Wide-Mouth Taper and Group-Based Termination

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.

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.

Python Library for Calculation of Balloon Properties

I have now put up a python library with numerical implementations of the fundamental relationships for pressure, volume, mass, etc. of a gravity balloon.

https://github.com/AlanCoding/gravitational-balloon-mathematics

The old work on this blog was done largely in an Excel spreadsheet with macros. In terms of the library of methods, I feel that the python version is now better and more correct. Some library methods haven't yet been converted, but the important ones will, and that should go quite fast.

Doing this allows me to put work in Juypter notebooks, which is much better for sharing my work down to the numerical implementation. For a demo, I have re-done the graphs for the PR and PV curve.

These are showing the same thing as the prior post did:

https://gravitationalballoon.blogspot.com/2013/03/gravity-balloon-pressure-volume-curve.html

That had some errors in it, and I'm now confident those are corrected.

The python library is much much easier to understand and modify, and any further improvements will become considerably faster.

A More Detailed Run-through of the Pressure-Volume Relationship

I've enabled MathJax on this blog and started repairing numerous equations, after a few years of the equations not rendering. Some parts have still not been recovered, but I've also realized that some parts are unclear.

So there will be value in running through the basic equations of the gravity balloon with fresh eyes.

Objective

The equations here will relate multiple quantities. At different times we are interested in different quantities. The most common is to seek pressure (P) and volume (V), given values for all the others. Given that a gravity balloon is to be built out of some asteroid, then available mass and density of rock is fixed.

Mass

We will temporarily introduce variables for dimensions. The big R is used for the radius of the inner volume of air - the inner surface of the rock. The little t is used for the thickness of the rock. Thus, the outer surface of the inflated gravity balloon would be (R+t). Less commonly, the original radius of the asteroid (assuming spherical) will be denoted $R_0$. Using those, we will use the general formula for volume of a sphere both before turning into a gravity balloon and after.

$$ M = \rho V = \rho \frac{4}{3} \pi R_0^3 = \rho \frac{4}{3} \pi \left( (R + t)^3 - R^3 \right) $$

Gravitational Field

Consider any homogeneous spherical planet, we have a simple $1/r^2$ formula for gravity on the surface. I'm keeping M, the mass of the planet, in there as an independent variable of the function, as this will be important.

Spherical Planet Field Surface and Beyond

$$ g_{space}(r, M) = G M \frac{1}{r^2} $$

As you consider the interior, Gauss' law dictates that we can use that same formula, if we include all the mass below the radius of consideration.

Spherical Planet Field Interior, not for Gravity Balloon

$$ g_{interior}(r) = G M_{inside} \frac{1}{r^2} = G \rho \frac{4}{3} \pi r^3 \frac{1}{r^2} = G \rho \pi \frac{4}{3} r $$

These are universal expressions for field inside and outside a solid sphere. I don't want to make them out to be anymore than that, because the important thing is how they get reused in for the gravity balloon.

Gravity Balloon Gravitational Field

The gravity balloon has 3 distinct regions:

• livable air on the inside
• rock walls
• space outside
  

I will write the gravitational field for the gravity balloon as a piecewise function covering all 3 regions here.

$$ g_{gb}(r) = \begin{cases} 0 & r > R \\ g_{rock}(r) & R < r < R + t \\ G M \frac{1}{r^2} & r > R + t \\ \end{cases} $$

As you can imagine, the hard part is that $g_{rock}(r)$, and that is what the rest of the work here is for. The right way is to use $g_{interior}(r)$ to find the field contributions from the rock, but this isn't valid by itself. Instead, we pretend that this is a solid planet of radius $(R+t)$, and write $g_{interior}(r)$ for that, but then subtract the field you would get from the air volume if it were made of rock. This subtraction ("superposition" if you will) is valid for Newtonian field calculations.

$$ g_{rock}(r) = g_{interior}(r) - g_{space}(r, M_{\text{air as rock}}) \\ = g_{interior}(r) - g_{space}(r, \rho \pi \frac{4}{3} R^3) $$

(ASIDE: this is the critical step, and it is easy to get it wrong. I have gotten it wrong before, that, and lack of clarity in prior posts, is why I revive this now. Although I did eventually correct my actual numbers, I also had a habit of skipping a ton of steps, so I'm publicly taking it slowly here.)

With pretty good confidence in this established, let's expand it because it will be integrated.

$$ g_{rock}(r) = G \rho \pi \frac{4}{3} r  - G \rho \pi \frac{4}{3} R^3 \frac{1}{r^2}  = G \rho \pi \frac{4}{3} \left( r  - \frac{R^3}{r^2} \right) $$

This wraps up the gravitational field. The field is fully described by the expressions for $g_{gb}$ with the supporting $g_{rock}$. There are other tangents I can go on, like contributions from the gravity of the air itself, but this should not be interesting until numerical solutions come into play. I have little very interest in air gravitational contributions as a calculus problem.

Pressure

To get air pressure we integrate the gravitational field, and then multiply by density. This is justified by our intuition that pressure is $\rho g h$, which is (density)x(gravity)x(height). This is the integral form, specific to the gravity balloon.

$$ P = \rho \int_R^{R+t} g_{rock}(r) dr  = G \rho^2 \pi \frac{4}{3} \int_R^{R+t} \left( r  - \frac{R^3}{r^2} \right) dr $$

Now we perform the integral.

$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{1}{2} r^2 + \frac{R^3}{r} \right) \Big|_R^{R+t} \\ = G \rho^2 \pi \frac{4}{3} \left( \frac{1}{2} (R + t)^2 + \frac{R^3}{(R+t)} - \left( \frac{1}{2} R^2 + \frac{R^3}{R} \right) \right) $$

I feel like it is important to write everything out here so that people can follow. That will simplify a great deal, which I do here.

$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{1}{2} (R + t)^2 + \frac{R^3}{R+t} -  \frac{3}{2} R^2 \right) $$

Prepare to combine the fraction.

$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{(R + t)^3}{2 (R+t)}  + \frac{2 R^3}{2 (R+t)} -  \frac{3 R^2 (R + t)}{2 (R+t)} \right) \\ = G \rho^2 \pi \frac{4}{3} \left( \frac{(R + t)^3 + 2 R^3 - 3 R^3 - 3 R^2 t}{2 (R+t)}  \right) $$

The cubic expands into a lot of terms, but the $R^3$ power from it cancels out with other terms.

$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{ t ( 3 R^2 + t (3 R + t) ) - 3 R^2 t}{2 (R+t)}  \right) \\ = G \rho^2 \pi \frac{4}{3} \left( t \frac{  3 R^2 + t (3 R + t) - 3 R^2 }{2 (R+t)}  \right) \\ = G \rho^2 \pi \frac{2}{3} \left( t^2 \frac{ 3 R + t }{R+t}  \right) $$ 

Years ago, I know that I did this many times on paper. Now, I realize that I just don't want any of it to get lost. The pressure equation is slightly non-trivial, but it's still within the realm of basic college physics / calculus.

How you use the equations is the one other slightly non-trivial part.

Usage

The equations above should be thought about in terms of their independent variables. We have functions to give one variable in terms of other.

$$ P(R, t) \\ M(R, t) $$

Usually, we prefer to put things in terms of volume, and this can be swapped one-for-one with R in the relationships above, because the relationship between M and R is trivial and only involves those 2.

$$ V = \frac{4}{3} \pi R^3 $$

This can be done as a preprocessing step in a method numerically. So we can always freely swap V and R as independent variables. I have more commonly written:

$$ P(V, t) \\ M(V, t) $$

Referring back to their definitions, neither of these methods are trivial to invert symbolically, as they carry cubic terms. It can be done, but it's not the best for technical communication.

At this point, I stop with math.

We have 2 equations and 4 variables. That means that, somehow, a user has to specify 2 variables, and the other 2 can be calculated. The system is fully defined for any correctly-phrased question. In my younger days, I was inclined to go further into problem solving through math. Now, I am more than happy to let code solve the rest. The only challenge I have not addressed is selecting workable initial values.

 I have posted one demo method here:

https://github.com/AlanCoding/gravitational-balloon-mathematics/blob/master/gb/inflation.py

This is the rebooted form. I used Excel Visual Basic macros before. I have successfully converted those to python, which I will use to bootstrap some initial testing.

Very Preliminary Thoughts on a Hybrid Taper Solution

Material strength is the enemy in the design philosophy of the gravity balloon, as I have laid it out. Honestly, I think that it is always the enemy. It is one more thing that can go wrong operationally, it's not something one would like to rely on for safety. It also lacks a sort of elegance needed for the massive scales and volume of industrial replicability that is needed for massive zero-gravity industry of the future.

Looking at both the approaches for the the task of tapering - bringing the friction buffer sheets into a smaller radius without defeating their economic point - I feel like I'm still missing something. Neither of the designs I wrote about does a good job of eliminating the need for tensile strength due to the different radial acceleration of the air between sheets. On that point, I think I might have already conceded defeat. In gross terms, the extra tensile strength isn't actually a problem. It would pale in comparison to what the rotating tube's hull itself would require, and that would, again, be vastly less than a comparable fully 1-bar pressurized hull. No, I think the problem is requiring both strength and numbers at the same time. The failure modes are not good in that case. There is a level of material quality assurance that must be very robust. Additionally, it has intense tie-ins with the stability questions still outstanding for the many-layer hydrodynamic stability. Oscillation is also a problem if the friction buffers have good mass to them, and the idea of them as something more ephemeral has always been something much more appealing from an engineer's perspective.

I have briefly mentioned a 3rd possibility in addition to the taper-nested and taper-zero options that I have been playing around with. You could basically combine the two. In particular, on the large scale I think that taper-zero is hard to avoid. It keeps the outer motion in the right kind of reference frame, the air ingress patterns give some very needed design flexibility, and it doesn't have those darned problems of undesirable connection points. It's the connection points that I think will sink the other design.

So it's worth while following this rabbit hole for some time. Trash the taper-nested option. Start with taper-zero, and use something apparently exotic - a hierarchical type of design to them. I've used that word before, but I think that "group" might be better, because there would only reasonably be 1 layer to the hierarchy.

The idea is that flow divider sheets are divided into 2 categories. One consists of infrequent "heavy" (although not all that heavy in absolute terms) dividers that hold a pressure boundary across its surface. These do substantial radial tapering toward the ends. The other type consists of a sheet that really has no material strength, and merely rests on air pressure. The connection points for the "flimsy" sheets are almost directly to the side, on the inner surface of their neighborhood "heavy" sheet. For the "flimsy" sheet, this avoids the problems of pressure ride-up in the taper altogether by outsourcing the task to the other type. For the "heavy" sheets, it consolidates the manufacturing and operations complexity by reducing the numbers to around maybe 4, when it might have otherwise required 20. This can also be a go-to solution for centralization of the pressure management of the "flimsy" sheets.

I'm still not sure how contact might be maintained between the heavy sheets and the flimsy sheets. There might still need to be some tapering... but maybe not.

I hope to return to this, and I'm sure I'll make a detailed post sometime after I can get around to sketching some of the basics and doing brief mathematics on it. I just want to throw it out there for now. I'm definitely thinking about it, and it absolutely has tie-ins to the most major problems of the gravity balloon design.

I also find it interesting that this makes vastly more sense as you talk about larger and larger artificial gravity tubes. I've kept assuming a 500 meter diameter, but realize that might be too little. Once you talk about > 1 km, then the non-hybrid approaches start to look more and more unrealistic.

Global Heat Transfer Without Alternating Layers

Here, I hope to offer an alternative to the previous method I discussed for exchanging hot air from the rotating tubes to the edges of the gravity balloon (from where they would need to go through another heat transport mechanism into the space radiator on the surface).

Because global heat transport is a relatively loosely constrained problem for gravity balloons of most conceivable sizes and densities, we are able to spend some of that margin in order to achieve an interior that may be more desirable to the inhabitants. The previous method is described here:

http://gravitationalballoon.blogspot.com/2014/12/global-air-heat-transport-in-gravity.html

The basic ideas of the first version are:

• The tubes are arranged in a regular lattice where each tube has a neighbor counter-rotating tube
• They are further arranged into cross-sectional layers where all tubes rotate in the same direction
• Sheets are placed spanning the space between similar-rotating tubes to block airflow going from layer to layer
• The flow makes a U-turn once it gets to the heat exchanger on the inner surface of the global gravity balloon wall and enters the neighboring sheet to continue a criss-crossing pattern

The potentially undesirable aspect of this is that the inner space has a great deal of clutter in the form of flow-dividing sheets. You could still have some holes in the sheets for travel of people and goods to go through, but the sheets would still be a nuisance. It would also be mostly mutually exclusive with large open spaces.

The alternative proposal is only marginally modified from that idea. My overall sketch is this:

Here, I am illustrating a pair of counter-rotating tubes. In the previous version of this idea, the air in the above diagram would be moving downward (by the directions in the sketch) within the space between the two tubes. The modification here is that we add a scaffolding around the surface of the tubes in this space. This achieves the goal of bulk flow in one single direction over a large volume within the gravity balloon.

QUALIFIER: Someone unfamiliar with the broader gravity balloon concept in this blog might find it easy to mistake the motion depicted here as directly corresponding to the outer surface of the artificial gravity tube itself. Instead, this is only the outermost friction buffer layer, traveling at a few m/s, instead of on the order of 100 m/s, which would be the outer hull of the artificial gravity tube itself.

What about the global circulation patterns? The air can't only move in one direction, it has to have a net loop in some sense. The best solution to couple with this design is to make the flow regions as large as possible, resulting in a "apple core" sort of circulation pattern. In this sense, there is one major river of flow going straight through the center, which fans out and goes along the outer regions to return to the other side and back again.

The main challenges, as I see them, are the management of the integrity of the shape of the outer layer friction buffer. It is true that I expect some natural wedge effect to help maintain stability, but there will be more deformation caused by the significant asymmetrical drag on the inner segment. Intentionally putting asymmetrical forces on the outer layer will also push them closer to the limit of the stability criteria (whatever that specific criteria may be) and may also increase the drag forces.

I started thinking about this topic more after seeing some artwork in the Accelerando blog. In future posts I do hope to provide more specific commentary and back-links those works. My intent here was just to put this concept out there.

Massive Topic List with Half-Finished Writings on Gravity Balloons

NOTE: extremely meta post follows.

Several past posts have been a dump of a large set of topics all balled into one. Now, I would like to do something different. I have used a text file as a staging area where I battled ideas against each other (in terms of where they rank in priority) and also just spitball ideas to see what sticks. While I still like to do these things, I'm depreciating the text file as a tool. I would rather keep the extremely premature ideas on the back of a napkin (or email draft), and use the blog itself as a better format for medium-low effort writings.

Even so, I still have that massive backlog of stuff that I never got to finishing. In my personal philosophy, I want to follow the open source model, and just let information free whenever there's no compelling reason not to. So here it is, my newly retired backlog:

http://pastebin.com/p1qSQkdu

If I'm too wordy in my general writings, then there won't be much of interest in there. Nevertheless, not everything is terrible, and I'm always somewhat taken aback when I read my old writings. It might be nice to polish it up and put it in a nicely displayed format (at least with working links). But let me just go through and dig a few things out of the dredges...

Small Gravity Balloons

 I attacked this concept from several different angles. One specific scale I was interested in was 1 km size asteroids, since these get closer to the NEA territory. Air pressure might still be used to resist against self-gravitation or some other uses, but exactly what is an open question.

Stability Topics

Nothing I've posted has come close to an exhaustive accounting of the stability topics which span from the gravity balloon part itself, to the internals, to the friction buffers. Then, multiply some of these by all the different size classes. Every problem you look at, you can probably think of at least five different mathematically simplified cases. Each one of those problems could have an enormous amount of analysis, and even radically different formulations.

Phobos Reference Values

The moon of Mars is just too interesting to give up on. But fairly small, and also close to the Roche Limit, this moon also presents a host of different mathematics that can complicate its scenario. In spite of that, there is still a strong motivation to give definite values for some kind of maximally populated colony.

Space Development Plan

Where does the gravity balloon exist within some kind of space roadmap? There are some efforts to make a detailed space development roadmap (I have one in mind that was on Kickstarter). These can offer an interesting starting place, but may be too near-term to have much connection to gravity balloons. The NSS also has some interesting roadmaps that involve extremely far-reaching development goals. I am interested in making an ordering. What is likely to happen before a gravity balloon is built? What is strictly necessary?

Cross-Structures in Artificial Gravity Tubes

Unlike most artist illustrations and typical guidance from 1970s era concepts, the artificial gravity tubes inside a gravity balloon would be extremely friendly for developers who want to build skyscrapers straight across the tube. In fact, it would be necessary if the mass was not evenly distributed (this is more important for gravity balloons, since the shielding mass isn't integral to the hull, making the livable structures relatively heavier compared to the walls).

Lower-Gravity Tubes and Microgravity Industry

Where would sewage processing happen? Probably in tubes that don't have the burden of friction buffers (accomplished by spinning at very low rates). This seems perfectly fine for algae and other smaller and easy to manage husbandry of animals, etc. What other industry (like shipyards) would happen in the microgravity (but not airless) space? Probably lots.

Procurement and Management of Air

I address "air" in the basic physical sense a lot, but the chemical realities of production of air is more challenging.

Other Agenda Items

These topics aren't in that list, because I've only recently been kicking them around:

• Looking into the work by Dr. Forward in his 1990s (and hard to obtain) books
• Of course, actually conducting the scaled experiment
• Inner solar system asteroid Delta V versus mass map (not perfect math, but good-enough with some help from JPL pre-calculated data)