Putting Some Numbers on the Taper Options

 See the prior post for the definitions here:

Illustrations of the Friction Buffer Tapers

Here, I just want to give more elaboration on the specific connection points because they were only drawn in the abstract before. To do this, I have a simple spreadsheet which I'll just leave a shared link for. To explain what I'm looking for, we'll go by the designs introduced in the prior post.

• taper-nested:
• The connection points can connect to a point along the triangular ramp which is at the end of the rotating cylinder. There is a constraint of a maximum radius where we can connect it, because connecting at a larger radius would leave us with a large relative velocity. The reason for existence of the sheets is to minimize drag, so we can't do that.
• taper-zero:
• Each connection point (confusingly) has to of a small enough radius so that it shields the sheet inside of it. This, again, results in a maximum radius value, beyond which the sheet inside of it will make contact at the air at too high of velocity.
• Note, however, that the design calls for the innermost sheet to envelope basically the entire ramp. This this brings the connection further in, to a smaller radius, it does not violate the maximum radius constraint.

This note on taper-zero is going to cause some trouble communicating, so I'm not going to plot its numbers directly (because they don't apply to all sheets), so I'll instead have a series "air-acceptable R" which is the radius at which any given sheet is moving slow enough relative to the static air so that it can be exposed directly to the outside micogravity.

One item not exposed here is that the access opening is assumed to be at a radius of 15 meters. That is largely set by the arguments around acceptable speed (the 3 m/s thing), so it shouldn't be surprising that no point in the graph dips below this radius.

The biggest thing I want to observe here is that the points are clustered fairly heavily towards the center (low values of R). This does quite a lot to change one's visual image, which were poorly represented by the earlier hand drawings.

Let's take taper-nested as an example. Start with the first sheet, and it can connect about 3/4ths the way along the ramp, next, maybe 1/3rd. But then numbers 6 through 17 are super close together. The sheets at their full cylinder radius should be a large distance apart, like 10 meters, and you won't have this automatically with the triangle shape. Thus, a key takeaway is that you would have to elongate the access tunnel to increase spacing. Because decreasing spacing increases drag, just like increasing relative velocity does.

So my revised mental image of the taper-nested looks more like this.

I've added an additional detail which is compartmentalization in the tapering region. This would be a leaky flow divider, and to be honest I arrived at this addition after a conversation with ChatGPT, where it was concerned about "pumping" being caused in the tapering region. I think it is still small, because the tapering region keeps velocities as low or lower than what they are at the full radius... but I still see the point that we have 2 axes of eddy creation, and a dumb divider is a cheap solution. We already have some controlled air ingress through the channels, so they would bend in the direction of the access tunnel.

Onto the elephant in the room - that seems inconvenient. This would make it harder to transport goods and people in and out. Yes, but it's an obtuse academic over-simplification. Given this reference design (17 sheets), there is clear advantage to having the first 3 or so sheets hug the tube, but beyond that, spending the material to wrap all the way to the access point is pure waste. The direct solution basically winds up being what I've already named taper-zero.

I do have many more thoughts on taper-zero, and I need to mature the numerical constraints for that design (angles get "weird", but this isn't... a technical statement). I almost might start over from scratch with a new approach that helps conceptualize the overall design space better. However...

Rejection of Hybrid Taper Solutions

I speculated in another design direction before.

Very Preliminary Thoughts on a Hybrid Taper Solution

I now believe this was an unproductive dead end. It does not solve any problem that mattered. Total quantity of material strength needed for the sheets will simply never be an issue, ever. You spend more on the ground itself. Sheet positioning is a much bigger issue. Keeping the fully or mostly tensile constructions (balloons) also has a big economic impact. Control systems for the air ingress mater, means of maintaining the seals matter. I think what that design direction was offering was just worthless. In the end, with new designs I'm still working on there might some some non-uniformity between different sheets, but nothing like different material composition from one to the next.