentially 'free' extra volume.

     – nirurin Nov 05 '19 at 22:43
  • In the vast majority of orbits, you don't really need radiation shielding on any part not directly exposed to the sun. If you're measuring total surface area, you're going to get a vastly inflated number from a torus. Depending on orientation, you could restrict shielding to only the outer edge, or to only the top (or bottom) faces, and you wouldn't need to shield most of the middle of the torus either. – CBHacking Nov 06 '19 at 00:06
  • This isn't being thought of as a LEO design. It would be for other parts of the solar system, so no protection from the magnetosphere. Mars, for instance, won't protect it much. Unless you stay shielded behind the planet, but then you can't use solar panels at all.

    Edit: Also I thought that cosmic radiation was at least as dangerous as solar radiation? So you'd need shielding on all surfaces.

     – nirurin Nov 06 '19 at 00:13
  • Here are 2 factors to consider. First, the shielding doesn't have to rotate. The centrifuge can be inside the shell of shielding. That reduces the structural integrity all that mass would need if it were rotating. It also reduces the gyroscopic effect a lot, allowing easier attitude changes. – Johnny Robinson Nov 08 '19 at 03:17
  • The other factor is how the weight ratio improves with size. If a half meter of ice is needed for shielding, that would be a huge portion of the weight for a habitat that is 3 or 4 meters across. However as the overall size increases, the thickness of the shield stays the same. If the habitat were 50 meters across or more, the shielding would be a much smaller portion of the total mass. – Johnny Robinson Nov 08 '19 at 03:23