I'm in the process of developing a proper web front end for exploring the Iliad, and in producing my deck directory, I ran into the problem of how to curve the decks. Beyond the obvious issues with living inside of a centrifuge, there is the problem of plumbing. What got me started on this issue was, oddly enough, the fate of the IJN Taihō.
The vessel was one of most state of the art carriers in Imperial Japan's Navy. And it was done in by a single torpedo strike. Not because the torpedo itself sunk the ship. Because the Torpedo disrupted a bunch of piping that led to aviation fuel forming pools inside the structure of the ship, and not draining. That fuel, over several hours, evaporated into clouds, and through a bit of ineptitude on the part of a green crew, essentially turned the entire vessel into a fuel-air bomb. A spark somewhere on the ship (inevitable on a vessel that size) set off fuel-air mixture and ... boom.
The tale made me think about the importance of proper drainage on a vessel. I work with the problem in passing in my day job modeling naval vessels. But mostly from a "is the drainage system working" perspective. I hadn't had a clue about how to properly design a drainage system.
And in true Sean fashion... I decided to teach myself. I'm going to discuss how water drains here on Earth, and then I'm going to expand on that to explain the difficulties on getting water to drain in artificial gravity.
Here on the Earth's surface, everything is accelerated toward the core of the planet. What holds us steady is the ground pushing back. In a drain system, we use this natural accelleration to guide water from where we don't want it to pool to where we do want it go.
It turns out there is a formula perfected over thousands of years that describe how steep a slope is needed to ensure that water moves from one end of a pipe to the other in the direction we expect it to go. Here's an external article that goes into detail. The reason why smaller pipes need steeper slopes is because of surface tension. More slope is needed to overcome the force of the water sticking to the walls of the pipe.
When I first designed the decks of the Iliad, I just kept things flat.
To the untrained eye, this would be the ideal arrangement for a ship under constant accelleration. A ship moving like this actually experiences proper gravity, as if the ship was just a building sitting on the surface of the Earth.
From a drainage perspective, though, it's not ideal. While you look at buildings and think the floor is flat, a great deal of care goes into sloping floors so that the occasional coffee spill or overturned mop bucket ends up in a drain. And that fluids that reach the drain are transmitted down the pipes and out to the sewer. The pitch is imperceptible, about 1/4 of an inch per foot.
When the ship starts rotating, however, that flat deck stops working nicely for you. At first I was considering the effect of gravitation on the crew members.
That diagram is a bit of an exaggeration, but what I'm trying to communicate is that the edges of the deck, because that are further away from the hub of the wheel, experience more accelleration. This means water spilled on the deck would flow away from the center of the deck and towards the edges.
Next I considered a deck that matched the curve of the imaginary radius from the hub of the wheel.
A deck that is a perfect circle spinning around a central hub will produce uniform accelleration along all points. In rotation mode, down is perpendicular to the deck. In constant accelleration mode, the deck is slightly hilly on the sides. You would think this would be perfect for drainage... but...
We have to consider Coriolis forces. The deck in rotation mode is moving. Water moving in the direction of motion is actually pulled backward. Water moving opposite to rotation is accelerated. We don't just have to factor on water moving outward. We have to factor that water is going to be propelled opposite the direction or rotation.
Long story short, if we want to look at where water is going to pool on a deck shaped like this:
Which is good to know. If we install drains on that side of all compartments, we will have a pretty effective drainage system. The problem is when we consider where the water is going to drain when the ship in in accelleration mode:
In that configuration, water will pool at the lowest part of the deck. Which is an entirely different part of the floor. That also dictates an entirely different direction to route pipes. At least if you want them to empty of water (and whatever was the water was carrying, namely sewage.)
There are a couple of schools of thought. One is to use pumps to actively move water around. Bad idea, pumps need energy. Pumps break down. The other thought is to have two different plumbing systems. But by that point you are negating the entire purpose of having the habitat rotate.
In my minimal research I stumbled on the fundimental design of the Centrifugal pump. What if we designed the floors of the vessel to mimic the volute of a Centrifugal pump? The gravity ring spinning would then be acting as one giant pump. One giant pump that we were intending to keep running anyway, for other reasons.
This is accomplished by building a bias into the design of our decks to reflect one design direction of rotation. Instead of a flat deck, or a circular section, we use a spiral. (Well section of a spiral.) That spiral constantly increases the radius of the deck as we travel opposite the direction of rotation.
I have to work out the exact equation for this curve, but essentially we match the curvature of the the radius of the centrifuge until we reach the bottom of the bowl. In constant accelleration, this arc is a gentle (ish) hill that may be slightly steep at points, but which will draw water down toward the bottom of the sphere. In rotation, this same portion of the curve is technically flat. But the Coriolis effect is going to pull any fluid resting on that "flat" surface in opposite of the direction of rotation.
Slightly before we reach the bottom of our bowl, we change the curve. From that point on, the slope needs to be as shallow as we can make it. Too flat and water will not drain in constant accelleration. Too steep and water will pick up some wicked speed through the pipes when we are draining. Fortunately there is some play in the plumbing math. While the minimum slope for small pipe is 1/4 inch of drop per foot, it can be up to 3 inches of drop per foot before we start running into trouble.
The next thing I realized is that all of our pipe systems are going to need somewhere to drain into once they reach the end of the deck. My first thought was a massive soil pipe running down the one side of the sphere:
And my immediate thought was "no way that would work." Water would pick up too much speed coming down those drainage stacks and cause all sorts of hate and discontent if something ever backed up. Well... I decide to look at drain stacks are designed for skyscapers. And lo and behold I learned that the speed of water through a drain pipe is governed by air pressure. Water is not compressible, so to leave a pipe something must take its place. Either more water or air. If a drain doesn't have a vent it doesn't drain. And the speed of the drain can be directly controlled by the size of the vent.
Drain pipe design solved (ish), I next had to come up with where the water was draining to. While the habitat is surrounded by water, you would not want to open a hole into that body of water and pump water through it. As soon as the pump stops, water will siphon in, and keep flooding the habitat until the water level inside the sphere equals the level outside the sphere.
You also don't want a giant tank at the bottom, because eventually that puppy is going to fill up. So I get the idea that we do the bulk of our waste treatment at the bottom of the sphere, and then pump that treated waste water up, out of the sphere, and into the giant tank that forms the cosmic ray shield. All it does it block radiation, we don't really care about how clean it is.
For agriculture purposes, that treated water can be pumped right back onto a field to irrigate crops. For drinking water and industrial purposes, reservoir water can be pumped out, purified and stored in purified water tanks for later use. The nice part is, but placing those tanks at the top of the sphere, either the accelleration of the vessel or rotation of the ring provide the water pressure for your system. Tanks on top with pipes running straight out of them to your end user.
But then we have to address an elephant in the room. Nuclear isotopes. The environment of deep space is constantly bombarding the vessel with cosmic rays and high-speed nutrons. Those rays and particles collide with molecules in the reservoir and produce exotic nuclear isotopes that, while in small quantities are not a health hazard, but as they build up over time, they have the potentital to cause growth issues for crops and illness in individuals. We also need to account for the occasional screw up where somebody accidentally dumps heavy water from the power system into the municipal water system.
The Iliad is designed to be a self-contained colony when it reaches its destination solar system. And part of that self-sufficency is an on-board heavy-water refining facility. Periodically, water is pumped out of each reservoir and replaced with depleted water from the Girdler Sulphide process. This will ensure that isotope concentrations remain well within safe guidelines for nuclear exposure.