Introduction of "Taper-Nested" Friction Buffer Connection Scheme

Suffice it to say that a minimum viable case has been made for the engineering of the friction buffer connection points. However, the very day after I claim to have "solved" that problem, I noticed that another scheme is possible, and possibly even better. I will make this post as a brief introduction, and I apologize for the painful lack of illustrations this leads to.

Let me clarify the naming - the names refer to whatever kind of logic sets the pressure around the (moving) connection points (seals). You can see that this, combined with the velocity constraint, forces all of the other parameters to follow suit. That's why this taxonomy makes sense. In the taper-zero scheme, all seals were approximately at ambient atmosphere pressure. Note that all friction buffer sheets are at a slightly positive pressure in order to maintain their shape with a controlled leakage, and this extra positive pressure is not accounted for directly in the math (partly because there is no lower-bound, and partly because it may be small enough to neglect).

Imagine, instead, that the seals connect to the tube itself. It's irresistible to call this the "hull" of the artificial gravity tube. The interior is obviously where people live, but the exterior may be just a metal wall. Picture connection points all along the sloped part of the hull. There are 2 options for how to determine the spacing between those connection points:

1. Constant distance between each connection
2. Setting connection location based on a invariant relative velocity limit

Once I ran a few numbers, it quickly became clear that option #2 leaves the majority of the connection points clustered very close to the end opening (at small radii to minimize the velocity difference between the sheet material and the faster rotating tube). After chewing on this a bit, I find that this sets the stage for the central engineering tradeoffs for the friction buffer connection engineering.

Engineering Showdown between Solutions

Taper-zero connects sheet-to-sheet. This taper-nested scheme connects sheet-to-hull. Making the connections to the hull will give better predictability and stability, because the other sheets and highly deformable. The advantage of the taper-zero approach is that the relative velocities at the connection points are very slow and consistent, while at the same time they are evenly spaced and open to atmosphere for maintenance.

Now compare to the taper-nested approach. This scheme puts each friction buffer sheet fully inside of the next outer-most one. Getting to that connection to do service work on it will be much more complicated. Also, they will require awkward clustering toward the end if the relative velocity is kept constant. Alternatively, we can assume the constant distance spacing, and we find that the connection points have variable, and often quite high, relative velocities. This is riskier (but might be preferable with the advantage of the stationary hull), and it also imposes a meaningful air drag penalty. The additional air drag may be partially compensated for by increased spacing between sheets compared to the radially symmetric portion.

We're not done yet. Recall the central concession of the taper-zero approach - that the friction buffer sheets must have substantial material strength. This is partly to compensate for the radial acceleration of the air in its region, but mostly as a design tweak to keep the seal at close to ambient pressure (thus the "zero"). For the taper-nested approach, leakage air is recycled from one stage to the next. That means that the sheets connect at a pressure which is already higher than ambient due to a non-zero radius. In taper-nested, you wouldn't strictly need holes in each sheet to allow ingress into the next stage, because the loss from one stage is also the loss for the next-most stage.

My initial hope was the the material strength of the sheets would be lowered in the taper-nested scheme, but so far I have not been able to nail this feature down, and it could go either way. Jury is out on that topic. It is also not obvious that one is simply better than the other, and I may be hedging my bets between the two for quite some time to come.