Personally I struggle to visualize how that transfer car concept is engineered to work. I'm not questioning it, I just wish I had a model, or some art or a video, something that could help me conceptualize it.
Imagine that the gravdeck is a long chain of subway cars bent into a circle. It runs in an endless, circular subway tunnel somewhere inside the WarShip.
Right beside that tunnel is another circular tunnel. Instead of being filled with a complete, rotating circular train, it just has individual, elevator-sized cars.
1. If you're in the non-spinning part of the ship, press the call button like an elevator.
2. A transfer car pulls up to your door, docks.
3. Door opens, you float in, door closes.
4. Hit the transfer button.
5. Transfer car begins moving, running on track beside the gravdeck.
6. When the transfer car matches the speed of the gravdeck, it pulls up beside a door on the gravdeck and docks.
7. Door opens, you walk out, door closes.
8. Transfer car is free for another call.
Reverse to go back to the non-spinning parts of the ship.
I wondered if there might be no spokes at all, if it might resemble something more like a train, wrapped around a cylinder. But I'm not sure that jives with physics.
That's how gravdecks and transfer cars work in ships. There's no need for spokes at all. Physics doesn't care so long as you're spinning in that circle.
Warship grav-decks don't have to be circumfural, do they?
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There's still stuff in there, and it needs to be secured unless you want to have it breaking lose and banging around. So, yes it does matter, it matters a hell of a lot unless you want to have a treadmill rip lose, bash its way across the gym, and then punch a hole in a pressurized bulkhead that exposes the entire gravity deck to vaccum.
Most gravdecks should be a ring around the KF core of a JumpShip or WarShip. When under spin, the floor should be aimed at the ship's broadsides. When under thrust, those floors will become walls, rendering the gravdeck uninhabitable. As you pointed out, care will be required in design of things like toilet lids. The issues of loose objects, piping, plumbing, etc. require attention to secure them, but they were largely solved by 1962. The RP Flip even retains usable bathrooms (toilets and showers) after gravity shifts 90 degrees on it:
https://en.wikipedia.org/wiki/RP_FLIPHowever, there's at least one exception to the "ring around the KF core" approach: Matt Plog gave the Athena off-axis grav decks in a way I never intended when I wrote up the ship. Those are still unusable under thrust but they could, in theory, have spokes to a central hub rather than using parallel transfer cars.
https://www.sarna.net/wiki/Athena_(WarShip_class)