tag:blogger.com,1999:blog-55156921647853283382024-03-05T02:30:10.010-08:00Gravitational Space BalloonsThis blog describes a space habitat concept where air is contained in a large volume by relying on the weight of asteroid rock to support internal pressure via self-gravitation. Centrifugal artificial gravity cylinders with pinched openings are surrounded by friction-reducing concentric flow dividers, enabling space cities with good economies of scale.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.comBlogger55125tag:blogger.com,1999:blog-5515692164785328338.post-56896752847354340362021-07-07T20:14:00.000-07:002021-07-07T20:14:24.473-07:00Python Library for Calculation of Balloon Properties<p>I have now put up a python library with numerical implementations of the fundamental relationships for pressure, volume, mass, etc. of a gravity balloon.<br /></p><p><a href="https://github.com/AlanCoding/gravitational-balloon-mathematics">https://github.com/AlanCoding/gravitational-balloon-mathematics</a></p><p>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.</p><p>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.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7X_91zzU9_M2kuhIArf0jv5C-_b-1qzUQ3PV3Xf835L-L_KVG1SfCyjfCt_dFA5OtFn4gGaNF9gXaXXXmCWtqHMq_fU28jrdN0KFc2KcXz2xwoqBFQAQwelazwHbtdxrOSXTOqXcXhzUv/s397/PR.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="278" data-original-width="397" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7X_91zzU9_M2kuhIArf0jv5C-_b-1qzUQ3PV3Xf835L-L_KVG1SfCyjfCt_dFA5OtFn4gGaNF9gXaXXXmCWtqHMq_fU28jrdN0KFc2KcXz2xwoqBFQAQwelazwHbtdxrOSXTOqXcXhzUv/s320/PR.png" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmQlUOOmrlEyv6r8bx5IWddTLxfUPEeidsxovnbdftw-0pkWaEcTcdJ_ZBkZjGYCjY2Hw6wYgN_13VnkAJoCX7JJ28Tqc5YweeOHKoTW_E686X3t5xKR8LZpfpKWI26h_0QVBnkPUBhicm/s397/PV.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="278" data-original-width="397" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmQlUOOmrlEyv6r8bx5IWddTLxfUPEeidsxovnbdftw-0pkWaEcTcdJ_ZBkZjGYCjY2Hw6wYgN_13VnkAJoCX7JJ28Tqc5YweeOHKoTW_E686X3t5xKR8LZpfpKWI26h_0QVBnkPUBhicm/s320/PV.png" width="320" /></a></div><p>These are showing the same thing as the prior post did:</p><p><a href="https://gravitationalballoon.blogspot.com/2013/03/gravity-balloon-pressure-volume-curve.html">https://gravitationalballoon.blogspot.com/2013/03/gravity-balloon-pressure-volume-curve.html</a><br /></p><p>That had some errors in it, and I'm now confident those are corrected.</p><p>The python library is much much easier to understand and modify, and any further improvements will become considerably faster.<br /></p><span><a name='more'></a></span><p>I already have a few new fun ideas. I tried very hard to write these as numerical solvers. This gives a lot of flexibility to modify the equations themselves. This easily opens the door to include things like gravitation from the air inside. It might even be practical to make the same equations apply to the super-large case where I account for drop in air pressure away from the center.<br /></p>Alanhttp://www.blogger.com/profile/16161965850899477592noreply@blogger.com2tag:blogger.com,1999:blog-5515692164785328338.post-19397319927294002132021-07-02T21:04:00.000-07:002021-07-02T21:04:01.068-07:00A More Detailed Run-through of the Pressure-Volume Relationship<p>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.</p><p>So there will be value in running through the basic equations of the gravity balloon with fresh eyes. <br /></p><h2 style="text-align: left;">Objective</h2><p>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.</p><h2 style="text-align: left;">Mass <br /></h2><p>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.<br /></p><p>$$ M = \rho V = \rho \frac{4}{3} \pi R_0^3 = \rho \frac{4}{3} \pi \left( (R + t)^3 - R^3 \right) $$</p><h2 style="text-align: left;">Gravitational Field</h2><p>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.<br /></p><p style="text-align: center;">Spherical Planet Field Surface and Beyond</p>$$ g_{space}(r, M) = G M \frac{1}{r^2} $$<p>As you consider the interior, Gauss' law dictates that we can use that same formula, if we include all the mass <i>below</i> the radius of consideration.</p><p style="text-align: center;">Spherical Planet Field Interior, not for Gravity Balloon <br /></p><p>$$ g_{interior}(r) = G M_{inside} \frac{1}{r^2} = G \rho \frac{4}{3} \pi r^3 \frac{1}{r^2} = G \rho \pi \frac{4}{3} r $$</p><p>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.<br /></p><h3 style="text-align: left;">Gravity Balloon Gravitational Field</h3><p>The gravity balloon has 3 distinct regions:</p><ul style="text-align: left;"><li>livable air on the inside</li><li>rock walls</li><li>space outside <br /></li></ul><p>I will write the gravitational field for the gravity balloon as a piecewise function covering all 3 regions here.</p><p>$$ g_{gb}(r) = \begin{cases} 0 & r > R \\ g_{rock}(r) & R < r < R + t \\ G M \frac{1}{r^2} & r > R + t \\ \end{cases} $$</p><p>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 <i>subtract</i> the field you would get from the air volume <i>if it were made of rock</i>. This subtraction ("superposition" if you will) is valid for Newtonian field calculations.<br /></p><p>$$ g_{rock}(r) = g_{interior}(r) - g_{space}(r, M_{\text{air as rock}}) \\ = g_{interior}(r) - g_{space}(r, \rho \pi \frac{4}{3} R^3) $$</p><p>(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.) <br /></p><p>With pretty good confidence in this established, let's expand it because it will be integrated.<br /></p><p>$$ g_{rock}(r) = G \rho \pi \frac{4}{3} r - G \rho \pi \frac{4}{3} R^3 \frac{1}{r^2} = G \rho \pi \frac{4}{3} \left( r - \frac{R^3}{r^2} \right) $$</p><p>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. <br /></p><h2 style="text-align: left;">Pressure</h2><p>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.<br /></p><p>$$ P = \rho \int_R^{R+t} g_{rock}(r) dr = G \rho^2 \pi \frac{4}{3} \int_R^{R+t} \left( r - \frac{R^3}{r^2} \right) dr $$<br /></p><p>Now we perform the integral.</p><p>$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{1}{2} r^2 + \frac{R^3}{r} \right) \Big|_R^{R+t} \\ = G \rho^2 \pi \frac{4}{3} \left( \frac{1}{2} (R + t)^2 + \frac{R^3}{(R+t)} - \left( \frac{1}{2} R^2 + \frac{R^3}{R} \right) \right) $$</p><p>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. <br /></p><p>$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{1}{2} (R + t)^2 + \frac{R^3}{R+t} - \frac{3}{2} R^2 \right) $$</p><p>Prepare to combine the fraction.</p><p>$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{(R + t)^3}{2 (R+t)} + \frac{2 R^3}{2 (R+t)} - \frac{3 R^2 (R + t)}{2 (R+t)} \right) \\ = G \rho^2 \pi \frac{4}{3} \left( \frac{(R + t)^3 + 2 R^3 - 3 R^3 - 3 R^2 t}{2 (R+t)} \right) $$</p><p>The cubic expands into a lot of terms, but the $R^3$ power from it cancels out with other terms.<br /></p><p>$$ P = G \rho^2 \pi \frac{4}{3} \left( \frac{ t ( 3 R^2 + t (3 R + t) ) - 3 R^2 t}{2 (R+t)} \right) \\ = G \rho^2 \pi \frac{4}{3} \left( t \frac{ 3 R^2 + t (3 R + t) - 3 R^2 }{2 (R+t)} \right) \\ = G \rho^2 \pi \frac{2}{3} \left( t^2 \frac{ 3 R + t }{R+t} \right) $$ </p><p>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 <i>slightly</i> non-trivial, but it's still within the realm of basic college physics / calculus.</p><p>How you use the equations is the one other slightly non-trivial part.</p><h2 style="text-align: left;">Usage</h2><p>The equations above should be thought about in terms of their independent variables. We have functions to give one variable in terms of other.<br /></p><p>$$ P(R, t) \\ M(R, t) $$</p><p>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.</p><p>$$ V = \frac{4}{3} \pi R^3 $$</p><p>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><p>$$ P(V, t) \\ M(V, t) $$</p><p>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.</p>At this point, I stop with math.<p>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.<br /></p><p> I have posted one demo method here:</p><p><a href="https://github.com/AlanCoding/gravitational-balloon-mathematics/blob/master/gb/inflation.py">https://github.com/AlanCoding/gravitational-balloon-mathematics/blob/master/gb/inflation.py</a></p><p>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.<br /></p>Alanhttp://www.blogger.com/profile/16161965850899477592noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-34874866091501314212017-01-31T19:45:00.001-08:002017-01-31T19:45:30.624-08:00Very Preliminary Thoughts on a Hybrid Taper SolutionMaterial 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.<br />
<br />
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.<br />
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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.<br />
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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.<br />
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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.<br />
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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.<br />
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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.<br />
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I also find it interesting that this makes <i>vastly</i> 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.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com3tag:blogger.com,1999:blog-5515692164785328338.post-91358561102191069712017-01-04T17:38:00.001-08:002017-01-04T17:38:37.890-08:00Global Heat Transfer Without Alternating LayersHere, 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).<br />
<br />
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:<br />
<br />
<a href="http://gravitationalballoon.blogspot.com/2014/12/global-air-heat-transport-in-gravity.html">http://gravitationalballoon.blogspot.com/2014/12/global-air-heat-transport-in-gravity.html</a><br />
<br />
The basic ideas of the first version are:<br />
<ul>
<li>The tubes are arranged in a regular lattice where each tube has a neighbor counter-rotating tube</li>
<li>They are further arranged into cross-sectional layers where all tubes rotate in the same direction</li>
<li>Sheets are placed spanning the space between similar-rotating tubes to block airflow going from layer to layer</li>
<li>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</li>
</ul>
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.<br />
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The alternative proposal is only marginally modified from that idea. My overall sketch is this:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2ndcM5mFsR7qTPXCgZARshRMcFkuDEsk5T9oT6SPovr0PS6zsAPIihKb4HooYUAgKAPrUdC4TdV8iM_7jyJbyuMgSlWcV7qgPNaKV6T7wLL_WjQiQPyYMMQRggKZ27iO2V_o9dw_WeiQ/s1600/single_direction_global_flow.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="187" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2ndcM5mFsR7qTPXCgZARshRMcFkuDEsk5T9oT6SPovr0PS6zsAPIihKb4HooYUAgKAPrUdC4TdV8iM_7jyJbyuMgSlWcV7qgPNaKV6T7wLL_WjQiQPyYMMQRggKZ27iO2V_o9dw_WeiQ/s320/single_direction_global_flow.png" width="320" /></a></div>
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
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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.<br />
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I started thinking about this topic more after seeing some artwork in the <a href="http://accelerando.tumblr.com/">Accelerando blog</a>. 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.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com2tag:blogger.com,1999:blog-5515692164785328338.post-25418207711284287002016-05-16T19:30:00.002-07:002016-08-17T18:50:45.812-07:00Massive Topic List with Half-Finished Writings on Gravity BalloonsNOTE: extremely meta post follows.<br />
<br />
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.<br />
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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:<br />
<br />
<a href="http://pastebin.com/p1qSQkdu">http://pastebin.com/p1qSQkdu</a><br />
<br />
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...<br />
<h4>
</h4>
<h3>
Small Gravity Balloons</h3>
<br />
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.<br />
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<h3>
Stability Topics</h3>
<br />
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.<br />
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<h3>
Phobos Reference Values</h3>
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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.<br />
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<h3>
Space Development Plan</h3>
<br />
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?<br />
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<h3>
Cross-Structures in Artificial Gravity Tubes</h3>
<br />
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).<br />
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<h3>
Lower-Gravity Tubes and Microgravity Industry</h3>
<br />
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.<br />
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<h3>
Procurement and Management of Air</h3>
<br />
I address "air" in the basic physical sense a lot, but the chemical realities of production of air is more challenging.<br />
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<h3>
Other Agenda Items</h3>
<br />
These topics aren't in that list, because I've only recently been kicking them around:<br />
<ul>
<li>Looking into the work by Dr. Forward in his 1990s (and hard to obtain) books</li>
<li>Of course, actually conducting the scaled experiment</li>
<li>Inner solar system asteroid Delta V versus mass map (not perfect math, but good-enough with some help from JPL pre-calculated data)</li>
</ul>
AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com6tag:blogger.com,1999:blog-5515692164785328338.post-61054334823140857502016-05-15T20:20:00.000-07:002016-05-15T20:20:27.847-07:00Tether Superstructure for Large Space CitiesGiven a large number of artificial gravity tubes located near to each other, they all need to fly in formation. A common picture of how to approach this problem is to have many orbital habitats in synchronized orbits. Since their mutual gravity is small, they all essentially trace their own ballistic orbit, and for many orbital locations (like some L4/L5 point) lots of stable non-crossing orbits exist. This does require some station keeping because we can not arrange the orbits with perfect accuracy to begin with.<br />
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Another approach is to tie together several cylinders together to create a larger space station. Like many of these deep-future scenarios I write about on this blog, massive structures would be much better off without needing manufactured steel beams with high compression strength. At a glance, working around the constraints to achieve this ideal might sound impractical, but it's actually entirely reasonable. I will address both scenarios of 1.) the superstructure inside of large gravity balloons and 2.) a generic case for orbital habitats in typical vacuum conditions. These are quite different, but some of the underlying principles are the same.<br />
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<h2>
Purposes of Tethers</h2>
Let's get the first things straight - what specifically the engineering role for a superstructure is.<br />
<br />
<ul>
<li>Rotation - spinning up and stopping the rotation of the tubes that creates gravity</li>
<li>Contingencies - if a tube breaks, there is a space traffic accident, or a host of other scenarios, the tethers must be in place to arrest the motion and avoid a local conflagration from destroying the entire space city in a domino effect</li>
<li>Position - must be maintained against tube-to-tube self-gravitation, external gravitational fields, momentum exchanges from transport, and so on</li>
</ul>
While this blog might have hit on one or two of these roles, I have never faced them all in any capacity. Elsewhere, I have not seen much of any analysis or reference to the superstructure notion to begin with.<br />
<br />
<h3>
Scale-Dependence</h3>
For a small gravity balloon, it might be completely reasonable to pull against a tether anchored into asteroid rock to maintain or start up rotation. On any larger scales, however, you would just use force-exchange with the neighbor cylinders for this task.<br />
<br />
Also, let me modify and expand on a statement I previously made regarding wall-connected tethers:<br />
<blockquote class="tr_bq">
These must be anchored deep into the asteroid rock</blockquote>
Larger gravity balloons will see different physics in this respect. The tethers can be (and likely would be) held in place by the air pressure itself. This will demand some curvature of the wall, as I illustrate in the sketch below.<br />
<br />
Going further, there are many many more interesting things that need to be taken into account on larger scales. As scale increases, the self-gravitation effect becomes larger and larger and for something like Virga, you might very need to imagine something like carbon nanotubes in order to keep all the habitats from collapsing in on the center.<br />
<br />
<h3>
Tensioners and Enabling Technology</h3>
For the superstructure concept to work, we need some form of control input. I have made several references to the generic type of technology whereby a tether can have slack pulled in (thus making it tighter) on command. This is the control machinery side of the equation - we also need good control signals. Simply put, on a large enough scale, the system must have more give than what simple material properties would allow you.<br />
<br />
As a counterpoint alternative, think about what the superstructure would be like if it were made of springs. This could accomplish most of what a control system could otherwise do.<br />
<br />
Momentum will be fully looked at as a commodity in this system. This implies it can be stored and transferred from one place to another as needed. There are large-scale balance equations that will eventually be satisfied, and a gravity balloon would presumably have an agency that followed these numbers (like the various energy agencies are to us on Earth today). <br />
<br />
<h2>
A Reference Case</h2>
Illustrating what I have in mind - tethers extend from the pressure liner into the habitat. These fork into different directions to connect with the different connection points (and have a curve so they can reach closer to the wall) and also with the rotating cylinders themselves. All throughout the middle space you must imagine a vast number of tubes. Each one of these tubes are connected into the tether network - and the tether network will do the work to hold them safely in place, depending on what the particular needs at the time and location are.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWg5gQkLSjQ4O0ozOJCRwIyTwfZE7totsJZGqgCCNn4ceAF6jCu81pLDaNiKSVnsfcndXKHGWsyuAmvFU2zn8Br0S8BAjhEKJT6LbEF7wfqLRFqYv1m6Owr-Z9bFzExj79vEoXLtB5GMQ/s1600/superstructure_illustration.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWg5gQkLSjQ4O0ozOJCRwIyTwfZE7totsJZGqgCCNn4ceAF6jCu81pLDaNiKSVnsfcndXKHGWsyuAmvFU2zn8Br0S8BAjhEKJT6LbEF7wfqLRFqYv1m6Owr-Z9bFzExj79vEoXLtB5GMQ/s400/superstructure_illustration.png" width="385" /></a></div>
<br />
I have drawn an empty space between the tethers and the liner. This isn't strictly necessary because you could just have more tethers connected to the liner. I did not go this route because I assume that additional connections would have an additional cost, but this is not strictly true. So you are free to imagine an innumerable number of tethers extending out from the wall and no "dead space" around the edges. Also, I am burdened by the need to illustrate <i>something</i>.<br />
<br />
You must also use your imagination to picture a network of ever-thinner tethers that reaches out to each individual habitat in the entire volume, and connects (eventually) to the superstructure.<br />
<br />
<h2>
Comparison to Vacuum Orbital Superstructures</h2>
In the cases I've described, air pressure is the "ultimate" tension force. That allows you to pull something away from the center. In an arbitrary orbital location, tidal forces might be one of the easily available options. Even a space elevator could be an extreme version of this.<br />
<br />
Going in another direction, an orbital ring can be used to pull in another direction. Combining tidal and the orbital ring tug, you could arrange habitats in a 2D plane which is essentially a disk around a planet. This structure could hold all the constituent colonies in place. But let me stress that in the radial directions, "anchors" are needed in order to get a good tug on the tether, while operating on habitats that have relatively small micro-g accelerations acting on them.<br />
<br />
These could also be very useful for other mega-structure projects, like solar power arrays, or electromagnetic launchers and catchers. These projects might need precise alignment, and you need something with which to <i>act</i> on in order for them to be viable. The disc-type megastructure might be the ideal option for that.<br />
<br />
Another option also presents itself (which I have sometimes briefly hit upon), you could have a large bag of low-pressure air that envelops a large space of orbital habitats just for the purpose of holding the tethers in place and keeping tension on them. This would enable massive 3D habitats, but would not allow free-air access to the different habitats. Since the latter (a full gravity balloon) requires access to a large mass source (a large asteroid), many locations would not have that option and may possibly find a space city of this type the best available option.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-3113775522082590152016-04-28T19:59:00.000-07:002016-04-28T19:59:54.268-07:00Scaled Experiment Metrics and Development PathwayStability remains an issue - it is one of the core weaknesses of the proposition for the gravity balloon concept. The issue isn't whether the fundamental principle of laminarization will work, or even necessarily that the channel flow physics are suitable for this problem, but the behavior of a complex and fairly high-energy system.<br />
<br />
If you took a simplistic picture of the wedge effect, the prediction would be a slight restorative force for each layer of the friction buffers. The exact directionality of this force gets complicated. It gets even more complicated by the non-rigid nature of the buffers. What we should really raise our eyebrows at, however, is what happens when you consider all the numerous sheets in tandem. Loosely connected dynamic systems can be prone to failure, and this situation seems like a candidate for that. But then again, maybe not. The solution becomes fairly non-trivial.<br />
<br />
Due to the complexity of the problem, our only best option left is to perform scaled experiments. Ideally, we would like to use a fluid that is more convenient, in that the same flow patterns can be produced at a smaller scale. To do this, we will look at the Reynold's number.<br />
<br />
Re = rho v d / mu<br />
<br />
We would like something with a high density and a low viscosity (in particular, relative to air). It becomes fairly obvious that water is our best option for this. Also, you can see that we have 2 dimensions over which to flex our abilities - that is the <b>velocity</b> and the <b>distance</b> metric. Now it seems pretty clear that we want the smallest structure that we can spin at workable speeds.<br />
<br />
These 2 degrees of freedom would still dictate a massive scale of experiment, if taken to apply to the entire system all at once. By that, you can say that d is the diameter of the outer-most friction buffer (for example), and that the system will be a scaled model in terms of all geometric dimensions. The enormous cost of this nudges us to seek cheaper solutions that might go 80% of the way with 20% of the effort. In a more accurate accounting, I'm looking for something more like 10% of the ultimate discoveries with 0.001% of the effort.<br />
<br />
Obviously, we might instead take d to measure the distance between sheets, while also relaxing the requirement for strict geometric similarity. This might be nice in order to make something testable by reducing the <b>number of sheets</b> compared to the gravity balloon reference design. Thus, the overall scale and velocities will be dramatically less, while still demonstrating channel-to-channel interactions with the same flow patterns.<br />
<br />
This still won't be sufficient to make an immediately tenable experiment. We'll need to relax something related to the channel flow pattern itself. The obvious candidate is to change the channel width relative to the overall tube diameter. However, I will not count this as an independent variable, because I think that (for most cases) it will fall out of the selection of the number of sheets. In any format you choose, it's likely that the ratio of the overall thickness of the friction buffer region will be about 50% of the tube radius. So greater channel width will follow with fewer sheets.<br />
<br />
Our hypothetical experiment has been cut-and-slashed a lot by this point, but we're not finished yet! What is truly the really important point? What would we want to learn from this? I would argue that it is the interaction of multiple friction buffers in a (generally sufficiently) turbulent flow regime. Even if you cut <i>that</i> out, there's still some value because it answers some questions about this broader notion of friction buffers (which can even have other applications). However, we do want to answer <i>questions</i> about the friction buffers used in a gravity balloon regarding their stability. We basically know that the answer will be different for laminar and turbulent (or at least somewhat independent). Let me illustrate my thinking in a sketch.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii6VWhuaI6y_BRMfmpFFOD6fz6gSgcYsZwUl8RrpVAWrHU9Ak0_aDVTz72ibJX4bKPo5omMtTa5X9jJyxABYuB898SvWBqAehBn1X7arctQqjEsyYg_sN4yfc1ybZ9mraTGCysF_JZI5s/s1600/friction+factor+experiment.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii6VWhuaI6y_BRMfmpFFOD6fz6gSgcYsZwUl8RrpVAWrHU9Ak0_aDVTz72ibJX4bKPo5omMtTa5X9jJyxABYuB898SvWBqAehBn1X7arctQqjEsyYg_sN4yfc1ybZ9mraTGCysF_JZI5s/s400/friction+factor+experiment.png" width="400" /></a></div>
(let me volunteer that I know I illustrated the transition region poorly)<br /><br />
Basically, we want to probe on the minimum edge of turbulent flow regimes with a multi-sheet friction buffer system. Just opt for an outright change of <b>Reynolds number</b> according to the abilities available for experimentation. This would be the 10% of ultimate knowledge I'm interested in. This would set the stage for everything that may (or may not) come in the future.<br />
<br />
The good news - all this slashing of the metrics gets our experiment size way down (the scale is highly sensitive to Reynolds number). And that gives us some wiggle room. With lower Reynolds number, we can play around with more sheets (even up to 10 or 16 as I'm dreamed about), while staying at least in the turbulent regime. With the same general equipment, dial the numbers the other direction, and see about higher Reynolds number channels with fewer sheets.<br />
<br />
Once you start chewing on this, something new starts to take form - a general format of the development path. Because as these numbers are dialed back up to the full scale (with more resources), its possible to speculate when many different components of the design will be proven in principle. After that, you can image at what point those components will mature into a representative suite of technologies. For instance, at certain numbers, the intra-sheet flow management will become testable. At another point later on, active controls for maintaining the seals could be strapped on.<br />
<br />
So now we've covered 4 (mostly) independent factors. I think this is probably the right way to look at scaling of real, physical, experiments. These can start on a household scale.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-77538992578855069852016-04-27T19:32:00.000-07:002016-04-27T19:32:01.945-07:00Illustrations of the Friction Buffer TapersThis is a fairly simple illustration of the problem that we start out with. The friction buffer concept was conceived of essentially within a cross-section of a gravity tube and the surrounding sheets. As the ends of the tube's hull is pinched, so must the friction buffer sheets as well. The problem comes down to how we manage the geometry of the sheets in this area, as well as how we make the moving connection.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8dDpLrEEnB37pGH8IjsEVA6hWrsYdPbedy_TXiw3ZIqHlKm0syyyp71lj42XedQdjbnIBw7P1T9CXctKh9-eRy4aCdJBuHh-cY-p78o1GWGKRGk9RfZdViVEPhXoBMnk6IyUgnNWlVGA/s1600/problem_statement.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8dDpLrEEnB37pGH8IjsEVA6hWrsYdPbedy_TXiw3ZIqHlKm0syyyp71lj42XedQdjbnIBw7P1T9CXctKh9-eRy4aCdJBuHh-cY-p78o1GWGKRGk9RfZdViVEPhXoBMnk6IyUgnNWlVGA/s320/problem_statement.png" width="320" /></a></div>
<br />
Two solutions have presented themselves as relatively strong candidates for an ultimate solution. They both have a similar pattern to them. The sheets pinch in with both ideas, but in the "zero" solution they terminate against the next-inner-most sheet, while in the "nested" solution they terminate against the hull itself.<br />
<br />
Here is a quick sketch of the <b>taper-zero</b> solution. Keep in mind that this is 1 quadrant of what is illustrated in the above problem sketch.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB1HJrz8C85V5uUKVnXcKYC51LNO7-lIIPcOVfkV9svvyd7mivOKxOHU19gngcb4cWbPVT8UJWUncD-8itORrwvjEOoMvja4A2mqhtJpQJmqiMmmyKYtiqELy2uwQTAFVtf-41zLen2Hg/s1600/taper_zero.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="263" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB1HJrz8C85V5uUKVnXcKYC51LNO7-lIIPcOVfkV9svvyd7mivOKxOHU19gngcb4cWbPVT8UJWUncD-8itORrwvjEOoMvja4A2mqhtJpQJmqiMmmyKYtiqELy2uwQTAFVtf-41zLen2Hg/s320/taper_zero.png" width="320" /></a></div>
<br />
Here is a quick sketch of the <b>taper-nested</b> solution. The calculation for the connection points is different from the taper-zero, and this causes the connections to happen at small radii, and possibly face higher velocities at the connection points. An advantage is that connecting to the hull is probably easier, since it is a hard surface.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdxi9QoUHIFyj6GWtdNhhGCr1wg8pzOU6vN0Y2H6Y8YgSzJAQMqdQtlPKwUvam1_EjbpsxDviz3K6hYROW3KZBiN8_nyWVjmIPs-Kp74P3jgkQr3AABYRO0NHqPJm6R5UWdi-SGutfXQU/s1600/taper_nested.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="289" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdxi9QoUHIFyj6GWtdNhhGCr1wg8pzOU6vN0Y2H6Y8YgSzJAQMqdQtlPKwUvam1_EjbpsxDviz3K6hYROW3KZBiN8_nyWVjmIPs-Kp74P3jgkQr3AABYRO0NHqPJm6R5UWdi-SGutfXQU/s320/taper_nested.png" width="320" /></a></div>
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For the connections themselves, I envision a tensile tensioner acting at the end of the sheet in order to control the clearance and positioning of the sheet. This applies for both of the concepts.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcOon8Ru3cxATXH0bn7sleQ-3uyfPigRy3eRXQDcDnvlmTfPlqB51mfexp3yosfpSOY6s-dlMcHkNlGa0ExmBzZnKBnYLSa36WLawJ6L9R1YPEMuax7IG-9krR-gyEwPoxh2ZFxsyv1v4/s1600/connection.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcOon8Ru3cxATXH0bn7sleQ-3uyfPigRy3eRXQDcDnvlmTfPlqB51mfexp3yosfpSOY6s-dlMcHkNlGa0ExmBzZnKBnYLSa36WLawJ6L9R1YPEMuax7IG-9krR-gyEwPoxh2ZFxsyv1v4/s200/connection.png" width="166" /></a></div>
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Hope these were fun to look at. I'm not much of an artist, but since the hand-drawn sketch is a popular style these days, I figure "why not" and avoid the tedium of creating these on a computer.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-86966337595471830312016-04-22T19:39:00.000-07:002016-04-22T19:39:22.151-07:00Introduction of "Taper-Nested" Friction Buffer Connection SchemeSuffice 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.<br />
<br />
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).<br />
<br />
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:<br />
<ol>
<li>Constant distance between each connection</li>
<li>Setting connection location based on a invariant relative velocity limit</li>
</ol>
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.<br />
<br />
<h3>
Engineering Showdown between Solutions</h3>
<br />
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 <i>advantage</i> 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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-82589200641588918892016-04-21T19:43:00.001-07:002016-04-21T19:58:19.575-07:00Artificial Gravity Tubes with of the Mashveya World with Friction BuffersThere are now honest-to-god friction buffers being utilized in fiction and world-building. Check it out at:<br />
<br />
<a href="http://accelerando.tumblr.com/">http://accelerando.tumblr.com/</a><br />
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This author illustrated the tethers used to spin up a tube, as well as a buddy system for spin maintenance. For future reference, <a href="http://accelerando.tumblr.com/post/143024728337/torque-axles-for-spinning-up-an-open-air-space">here is one</a> post that contains both pieces of content. This has a great deal of technical accuracy. You can see in the axle mount system (buddy system) that there are trusses necessary to handle the varying compression / tension action with changing the direction of angular acceleration.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9_qEwiR5i61lJ5THI80RFwKSmniVUDhUzFa5e0LoRTB7K0GqC7lon6ZQyBq7h087tP6xeWUZ_rH8IWN2FMvKJOmtfH_1tRSVKFM8S6Tc-1SFGTbSb2AmbgB8qYh0Q39Z43FOC-2msf6Y/s1600/tumblr_o5tq6wId8a1vqm28yo1_1280.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9_qEwiR5i61lJ5THI80RFwKSmniVUDhUzFa5e0LoRTB7K0GqC7lon6ZQyBq7h087tP6xeWUZ_rH8IWN2FMvKJOmtfH_1tRSVKFM8S6Tc-1SFGTbSb2AmbgB8qYh0Q39Z43FOC-2msf6Y/s400/tumblr_o5tq6wId8a1vqm28yo1_1280.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimlxskXOSbgt884V64daMqttaBlqO4qLRo2WOF2bAQn5XTedKgm50fuOJ7woBsfdjmbTGlqHnDFjQtiqUK0p-HrK0oBEPOfAp_scRPSy3dE-LvscU1K47yaiUEviLrnt3ak_kgopPnNYw/s1600/tumblr_o5tq6wId8a1vqm28yo2_1280.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimlxskXOSbgt884V64daMqttaBlqO4qLRo2WOF2bAQn5XTedKgm50fuOJ7woBsfdjmbTGlqHnDFjQtiqUK0p-HrK0oBEPOfAp_scRPSy3dE-LvscU1K47yaiUEviLrnt3ak_kgopPnNYw/s400/tumblr_o5tq6wId8a1vqm28yo2_1280.png" width="400" /></a> </div>
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Images from <a href="http://accelerando.tumblr.com/">Erin Accelerando Content Creator Blog</a></div>
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The world these designs exist in is called Mashveya, and uses transportable fuels (like hydrocarbons) for their energy economy, so these are free floating and exist in a smoke-ring type world with a fairly low density of habitation. I find this image with additional world context quite stunning. Calling this a catamaran system makes a lot of sense.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKRRONELAnGmHxoKAo3kc7be6NxYPVWd-CKztM-SmZXDdIvTi06SuuDEup6bJQkX6rl8LGGUVpgHdmwTcHT_J9lqupdBDU-kGJKW_8cZElrLmNzWeNCmSAX_T_G9OnG2UVL2g5R8pSidI/s1600/buddies.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKRRONELAnGmHxoKAo3kc7be6NxYPVWd-CKztM-SmZXDdIvTi06SuuDEup6bJQkX6rl8LGGUVpgHdmwTcHT_J9lqupdBDU-kGJKW_8cZElrLmNzWeNCmSAX_T_G9OnG2UVL2g5R8pSidI/s400/buddies.png" width="400" /></a></div>
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Images from <a href="http://accelerando.tumblr.com/">Erin Accelerando Content Creator Blog</a></div>
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Quite a few possibilities jump right out at me. Many different methods of navigation would be possible. You could use some flow control to direct air out one end to power flight in the axial direction. It would even be possible to fly perpendicular by allowing the outer-most sheet to spin freely, and blocking flow around the middle portion or on the two sides. I might diagram some of these later. These are extremely cool. Seeing these brings an entirely new perspective to some of the underlying concepts.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com1tag:blogger.com,1999:blog-5515692164785328338.post-79160106078260079072016-04-20T19:44:00.001-07:002016-04-20T19:44:13.427-07:00The "Taper-Zero" Design for Friction Buffer Tapering and PressurizingGravity balloons, with friction buffers to allow artificial gravity inside them, have so-far had one major design aspect missing. There are a few reasons for this. Partly, it was an non-intuitive problem, and every time I returned to it, I started out going down the wrong track with a careless sign error somewhere in there. Another reason is that it's genuinely a hard problem. But the main reason it has taken me so long to present a full solution is because I didn't want to accept what the math was telling me. Up until this point, I have always wanted to imagine the friction buffer sheets as something with a zero-thickness limit - something that could be literal paper, aluminum foil, or some other absurdly thin material. This was unrealistic and didn't fit with the other basic realities of the turbulent reference design parameters. I also resisted a 2nd obvious design decision, which was to have the moving seals connect sheet-to-sheet as opposed to sheet-to-center-line-structure. I may go into those trains of thought, but in this post I mainly want to communicate the bare minimum to lay out this design.<br />
<br />
The problem is how to "terminate" the friction buffer sheets. For the bulk of an artificial gravity tube, there is radial symmetry, so the problem is relatively easy to envision. The fluid flow between sheets is very nearly approximately a parallel sheet flow problem. The basic mechanism to reduce friction is flushed out in the radially symmetric form. Intuitively, it seems "messy" to picture how the sheets pinch at the end, similar to the tube itself. No matter what specifics you opt for, this also introduces a moving seal, at which point an engineer may think "yuck", but still accept that there's no choice but to deal with some seals. We take comfort in the fact that, while the seal length is large, it is at low speeds and low pressures. The problem that really blows down the house of cards is the realization that, as the sheet pinches to the contact point, the air pressure in its volume decreases - and that different layers decrease at different gradients.<br />
<br />
I've summed up some details of this problem space in the last post and at other times in this blog. So here I want to jump right into the solution space.<br />
<br />
<h2>
The Solution Space</h2>
<br />
A design solution starts by holding something specific constant, and then fills in the rest of the values from there. I will name the different solutions according to that assumption. The first intuition I had was to terminate all friction buffer sheets very close to the tube's end opening, which I will call the <b>taper-center</b> design. This is still a possible solution, but I believe it's inferior due to the complications of making the seal act between the flexible sheet and the stationary connection point around the tube ending.<br />
<br />
As I came to better understand that the pressure distribution within the friction buffer region would be a problem (at all), my natural intuition was to imagine that there is no pressure difference over the radially symmetric part of any of the friction buffers. I would call this the <b>sheet-isobaric</b> solution method. This start with the assumption that we will preserve the "no strength" requirement for the sheets, and figures out where to go from there. The problem comes when you pinch in toward the end opening - even the slightest bit. The pressure drops as you decrease radius, but the real kicker is the fact that pressure drops (a) below micro-gravity ambient and (b) faster for the innermost sheets. This means that in the taper region the sheets will be "sucked" in towards the tubes. Combating this would require complex, rigid, and moving parts. I hate all 3 of those adjectives! The fact that the sheets can't passively maintain their shape if they don't have a positive pressure is what I will call the <b>convexity-constraint</b>. How often do you see a balloon with sharply convex shapes? Never, exactly. Now, the balloon notion here is different from that of the overall gravity balloon. But for simplicity of operation, we all but demand that the friction buffers act sort-of like a balloon so that they don't need rigid members. Moving on, why does this constraint create any problems? Why do we need to taper (pinch at the end) the sheets at all? Why can't we just terminate them against a rigid structure at the radius they start out at? Because that would demand a moving seal at > 100 mph, and defeat most of the purpose of the friction buffers in the first place. This is what I will call the <b>velocity-constraint</b>.<br />
<br />
Maybe we can come to something of a compromise here, and now we arrive in a design space that I found to be a large bit of a pitfall myself. I imagined the sheets terminating against a rigid structure that fanned out from the end opening. This increases the radius in a graded system, and thus largely avoids the velocity-constraint. I might call this the <b>center-graded</b> deign, and it has some neat properties, but those properties wound up being largely irrelevant to the problem. These configurations just couldn't save us from the convexity-constraint. By connecting to a seal with a rigid structure at low radius / low velocity, you are still going to run into that sucking problem and have to use a massively expensive system to partially pin the moving sheet to the rigid structure. I struggled in this logical knot, trying to somehow make the pressure gradient turn around in my mind. Alas, when you rotate stuff, it wants to fling <i>outward</i>. Fighting that is a fool's errand, and tension is better than compression by 10x factor or greater.<br />
<br />
So let's move on to accept <b>taper-zero</b> hypothesis and design. The cold logical facts are telling us that the friction buffer sheets (1) are concave geometries (2) must have positive pressure compared to ambient and (3) must have positive pressure relative to the next outer-most sheet. This is a mouthful, it is <i>weird</i>, and it sacrifices some of the most beloved assumptions up until this point. I believe there is a logical train of thought directly from these principles (hard-fought conclusions from the previous failed design spaces), and I will probably not do that train of thought justice here, and I will be skipping some. But the final insight is pretty cool.<br />
<br />
<br />
A combination of two, and somewhat a 3rd one, factors suggests that we don't connect the sheets (moving joint) to a rigid structure, but instead to each other. Those are the convexity-constraint and the velocity-constraint together. We want the outer sheet to connect at large radius (velocity, combined subtly with a desire to keep strength requirements low), but we also want to keep the friction buffers "puffy". We wind up with a vision of one puff puffed out on the outside of another puff. Now, for pressure, this suggests that the connection between the puffs is just a little bit higher than ambient. This directly suggests what the pressure of each stage will be like (assuming you have values of radii for connection points, which you can just get directly from the velocity constraint).<br />
<br />
<h2>
Taper-Zero Design Specifics</h2>
<br />
Each sheet connects at a different radius - smaller radius for the innermost sheet, and large radius for the outermost sheet. The exact picking of connection points can be engineered to your own desire. Here, I'm going to be using the velocity constraint to have all sheets move at the end-opening speed at their connection point. I'm using 10 sheets in this reference design, because 16 (a previous benchmark) is just too labor intensive to illustrate.<br />
<br />
These sheets will actually have a pressure at some minuscule value over ambient at the seals, and they will be constantly leaking air (I'll talk more about this later). Additionally, there will be no complicated system maintaining the pressure and position. Instead, the 2 ends of the friction buffer sheet will have a simple remote-controlled tensioner unit which can increase or decrease the clearance distance (thus impacting the leak rate and the pressure).<br />
<br />
Start from the seal, and move outward toward the center of the channel in the radially symmetric portion of its geometry. The pressure increases, depending on how fast that stage is rotating. The ultimate pressure in the channel is almost entirely a consequence of the rotation speed of the stage. Next, observe that inside of the channel there is some radial pressure gradient, but the sheet is also holding back some amount of air pressure as well.<br />
<br />
I don't know if this fully illustrates it, but it is an attempt. This graph is telling the story for each stage, going from the connecting point (venting air to atmosphere) to the channel interior.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx17QiqD8pPohSwEFI4DZKkZ9XogavjtG93yIwZdMTPa1I9Fc8BTuIMcf8yHAbnXDRLY-UqlweTDzXODh9DwwHDWpXeBGGW-7K95m0N2bbhD3Vyv0DkhfcYvw4XFpCOocSyMqKYBgzVXs/s1600/Screenshot+2016-04-20+20.54.15.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx17QiqD8pPohSwEFI4DZKkZ9XogavjtG93yIwZdMTPa1I9Fc8BTuIMcf8yHAbnXDRLY-UqlweTDzXODh9DwwHDWpXeBGGW-7K95m0N2bbhD3Vyv0DkhfcYvw4XFpCOocSyMqKYBgzVXs/s320/Screenshot+2016-04-20+20.54.15.png" width="320" /></a></div>
<br />
Next, let's look at the profile as you increase radius from the center-line in the center of the tube. You can't literally traverse this path, and this is just an illustration. The tube itself has a pressure increase from ambient, dictated by its rotation. The innermost friction buffers mostly inherit these same numbers.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkDh5ZMEg3OXHcwqRITlx-dtQ37VbaYhXCmYN6Dee-DfFn40jDtca4UVaIFWCjB6suiVV47jfBjA63mk7j2a5GKssZwSPxiAbzqjyA4AJDvznZlsAsTvnTbxHr0V2QScvAwXdTxknDxMI/s1600/Screenshot+2016-04-20+20.55.12.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="247" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkDh5ZMEg3OXHcwqRITlx-dtQ37VbaYhXCmYN6Dee-DfFn40jDtca4UVaIFWCjB6suiVV47jfBjA63mk7j2a5GKssZwSPxiAbzqjyA4AJDvznZlsAsTvnTbxHr0V2QScvAwXdTxknDxMI/s320/Screenshot+2016-04-20+20.55.12.png" width="320" /></a></div>
The big point I want to make here is that the friction buffer sheets are <i>fighting</i> the radial gradient of air pressure. In the 2nd graph, you can also make note that the saw-tooth looks different. The "step" part of it has a slope to it that the outer layers don't share. This is because the inner layers are rotating faster. That shows the presence of a strong radial air pressure gradient toward the inner-most layers compared to the outer layers that are most stationary.<br />
<br />
<h3>
Air Flow</h3>
<br />
The floor of the artificial gravity tube, and the sheets themselves, would have holes in them. Not a huge number - there is no obvious lower limit. The inner layers would have more holes than the outer layers, because air must flow through them all to get to the outer layer while ever layer loses about the same amount to leakage.<br />
<br />
In this scheme, while the air flow percolating through the layers can be actively controlled, it is not necessary. It would be more simple and still effective to just operate the tensions that control the leak rate along the seals, and these would be tremendously simple seals.<br />
<br />
In retrospect, abandoning the dream of zero-strength requirement sheets bought us <i>a lot</i>. It's that simplicity that I see coalescing the design where someone can put their foot down and say "yes, this all is consistent and coherent now". I still see possible improvements to this, but the important thing to note is that I see them all starting from this design as a template.<br />
<br />
What's left to do? I need to revisit the impact of elasticity. It was never really an issue before now, but with the sheets holding back some quantity of air pressure, it will be relevant again. Trickier - it may change as the rotation rate changes. That demands some extra engineering of the seal actuation during spin-up and spin-down. Nothing crazy, I can already mentally picture a lot of the specifics. It's likely that the tube would have auxiliary compressors that will intentionally inflate the friction buffers while the tube is not yet rotating. Predictable movements in this phase of spin-up will give confidence to begin rotating the entire tube.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-10266103062337288112016-04-18T20:42:00.002-07:002016-04-18T20:42:43.936-07:00Runthrough of Friction Buffer Management ChallengesI have been long-overdue to share even some of the most basic thoughts I've had regarding specifics of the configuration of the friction buffers. To recap some basics, this blog describes open-air rotating tubes to create artificial gravity. The ends are pinched (to perhaps 1/8th or 1/10th the surface radius) with air flowing freely through the inlet and exits (aside from flow control clutter I've written about). The rotation can be maintained at a low energetic cost by multiple layers of sheets surrounding the tube.<br />
<br />
Problems only become glaringly apparent when you combine all of these construction elements into a single package, and realize a component which was helpful in one respect is messing up the design in another respect that was hard to imagine. In particular here, I have in mind the combination of 1) the taper and 2) the friction buffer layers. The obvious conception is that the friction buffers (just like the ground itself) tapers up toward the opening. But this comes with hazards.<br />
<br />
I don't mean to claim this is the only engineering problem within this general topic. However, I also want to stress that I see none of these inflicting anything close to a mortal wound. They are, for the most part, problems with foreseeable workarounds. I only intend to articulate how these workarounds constrain the design space. I will have to start by naming the problems in the first place<br />
<br />
<h3>
The Balance Problem</h3>
<br />
The inside air of a tube falls with radius from the center-line. This is true for any rotating artificial gravity habitat. The point I want to stress here is that we also have to think of this in the context of the friction buffers.<br />
<br />
Let me get one thing straight - the relative rotation speeds of the friction buffers are dictated by the fluid mechanics. For complex geometries, you can't even predict this perfectly in advance.<br />
<br />
Now if the air is falling in pressure because it is rotating inside the tube, then it is also clearly rotating between the friction buffers, but at a staged rate. So the math is different, but there's still a pressure gradient - and pressure falls as radius increases. Carry this to its logical conclusion and you'll arrive at a contradiction. Walk from the center-line to the outermost friction buffer, and the pressure goes down over the entire trip. But the center-line must be the same pressure you started with. The discrepancy is because the tube will act like a centrifugal pump if you let it. Our intent is to avoid that by implementing a barrier to the flow somewhere (as an absolute necessity).<br />
<br />
Solutions:<br />
<ol>
<li>Maintain a pressure barrier as part of the outermost friction buffer, keep pressure drops over all other sheets (and the surface) small</li>
<li>Maintain a substantial pressure barrier in the floor itself and allow the sheets to keep a small delta P from one to the next</li>
</ol>
<h3>
The Taper Problem</h3>
<br />
This is the most critical and most interesting problem to me. It's also hard to explain. Start out the outer surface of the outermost layer of the friction buffers. The pressure drops as you go to lower radius. But (and here's the kicker), as you climb the taper at the end, the rotation rate drops too.<br />
<br />
Firstly, this presents a problem that you will have trouble maintaining a positive pressure compared to the ambient atmosphere as you climb toward the end opening. Secondly, it means that the problem repeats itself for each layer of friction buffer compared to the next.<br />
<br />
Why is this a problem? Consider a balloon (no word tricks here, a literal balloon). It has a positive pressure, and it maintains its shape because of that pressure. If some part of the balloon transitions to a negative pressure, what happens? That parts caves in on itself. That's the problem we are dealing with in the taper regions. <br />
<br />
Solutions:<br />
<ol>
<li>Design the sheet-by-sheet over-pressure to be greater than the pressure change drop as it climbs the slope toward the end opening</li>
<li>Implement the seals in a graded pattern outward from the end opening</li>
</ol>
I know this is getting hard to visualize. Here is a token attempt to sketch it. (please ignore the lines in the upper right, it's just too late to edit them out right now)<br />
<br />
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It's hard to keep in mind the speeds when you look at this. All friction buffers have about the same speed difference relative to its neighbor, and the outermost sheet is almost stationary relative to the ambient air. So this does not introduce any extraordinary speeds, because while the innermost sheet is moving fast, the taper brings it down to a manageable speed.<br />
<br />
<br />
<h3>
The Seal Problem</h3>
<br />
This is the most obvious of all - the connection between the sheets is a moving seal over a long distance, and this can easily get expensive. Solutions:<br />
<ol>
<li>Mechanical tracks to maintain the coupling and minimize the air ingress</li>
<li>Passive ring that can be tightened dynamically to keep the clearance distance small</li>
<li>Labrynth seals </li>
</ol>
Points #2 and #3 are mostly complementary.<br />
<br />
My own vision is a combination like #2 for the balance problem, #2 for the taper problem, and #2 for the seal problem.<br />
<br />AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-13546211026741999512016-04-11T18:27:00.001-07:002016-04-22T18:51:37.346-07:00Small Balloon-Tubes Systems, a Gauntlet of Wires, and Sucking Sheet PinchesThis is a fairly general brain dump of a collection of topics. I could see them all being posts, but not all of them are likely to become posts, so I want to get them out while the concepts are fresh in my mind.<br />
<br />
<h2>
People-Units </h2>
<br />
While working on the math for this stuff, I keep coming back to notions of "magic" numbers. There are very defined numerical parameters that we can spin our own abstract tapestry. What's most unique about this project is what defines those bounding parameters - they almost all come down to human biology. Why is a gravity balloon a certain size? Because humans need a certain pressure, and this combines with the _fundamental_ gravitational constant to produce a tangible number.<br />
<br />
All this reminds me of the notion of "god" units, or Planck units. The fundamental units span the full range of physical values. Because of this, you can measure practically any complex quantity as a combination of the fundamental ones - like volume.<br />
<br />
People units constitute a rougher and more gray set of fundamental constants. Combining the gravity people need with the air properties they need, you can get the characteristic height of Earth's atmosphere, but there are lots of other ways you can come up with different length units.<br />
<br />
<h2>
Minimum Size for Friction Buffers</h2>
<br />
Lately on NASA Spaceflight forms, I've seen artificial gravity inside of balloon envelopes come up. This has a rather strange similarity to what I've talked about in this blog. The motivations given for this design are predictable - space stations can continue to be thought of as a nice inertial frame of reference, like the ISS, while adding centrifuges in a limited domain. The basic idea is to take a large Bigelow module and put 2 counter-rotating centrifuges. The two can be spun up at the same time so they have minimal effect on the rest of the station.<br />
<br />
The minimal effect principle is an objective very much worth pursuing. For near-term space stations, we will expect many roles to be fulfilled by the station, and external operations can not be compromised for the logistics of a spinning module. In this context, it's hard to imagine that anything other than a fully enclosed centrifuge can make sense.<br />
<br />
But where does this lead us? Operationally, I can paint somewhat of a picture. If you moved around in such a centrifuge, vomiting seems inevitable. However, limited time spent for the purpose of maintaining health seems possible if you limit people's activities (and compare to the fact that they'll be feeling sick anyway). But what about drag? For something just a few 10s of meters, it's likely that you would leave the annular space alone between the centrifuge and the balloon wall. But at what size will it make sense to add any friction-reducing buffers? It depends on how much energy you're willing to put in, but it seems simple to compare this to the energy expenditure of other station systems.<br />
<br />
That sounds like some pretty low-hanging fruit for developing a practical case for more investigation into this tech. Importantly, some push into this area would raise some obvious experimental pathways to establish the friction buffer sheet stability.<br />
<br />
<h2>
Scaled Experiments </h2>
<br />
Stability of the friction buffers is a tough topic, so it makes sense to give up on the analysis and defer to experimental evidence at some point. Fortunately for us, the available fluids helps to make the problem easier for us. Air is a low density and low viscosity fluid. Water an extremely obvious stand-in for scaling based on similar Reynolds numbers.<br />
<br />
I have two types of things in mind:<br />
<br />
sheet Reynolds number<br />
true scale model<br />
<br />
You could scale the entire system of an artificial gravity tube by selecting an experiment geometry that is exactly similar to it but on a tabletop scale. In practice, however, this leads to sizes or speeds and torque that are just not workable. This could not be a tabletop scale experiment.<br />
<br />
Instead, it will make more sense to emulate the separation distance and speed of the friction buffer layers, and see how the multi-sheet stability looks with different kinds of configurations.<br />
<br />
Problem with all Center Connections<br />
I misspoke somewhat in my previous post introducing transport of commodities. I had presumed that some commodities could be sent through connections that existed exactly on the axial line. This can not possibly be the case.<br />
<br />
It is an easy mistake to mistake. You can simply imagine that cargo moving through the center can move slightly to the side of the axial line itself. The rotation speeds will not be substantial for a great distance beyond this, and the weight itself would not be overly burdensome. The problem comes when you realize that the rotating part... well... rotates. You can't simply move cargo to the size of the connection and move it along, because the line (pipe, wire, etc.) going to the colony rotates. If the cargo stalled inside of the plane that this line rotated in, then it would collide with the line.<br />
<br />
This seems impractical in my vision of the economy. It would be far better to keep the center-line of artificial gravity tubes completely empty aside from rails which which cargo is moved along with. The challenges for connecting at a larger radius for power, water, information, etc. are completely solvable. Transit of bulk materials is much trickier, so the center line would need to be reserved for these activities.<br />
<br />
<h2>
Relative Movement of Tubes and Balloon</h2>
<br />
I must take some time to argue with myself on the subject of how the artificial gravity tubes move relative to the balloon "wall". The most simple solution is that they don't move. Actually, this is quite practical in terms of the inflation physics. Halting the rotation of an asteroid in general isn't a hard problem. With a strong tether, you can dangle a large rock from the equator, slowly releasing it to a large radius, pulled by the rotation of the asteroid. This is a cheap way to expel a great amount of the asteroid's rotation. You may still keep a small amount of rotation to stay sun-synchronous. The inflation process itself also reduces the rotation speed. The only cases where this is not practical are small asteroids. Those will be easier to manage in general, and will probably have rotating joints for electric connections.<br />
<br />
So I envision artificial gravity tubes fully tethered to the wall. This will help to keep them suspended in-place inside of colonies with insanely huge scaling. It will also develop a hard electrical connection between the tubes and solar panels that may lie out the surface of the asteroid (or slightly off). Things can be balanced by a tether at the asteroid-sun L2 and L1 points (these are not impractically far away either).<br />
<br />
Because of this, I will personally have to abandon the idea of the geosynchronous washer-shaped radiator. It's better to not rotate and tie the tubes to the walls (if sufficiently large).<br />
<br />
<h2>
Pressure Management and End Seals</h2>
<br />
Friction buffers are not rigid. I mean, they're monstrously huge. Instead, they would maintain their shape by having some positive pressure inside of them. Note that this positive pressure is relative to the next outer-most friction buffer sheet. This constitutes some fluid management constraints. Keep in mind that air pressure changes with the rotational acceleration (like a gravity gradient). Because of this, we can draw a graph of the pressure over an outward line from the axis to somewhere on the surface of the outermost friction buffer.<br />
<br />
Are there any complications with this scheme? Of course there are. The ends are pinched, remember? As you get closer to the end-cap, the friction buffer sheets pinch in as well. This means that the acceleration gradient will be more gentle. In the limit case, consider that the outer-most sheet is almost stationary, but the 2nd outermost sheet is rotating very slowly. Going from the outside to the pinch point will be a small change in pressure. On the other end of the spectrum, the air pressure changes a great deal from surface to axial line inside the tube itself.<br />
<br />
We would like to equalize all the different pressures around the end seals (this would make it easier to seal, clearly), but this isn't possible due to the pressure demands of the friction buffer layers at their full radial position. The real problem comes at both ends of the tube where we should maintain a negative pressure inside the spaces between the friction buffers. Positive pressures are easy, negative pressures are tricky. I'm not sure exactly how this problem would be solved, but I think there are a lot of tricks to mitigate the challenge.<br />
<br />
To be clear, I think this is one of the biggest problems for the viability overall. It probably comes somewhere close to the stability of the buffers in general.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com7tag:blogger.com,1999:blog-5515692164785328338.post-32975098052183303262016-03-26T20:06:00.000-07:002016-03-26T20:06:07.411-07:00Water & Sewage Service Between Space ColoniesA space colony must have a closed water cycle. Any place short of living beside a freshwater ocean will see extraction costs of new water too high compared to recycling the existing inventory. For a gravity balloon with multiple independently rotating tubes floating inside, however, it makes little sense to constrain that closed cycle to the same tube where the water is consumed. This is because the economy of scales are overpowering. Reprocessing water from 1 billion people is a very different challenge (and actually quite doable on a per-capita basis) than doing the same thing for a small municipality of 20,000 people.<br />
<br />
So let's take a peek into this strange engineering problem, and the tremendous surprises that it holds for us.<br />
<br />
<span style="font-size: large;">Formulating the Problem</span><br />
<br />
Economically, pipelines are good. Any place that can avoid trucking in water does so. Consider that we could transport water in batch processes. This could be done in vehicles existing in zero-gravity, and vehicles specialized to making the same trip in repetition. So it's not that we can't, but we would still prefer not to.<br />
<br />
On the other hand, there is a certain critical resource in a tube that we want to avoid tying up - the center axial space. Virtually every transport necessity is competing for that same space.<br />
<br />
This makes the final solution seem obvious.<br />
<ul>
<li>Water reprocessing will happen in dedicated facilities outside of the tubes where it is consumed</li>
<li>It will be delivered and collected by pipes (no batch processes)</li>
<li>This will avoid occupying the central axial space</li>
</ul>
<br />
<span style="font-size: large;">We Can Satisfy Those Requirements</span><br />
<br />
Fascinatingly, it's the liquid phase of water (versus air) that makes it possible to satisfy all these stipulations without requiring any insanely speculative technology. Water can maintain a level inside a gravitational field, and this is the obvious property to exploit.<br />
<br />
After thinking through the basics, here is my mockup. I actually got the rotation direction wrong. This diagram would actually apply for scooping up sewage (closed system, right?), and for pumping in fresh water, the tube exit should point in the direction opposite of the rotation.<br />
<br />
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<br />
We have maintained 2 frames of reference. One is stationary (non-rotating), and the other is the rotating colony. The water level exists within a very low artificial gravity field. For the purposes of argument, I imagine this to be 1/10th Earth gravity, the same as on the inner surface of the tube.<br />
<br />
This raises another objection - that the low gravity makes the water prone to splash out. This is why I anticipate some amount of buffer room above the water level so that it can eventually fall back down. This exists in the rotating reference frame as well. We can do even better - overlapping sheets (not even touching) can capture water trying to get out and allow it to slowly drip back down. With this, the lower gravity level should not present much problem.<br />
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<br />
One could continue with more granular problems to solve. You may need some special couplings in order to keep them aligned nicely even when the entire station has some change in movement. Additionally, you would need some way to put it together in the first place and a way to separate the splash guards and allow temporary disconnection. A spin-down, spin-up process is expensive.<br />
<br />
I found this solution to be surprising, and downright delightful. I think it's a reasonably robust design to maintain a <i>continuous</i> service. The ability to have such a thing is critical to provide economic benefits of a space mega-city, and it makes it feel more human, in a way. Some people want to live off-world, but still like taking showers.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-30841368443265325672016-02-20T21:19:00.000-08:002016-02-20T21:19:01.879-08:00What About Transport of Utilities Between Space Colonies?Much of what I write here is an extension of the idea that our conventional vision of orbital space colonies involves an impractically small population size. This is natural to think about in terms of movement of people, but it’s even more painful if you compare it to how we provide mundane utilities to cities on Earth today.<br />
<br />
<h2>
What Utilities Are Involved?</h2>
Space colonies may have somewhat different needs than Earth cities, but we're all human, after all. Provision of utilities is all very scale-dependent. In my reference size of an artificial gravity tube, there are about 20,000 people. Compare to a city on Earth, what utilities are distributed on a scale larger than this? The answer is “just about everything”.<br />
<br />
Things that must be distributed between tubes: <br />
<ul>
<li>Electricity</li>
<li>Communication</li>
<li>Goods</li>
<li>Industrial Fluids</li>
<li>People</li>
<li>Water / Sewage</li>
</ul>
I’m using a catch-all of “industrial fluids” to denote anything that is remotely similar to the role that oil plays in the world today. We transport oil through pipelines because there is <i>SO MUCH</i> of it to move that we need good efficiency. A space colony wouldn’t use hydrocarbons in the same way, but they may use fuels like Hydrogen. All these things would necessarily need to be managed among several tubes at once, and possibly throughout the entire gravity balloon. But I do want to make mention of at least one thing I can imagine for which the multi-tube assumption is not (can not be) true for.<br />
<br />
Things produced and consumed inside a single tube:<br />
<ul>
<li>Light </li>
</ul>
The psychological impact of light can’t be discounted, but when we’re talking about a colony that has a wall over 10 km thick, then it’s pretty impractical to pipe natural sunlight through this barrier, and then pipe it through complicated snaking channels into a cluttered and rotating tube.<br />
<br />
<h3>
But Physically, Where Will These Go?</h3>
Artificial gravity tubes have an access limitation around the outside due to the flow dividers to reduce drag. That means that all utilities, like people, need to go in through the tube openings on either side. For most of these utilities, they will need to access some connection points near the axial line, and then be distributed to the inner surface through “vertical” pipes or elevators (elevators are in the case of batch processes).<br />
<br />
The challenge is that you want to avoid moving things in batch processes as much as you possibly can. Batch processes are tremendously economic. A bath process going through an airlock would be much worse - thus, the entire motivation for a gravity balloon.<br />
<br />
<h2>
How Can They be Moved?</h2>
<b>Electricity</b> probably has the simplest answer, and is a total cop-out. We use slip rings all the time for electric machinery, some of which are the largest units on the grid, supplying more than the population of one of these tubes. The power constraint itself should not be a problem, but there will likely be a voltage constraint. Several kV shouldn’t be a problem, and this might constrain the transformer architecture a little bit. Let me elaborate a little more specifically. Imagine that there are 2 levels of transformers to get electricity from the zero-gravity high-voltage electric transmission system to someone’s home on the inside of the tube. You will need one transformer to step it down from, say, 750 kV outside the tube to, say 10 kV, going into the tube. After that, you’ll need another transformer to take it down to 100-200 V for residential use, as needed. This is because the slip-rings connect the tube electric distribution system to the outside by brushes that slide along a conductor while the tube spins. These brushes wear out, and they will wear out faster at higher voltages. There is a practical limit, and also other hazards due to the larger footprint of the slip rings.<br />
<br />
<b>Communication</b> also has an easy cop-out, which is wireless technology. Again, this might be a slight headache for the experts (in this case, networking experts) who build the system. Alternatively, you could (again) use slip rings in this case as well. Even better, it might be possible to create a coupling for a fiber-optic cable that allows both ends to rotate relative to each other. This wouldn’t even necessarily have to connect near the tube’s axial line (I guess the same could be said for electricity, but it’s a harder sell).<br />
<br />
<b>People</b> - I’ve mentioned moving people in and out in other posts. In short, you will need elevator transport to and from the axial line, although I am partial to the idea of entering the tube through a literal slide.<br />
<br />
<b>Goods</b> - again, there’s no other choice but to move shipping containers through the axial line and lower/raise through elevators. Combined with people, the staging areas for these are sure to occupy the majority of the bottleneck of the tube-end openings.<br />
<br />
Air - I have not mentioned among the others, because it must be handed in the same distribution system that temperature control operates in. It’s not a “visible” distribution system, although barriers to control the movement of air will be a major source of clutter in the tubes.<br />
<br />
<b>Industrial fluids</b> - this is where the problem gets hard. If you did need to transport oil or natural gas, you would likely have to do it in a batch process along with the rest of the goods transported. There is still the possibility for a local distribution system on the inner surface of the tube with storage just for that 20,000 person (or however many) population. A rotating joint for this type of stuff is not easy.<br />
<br />
<span style="font-size: large;"><b>Water / Sewage</b></span> - You would think that the same principle might apply here - that there’s no other option but to ship in water trucks through the axial line and have them disembark, unload, and exit alongside sewage trucks taking the used water back out to shared process facilities among many tubes. But I think this is where it gets interesting.<br />
<br />
Water is different than something like natural gas because contact with ambient air isn’t necessarily bad, and because it has a definite phase difference. This allows for a different kind of coupling… a weird one that I can’t imagine would ever come up except for in situations like the tubes in a gravity balloon. In short, I think you would use something like a toroidal water-garden at a partial gravity level. There, you can allow a glorified straw to add water to the partially-filled torus, or to suck up sewage.<br />
<br />
At this point, it’s getting weird, and I like that. But the conversation about water distribution is going to be more involved. This is something I hope to cover in my next post, and I think it touches on some very cool and very novel concepts.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-37725088167360133492016-02-16T20:31:00.000-08:002016-02-16T20:31:04.601-08:00But Would the Nested Flow Dividers Really Work?People coming from different backgrounds will have trouble with different parts of the gravity balloon concept for space colonies. However, the one criticism I am most excited to receive is that the flow dividers might not work. This came up on a <a href="http://www.reddit.com/r/Futurology/comments/368jge/gravitational_space_balloons_possible_kind_of/">reddit thread</a> sharing this blog. I am overjoyed to hear this criticism - because it means that the critic has understood all the big details. They are up to speed, and that means they are ready for the <i>meat</i> of the conversation.<br />
<blockquote class="tr_bq">
Now, having something spin in an atmosphere presents issues of its own,
and the author proposes a complicated scheme involving nested shells to
avoid turbulence. This feels like the sketchiest part of it to me -
there's a lot of handwaving involved.</blockquote>
For too long, I have neglected to argue the core mechanical details on this blog. I can't give it the full treatment it deserves in limited time, but I'll break out the big guns (even if that only means labeling them).<br />
<br />
<span style="font-size: large;">Why the Balloon is Not Disputed</span><br />
<br />
Other scientists and engineers have already covered the basic physical mechanism of a gravity balloon with no rotating structures inside. In every case, educated people who looked at the problem said "yeah, of course that would work". The core prediction comes from Newtonian gravity.<br />
<br />
Take a moment to appreciate this fact: A gravity balloon construction has never existed. Even if someone tried to replicated it within a present-day space station, the other (mostly molecular) forces would dwarf self-gravitation. It is a purely hypothetical construction. Yet we are all agreed (all of the informed, for whatever it matters) with 100% certainty that it would work.<br />
<br />
<span style="font-size: large;">Conservative Approach to Flow Dividers</span><br />
<br />
What is the "sketchy" part of the flow dividers? Like any engineering, the concept originates directly from the equations, given specific assumptions.<br />
<ul>
<li>Equations - Parallel plate turbulent flow (or laminar, if needed)</li>
<li>Assumptions - The geometry and movement of the flow dividers </li>
</ul>
<br />
You probably need a fluids expert to comment on this. One problem might be that those equations are not exact... but this is unconvincing. Turbulent flow models don't run the risk of dramatically <i>underestimating</i> the drag. The transition point from laminar to turbulent is also highly uncertain. That would chip away at the laminar flow designs I have entertained before.<br />
<br />
Also, there's more to flow than the global sheer forces. We have eddy currents. Those can form resonant patterns of certain kinds, you could posit that those might be destructive. But that claim is just plain wrong - because the exact problem has been studied before. It's called Taylor-Couette flow. For the most part, this leaves the flow circling in cylinders between the sheets. No, I don't have the exact flow description for the (very turbulent, very big) geometry described here, but there's nothing spectacular about the flow regime.<br />
<br />
Geometry is the most challenging part of this all. The flow solution is all well-and-good, but it assumes that the sheets are in certain places. This requires them to be held there. That could be difficult, maybe even impossible. That might demand large steel scaffolding holding the flow dividers in place, along with mechanical joints and wheels to maintain separation between the nested sheets. This could become quite expensive. I'm not even willing to concede that this scenario makes it totally nonviable in all foreseeable circumstances.<br />
<br />
Just take a moment to accept, however, that demanding assumptions of large structural supports (to resist air currents) is the most conservative academically honest position you could take. The flow regimes have already been in literature. All I'm asking is to apply them to a fictional geometry.<br />
<br />
<span style="font-size: large;">Very Liberal Approaches</span><br />
<br />
The sell gets difficult when we start attempting to strip down those supports for maintaining the geometry. As I've argued, you can try using flimsy sheets. Perhaps you apply some positive pressure to them so that they hold a pseudo-rigid cylinder shape. But maybe not. We can just handwave these complications away.<br />
<br />
In fact, there are two components to maintaining the geometry.<br />
<ol>
<li>Keeping the flow dividers from colliding or jostling</li>
<li>Keeping the flow dividers shape in tact</li>
</ol>
Violating #2 might also imply a violation of #1, but I'm not worried as much about #2. Balancing the pressure in each layer will likely maintain shape as a side effect.<br />
<br />
I've received <a href="http://physics.stackexchange.com/questions/55387/can-a-divider-laminarize-turbulent-flow-and-thus-reduce-friction/190295#190295">one interesting response</a> that seems to argue that the sheets may not even be necessary because the transition to laminar flow isn't clearly defined and may not necessarily exist if certain precautions are made (what exactly, I don't know). That sort of position is too liberal for me.<br />
<br />
You might even build flow dividers with massive holes in them. Flow dividers which are more of a suggestion for the flow than a solid rule might be entirely sufficient. As for myself, I pull back a little bit from that vision. There is a lot of energy in the system, and the movement makes it difficult to identify a clear lines to the isobars in a mostly open system. If this were simply cylindrical geometry, I would be more inclined to the idea, but the end tapers wreck havoc on the flow complexity. I'm mainly speaking from intuition here, and I think that partially-open flow dividers are in the engineering battleground.<br />
<br />
<br />
<span style="font-size: large;">Mechanical Stability (the meat of the discussion)</span><br />
<br />
There is something called the "wedge effect", but it might not be called exactly this depending on the source. Lots of large machinery levitate a rotor on a fluid. Some of that machinery rotates at tremendously high speeds. Essentially, the combination of the rotation in conjunction with the <br />
<br />
You can find plenty of literature on the subject. Go look at <a href="https://books.google.com/books?id=7QNWNReOUocC">chapters 2 and 3 of this book</a> for some basic theory. This is what makes me largely an optimist, because it argues for a mostly passive answer to component #1. Additionally, it's an answer that is quite hopeful to aid in the concerns of component #2. Oscillations aren't really going to lead up to a Bernoulli effect like a naive reading might seem to suggest. The forces in involved have most to do with friction and a roughly static pressure profile.... if its fully laminar. As we get into turbulent territory, there is some wiggle room for pessimists, but it's more unknown than anything else.<br />
<br />
Well, I just wanted to get that out there. Consider the surface to be scratched.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-53260422335948311532015-03-19T22:17:00.000-07:002015-03-19T22:17:56.659-07:00Construction of a Space Mega-City from a Bald Balloon Frame<br />
Over on Orion's Arm, they put out a <a href="http://www.orionsarm.com/eg-article/54a180bebfacc">very cool article on gravity balloons</a> (link also in sidebar nav now). In the process, they just happened to propose a new construction method as well. I had not gone this direction because I thought the asteroid in-situ use is critical for nearest-term viability because it avoids large material movement. That assumption, like all others, can change depending on unknown future capabilities. Not only is the method possible, it's actually more material efficient due to a roughly 2/3<sup>rd</sup>s power scaling benefit due to decreasing the surface area to volume ratio. In other words, it lets you combine smaller asteroids into one colony which will be more mass-efficient than any of the individual asteroids alone.<br />
<br />
Also, there is some amazing eye candy far beyond anything in this blog. The things which look like sesame seeds are broken pieces of asteroids. The balloon is a membrane with a small pressure tolerance, and those rocks are placed (or sprinkled) on evenly so that the pressure is increased through mutual gravitation. The red thing is <a href="http://gravitationalballoon.blogspot.com/2013/12/population-limits-of-large-space.html">a specific radiator design</a>.<br />
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<div style="text-align: center;">
<i>Image and copyright of <a href="http://www.orionsarm.com/forum/showthread.php?tid=629&page=2">Steve Bowers at Orion's Arm</a></i></div>
<br />
Some specific constraints on how you can move the rock material will come up with this method. However, I see two competing frameworks for developing a model. One fundamental constraint would be to avoid any angles larger than the tumbling angle for rocks. Another constraint is that your material strength must be enough to support some curvature due to ballooning out between the rocks. You could use any Platonic solid to create a model of this, although I would prefer to just start with a tetrahedron. Also, I'm not sure if the balloon should be considered to have some linear mass, or the rock placement should form some kind of regular summation. There could be some similarities to the rockfill problem I wrote about, but with even more potential directions. I don't think this would be an easy problem, but that depends on the approach and how the math turns out.<br />
<br />
If you consider the balance between the membrane's material strength and the number of trips needed to add the rocks, that forms a very coherent mathematical problem and I would love to have a crack at it sometime. AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com1tag:blogger.com,1999:blog-5515692164785328338.post-37322175464779410332015-03-19T21:59:00.000-07:002015-03-19T21:59:12.327-07:00Impact of Rotating Asteroid on Orientation of Artificial Gravity TubesIn a <a href="http://forum.nasaspaceflight.com/index.php?topic=36991.0">NASA Spaceflight forums discussion</a>, I had a new complication pointed out to me that I'm surprised I had not thought to cover on this blog before. The artificial gravity tubes are rotating, but the asteroid is as well. We can distill the implications into 3 options. Either:<br />
<ul>
<li>the tube's axis of rotation will appear to move relative to the walls as the asteroid</li>
<li>you will have to use some complicated form of "compound" rotation</li>
<li>you will align the axis for rotation of all tubes parallel to the asteroid's axis of rotation</li>
</ul>
Aligning all tubes in the same direction is the most obvious and cheapest option. In the <a href="http://gravitationalballoon.blogspot.com/2014/12/global-air-heat-transport-in-gravity.html">last post on global heat removal</a>, I inadvertently designed this in. If you follow the implications a little bit, that implies that the majority of the heat exchangers are toward the asteroid's poles. This is intriguing because that would be the ideal place for space radiators in the first place. However, if the colony is pushing the spherical black-body limit, then it's not as good because the GEO radiator is toward the pole anyway.<br /><br />Actually, an ability to precess was <a href="http://en.wikipedia.org/wiki/O%27Neill_cylinder#Attitude_control">already designed into some O'Neil colony designs</a>. With 2 artificial gravity tubes near to each other, they can push and pull so that they change the direction they face. This was proposed as a way to keep facing the sun, which obvious means they turn a full circle roughly every year (depends on the orbital position). For the asteroid rotation, we could be talking about rotation rates of 8 hours or less. Whether the forces involved and the unwanted acceleration on the surface are small enough is a question that is still unresolved.<br /><br />This is a type of topic which I might return to sometime, but I've decide that I'm going to do a few micro-posts from the long list of things in my backlog where I introduce the subject in a few paragraphs.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com1tag:blogger.com,1999:blog-5515692164785328338.post-85143749717366707562014-12-18T14:31:00.000-08:002014-12-18T14:31:03.749-08:00Simplified Fully Turbulent Argument for Flow DividersRecently thinking about the core technology for a gravity balloon habitat (the friction buffers in my prior terminology), I realized that I have yet to confirm that I have convinced anyone of its function. Further deconstructing the disconnect, I'm not sure how many people have been convinced of the <i>problem</i> (a few, at least), and only that subset of people are eligible to understand the proposed solution in the first place. My current guess is that time is just needed to process it. This concept took me quite some digesting at first.<br /><br />The underlying equations can be as simple or as complicated as you like. A true freely rotating cylinder isn't nice to work with, and for the laminar solution it even has <a href="http://en.wikipedia.org/wiki/Stokes%27_paradox">a paradox</a> for it. Since <a href="http://gravitationalballoon.blogspot.com/2013/04/turbulent-friction-buffers.html">my prior post</a> which handled the issue was relatively general over all flow regimes, it was also less easy to understand. Here, I'll simplify things to show the scaling that will most likely be relevant.<br />
<br /><span style="font-size: x-large;">Extremely Simplified Argument</span><br />
<br />If you'll indulge only the most basic dimensional analysis intrinsic to almost all turbulent drag calculations, the motivation and operation behind the friction buffers becomes clear very quickly. Imagine a baseball flying through the air. Most physicists wouldn't hesitate to quickly categorize the force as being proportional to v^2. If you want to think in terms of units of power, it's a very quick step to say that (power) = (velocity) x (force). That means that power has a form of v^3 in the same way that we said that force has a form of v^2. With this, we can get a dependence on the number of sheets.<br /><br />Variables Needed:<br />
<ul>
<li>N: number of sheets</li>
<li>tau: shear pressure on outer wall of habitat (Pascals)</li>
<li>f: Darcy friction factor</li>
<li>rho: density of air</li>
<li>v: velocity of air within a single channel</li>
<li>V: outer velocity of the habitat itself</li>
<li>P: power per unit area</li>
</ul>
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<br />The argument is accomplished here in its most simple form. Our equation for shear pressure (the retarding force per area on the cylinder) only involves the velocity out of all variables impacted by the number of sheets. Since the relevant channel velocity is divided by the number of stages, power ultimately goes with 1/N^2. Clearly, adding more layers of sheets will reduce friction.<br /><br /><span style="font-size: x-large;">Including Friction Factor</span><br />
<br />But why does this not involve the width of the channel? Because to a first approximation, the width of the channel doesn't matter, and that is hidden as a dependency of the friction factor "f". Of course this is a bad assumption. Intuitively the friction between two sheets moving parallel depends on the distance between them. The root of the prior formulation is that fluid velocity only increases <i>logarithmically</i> from the distance to the wall. Given high enough Reynold's number ln(x) is kind of a little bit flat-ish.<br /><br />Clearly this is unsatisfactory, so to remedy this we merely rewrite things with a form for the friction factor - which is where this dependency lies. This is commonly illustrated in the <a href="http://en.wikipedia.org/wiki/Moody_chart">Moody Chart</a>. Here I have reproduced that chart from the Colebrook-White equation.<br /><br />
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<br />Many approximations exist for the friction factor, but we know almost exactly what regime we'll be in. I plotted those points for different numbers of sheets, along with an approximation for the reference tube design. We'll plug that approximation into the prior format.<br /><br />As a minor detail, Moody's chart has the roughness in it as well. This will penalize adding more sheets technically, but it doesn't matter in the end. The reason is because decreasing the channel width increases the size of the roughness to channel size. However, even if we have 20 sheets, that leaves something like 5 meters. The sheet itself should only be a few milometers in my view, so clearly the roughness can't be more than this. Comparing to the values displayed here that's off the chart. Might as well consider it smooth.<br /><br />New Variables:<br />
<ul>
<li>d: half-width of a single channel</li>
<li>D: width of entire friction buffer region</li>
</ul>
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<br />With this specific approximation, we can plug back into the previous equation in order to have a very definite form for the shear stress. To go from this to power, multiply by the overall V. This involves a few steps and a little bit of math, but at the end we'll have a very useful form.<br /><br />
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<br />Let me stress that this is an accurate representation of our situation as long as we're in the turbulent regime. What is this constant on the top though? That's the power you would have in the case of N=1 for a specific reference case. That still doesn't represent a rotating cylinder in a free atmosphere, because it utilizes a standard channel width of about 100 meters.<br /><br />I find it entirely arguable that you would have to install a flow arrester like this if you built any kind of in-atmosphere artificial gravity tube... because if you don't you'll have very high air currents to deal with. Using this flow arrester will increase drag somewhat from the scenario where you don't use it. Anyway, it forms a reference case that I need in order to make this math comprehensible.<br /><br />So the basic proposition rehashed is:<br />
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<br />The economic case seems pretty clear. Even in Manhattan people average something like 30 square meters of land per person. In the reference case, that would amount to 15 kW per person, which would likely dominate energy consumption. This doesn't mean it's impossible. You could do this, but if you did, thermal and energetic constraints would be setting your engineering limits at just about every turn. Clearly you wouldn't go this route if a better alternative existed - and it does. The formula is quite simply to scale the number of flow divider sheets to achieve the necessary power level.<br /><br /><span style="font-size: x-large;">Power Calc Stage-by-Stage</span><br />
<br />One might also be confused by the calculation of power. Indeed, for the fluid dynamics calculations we used "v", lower case v, which is the half-velocity within a channel. But to get total power consumption, we multiply shear stress by "V", the total velocity shift over the entire friction buffer region. This is justified because the torque to keep the tube rotating is applied relative to the stationary reference frame, but it is dragged <i>on</i> by the fluid forces present in only one layer.<br /><br />But I don't expect everyone to believe that right away, so I'll show the other approach as well. Let the index _i mean that a quantity is for a single stage. To sum up power, we have to add a factor of 2 because these aerodynamic forces exist on both sides of the sheet.<br /><br />Variables:<br />
<ul>
<li>P_i : power for a single stage</li>
<li>P : total power summed for all stages</li>
<li>tau : shear stress, there is only one value of this, because force is transmitted over all layers</li>
</ul>
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<br />I don't think this is particularly profound, but perhaps it needed to be stated.<br /><br /><span style="font-size: x-large;">Appendix</span><br />
<br />The expression for "tau" uses 4 f in it. This is done in order to employ the Darcy friction factor. If you used the Fanning friction factor instead, you would just use "f".<br /><br />Reynolds number contains "d" for the width of the channel. We know there are N channels, however, the equation for shear stress doesn't apply directly to Couette flow, but instead a channel with one free end. This is mathematically the same as half of one of our channels, so the operative d would be D/2. However, hydraulic diameter in Reynold's number must be found by using 4Ax/Dx, where Ax and Dx are the flow area and diameter. This comes out to 2 times the width of the channel in question. Combining these two factors, we see that the linear dimension to be used in Reynold's number is D/N.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com1tag:blogger.com,1999:blog-5515692164785328338.post-77670818103795177812014-12-17T06:40:00.000-08:002014-12-17T06:40:56.502-08:00Global Air Heat Transport in a Gravity Balloon<br />
The complete scheme for heat transport within a gravity balloon habitat with artificial gravity cylinders can be segmented by following general outline. This tells the story of the path of heat as it's generated where people live through the point when it eventually gets emitted out into space.<br />
<ol>
<li>Heat generation occurs inside a artificial gravity tube</li>
<li>Hot air flows out of the outlet window of the tube</li>
<li>Hot air flows to the walls of the gravity balloon</li>
<li>Heat energy passed through a heat exchanger to some non-air medium</li>
<li>Non-air medium passes through a space radiator as the ultimate heat sink</li>
</ol>
This post will focus on how the air currents transfer the heat from the outlet of a tube to the wall of the gravity balloon where the heat exchanger then picks up, #3 in the above list. The previous post outlined one valid scheme for #2. In the past I've entertained several bad ideas for a scheme that accomplishes #3. Notably, since the currents need to occur over such a large area and only need to move so slowly, I imagined an impossibly large fan many kilometers across. If possible, apparently absurd or extraordinary schemes should be rejected (unless the problem it solves is, itself, extraordinary). In this case, just like in the last part, a much more elegant solution presents itself.<br /><br /><span style="font-size: x-large;">Outer Sheet as the Air Movement Mechanism</span><br />
<br />Just like heat transport out of the artificial gravity tube, it would be preferable to reduce the number of parts, so if there's a device already called for by the design we would prefer to configure things so that one device solves multiple problems at the same time. Thankfully, that exact thing is possible. We will pump the air ultimately by using the driving force applied to keep the artificial gravity tubes spinning.<br /><br />But first, I must specify that I imagine a stationary lattice which is connected to the asteroid rock and can accept forces. This is absolutely necessary for the motors to push against which keep the cylinders spinning, but they shouldn't be particularly difficult to build. A key distinction now comes in how we configure the outermost layer of the friction reducing flow dividers (friction buffers). That outermost layer could conceivably be connected to the stationary lattice structure. Up until this point my math has assumed this is the case, but that was only done for mathematical simplicity.<br /><br />In fact, it would be best to allow the outermost layer to freely rotate. For some numbers, let's say that the speed of the habitat on the inner surface of the tubes is 100 miles per hour and there are 20 flow dividers. Each stage then sees roughly 5 mph relative speed to the next stage. What will be the velocity of the outermost layer? Answer: considerably more than 5 mph.<br /><br />To understand this, I will offer a concept of "resistance to movement" between each layer of flow dividers. Given that the stages have constant spacing between them, this is roughly the same for them all (with some difference due to varying radii). However, the distance between the outermost layer and the bulk atmosphere isn't something which can be clearly defined. If we imagine the point of "r=infinity" to be another flow divider, the spacing between that and the outermost flow divider is clearly more than the spacing between the other dividers.<br /><br />Given that the outermost sheet sees less resistance to its motion, its natural preference will be to couple more strongly to the speed of the habitat (100 mph) than to the bulk atmosphere (0 mph) than would be predicted by it's share of the speed divided evenly among the flow dividers (5 mph). But we have yet another pesky effect that we have to deal with. If multiple tubes are in the same general vicinity and their air currents compliment each other, this could increase the ultimate speed that the outermost layer equilibrates to. Those are potentially two factors which push it above the 5 mph prediction for this case.<br /><br />For all of these reasons, I believe that the outermost layer will have some kind of "brakes" on it which prevents it from speeding up too much. Even better- if the motor is attached to the outermost layer this will improve efficiency somewhat, although it would require an additional motor to keep that layer rotating slightly relative to the stationary lattice. Even if you simply threw away the extra energy, the scheme will see a very small efficiency reduction and will work just fine. Accept a little extra energy consumption or a little extra complexity - the choice is yours.<br /><br />All of this is only to say that the velocity of the outer layer can be selected to some degree.<br /><br /><span style="font-size: x-large;">Direction of Thermal Gradient</span><br />
<br />The ability to move flow in the local vicinity between tube would be pointless anyway if there wasn't some coherent path that takes the tube's hot air exahust to the wall's heat exchanger in order to ultimately dissipate the heat. Because of that, I'm making the obvious claim that every tube has its flow connected to two different channels. It obtains its intake air from one channel and exhausts hotter air into the other channel.<br /><br />Picturing this takes a little bit of creativity, and my illustration skills might be lacking. The divider between the global channels (different from the friction buffers themselves) is a 2D sheet that cuts accross multiple artificial gravity tubes. For the most part, this plane cuts through the tube's axis of rotation. We just apply a slight skew or deviation in order to allow the exhaust and intake ends to connect to their respective channels. Here is my illustration of the situation:<br /><br />
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<br />Some attributes are exaggerated in this figure. The exhaust and intake windows are only 10% of the habitat's radius in most reference designs I've used. Thus, this slant we're working with might only be slight. Alternatively, the sheet could be completely parallel to the axis of rotation, and the windows will connect into small local depressions. Well "small" in this case would still be around 25 meters, but that's small compared to other stuff involved.<br /><br /><span style="font-size: x-large;">Hot Channel Calculations</span><br />
<br />Moving on, we need to figure out what limitations this scheme places on the overal gravity balloon size and/or population. I will return to my reference design in order to illustrate a pattern of air flow. Flow dividers must be added between a series of artifical gravity tubes, and then air flows in different directions on both sides. This produces an interlocking pattern of air currents.<br /><br />
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<br />Putting that in perspective of the entire balloon, I have the following image in mind. Here, I have included the presumed heat exchangers on the wall. I hope that makes it clear what kind of back-and-fourth pattern the flow is traveling in, and how it gets hottest right before it gets to the heat exchanger.<br /><br />
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<br />We can set the temperatures to whatever is desired at the start and endpoint for these flows. However, since the flow travels in a straight line, it seems fairly clear that the highest temperature change will be experienced by the line of colonies that goes straight through the center of the sphere. It is this row that sets our limit.<br /><br />I would imagine this limit will be around 10 degrees C or Kelvin. Perhaps 20 degrees. If you refer to the heat transport within the tubes, that is certain to be on the order of 5 degrees, and some colony will experience the extremes of these temperatures. As such, it's probably best to keep it to 10.<br /><br />As long as we're accepting my reference design, that has 22,000 people, and I'll stick to the claim that they're using 2 W each, for a total of 44 MW. On average, there is one colony per 1 km^3 lattice. The colony takes up a small fraction of the total volume (about 27%). Thus, the effective flow area is about 0.86 km^2. With all these ingredients, we can formulate the heat balance relationship for the balloon-level flows.<br /><br />
<div style="text-align: center;">
Heat Balance for Global Heat Transport Channels</div>
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<br />Selecting the Delta_T value is related to biological and comfort limits. Heat transport within the tubes themselves is already known to require about 5 Kelvin of temperature change in order to employ natural circulation at the desired population density levels. If we add much more variation, then we could have undesirable large temperature swings. I would imagine that a number under 5 Kelvin would be acceptable.<br /><br />As I previously argued, v is a tunable variable up to a certain limit, and that limit relates to the degree of friction reduction in maintaining spin. Presumably, this would be under about 3 m/s, but it could be a good deal more. With this piece of info, we have a fairly strong argument for what the bounds on these variables are.<br /><br />For a given Qdot, we can find the number of colonies which can be served. Referring to the previous illustrations of the scheme, there is on average one colony per linear kilometer of flow chanel. That means that Qdot/(44 MW) will yield the maximum number of colonies it can serve. Since the hot channel's length is equal to the diameter of the gravity balloon, dividing by 2 can give us the radius of the maximum size (in km of radius) that the scheme can thermally support. I present those cases in this table:<br />
<br />
<div style="text-align: center;">
Thermal Limitation of Gravity Balloon</div>
<div style="text-align: center;">
Based on Global Heat Removal Channels</div>
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<br />These are large sizes, and the assumptions about Delta_T and v are quite conservative.<br /><br /><span style="font-size: x-large;">Implications</span><br />
<br />This problem, in particular, would seem to be extremely easy to solve and pose little constraints on engineering of other related systems. There are multiple parameters that you could scale up in order to efficiently globally circulate air in a gravity balloon for just about any practical scale.<br /><br />A large area for the flow channel was key in making this so easily solvable. Even if the generous parameters for maximum balloon size were not sufficient for someone's desires, there are multiple ways of pushing the envelope further. For instance, increasing the spacing between artificial gravity tubes or reducing the number of friction buffers. Even these methods would only need to be applied in a select regions which are subject to the extremes of the hot channel temperatures.<br /><br />Another major benefit of this system is that the driving force is applied constantly. It is somewhat concerning that the flow path isn't completely straight, but I doubt that any really good solutions to this problem exist. You could conceive of extreme solutions, like flow divider sheets that are partially friction buffers for the tubes and partially friction buffers for the global flow channels, but this is certainly not necessary. The most important benefit of the continuous driving force as well as frictional losses is that no major pressure differential exists within the whole of the gravity balloon. This means that no hardened airtight doors will be necessary for people and goods passing between the different flow channels, which is sure to happen often.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-5465611678679526262014-12-16T19:44:00.000-08:002014-12-16T19:44:35.919-08:00Natural Circulation Heat Removal from Artificial Gravity TubesIn <a href="http://gravitationalballoon.blogspot.com/2013/12/thermal-engineering-of-free-floating.html">a previous post</a> I concluded that natural circulation of air was an attractive method of removing heat produced by a population living within an artifical gravity tube within a gravity balloon. This notion was still very vague, so I want to place some numbers on that, and also potentially define the scale at which it would be economical.<br />To summarize the idea, the airflow goes in at one end and out the other with no pumping. This is made possible by the fact that heat is produced by the inhabitants in their everyday lives, and also by the designed geometry of the cylinder which lets the hot air rise up to the outlet while preventing cold air coming from the inlet from reaching the center.<br /><br />Forms loss (I'll sometimes call k-loss) is a means of grouping together various resistances to flow along a flow path. This is always referenced to a specific cross-section on the path, and I will reference it to the pinched open end. For a free jet condition, it is somewhere around 1.0 generally. In our case, we have a large stagnant atmosphere outside of the tube as well as a mostly stagnant atmosphere inside the tube. That causes both the inlet and outlet to be something close to free jet conditions... with a lot of qualifiers. Since the flow is expanding radially, it must also exchange a great deal of angular momentum with structures attached to the rotating tube, similar to the case of a centrifugal pump. This should substantially affect the k-loss value, but probably not by more than, say, a factor of 2. Given that we have 2 free jet conditions, I would most likely expect k to fall somewhere in the neighborhood of 2 to 4, but this is a highly imprecise science at this point. Thankfully, as long as it's somewhere close to that range it shouldn't critically wound our overall conclusions.<br /><br />Tube radius, heat production, temperature range, end opening size, and air flow velocity are all important things which have very practical relevance to the design of an artificial gravity tube. Armed with some educated guesses for the k-loss factor, we can set constraints on these parameters. Firstly, I'll divide up these values which are absolute, fungible, and independent variables.<br /><br />Parameters for air:<br />
<ul>
<li>density rho0 ~ 1.3 kg/m3</li>
<li>heat capacity Cp ~ 1,005 J/(kg-K)</li>
</ul>
Relatively fixed variables<br />
<ul>
<li>temperature of the environment T0 ~ 293 K</li>
<li>gravity in the living areas of the environment g = 9.8 m/s^2</li>
<li>Power consumption per inhabitant gamma ~ 2 kW</li>
<li>Window edge radius relative to habitat radius Rw/R ~ 0.1</li>
</ul>
Independent design variables<br />
<ul>
<li>Radius of the tube</li>
<li>Change in temperature across the tubes</li>
<li>Velocity of the air at the end seals</li>
<li>Population of the society</li>
</ul>
<br /><span style="font-size: x-large;">Equations to Relate Variables</span><br />
<br />By definition, the k-loss equation is the following. This quantity represents the frictional pressure head fighting against the direction of flow.<br /><br />
<div style="text-align: center;">
Pressure Drop due to Friction</div>
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<br />The essential idea of natural circulation is that heavy cold air flows down from the inlet to the surface habitat, and then less-dense warmed air rises from the habitat toward the center-line point. To find the change in density we must return to basic PV=nRT gas law concepts. Compared to the magnitude of the temperature change, the pressure changes very little relative to its environment value. Thus, to deal with the density change we can just imagine that it changes linearly with the temperature change.<br /><br />
<div style="text-align: center;">
Density Change Given Temperature Change</div>
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<br />It is this density change which gives rise to the natural circulation driving force. This works by the analog of (Delta_P=rho g h) in constant Earth gravity. But gravity varies with radius in the case of artificial gravity. Since the driving force is the <i>difference</i> in hydrostatic pressure change with altitude, it goes with the change in density as opposed to absolute density.<br /><br />
<div style="text-align: center;">
Natural Circulation Driving Pressure</div>
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<br />Driving force then exactly matches the frictional losses experienced over the flow path. Thus, we can set the two expressions to be equal. This constitutes the momentum balance for the natural circulation heat removal system.<br /><br />
<div style="text-align: center;">
Momentum Balance Final Form</div>
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<br />Variables involved in design:<br />
<ul>
<li>Delta_T</li>
<li>R</li>
<li>v</li>
</ul>
With this relationship nailed down, we can consider the limitation on heat production. Along with this we have a litany other other supplementary relationships introduced. The mass flow rate through the tube is connected to the end window size. The area of the end window is related to the window's aspect ratio as well as the overall radius. Total heat production goes with total population as well as the per-capita energy intensity of the society (I call gamma).<br /><br />Writing these all out and then combining them:<br />
<br />
<div style="text-align: center;">
Population / Heat Relationship</div>
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<br />Additional variables involved in design:<br />
<ul>
<li>P</li>
</ul>
So while we added another equation, we also added another free variable. In other words, this doesn't add any dimensionality to the problem, it's just an auxiliary equation that I'll use to calculate a population limitation given the other parameters.<br /><br /><span style="font-size: x-large;">Numerical Values</span><br />
<br />With more-or-less 3 variables and 1 equation, we have two degrees of freedom. The relationship is pretty straightforward but it's not very helpful in that form without comparing it to some reference designs or tangible speeds and sizes.<br /><br />As a simple applcation of the equations, here are some values for 3 cases of radius, 3 cases of temperature, and 2 scenarios for the k-loss value. That is 3x3x2=18 total numbers. In each of those cases, we have dependent variables of "v" (the velocity at the end windows) and "P", the population.<br /><br />For some further notes, I've included the velocity of the edge of the window for all the cases for different radii. These are assuming that the windows are 10% of the radius of the habitat surface. I've distinguished between that as "V edge" and the flow relevant to heat removal as "V flow". As you can see, the window edge velocities tend to be even higher than the outward and inward flow for the other parameters I've selected. That, itself, might be a problem but it's a geometric consequence of the window size. The window could be made smaller while accepting some other sacrifices.<br />
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<br />
<br />The population limit reported here is then divided by the livable area within a habitat. It is assumed (as in the reference design) that the length of the cylinder is equal to its diameter and no credit is taken for the are on the pinched ends.<br /><br />
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<br /><br />I put NYC and Manhattan on this as well for a reference. Note that in my reference design for the artificial gravity tube, density is still incredibly high - about that of Manhattan. This applies for the scenario of Delta_T=5k, R=250m, and k=4, where the population constraint comes out to be about 20,000 people.<br /><br />To me, this still seems to be about the most reasonable reference design. I will elaborate on that a bit more in the conclusion.<br /><br /><span style="font-size: x-large;">Carbon Dioxide Removal and Other Undesirables</span><br />
<br />The design principle of the gravity balloon is more-or-less to locate industrial facilities that don't need gravity (or strong gravity) within the open air microgravity environment between colonies. It is crucial that we can show that critical services (like heat removal) can be viably provided outside the gravity tubes. For heat removal, not only can this be done, but it can be done at incredibly low cost using natural circulation. But that's not all we have to worry about.<br /><br />Possibly the most vital metric to control within a space habitat is carbon dioxide levels since this will cause negative health effects before lack of oxygen, however the limitation relative to the habitat's heat removal is less clear. Let's just look at the comparitative limits between these two. Consideration of the specifics of an artificial gravity tube isn't necessary. I'll just consider what temperature rise would also correspond to a dangerous rise in CO2 levels.<br /><br />Certain specifiers are needed, but I'll consider the most active society possible in order to be conservative. A human doing normal work will emit <a href="http://www.engineeringtoolbox.com/co2-persons-d_691.html">0.08 to 0.13 m3/h of CO2</a>. Using this information as well as the scenarios I've defined, we can find the increase in CO2 parts per million (ppm) as the air flows from the inlet window to the outlet window. Here are my estimations:<br />
<br />
<div style="text-align: center;">
Increase in CO2 Concentration</div>
<div style="text-align: center;">
for a Given Rise in Temperature</div>
<ul>
<li>2 K : 31 ppm</li>
<li>5 K : 78 ppm</li>
<li>10 K : 155 ppm</li>
</ul>
None of these are particularly deadly. Humans can easily tolerate increases this much or greater. However, these were only formulated based on the assumpting that people were consuming 2 kW on average. That was supposed to be a conservative assumption, but in this case lower values might put us in a bit of a bind. If that was reduced to a value closer to the biological limit of around 200 W instead, then the above temperature changes would correspond to a dramatically higher CO2 concentration rise. As such, it's plausable to create scenarios where CO2 removal would be the overriding constraint on the allowable population of the tube... but this probably wouldn't be likely under normal conditions.<br /><br /><span style="font-size: x-large;">Big Picture Conclusion</span><br />
<br />My pessimism in the last post on this subject is lessened substantially. We can state a number of relatively attractive combinations of parameters which would be economically desirable and physical plausible. However, there is still a bit of a tight design envelope to fit.<br /><br />The heat production limit would likely constitute the gravity balloon's version of a "<b>fire code</b>". You could certainly pack more people into the tube, but the temperature would rise slowly. Except for some possibly extreme circumstances, it seems unlikely that CO2 removal would become more restrictive than heat removal.<br /><br />I find it hard to argue against natural circulation as a means of cooling the tubes themselves. The benefits compared to the alternatives seem immense. The air flow rates are unlikely to surpass the speeds which will be encountered near the windows anyway, and being a fairly localized thing, I don't expect the end seals to have a dramatic impact on the overall drag anyway.<br /><br />In fact, in some cases the air flow would be so low that in the center you couldn't rely on it to move out of the tube (starting at centerline) in a timely manner. For these cases, you would need a conventional transport system or elevator-like system. Since the heat production rate will vary throughout the day, this seems inevitable anyway.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-21089071987421804932014-12-09T21:04:00.001-08:002014-12-09T21:04:17.736-08:00Transit within Space Mega-CitiesThis is intended to be the first post in a series on transport issues applicable to moving between one artificial gravity cylinder and another (not necessarily specific to a gravity balloon). The growing list of topics under this umbrella, new and old, have grown so much that a full series is needed. This post acts as a summary of those topics and establishes a central claim.<br /><br />In particular, I want to talk about a billion person city. That is, a 3D city in space or inside an asteroid which has on the order of a billion people. For the purposes of this topic, I will use the term <b>colony </b>to denote a rotating artificial gravity cylinder in such a cluster, and the word <b>city</b> to refer to the entire cluster. In previous posts, I outlined how 1 billion people is just on the elbow of population constraints shifting from packing density to heat removal. Even that latter constraint isn't absolute, but it's not important because transportation times will put larger sizes in a different stratum anyway. The level of cultural connection is fundamentally different between occasional travel versus daily service.<br /><br />Just that word "daily" introduces all kinds of qualifiers in the first place. Any concept of a day/night cycle would be artificial. My position is that this is only slightly different from modern cities on Earth since artificial light became rife, except that there's no natural suggestion from nature. The specifics of how a society manages the biological need for a day/night cycle is one thing I don't care to take a position on. The only kind of assumption I'm interested in here is how many trips per day someone takes between seperate colonies. Ideally this wouldn't include grocery trips or other relatively fungible activities. However, the entire draw of such a city is the connectedness, so I expect the relatively routine days of living in one colony and working in another would be balanced by extremely active collaborators. If you only go between your work and home colony that will obviously result in 2 trips. To balance things out, I'm saying 4 on average per person per day, for 4 billion A->B trips each day.<br /><br />How you accomplish this volume, and the specifics of the physical manifestation is what I'm interested in here.<br /><br /><span style="font-size: x-large;">1. The Comparison</span><br /><br />As an alternative hypothesis, this discussion will entertain the idea of lots of conventional artificial gravity habitats packed closely together. That <b>conventional</b> concept is an independently pressurized colony that rotates to create gravity. The problem I'm interested in here is inter-colony transport. Inter-city transport would be very different, the demand for it isn't well established, and there's not much I could say anyway. Comparing to the gravity balloon, the one obvious difference is that the space between the colonies is vacuum.<br /><br />This still accomplishes the argument that a larger number of smaller colonies will have more surface area than a large single colony with the same volume. Transit is a lot easier with this system. Transportation within a colony is not much easier than transportation on Earth since it is a terrestrial-like environment. With no convenient fossil fuels you'll find public transportation more appealing too.<br /><br />It should also be noted that these colonies would need to be tethered together in some way to avoid eventual collisions and resist destruction due to any perturbation. For instance, if a transport ship lost its pressure boundary, that air will then impart an impulse to the nearby colonies. It's obviously necessary to prevent those disturbances from causing millions of people's death by slow drift and collision of their colonies.<br /><br />My reason for introducing this dichotomy is to identify very stark different between the gravity balloon and the conventional scenarios. Starting out, we don't want to prejudice ourselves to one or the other. Indeed, I think there are scenarios where the conventional approach might be better. It all comes down to what it is that you value. My predictable insinuation, however, is that if you desire a hyper-connected community of a billion people, the gravity balloon is almost certainly your best option... mostly because it doesn't need airlocks for intra-colony transportation.<br /><br />But first, we need to formalize why airlocks matter.<br /><br /><span style="font-size: x-large;">2. Transport Network Topologies</span><br /><br />Transportation can either be <b>on-demand</b> or <b>mass</b> transit. On-demand can entail either a personal or a shared vehicle. It also doesn't have to be the case that an on-demand vehicle is for a single person, but if it's not this will impose additional constraints which I don't want.<br /><br />My perspective is that whether a trip is serviced by on-demand or mass transit depends on the volume of demand for the trip, measured in people per second. While the ideal volume for mass transit is disputable, I put it roughly in the range of 1.0 people per second. However, the minimum acceptable volume also depends on the number of transfers someone has to take during their trip. Doing 5 transfers at a cost of 1 minute each is taken to be equivalent to waiting 5 minutes for direct service.<br /><br />Quantifying the difficulty of a transfer isn't precise but is still obvious. Going through an airlock is going to carry a higher time cost than stepping from one platform to another.<br /><br /><span style="font-size: large;"> 2.1 Spoke-hub</span><br /><br />On one extreme, the spoke-hub network topology is heavy on transfers. If all colonies only connected to one hub by their own dedicated <b>route</b> (or "spoke"), then even to get to your neighbor colony you'd have to travel to the very center of the city, transfer, and travel to the destination.<br /><br />This complexity buys you a reduction in the total number of routes that have to be planned and maintained. Since the number of travelers is a constant, this increases the volume that each route sees. The 1 central hub is the extreme example, because there's only 1 route per colony.<br /><br />Such extremism is not necessary. If you turn this into a hierarchy then the more central routes and hubs will have even higher volume than the local routes. As such, this method lends itself nicely to mass transit. The local routes will inevitably see usage rates 8 times the population of the colony per day. Since this will be in the 1,000s at least, any literal hub-and-spoke topology could be serviced entirely with mass transit.<br /><br />Relaxing the extremism a little bit more, you would likely add cross-links either between colonies or regions. Since the volume is so high, this can be done while keeping mass transit viable, but still reducing the number of transfers.<br /><br />Our tradeoff for extremely high volume is a larger number of transfers. I'll call the number of hierarchy levels I, and the number of regions/colonies serviced by a hub N. Then the total number of colonies is N^I. This established, the maximum number of transfers would be 2*I-1. If you used the smallest possible value of N, N=2, then you could be facing on the order of 30 transfers.<br /><br />Such transfers would have to be virtually instant in order for the transportation system to be practical.<br /><br /><span style="font-size: large;">2.2 Point-to-Point</span><br /><br />By putting people into colonies, we are dividing up our billion people into groups which are probably 10,000s to millions of people. Even the smallest realistic number of colonies is around 1,000. Even with this number of people, mass transit could only be minimal in a point-to-point system. This is because the number of routes in a full point-to-point system goes with the number of colonies squared. You'd be looking at 2-3 people for every route every minute.<br /><br />This still forms a decent alternative hypothesis. By making the colonies large (although practically so), regular flights between colonies can be possible with the ridership being a handful of people.<br /><br />
<span style="font-size: large;">2.3 Penalties for Distance and Transfers</span><br /><br />A space city might find either one of these topologies favorable depending on the type of city and available transportation technologies.<br /><br />Broadly, larger colonies are associated with conventional colonies because the task of reducing air drag in a gravity balloon becomes more onerous. Larger colonies are also associated with greater propensity to point-to-point transport topology.<br /><br />More transfers are also disassociated with conventional colonies. The self-evident facts are that all colonies maintain their own atmosphere, and that colonies are stationary relative to each other. That means that you will use a minimum of 2 airlocks. If find it unlikely that any system designer would want to do any more than this. Any mid-range transfers would likely avoid merging the atmospheres of the vehicles if at all possible. Airlock cycling is slow and expensive.<br /><br /><span style="font-size: x-large;">3. Physical Mechanisms</span><br /><br />Routes and transfers have been addressed in the abstract sense up until this point. That is, a route connects a hub or a colony to another hub or colony, while a hub is a point where one can exit one vehicle and enter another.<br /><br />Even without any statements regarding the possible or likely network topology, a great deal can be inferred about the transportation system of a future space city from the underlying technologies. Popular illustrations of space colonies with artificial gravity sometimes add one or two details of ships entering and exiting... but if you start increasing the expected volume things start to get real weird real fast.<br /><br /><span style="font-size: large;">3.1 Means of Docking</span><br /><br />By docking, I mean mean moving in and out of a colony or a transportation hub. Docking entails getting on a shuttle, getting off, and even the process of finding your next shuttle.<br /><br /><b><span style="font-size: small;">3.1.1 Conventional</span></b><br /><br />Ports are most commonly depicted on the axis of a rotating space colony. For a cylinder, these are the two ends. For a sphere, these are the two poles on the axis. This rotates along with the space station, but the rotation rate is slow, and the accelerations mild.<br /><br />But this is inherently one-lane. You could dock off-center but this will use propellant which I find to be incompatible with a large space city because the propellant demand for billions of trips would be huge. The only alternative would be to surround the city in a barrier and recover and recycle propellant. As such, I find the only valid solution to be sending larger ships through the airlock. This will likely be a ship that carries other ships in order to satisfy the point-to-point topology.<br /><br /><b>3.1.2 Gravity Balloon</b><br /><br />A colony inside of a gravity balloon has open ends. This means that, hypothetically, someone could just walk off the edge. For our (more serious) purposes, we need some kind of architecture that gets them somewhere else after leaving. Since most of my reference designs have ends 30 m in diameter or more, this will entail collecting the people into a smaller space.<br /><br />The solution I've been leaning toward is to have people's path through the colony mirror that which the air flow takes. Come in at the edge of the inlet end. Either take an escalator, shuttle, or a slide down to the terrestrial environment. Once they decide to leave, a building which spans the full diameter of the colony rises to the center-line. Here, they enter a tube where the low gravity and air flow move them out.<br /><br />Individuals still need to make their own decision about what route to take, so you would essentially need a lot of handles and rails so they can move through the hub to their transport, which will be mass transport. Other than this, there's not much else to figure out. The atmosphere is continuous, so the only reason for doors in a transit shuttle is to keep people from falling out. A similar logic will apply for the transit hubs.<br /><br /><span style="font-size: large;">3.2 Means of Moving</span><br /><br />The primary difference between the gravity balloon and conventional cities is the existence of an atmosphere in the former. This is a detriment to power consumption and speed limits in transit. However, it also can be a nice thing to have something to push against.<br /><br />My position is that whether an atmosphere is a merit or a disadvantage is a function of the total size we're talking about. Since a gravity balloon can more easily host an extremely high density, these attributes somewhat make sense in conjunction. Alternatively, some methods might be available to get extremely high speeds in less dense clusters of conventional colonies.<br /><br /><b>3.2.1 Conventional</b><br /><br />In the conventional space city concept, we are forced to move relatively small shuttles through the vacuum between colonies. I'll start out with the assumption that these shuttles are mostly free-flying and I'll classify the issues into 3 major parts, and only briefly touch on them here.<br /><br />After departing the docking facilities of a colony, the shuttle obviously has to first <b>accelerate</b>. Since we're not very interested in multiple km/s speeds, this can almost certainly be accomplished mechanically. But we also must keep in mind Newton's law of motion. The transit volume almost certainly rules out reaction engines, so the shuttles are necessarily pushing against either the colony or some ancillary structure. I would favor the latter. A non-rotating envelope could surround the colony to provide easy access and also transfer momentum to and from the colony through axial bearings. So this non-rotating structure could launch shuttles through mechanical tracks or even mechanical arms. However, each shuttle is going in a different direction. The shuttle departure and arrival rate is also fairly high, so you would likely have many of these systems serving a single colony.<br /><br />Once you get going, there will necessarily have to be some <b>avoidance </b>software, if we assume a mostly crude method of moving in the direction of the destination colony. If I assume a shuttle is about a square meter in cross-section, then random walks through my reference space city would result in roughly 1 collision every week. This is probably most surprising in illustrating the enormity of the 3D space. This is even after subtracting the volume of the colonies themselves. Avoidance might be one thing for which propulsive maneuvers makes sense because they are both infrequent and random.<br /><br />Not only do you have to avoid other shuttles like yourself, but the lattice of colonies needs to be navigated around, but I classify this differently in the category of <b>steering</b>. Because you'll be going on movingly a preplanned route, it's thinkable that your redirects can be done by stationary infrastructure along your way. I would imagine that magnetic forces would be the most ideal for this because frequent catching and relaunching would make for a very uncomfortable ride.<br /><br />Lacking a good vision of implementation of a system that handles these issues, I'm tempted to say that free flying shuttles won't exactly be the architecture that a conventional space city winds up with. I think something much more akin to roads are likely, but very different space roads. I would imagine these are steel guiding rails which the shuttle only makes contact with during acceleration, braking, and steering. This road network, thus, would still somewhat resemble a hierarchical network topology, although certainly not spoke-hub. I envision something much closer to an interstate system. For the large volume routes, the shuttles might even combine themselves in something resembling a mass transit system, but still while avoiding connecting via an airlock. <br /><br /><b>3.2.2 Gravity Balloon</b><br /><br />Moving through a continuous microgravity atmosphere is the same as planes on Earth, except without the added complication of gravity. Thus, no novel technologies are needed and we can concern ourselves only with the economics of the system. If we use an extremely hierarchical transit system, the basic unit of transportation would likely be the individual and they would make decisions about where to go by grabbing onto guiding anchors as I argued before. Starting from that point, we only need to further identify the technology options for high-volume routes. These could use several mechanisms to minimize air drag, but the logistical implications of these approaches are also important.<br /><br />One approach might be to just not worry about drag. You could even use a <b>rope tow </b>to transfer people relatively locally between colonies of the local hub. That is essentially a simple pulley in zero gravity. Many of these trips would be around 1 km in length, but they would need to be completed quite fast and very safely. The biggest problem with a person directly holding on to a fast rope tow would be the they can't breathe. If everyone wore aviator masks, the speed could potentially be rather high. That raises another complication - of how to grab on in the first place. This could likely be solved by a series of rope tows in steadily increasing speed, but all within arm's reach to the next stage. This also sounds somewhat dangerous, so a simple alternative might be a shuttle moving along a rope. It could accelerate with its own wheels, or it could just be on a pulley system. The only drawback is the relatively inflexibility since these approaches very strictly connect either two places or a loop.<br /><br />The rope tow might be the most simple system I can think of. However, if we want to go in the extreme of maximizing logistical prowess while still not worrying about energetic efficiency, even a <b>pneumatic tube</b> starts to look like a valid option. If a traveler's destination was obvious (as in a true spoke-hub topology), the system planner can avoid a transit center where the person chooses where to go, and simply opt to suck the people up with a current of air. Yes, like the Jetsons. Actually, this could boost a much higher throughput with much greater simplicity than any other alternative. On the other hand, it can't be very fast (without killing people), and it would be highly inefficient.<br /><br />Fixing the problems with the pneumatic tube by adding greater complexity would, in fact, be possible. You could actually invent a system that borrowed the physical principle from the friction buffers that I've discussed for the rotation of the colonies themselves. This concept was obvious to me a while ago, but I found it completely ridiculous. However, after studying the nature of hierarchical transit systems, it seems that the most central transportation routes can quite possibly get used by a large fraction of all the trips taken in a day. I mean, one route might service 2 billion trips per day. This is 1,000s of people per second. Even at 100 miles per hour, you could have 100s of people per meter. Any conventional system would involve massive docks or massive ships. The logistics of getting people in and out of a shuttle would be mind-boggling at these volumes. So a pneumatic tube isn't absolutely a terrible idea.<br /><br />Considering these economic pressures, let me propose a ridiculous idea which would feasibly service the ridiculous populations of a space mega-city. Take a closed tube that goes in a large loop - a torus. Now surround this tube in another tube. Do this over many tubes. Have the inner tube rotate about its perpendicular axis at the desired speed. Each enveloping tube will move slightly slower. Let's say 5 mph over 20 tubes for a total of 100 mph travel speed. Then, of course, you would have doors in each level of tube so that someone could eventually make their way to the central tube. This could handle extremely large volumes, would be 100% continuous, and the power requirements wouldn't be all that high because the flow is controlled carefully. The main problem, I would imagine, would be training people to use it.<br /><br />For people desiring methods which are more familiar, borrowing from planes, both jet and propeller craft are possible. You would only exchange the wing for another control surface or two. For the biggest legs of a mass transit system, air-breathing shuttles could reduce energy consumption and increase speed by increasing their scale. This is a coherent vision, but I doubt that the air-breathing engine would be the ideal choice for acceleration at the start of the trip since a simple mechanical boost at the start would be fairly trivial. Direction changes can be handled slowly over the course of the trip by control surfaces, so any launcher wouldn't need to aim either.<br /><br />We don't necessarily have to consider on-demand transportation, but that is also relatively easy. It might also be a preference under certain circumstances, or just plain fun.<br /><br /><span style="font-size: x-large;">4. Gravity Balloon Connectivity Argument</span><br /><br />Here's the point:<br />
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Why build a gravity balloon space city instead of the alternative?</blockquote>
I've been as general and generous as I can with the conventional type of space city. Indeed, I'm not trying to argue that any particular reference design is bad, just different. The attribute where a gravity balloon is appealing is transit connectivity. One real reason for pursuing a gravity balloon is desire for an interesting, vibrant, and interconnected city in space. I did not go into numbers here, although I hope to get to those in later posts, so you'll have to take my word on matters of degree. I wouldn't be saying any of this if I didn't have some empirical basis ready.<br /><br />The desire to mingle among a billion person community daily might be somewhat difficult to reconcile with conventional space colonies. Even if one favored the extreme over-sized space habitat of a McKendree cylinder, it would take a heroic technology effort to make daily transit among the entire pseudo-terrestrial area viable.<br /><br />As we try to get design convergence in the reference conventional I mention, several issues pop up. Smaller colonies result in greater transit network challenges and shorter average travel distances. However, larger colonies raise some serious safety concerns due to the speeds of the rotation. Even on the large side of ideal design range, I'm absolutely sure that the space between colonies would involve a large amount of clutter in order to make the formation of the movement of shuttles workable and comprehensible.<br /><br />A gravity balloon, on the other hand, has really weird possibilities for the transportation routes, and considering the size that we're talking about these might even be relevant. Either way, having air to push against is a huge benefit. Also, no separate life support system is needed for every trip and people can live without constant airlock cycling. Those issues with conventional colonies are not deal-breakers, but the gravity balloon clearly has much greater desirability in this context.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-39922546771419124302014-12-04T21:32:00.001-08:002021-06-20T20:26:57.432-07:00Rockfill Pressure Boundary in Asteroids<p><span style="font-size: large;">Context of Void Use</span> <br />
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This post expands on concepts introduced in a <a href="http://gravitationalballoon.blogspot.com/2013/11/why-not-live-in-empty-spaces-inside.html">previous post about living in the voids in asteroids</a>, and it is the writeup of the fractal image I presented in the post right before this one. I've come to call this scenario "under-pressure" because it entails using a pressure below what's necessary for the rocks to fully float against the atmosphere pressure. In the present context, the gravitational balance is really the upper limit to the pressure and radial extent for using the voids in the way I'm talking about here.<br />
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In that previous point I laid out a very vague idea of how a collection of smaller rocks (within a lattice of larger rocks) might form the backstop for the airtight lining. I'll look into this with a little more detail in this post. Rubble piles are likely to be a collection of (former) asteroids which are resting in contact with each other, held by gravity. We don't know much about these structures yet, but the general idea is something like this, from a 1999 Nature article, <a href="http://www.nature.com/nature/journal/v402/n6758/full/402127a0.html">"Survival of the weakest"</a><br />
</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAL6MoiSbM2jWs7_SKpqmRoA9qIpoVAQi7EtTQ71-TyLWBVebcvkIIhhEkNIQCcLykk6VNwn9xE0_AoJ96_X41jq5zEQuqHEMkdrOITqllRAxcYuxs6D4jAK63seTOa6hlMIVOy0tmeqkE/s600/402127aa.eps.2.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="447" data-original-width="600" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAL6MoiSbM2jWs7_SKpqmRoA9qIpoVAQi7EtTQ71-TyLWBVebcvkIIhhEkNIQCcLykk6VNwn9xE0_AoJ96_X41jq5zEQuqHEMkdrOITqllRAxcYuxs6D4jAK63seTOa6hlMIVOy0tmeqkE/s320/402127aa.eps.2.gif" width="320" /></a></div><center>
Visual Conception of Rubble Pile Interiors</center>
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As the different scenarios in the above image suggest, this illustration is essentially a guess at the interior of asteroids. The constituent parts could be small, large, or a combination of them all. Furthermore, there are a large number of candidate asteroids. There could be a great diversity in their different interiors.<br />
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In order to build a space habitat in a cavity within one of these rubble piles, I would imagine that the ideal interior structure would be composed of rocks on the 1 km scale. This is approximately the minimum scale needed to produce artificial gravity at acceptably low rotation rates. It is reasonable to believe that an ideal candidate asteroid exists out there somewhere, although we can't say which asteroid that is. It's certain that many of them have unusable interiors for this type of habitat, so the problem is just narrowing down the sample space.<br />
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Another issue is how one might <b>seal</b> off the pressure boundary around the empty space to be transformed into a habitat. If you plan to ship in material to cover a kilometer scale gap, then you've obviously defeated the impetus of the concept altogether. We are obligated to think of approaches more clever than that.<br />
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<span style="font-size: large;">Lattice Structure of Unmovable Rocks</span><br />
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As a best guess, we might as well imagine the interior to be some lattice structure. We might also imagine that the rubble is roughly spherical rock. The <a href="http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres">3D packing of spheres</a> is a well-studied problem, particularly in material science. There are several configurations that an infinite lattice of this sort might have, but the most efficient structures are only 2, which are "face centered cubic" and "hexagonal closed packed". For the purposes of this study, there is no reason to distinguish between them. They are different geometries, but the important numbers such as coordination number and packing density are all the same. <a href="http://commons.wikimedia.org/wiki/Category:Face-centered_cubic_lattices">The FCC structure</a> looks like:<br />
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packing density = 0.740<br />
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Compare this packing density to the measured asteroid macro-porosity values. You can see that asteroid porosity is all over the place, but seems to be roughly constrained by the FCC density as a maximum.<br />
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This makes a lot of sense. Since FCC is has the most efficient packing density, and we expect that not all asteroids have differing degrees of porosity. It also makes it clear that if you want to find the kind of ideal body I'm referencing, you really will have to cherry pick. Of course, the above data set isn't comprehensive either, so there's plenty of space to find a body which approximates an FCC structure of the desired size.<br />
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<span style="font-size: large;">Movable Rock for Boundary Formation</span><br />
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So we have our perfect candidate, what now? The habitat (or at least the early version of it) will go in the interstitial space. That space is an odd one, because it doesn't start out enclosed. That leaves the builders with the burden of enclosing it. This is a self-obvious reality of the gravity balloon idea. If no excavation is necessary to get to the center, they the center obviously shouldn't be expected to have a well-defined cavity. From there, we have to make it into a well-defined empty space. That means sealing off a boundary within this contiguous interstitial space. That would be very difficult if you used manufactured materials. In fact, it would defeat the entire point.<br />
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The obvious solution is to seal off the surrounding pathways between the rocks with other rocks. Refer to the FCC diagram. The interstitial space has 4 close-by rocks, for which the centers are arranged like a tetrahedron. Looking toward one "exit" of this space, we see 3 rocks arranged in a triangle. This strange triangle space is what needs to be blocked. It's not hard to set a minimum amount of rock needed to accomplish this, because we could just fill it in in 2D. I took a fractal approach:<br />
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Specifically, I used <a href="http://pastebin.com/x0BTTdcB">a program</a> to place circles in the empty spaces between the previous level of circles. This has an obvious branching of 1->3. With each level you'll increase the number of circles you're adding by a factor of 3, but not all of these will be the same size circle. Because of this, I found it easier to add circles in order of their size. Then, using the handy svg markup, place them on a palate. The presentation of this graphic does falter a little bit, because the circles can only be specified by integer values for their location and radius. This causes some of the smaller ones to be displaced a bit from where they should be.<br />
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This is useful because it provides a long list (as long as you want it) of circles that allows us to map the connections between volume and area. Importantly, this theoretically lifts the requirement for the liner which hermetically seals the air inside the habitat to have any material strength as the number of rocks diverge to infinity. In practice, the areas very quickly fall off to imperceptibly small values, which is expected in these fractal scenarios.<br />
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But now how do we resolve the problem of carrying this out in the real world? In the previous illustration you would have to commit more resources to secure these rocks in place. In practice, you would prefer to use a rock which is larger than than the hole, and sufficiently large so that its compressive strength holds up against the atmospheric pressure. This is a function of the contact angle and more complicated structural engineering, which I will not get into. For a vague idea of what we would do, I just multiplied the size of all the circles by a constant factor, which would seem to be mathematically sound. So collapsed to a 2D view, it would be something like this:<br />
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Now returning to the volume vs. area correlation, we can produce some graphs from the realistic over-sized rock scenario. It will then tell us essentially what volume of rock we need to move into place, based on the assumption that we can find any size of perfectly spherical rock just laying around inside the asteroid voids.<br />
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Obviously that last assumption was stretching, so let me talk about where I intended to go with this.<br />
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<span style="font-size: large;">Blasting or Cutting or Shattering?</span><br />
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Originally, I had wanted to get a figure in terms of tons TNT that would be needed to blast rock in order to create the size distribution of rock that I worked with in the above figures and graphs. However, once it was finished, it became apparent that this was a fool's errand. Firstly, how the heck do we quantify a metric for mass of TNT per fracture area of rock? Actually I found <a href="http://www.austinpowder.com/blastersguide/docs/Coversions%20and%20Tables.pdf">some useful references for this (pdf link)</a>. <br />
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All kinds of variables are involved, but you can still get a metric for mass of TNT per square foot of the fracture you're creating. At first, the reference gives mass of TNT per foot of borehole, but this is a function of the spacing of the boreholes and the burden above it. Obviously, combining the linear mass density of TNT of the borehole with the distance between the boreholes gives a area mass density over the fracture area. But what exactly should those parameters be? The overburden is completely non-applicable in the space application we're looking at.<br />
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Nonetheless, I picked some parameters just to see. My estimate was about 12 kg TNT / m<sup>2</sup> of fracture. However, if you used this to cut all of the needed rock, you will quickly find that you'll be sending more explosives than what you would otherwise be sending as a pressure vessel to cover a similar volume. This would make the proposal absurd and clearly uneconomic.<br />
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Are there other ways to fashion rocks in the way you want without explosives? I picture space probes with chainsaw-like things attached. This would have complications too, since most of their cutting would be done on the center piece, they would either need really long cutters or they would need to excavate a very wide fracture so they could fit into it. Alternatively, a more simple and primitive method may suffice. Why not just bang rocks together in order to break them up? Nothing about this proposal actually required a well-controlled shape. So sure, why not? Although this assumes movable large monolithic rocks available to begin with. Plus, how do you shatter the largest rock if it's the biggest one around?<br />
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Finding out how much area needed to be cut turned out to be disappointingly easy. This is because the 2D cross section is a straightforward multiple of the spheres that would occupy it. It's just 4 Pi r<sup>2</sup> / 2 divided by Pi r<sup>2</sup>, you get 2. But now what is the total area that we're dealing with in the first place? This requires the advanced science of calculating the area of an equilateral triangle.<br />
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For reference, the ballpark figure I'm looking at is D=1 km. Maybe more. In order to get the area of the rocks with the slight over-sized method I mentioned previously, you'd multiply it by that over-sizing factor. Again, none of this was particularly difficult or insightful, and it's not clear what the application would be in the first place, since smashing rocks together doesn't have an easily quantifiable cost.<br />
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<span style="font-size: large;">Inside-out Regolith, Carried by a Million Robots?</span><br />
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In spite of all this, we're still not lacking for an argument that voids can be sealed with a hierarchical distribution of rocks. Why? Because nature already did it. We are relatively confident that many asteroids have large voids inside, and we are also confident that they have something kind of like a contiguous (even if dusty) surface on the outside. At first these facts seem contradictory. But it makes sense when you consider that 1) first large rocks congeal into a pile and then 2) smaller rocks continue to fall onto this pile. While some small rocks will fall between the larger rocks, some will get stuck. As more and more get suck, the probability that the next rocks that fall onto it will get stuck increases, up until the point when the surface is effectively sealed. Not sealed against gases by any means, but against particles falling on the asteroid.<br />
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As a bit of a troll argument, you could simply rearrange the rocks from the outside regolith into the structure to seal a void which I have discussed here. That would require nothing more than pushing them around. But this would be a complicated low-gravity maneuver of moving many rocks around the surface and interior of an asteroid.<br />
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But we have another point to grapple with - loose material still exists within the interior of the asteroid. Hypothetically (and somewhat realistically) you could run an inventory of all the rocks around the asteroid, and chances are that you'll have a good shot at finding a sufficient size distribution to make your seal without any blasting. Some will only need to be moved a small distance, for instance, from one void into the next, but many others will need to be dragged through the byzantine path through the asteroid pores. The largest rocks will be the worst.<br />
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In fact, the very largest one, the center stone, is the problematic one here. By the very fact that it can't FIT out of the void's entrance-way, we would expect that it can't fit INSIDE in the first place if we're hauling it from somewhere else. This isn't strictly geometrically true, but it's close enough. This leads to a dilemma. Maybe you cut the center-stone, and then glue the pieces back together. Thankfully, no glue is strictly required. If the forces balance correctly, then it can just "sit" there, held by the outward force from the habitat's pressure. I'm not very concerned about that detail.<br />
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The only real problem is that you'll have to move a lot of rocks. Exactly how many depends on the convergence between the price of moving stuff and the strength of the pressure liner. I would assume that the robots would move non-propulsive in a method similar to <a href="http://en.wikipedia.org/wiki/Lead_climbing">lead climbing</a> in the outdoor pastime of recreational climbing. By attaching anchors and ropes at various points, there should be enough degrees of freedom to get where you want to go.<br />
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<span style="font-size: large;">A Big Dump Truck of Tiny Qualifiers</span><br />
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I don't think this discussion is pointless. I think there is a compelling argument, but there are far more unknowns than what there are certainties. Also, an analytical approach isn't nearly as helpful as what I had hoped.<br />
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But none of this suggests that we should toss the idea out. We don't know if this method will be viable, but our best understanding lightly suggests it will work. This is still saying nothing of the vastly complex structural engineering problem that comes along with potential re-seating of the structural rocks. Once again, this doesn't appear as a game changer to me, it just seems like a tremendously complicated analytical task.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-86966482117818724452014-01-15T13:50:00.000-08:002014-01-15T13:50:14.263-08:00SVG Version of Fractal Rock Filling PatternThere will be another post on this soon, but I want to avoid testing a new trinket in the middle of a larger post. The figure below is the output from a code I developed in order to quantify things that will be needed for the cutting of rock to section off an area of a porous asteroid.<br />
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<div style="text-align: center;">
<i>Rock Distribution to Plug a Porous Interstitial Site of Regular Lattice of Spheres</i>
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<embed height="500" src="https://dl.dropboxusercontent.com/s/7lu91s0ymgqc38m/output_cutoff.svg?token_hash=AAGg6flINkob_I_AEGGtJdgj8zFNdnwhT3kgo2SzbOrmFA" type="image/svg+xml" width="500"></embed>
</div>
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This is an svg element, which is a vector graphics format. That means that every circle is specified by markup language saying where it is, what color it is, and so on. When I post details, I'll restrict myself to png images.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com0tag:blogger.com,1999:blog-5515692164785328338.post-81728469716138758152013-12-11T15:48:00.002-08:002021-07-13T06:28:34.096-07:00Ederworld Analyzed (Concentric Gravity Balloons to Maximize Volume)From the Orion's Arm website, <a href="http://www.orionsarm.com/forum/showthread.php?tid=629">I have been directed toward</a> another similar design. The original proposal seems to <a href="http://yarchive.net/space/exotic/bubbleworld.html">trace back to Dani Eder</a> (possibly in 1995). I believe this is the same person who wrote <a href="http://en.wikibooks.org/wiki/Space_Transport_and_Engineering_Methods">the Space Transport and Engineering Methods Wikibook</a>. In that discussion, people were trying to ask what the largest realistic structure that could be built is. He correctly concluded that this would be a gravity balloon of Hydrogen, made even larger by rotation. Wording used there was a "Bubbleworld", which appears to be the concept I call a "gravity balloon". This Bubbleworld is much more relevant, but I can find very little information on it. Worse, I had passed over the concept in the past because it shares a name with <a href="http://en.wikipedia.org/wiki/Bubbleworld#Other_designs">other proposals</a> that are not relevant to this blog. I would like to find more writing on this Bubbleworld, but I'm not sure if I will. The wording used for Ederworlds on Orion's Arm is <a href="http://www.orionsarm.com/eg-article/48472f9d56859">"Inflated, self-gravitating megastructures,"</a> which is very promising to me. However, it seems that the title of "Ederworld" should be reserved for the goal of creating the maximum possible living space, which is the quirky design that I'll get into here.<br />
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I've repeated the calculations for the Ederworld described in the email that it apparently comes from. It is a serious mind-twister. The goal is to create the largest possible living area in terms of volume. Previously, I have entertained the concept of the Virga world, which is the largest world you can create with a simplistic gravity balloon concept. In order to go further, Ederworld introduces a bubble of Hydrogen gas in the center, which is prevented from mixing with the ordinary air on the outside. As you increase the size of this central Hydrogen bubble, the thickness of the air shell decreases from Virga's dimensions. That means that you're accepting a reduced thickness of the living area in favor of an increased radius. Exactly where the optimal point will fall isn't trivial.<br />
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If you assume that the Hydrogen gas isn't compressed any, then it turns out the optimal point is infinity. This problem is fairly sophisticated, but can be done with simple algebra. I've done that, and taken the limit for large values of R. In the final form, you can see that the volume scales with <b>R<sup>2</sup></b> times a constant that comes from the problem parameters.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtaih7f8bFHYVHUzTefq7b3ykQqbAZW9F7QiThf9tMn9p0jkZmzd22uv2OCx5k2uOJxQgPEaZrHFoS96OTX71IaWz7mJFoE6IEWy4dXYuhBRr7GoFvPjaFhhlRaKwrUM_Clew9ouUzL5Y/s1600/eqn+without+H2+compression.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtaih7f8bFHYVHUzTefq7b3ykQqbAZW9F7QiThf9tMn9p0jkZmzd22uv2OCx5k2uOJxQgPEaZrHFoS96OTX71IaWz7mJFoE6IEWy4dXYuhBRr7GoFvPjaFhhlRaKwrUM_Clew9ouUzL5Y/s1600/eqn+without+H2+compression.png" /></a></div>
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This means that a larger Hydrogen balloon will always give you a larger livable area - and it means that our assumption was wrong. At sufficient sizes, it's obvious that Hydrogen gas compression will be significant. In fact, it is this factor which will ultimately dominate. That also makes the problem very very difficult to solve. I used the numerical integrator which I described in my post on superlarge gravity balloons. That is applied for the Hydrogen core. After that, the "large" assumption is appropriate for the livable area and outer shell.<br />
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With that numerical integrator, we can start with some central pressure and then find the radius at which the pressure has dropped to <b>1 atm</b>. That's the condition for the interface between the Hydrogen gas and normal atmosphere. The result of this inquiry is quite fascinating. Beyond a point, adding mass to a ball of gas actually decreases its size. Of course, a ball of gas with these central pressures would not be viable naturally. They would evaporate away. However, this is still the same basic idea as with our gas giants. In a simple model, they just lie further to the right on this curve. However, some phase changes happen, so it's not actually so simple...<br />
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<div style="text-align: center;">
<i>Ederworld Inner Hydrogen Balloon Radius</i></div>
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<i>Adjusted by Attempting Different Central Pressures</i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidyDPL84z7p0UpKOVNeL6XRlR1bHrPr5E59BmTmoZVZgYhaE0pPKPC5_UBytNviGIjz6dho7PtKtaLOOWqfLH0sP92xgAwLIedkQV6P6dj7zXl0_tk6PaDyJdgg1usJtn1RaWBnrFit9s/s1600/Radius+given+central+pressure.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="278" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidyDPL84z7p0UpKOVNeL6XRlR1bHrPr5E59BmTmoZVZgYhaE0pPKPC5_UBytNviGIjz6dho7PtKtaLOOWqfLH0sP92xgAwLIedkQV6P6dj7zXl0_tk6PaDyJdgg1usJtn1RaWBnrFit9s/s320/Radius+given+central+pressure.PNG" width="320" /></a></div>
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You can see that the radius itself hits a maximum. So obviously adding more Hydrogen won't get you more living area, because at that point it decreases both dimensions, the thickness and the radius. The volume peaks at a slightly smaller radius. Going between radius, mass of the Hydrogen, and thickness is a little bit detailed, but involves the same equations that I posted above, for the case without considering Hydrogen compression. The volume of the living space is obviously <b>4 Pi R<sup>2</sup> t</b>, where R is the radius and t is the thickness.<br />
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<div style="text-align: center;">
<i>Graph of the Living Space Volume</i></div>
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<i>The Central Pressure is the Pressure at the Origin in the Hydrogen Balloon</i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWhXOkJHuZmlkpHGpxmRzb3CXYg232Yf7DUTtuvcSViK0lUiJEJL5eScgRhhi9HnJca1kHKWeOW688q-b3MxNi7h7_fnbJTmo5POzQa2UfrlcE64IHm_IzPLSXkxts2n0HWKNw_OKK4mI/s1600/Habitat+volume+w+central+P.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWhXOkJHuZmlkpHGpxmRzb3CXYg232Yf7DUTtuvcSViK0lUiJEJL5eScgRhhi9HnJca1kHKWeOW688q-b3MxNi7h7_fnbJTmo5POzQa2UfrlcE64IHm_IzPLSXkxts2n0HWKNw_OKK4mI/s320/Habitat+volume+w+central+P.PNG" width="320" /></a></div>
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Again, these are all done by the integrator for spherical distributions of gas that I made. With the above graph, we pinpoint the absolute maximum living space that can be made by this method without rotation. For the big picture, here is a table of my numbers:<br />
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<center>
<style type="text/css">
table.tableizer-table {
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<tr class="tableizer-firstrow"><th>Region</th><th>Thickness (km)</th><th>Mass (kg)</th><th>Volume (km<sup>3</sup>)</th><th>Average<br />
Density (kg/m<sup>3</sup>)</th><th>Surface g (m/s2)</th><th>Inner<br />
Pressure (atm)</th></tr>
<tr><td>Hydrogen</td><td>237830.5</td><td>7.50E+24</td><td>5.63E+16</td><td>0.13</td><td>0.0089</td><td>3.5</td></tr>
<tr><td>Living</td><td>2719.7</td><td>2.36E+24</td><td>2.14E+15</td><td>1.11</td><td>0.0114</td><td>1.0</td></tr>
<tr><td>Wall</td><td>0.461</td><td>4.31E+22</td><td>3.80E+09</td><td>11340.</td><td>0.0114</td><td>0.7</td></tr>
</tbody></table>
</center>
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No doubt, this is way larger than Virga. To illustrate, here is what I'm describing:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTiDDNa0nMIYWbObXvz4O5e0aOIMo2U4SLi4a6aSQSFeDIJIYs2My3fkrRG3dDMNJvPNVkCUMyM7OZkWkTsqGJqnWlR_VKICJuLrpU123uZSaKDsgnCsLG6xN1A-bUpE519o81wwmzVQ4/s1600/Eder+maximized+volume+-+my+version.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTiDDNa0nMIYWbObXvz4O5e0aOIMo2U4SLi4a6aSQSFeDIJIYs2My3fkrRG3dDMNJvPNVkCUMyM7OZkWkTsqGJqnWlR_VKICJuLrpU123uZSaKDsgnCsLG6xN1A-bUpE519o81wwmzVQ4/s400/Eder+maximized+volume+-+my+version.PNG" width="400" /> </a></div>
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(Hydrogen gas isn't actually red, I couldn't</div>
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think of another color to differentiate it) </div>
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We have a central bubble of Hydrogen, for which the pressure shifts significantly. Interestingly, even the density at the center of the Hydrogen bubble isn't quite up to the density of normal air. Hydrogen spans a range of about <b>0.08 kg/m<sup>3</sup></b> to <b>0.3 kg/m<sup>3</sup></b>, and air is closer to <b>1.3 kg/m<sup>3</sup></b>. The parameters here actually match the previous work by Dani Eder surprisingly well. He said:<br />
<blockquote class="tr_bq">
If we assume that the bubbleworld is non-rotating, and the living space is at one atmosphere at the gas interface, the gas used is hydrogen, and the gas is at the same temperature as the living space i.e. 300K, then the answer is a sphere about 240,000 km in radius.</blockquote>
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That's essentially what I obtained. The major reason for the difference is probably that he assumed a temperature of 300 Kelvin, while I used <b>293 Kelvin</b>. Considering what it takes to get this number, I'm actually surprised that he was able to get this. However, I think there is a little bit of misspeak in the proposal here:<br />
<blockquote class="tr_bq">
If we assume that the living space has an average density of 10 kg/m<sup>3</sup> (air is 1.2 kg/m<sup>3</sup>, the balance is people, houses, trees, etc.), then the living space has a limited thickness based on breath-ability. After 2400 km of thickness, the air will be at the equivalent of 3000 m above sea level on Earth, which is about the limit of ordinary breathing with no problems.</blockquote>
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The livable portion is about <b>2,400 km</b> if you use 1.3 kg/m<sup>3</sup> as the density, not 10 kg/m<sup>3</sup>. Using the former, the thickness comes out to only 300 meters. However, I think that 10 is a little bit too high for this metric. The reference tube design I described contributes a mass of only about 2.8 kg/m<sup>3</sup>, for a total of <b>4 kg/m<sup>3</sup></b> if you include the air. I have a hard time imagining a comfortable environment where things are packed more tightly than this. After all, if you've made a habitat so absurdly huge, you would think that you wouldn't run out of space. But I guess that's a subject for the sci-fi writers.<br />
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The density of the livable portion doesn't affect the calculations for the Hydrogen part, because its boundary condition is 1 atmosphere of pressure either way, and shell theorem prevents any gravitational effects. However, the density does affect the total mass. It is also quoted that:<br />
<blockquote class="tr_bq">
The bubbleworld is too diffuse to hold the atmosphere in by gravity, so an outer shell (steel is handy) is used to keep it in. It works out to 500 m in thickness. The total mass of such a world is 3x the Earth's, so there should be enough raw material to build one out of a typical solar system.</blockquote>
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You'll get 3x of Earth's mass (of almost this) if you use 10 kg/m<sup>3</sup> for the livable area. But this isn't compatible with the thickness of that area of 2,400 km. Otherwise, the calculations for the "wall" are the same as mine. I find about 500 m if you assume a density of lead, which is extremely heavy at <b>11.34</b> specific gravity. If you change this density, it doesn't change the total mass of the construction.<br />
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If you return to the assumption of a 1.3 kg/m<sup>3</sup> living space density, then the mass is about <b>1.7x Earth</b>. <br />
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<span style="font-size: large;">Buoyancy (Actually Differentiation)</span><br />
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It's also not stable, naturally. You can say that no gravity balloon is stable.. but you would kind of be wrong, unless you're counting the liner to keep the gas inside. A gravity balloon should have a gas on the inside and a solid as the wall. As a rock-like substance, the rock has some strength to it. It's not going to start tumbling due to the presence of microgravity due to a slight displacement from perfect spherical symmetry. That's because we're dealing with a fluid underneath a solid. For the Ederworld, we're dealing with a fluid under another fluid.<br />
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Fluid-fluid constructions are extremely unstable if not already differentiated. By that, I mean that the Hydrogen gas is lighter than air, and because of that, it wants to rise to the top. The air wants to fall to the bottom. This is an issue, because you have to stabilize the Hydrogen balloon. Any off-center movement will want to grow, and that will be a big problem. This construction is so large that you really can't credit much material strength. However, since the livable space is only a few 1,000 km across at most, it's reasonable that this could be spanned with stabilizing tethers. This is obvious - stability is never absolutely limiting. It's only a complicating factor in an engineering sense.<br />
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Aside from stability, I was also convinced that tidal forces would be a big problem for a balloon of this size. I was very convinced of this, but it turns out that I was wrong. You would have to be within 1 AU of the sun for the tidal forces to approach the surface gravity of this, which is the general metric I would use to set expectations. It would appear that it could sit in many places in the solar system and still be viable at the stated pressure and size without tidal forces ripping it apart.<br />
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Qualifier: This goes into the library of physically viable constructions, but it would take a society far beyond anything that we have ever known on planet Earth. This is something to "outdo" the Virga design - which is the extreme of a Bubbleworld, which was the starting point for the Ederworld. The Virga design is vastly beyond what we could hope to do as a society that resembles what we have today. Even the designs I refer to as "Anahitan" and "Sylvian" are mind-bogglingly massive constructions, and those assume all kinds of shortcuts taken to reduce the needed resources.AlanSEhttp://www.blogger.com/profile/08119889774421336682noreply@blogger.com5