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August 12, 2012 at 8:35 pm #20919
The idea is not old. Jonathan Swift described “Laputa” in 1726, (Gulliver’s Travels). Technology described was magnetic suspension, not useful. Buoyancy by helium? Helium escapes from darn near anything useful, it’s expensive, and industrial demand is rapidly outstripping supply. It won’t be helium. You want a Cloud Nine City.
Several decades go, R. Buckminster Fuller stated that the geodesic dome is a structure which becomes much stronger as it becomes larger, (mistaken, sorry), that a geodesic sphere, a half mile in diameter, with all of its structure would weigh only one thousandth the amount of the weight of the air trapped inside, and that a sphere one mile in diameter, with an interior air temperature rise of only one degree would function as a huge hot air balloon and could support several thousand people. Naturally there was a lot of pretty artwork and a lot of speculation about social and political impacts, much of it along the same lines I see here decades later. Well, I have discouraging words for you. The pretty pictures aren’t gonna get past the Big Screen and video game stage, because the best materials we have are only suited to making one that floats free. Once you tether it to something it’s curtains for you. You see, there’s this pesky little mathematical relationship that I call the the Square:Cube Law. Essentially, many basic properties of structures, life forms and machines are dependent on scale. If that scale is changed, (example: doubled), all properties dependent on area, (such as physical strength of parts and sections), change in proportion to the scale squared, (in this example, quadrupled), while all properties dependent on volume, (such as mass and weight), change in proportion to the scale cubed, (in this example, octupled), with the result that the strength-to-weight ratio is inversely proportional to scale, (much to the detriment of our mass media). The larger the scale, the greater the strength required for the materials used. To build something really big, (Robert L. Forward’s tether technology), we must consider tapering things toward the ends, (factors of a hundred to one have been suggested), and the development of new high-strength materials, (like carbon nanotubules). I don’t see any structure, tensegrity spheres included, being immune to this.
Large domes and spheres have some advantages in that atmospheric buoyancy is volumetric, but we must remember that the skin will be supporting the frame, the safety factors may be small, and the buoyant forces will only be acting on surfaces with a horizontal component, (vertical surfaces must still support their own weight).
The next issue is the matter of biological environments:
The operating ceiling for a Cloud Nine may be very high, but without pressurized, habitable compartments, the humans in it are limited to an operating ceiling of about twenty-thousand feet, less than four miles, (or less, fifteen thousand for long periods)?. You can’t pressurize the entire, gross volume without a severe loss of buoyancy. All of that pretty artwork depicting flocks of pretty bubbles will be hard to realize. I’m used to thinking in terms of four general classes of engineering and construction:
Class 4: It Leaks (Frank Lloyd Wright has lost my respect),
Class 3: It Sheds Water (even the ancients were pretty good at this),
Class 2: It is Closed (keeps out vermin, maybe even dust),
Class 1: It is Sealed Against Pressure (aircraft, submarines).
You can imagine how these compare in cost. On the whole, though, you do want substantial altitude on your side if you can afford it, as it puts you above destructive weather patterns and gives you a safety factor, (one which you might need in the face of overnight cooling). Additionally, buoyancy and altitude are about the only things that you can control in navigation, (on water, the shear means that you can _tack_), and outside of them you pretty much have no other choices: you are the wind and you go where it takes you. I don’t know enough about prevailing winds and planetary weather patterns. I know that the bands of air circulation reverse with every 30 degrees of latitude, but that’s at the earth’s surface. I don’t know if the high altitude pattern turns it into a spatial corkscrew, (meaning that you have no choice but to circle the globe), or if it’s a true reversal, (allowing you to cross the U.S. diagonally from Southwest to Northeast, then return at high altitude). To be able to take advantage of these options, your habitable space within the sphere would probably take the form of a network grid of pressurized tubes, perhaps of Spectra-reinforced Tefzel film, and the rest of the sphere might be sustained at an uncomfortably warm temperature for buoyancy, depending upon payload weight.
Next issue, thermodynamics:
two primary equations will handle most of this reality for you, PV = nRT and PV^1.4 = C. The first equation, the Ideal Gas Formula, relates absolute pressure, volume, absolute temperature, mass and chemical composition for any ideal gas or mixture of ideal gases. This can be used to solve for buoyancy and many other desired values. The second equation, the Adiabatic Gas Formula, relates absolute pressure to volume when an ideal gas is compressed or rarified rapidly enough that no heat energy enters or leaves the system. If these formulae are used together, they predict how air and other gasses will heat when compressed, and explain why low-pressure air at high altitudes is colder than at sea level. More of our popular myths fall, including our “Day After” scenario of super-cooled air descending from the troposphere to freeze the landscape at 150 degrees below zero. Compress air to a pressure, and its temperature rises to correspond.
Next issue, Heat Transfer:
solar gain is how you will heat the air trapped inside the sphere. A light-absorbent system, (black materials), will enable you to capture heat from sunlight at close to a kilowatt per square meter. For a structure of this size, that’s a lot of power, and the issue becomes one of control. It is not enough just to heat things up to the temperature that you want and then ventilate to keep them there; you must control solar gain. The reason why you must do this is because the heat transfer processes are reversible. During the day, your black, solar heated film or fluff is heated by the sun and cooled by the convection of your trapped air, but at night, this process reverses and your black absorber becomes an emitter, cooling your air mass and radiating the energy into the night sky, (don’t discount this effect, night sky radiation is how the ancients made fruit ices in the desert). If you don’t want to touch down somewhere and roll across the landscape, you will stow the black sails at night and cover the photovoltaic solar panels with aluminized Mylar. Insulating the outer skin could be pretty important too, and might result in a pillow dome resembling the Eden Project in Cornwall.
Next issue, Structure:
I read somewhere that Bucky Fuller first hit on the GeoDome concept in his Dymaxion House days. The question had been, “How big should the mast be?” …and the math just kept pointing to tubes that were larger and thinner without limit. This led him from mast-mounted structures to domes. Funny things happened, though, as the domes got bigger: if the frequencies got too high and domes got too spherical, they collapsed. The headings for this in Mechanics of Materials are Truss Structure Failure and Buckling of Slender Columns. I don’t know how much you want to get into this, but the joints in a truss are typically angularly elastic enough that little, if any, of a bending load can be transmitted through the joint to induce bending eccentricities in the other members. Buckling of Slender Columns is a mathematically difficult problem, but it occurs within the elastic range for most useful materials, and none of the enhancement treatments we’re used to (tempering, hardening, etc.) make any difference. The failure would still have occurred if the material had been stronger; what it needed was to be stiffer. As the sphericality of domes increased, the leverage factors increased, magnifying the stresses produced by radial loading conditions tremendously. The answers to this were the addition of short, radial struts that were then connected to surrounding vertices by cables, or another inner or outer dome connected by diagonal members to create a space truss, (this may have also been called a ‘Star Dome’, I’m not sure). Beyond a point I’m not certain of, all of Bucky’s large, high-frequency domes were of one of these designs, at least before he got into tensegrity structures.
There are still some things going on here of which I’m not certain. For one, there’s the statement that “The geodesic dome is a structure which becomes much stronger as it becomes larger.” And the statement that tensegrity structures are capable of high frequencies without limit. I didn’t understand what Bucky meant until 2007. What I knew was that the struts in a tensegrity dome crossed at about the midpoints of struts that they were connected to at the end slightly displaced and not in direct contact, (cable connections only). If the surface of the assembly becomes too planar, the frequency too high, the structure approaches a planar grid of hexagons and triangles, and eventually the struts touch where they cross. Additionally, the cables approach parallelism with the struts. Parallelism means infinite leverage, i.e. any loading force results in extreme stress, and any contact between struts except at the ends results in deflection and eccentricity which figures strongly in buckling failure of the struts. What I had hoped to find, was that in addition to tensegrity masts, polyhedra and domes, Bucky also had a tensegrity design for a space truss that he had adapted for use as a truss dome. What he had done, however, was to propose replacing the struts in a tensegrity structure with tensegrity masts on a finer scale, possibly even additional recursive replacements without limit. Eventually it looks like nanotech.
My feeling is that what this calls for is proper engineering studies with simulated loadings and analyses with appropriate safety factors. One thing that is intuitively obvious is that a free-floating cloud nine with only localized differential atmospheric loads to deal with will face a great deal less stress than one that is tethered, anchored, mast-mounted or connected to anything else, even another cloud nine. I would not be surprised if designing for such load multiplied the required weight of the structural material and outer skin many times over.
Next issue, Ecology:
Importing food and other necessities would be expensive. The failure of BioSphere 2 has shown that with regard to closed systems we don’t know what the heck we’re doing, (though I may be out of date here). Perhaps a stable, pressurized, sealed and self-contained system would be a long-range ideal, but in the beginning the solar power system, whether photovoltaic or solar-thermal, must be sufficient to pressurize and provide climate control for the habitat like a passenger aircraft, to condense needed water from the air, to support communication with the surface, and to illuminate the anti-collision beacons to warn air traffic at night. Rechargeable batteries will serve for electrical power storage in the beginning, but composite graphite power flywheels would be a much better long-term solution.
Next issue, Construction: How to build?
First, you need a good design and the analysis to back it up. The design is somewhat problematic, as from the outside the structure looks like an array of cables of almost infinite complexity, and from the inside, one of struts, and how do you seal a membrane to this thing? It’s like coarse cloth or a woven basket. Does the membrane support the structure or vice versa? Both, it seems! It’s somewhat reminiscent of the old pillow domes, in which two layers of plastic film were draped over the tubular dome frame and afixed with curved strips and screws. The screws penetrated the film, but the load from the strips sealed the works. The corners were unimpeded, and when the space between the layers was inflated, the dome was thermally insulated by the pillows that formed. If the cables are already coated with the right kind of plastic it should be possible to heat-seal the film to them, and if both inner and outer membranes are used, should also be possible to seal film-to-film at the perimeters of the large openings.
I recommend that a fully robotic test model with a full sensor and telecommunication array be tested before anything manned is completely designed. It need only be a fraction of the size of the inhabited ones, but should be large enough for proof of concept on altitude control, thermal capture, overnight stability aloft, trajectory control and navigation, something to deliver enough data to support the first manned designs beyond question or doubt. Second, you need land, preferably something like Meteor Crater in Northern Arizona. Start with a polymer membrane and a few struts, and tension the cables to erect the section. Pressurizing the membrane section can also be used to support the tensegrity truss during construction. By this method, all construction can be done at ground level. Beyond some undefined point in the construction, the buoyancy of the air under the dome will likely eliminate the need to pressurize the air for support at all, at least during the daytime, but to maintain control you will need to be able to vent hot air from the top center area to keep it manageable.
The middle height of the spherical volume would probably be the best place to add a planar truss structure for the habitat, and a system of vertical cables from the upper dome structure will enable the planar truss to handle the habitat weight load with far less invested material and weight than otherwise. Ideally, both a system of suspension cables and a polymer support membrane should be included for suspending the habitat planar truss. With proper control of interior pressures and volumes, the upper dome, lower dome and habitat truss could all be air-supported, the trusswork only required for localized stress concentrations.
Next issue, Safety Factors:
No engineer in his right mind would design something like this without substantial safety factors. It is rare to see anything in use, where human lives are involved, with a design safety factor of less than five. NASA runs some things as low as 1.2, but they test eight of ten to destruction to achieve that. Most non-ferrous metals fatigue at nothing, and ferrous metals start to fatigue at 25% of yield, (okay, it’s more complicated than that, the issue is FCC vs. BCC crystal structure metals), improving with improved surface finishes to a max of 50% at a mirror finish. For polymers, a factor of ten would not be unheard of. Consider an aggressive maintenance schedule, while bearing in mind that much of the work will be done by hand by men in pressure suits. I also recommend multiple redundant buoyancy cells with independent heat collectors, just in case there’s a containment loss. Don’t expect any of the membranes to be stretched tight as a drumhead, or the cables to be tight as a banjo string, except near the equator where there is no buoyancy force. Expect things to bow, sag, droop and balloon in response to the pressures. Anything but a truss or strut that’s too straight or too flat would be under too much preload.
Next issue, Access, Arrivals and Departures:
I don’t see landing passenger aircraft on this without tailhook enhancements and a truss-supported landing platform on top. Trying to add landing bays in the habitable midlayer would probably be a big mistake, as aircraft pilots like large, open spaces, and most of ours would probably be punctuated by cables. Additionally, any attempt to fly under a ceiling to land inside may become subject to a sort of ‘reverse air cushion’ that would tend to stick the landing craft to the ceiling with disastrous results. For individual, low-altitude access I can foresee the possible development of a ‘cablevator,’ a sort of one-ended elevator system that would use a circular platform suspended by three cables in combination with a tube that would slide on those cables, and would be articulated by two or three others. Whether or not a cablevator would be of much use would depend on altitude, how fast the Cloud Nine is drifting, and how well ‘guidance fins’ can be used to direct the assembly during its descent. Ideally, the cablevator would drop fast, land directly in front of the passenger, he or she would have a minute or two to get within the perimeter of the platform, (identifiable by infrared optics), then the tube would drop to the platform and the whole substructure would rapidly ascend to the cloud nine, (hopefully without dragging across the landscape). Other methods of access both ways include parachute, parafoil and autogiro, (an unpowered autogiro, dropped from twenty thousand feet, can glide for about twenty miles).
I do have a tentative design concept but I can’t recommend it, as it would require far more expensive and exotic resources to build than a Seastead, (the Tefzel fluoropolymer film alone would be over $100M, and I wouldn’t trust this to anything less, because I know of nothing less that will survive the UV long term), you would face all of the problems that I have listed previously, much greater legal and political problems with no mobility control, (imagine being blown over North Korea), and no provision to ever dock, moor or land it. How would you finance this thing? Selling megapixel images? I wouldn’t invest the money if I had it, but it would cost a lot to send one up even if it only carried robotic cameras and needed no life support system.