[Spaceships] Cosmic rays and mass shielding

[Michael Thayne]

TLDR; I'm wondering if the rules for radiation in Spaceships 5 grossly understate the effectiveness of mass shielding against cosmic rays. Possible fix: cosmic rays divide e.g. vacc suit Protection Factor (PF) by 100, but very thick mass shielding (like you'd use on large stationary colony) provides full PF.

Rationale: according to Wikipedia, a NASA study suggested you'd need about 4 metric tons of shielding per square meter to get radiation exposure from cosmic rays down to levels experienced on Earth's surface. Four metric tons per meter is a lot when you'd need to launch the shielding into orbit using TL8 chemical rockets, but a back-of-the-envelope calculation suggests it's possible for a small habitat module on a ~SM+7 vehicle, if the "habitat" section of the ship is mostly mass shielding.

Don't take the SM+7 to literally; I originally tried to make some pessimistic assumptions and got SM+8. The point is that it's much smaller than what you'd get if you assume the desired level of protection from cosmic rays is a PF of around ~20,000, which (extrapolating out from the table in Spaceships 5) requires a space colony of SM+19 or more.

Am I right that the "divide PF by 100" rule shouldn't be used for mass shielding? Or is Wikipedia woefully out of date?

[Anthony]

The rules for PF in Spaceships 5 don't scale properly with thickness, though I think you're doing math wrong as well.

A SM +7 habitat module is 15 tons mass. If we assume 12 tons of that is shielding, it's enough to shield a 0.5 meter sphere (surface area 4pi*r^2, or pi square meters). That's not enough to fit 2 cabins.

Spaceships largely abstracts volume, but according SS1 p7, a sphere will be half the length, so a SM +7 ship would be a sphere with a radius of 7.5 yards or 6.85 meters. That works out to a surface area of 591 square meters. One armor module shields 1/3 of the surface, and has a mass of 15 tons or 13.6 metric tons, for an areal density of 0.07 tons per square meter. That is, incidentally, a thickness of about 9mm steel and would have DR 25 for steel, which is decently consistent with the armor rules.

To get 1 module up to 1 ton per square meter requires SM +14 (so 4 armor modules per section will do the job); to get it up to 4.5 tons per square meter requires SM +18. Note, however, that just about any non-habitable module can be used as shielding, not just armor, so SM+14 will likely do the job.

[AlexanderHowl]

If you assume that fuel tanks have enough volume for liquid hydrogen (~14 cubic meters per metric ton) and generalize that volume equivalent for all components, then the protection makes sense. An SM+10 spacecraft would be 140,000 cubic meters and, with a length of 100 meters, that would make it a cylinder with a radius of 20m (which fits with the spin gravity capabilities of unstreamlined spacecraft). It would have an area of 15,000 square meters, meaning that habitats in the core would benefit from a maximum of 2.6 metric tons per square meters with full fuel tanks (assuming an area of 3500 square meters). As fuel tanks become empty, mass shielding decreases, but the GURPS figures seem to be an approximate average when it comes to cosmic rays. The spacecraft would also have 100 kilograms per square meter of armor (assuming one armor component per section), which would translate to 10 grams per square centimeter (would would be 12.5 mm of steel).

[Michael Thayne]

Originally Posted by Anthony

The rules for PF in Spaceships 5 don't scale properly with thickness, though I think you're doing math wrong as well.

A SM +7 habitat module is 15 tons mass. If we assume 12 tons of that is shielding, it's enough to shield a 0.5 meter sphere (surface area 4pi*r^2, or pi square meters). That's not enough to fit 2 cabins.

Spaceships largely abstracts volume, but according SS1 p7, a sphere will be half the length, so a SM +7 ship would be a sphere with a radius of 7.5 yards or 6.85 meters. That works out to a surface area of 591 square meters. One armor module shields 1/3 of the surface, and has a mass of 15 tons or 13.6 metric tons, for an areal density of 0.07 tons per square meter. That is, incidentally, a thickness of about 9mm steel and would have DR 25 for steel, which is decently consistent with the armor rules.

To get 1 module up to 1 ton per square meter requires SM +14 (so 4 armor modules per section will do the job); to get it up to 4.5 tons per square meter requires SM +18. Note, however, that just about any non-habitable module can be used as shielding, not just armor, so SM+14 will likely do the job.

Two issues: first, Spaceships doesn't say spherical ships will be half the listed length, it says less than half. Your numbers give a density of 20% of the density of water, which as Alexander Howl notes is possible for a ship using liquid hydrogen reaction mass, but if much of the ship is armor, water tanks, etc. the radius will be smaller than you assume. If the ship is exactly equal in density to water, the radius will be roughly 4 meters.

More importantly, the surface area you need to shield is the surface area of the occupied systems—not the surface area of the whole ship. In the extreme case, imagine only two core systems are occupied, the rest of this spherical ship can serve as mass shielding. And suppose (again this is very rough, like Spaceships built on hand-wavy approximations) that all systems are equally dense. Then occupied systems are 10% of the sphere's volume. If they themselves are a sphere at the center of the big sphere, the little sphere will have a radius of 4/cbrt(10) ~= 1.87 meters. So your mass shielding will be 2.13 meters thick.

Since 1 cubic meter of water = 1 metric ton, that's the equivalent of 2.13 metric tons of water mass shielding. That's not quite enough, but we can get what we want at SM+9—going up to SM+14 might be nice if we want a large proportion of the ship to be open space, but it's not strictly necessary.

Now here's where the big discrepancy with Spaceships rears its ugly head. The table in SS5 indicates that 6 systems of mass shielding + SM+9 = PF 450. But since it's a core system, we need to double it. So PF 900. If we're dividing PF vs. cosmic rays by 900, though, that's only a PF of 9! So if this SM+9 station is, say, an Earth-Moon Lagrange point colony, you're taking 1 rad every 9 weeks. That's acceptable if you're an astronaut spending a few months there, but bad if you want to spend your whole life there.

If we divide PF from heavy mass shielding vs. cosmic rays by 5, then we get a PF of 180, which seems roughly consistent with Wikipedia.

[Anthony]

Originally Posted by Michael Thayne

Two issues: first, Spaceships doesn't say spherical ships will be half the listed length, it says less than half. Your numbers give a density of 20% of the density of water, which as Alexander Howl notes is possible for a ship using liquid hydrogen reaction mass, but if much of the ship is armor, water tanks, etc. the radius will be smaller than you assume.

Most designs will have a substantial amount of empty space. 20% of the density of water is a fair estimate for the density of a vehicle that includes habitats and maintenance access spaces, though density can be higher for some specialized vehicles.

Originally Posted by Michael Thayne

More importantly, the surface area you need to shield is the surface area of the occupied systems—not the surface area of the whole ship.

Which are notoriously low density components, and should be assumed to have a density of less than 10% of water.

[Michael Thayne]

In Spaceships, "occupied systems" aren't open space. A bunkroom on an SM+7 ship, according to Spaceships, is 6.7 tons of life-support systems (plus places to eat and sleep and go to the bathroom), and 0.8 tons of people. The "deck plans" section of the Spaceships designers notes assumes habitats are less dense than most other systems, but not that much less dense. It also recommends no more than 15 1-yard hexes for an SM+7 system. Since a unit hex has an area of 0.87 square units, and assuming a height of eight feet, that's about 35 cubic yards for one system, or 53 cubic meters for the two core systems in the math above. In spherical form, the radius is ~2.3 meters. A little more than in my previous math, but closer to my math than your assumption that we need to shield a sphere of 6.85 meters radius.

[Michael Thayne]

Spaceships is obviously not wholly realistic, but seems to be broadly in line with stats from the Space Shuttle. The total volume of the crew compartment is 2,325 cubic feet (~66 cubic meters), but that's not all habitat—it also includes the flight deck (Control Room, in Spaceships terminology).