Wide-Mouth Taper and Group-Based Termination (Staggering)

Here, we will entertain an alternative to the tiny access center-hole at the ends of a rotating tube in a gravity balloon (or generally, artificial gravity integrated into atmosphere). Return to our reference design:

• Radius of ground: 250 meters
• Access hold radius: 15 meters

The 15 meters could be pushed, of course. Because it's not that large to begin with, we may be able to accept a larger relative velocity to get, say, 20 meters radius for this access opening at the cost of slightly faster edge speed. That is 40 meters wide. While, to me, this seems sufficient to supply such a tube, it's not the only option and I want to give proper treatment to the alternative.

To start our goal - this is asking for a greater area at which the tube can interface with the surrounding atmosphere. Similar to cans going from the traditional opening to the "wide mouth" opening.

Wide-Mouth Can

Unlike the cans, however, we will go as big as we can, up to occupying the entire cross-section of the tube. Erase everything I've written about the termination of the friction buffers. We have a tube (like the tube of a toilet paper roll), and we know we need the friction buffers around them, and we know that the tube will be moving too fast relative to the atmosphere if we leave it as-is.

Making the Floor Itself Move

To make this work, we will move the ground itself. Similar to how (in any rotating artificial gravity habitat), you can get lower gravity by climbing a ladder, in our new innovation here, you will get lower gravity by walking onto another segment of the tube that rotates more slowly. Yes, this will require some kind of mechanical, moving, coupling between the floor moving at different speeds.

What else do we need? The moving floor segments will be connected to a friction buffer at the matching angular velocity. This connection happens under the floor, so would not be observable to residents. Now we have a tube that rotates fast in the center, and then rotates at decreasing speed as you go to the edge. For less obvious fluid mechanics reasons, this will not be sufficient either. There is quite considerable pumping you will get from this unless the length over which this happens is really really long. That would be possible, but wouldn't be practical. So to smooth out this flow, just like in the other friction buffer termination design, we have to add dividers and this time it goes into the interior of the tube in a very obvious way to the residents. We have enough to sketch now. This starts from the cross-section perspective I've used in prior posts and illustrates the described setup.

Wide-Mouth Tube with Variable Speed Floors

You need a lot of imagination for human-scale stories happening here. The diameter of the large tube is 500 meters, and a human is less than 2 meters. The relative speed between each segment of floor is the same as the existing reference design, 2.9 m/s, 10.5 kph, or 6.5 mph. Speaking personally, my running speed is 7.5 mph, so physical able humans can physically jump from one to the next (assuming no "video game platformer" gap). Moveable walkways travel at more gentle speeds of 2 mph, but the internet informs me that some go up to 9 mph. So real-world movable walkways could cover this, and one on both sides could easily cover it.

Because of these factors, I assume some minor assistance would be added if the gaps were to be traversed on foot, specifically one or two literal moving walkways. What happens after stepping onto the next segment? You are faced with the flow divider. Could a hole just put be in that? Maybe. There is expected to be some pressure gap between one stage and the next, so if there is a door I expect some door-opening resistance, and if it is left open, I expect some notable airflow that contributes to losses. To avoid travel delays, you would need doors along virtually the entire radius so I could see this being a problem. Reminder - if the pressure difference is too great, you can do the good-old 2-doors and a room in-between trick. This is similar to an airlock, but... just ordinary doors.

How would a vehicle travel from the tube interior to the edge? I'm at a loss. You wouldn't use a railed vehicle (how do you match the tracks on the next shell?). A rotating mechanical device to pick up the vehicle and place it at zero velocity on the next shell sounds expensive, but trivially possible. I think my favorite idea is that each shell has ramps built into it, and the vehicle goes in the circumferential direction and jumps to the next shell? Sounds fun.

I frankly have no idea how truly practical it would be to travel this way, it is an exercise left up to the reader. All I have to offer is the observation that it is an additional option. The above-illustrated design does not lose any utility compared to the other designs seen in taper-nested or others throughout this blog. You can ride a lift to the center-line, and then ride a gondola through the center hole into the microgravity space. This checks all of the boxes of being physical, economical, and practical. I just have no idea whether it is useful. If I'm maintaining a list of canonical ideas, things I accept as being in the real design space, count wide-mouth in!

Reducing Clutter, Group-Based (Staggered) Termination

While I'm iffy about the usefulness or need for this, it is academically useful to me to clarify the remaining work we need to optimize the termination of the friction buffers. As you can see in the diagram, this really is the same thing as the other designs, just with a different curvature to the geometry of each sheet (and a floor added, not relevant here).

Let me describe the obvious issue - at the edge of the access space, the sheets are moving at a relative velocity of 0.3 m/s, or less than 1 mph, all while assumed to have the same spacing between sheets as the rest of the geometry (it must, due to the velocity at the floors). This is much less speed reduction than what we need. We can pull that back for some sheets (make the center hole bigger)... but which sheets specifically?

Re-stating our constraint - the relative speed of each sheet must not be more than about 3 m/s relative to its neighbor. But if you reduced the inner radius of all expect the 1st and last, then the relative speed of the 1st and last becomes too high... as they kind of become neighbors. This leads me a form of grouping, like the markers on a ruler.

Center Opening Widened, Relative Velocity Still OK

This is a strange outcome, but I believe it to be legitimate. This also lifts the concern about traffic jams due to a very long and relatively skinny access tunnel. Yes, we still retain a single choke point, but it's not a choke tube. It opens up the atmosphere in the transition region... somewhat.

Implications of Group-Based (Staggered) Termination for Other Designs

This also helps clarify what the actual minimum clutter is in all designs. Through this sketching, I have learned something new about what is possible with almost all friction buffer termination solutions. For taper-nested, a brief sketch:

Taper-zero with Staggered Termination

For years, I have had a gut feeling that something was still off in how I was drawing these, and I believe this is it. The reason it was hard to find was that it was so non-obvious how to state the maximum relative velocity constraint, because it applies to the revealed neighbor sheet, not just the N+1 sheet. It also makes sheet numbers of 2^N desirable.

Even with the briefest visual survey of the taper-zero-staggered sketch, you intuitively see less clutter going towards the center. This concept of staggering the circular opening of each sheet is going to be assumed in most designs going forward.