Floating geodesic domes of concrete?

[georgeberzSubscriber]

Imagine a giant concrete geodesic floating house. think of a giant bouy?

What would happen if you made a forum in the correct triangular specifications out of steel with hinge pins to disassemble after casting.

laid them on flat ground with a piece of plastic tarp on the bottom to keep the concrete form sticking.

when cast and setup unpin the metal frame and you would have a perfect shaped concrete geodesic triangle.

Cast each so its like 12-24″ thick.

devise a method of pinning one to the next.

Say your dome was 50′ diameter struts on a 3v triangle would be about 13′ to 15′ so your triangle essenialy is a large flat slab.

Place the 1st one in the wateraround 15-20′ deep on the bottom of the harbor, then bring the nect one in place and pin it in etc with a crane until you get 1/2 spehre

Put some caulking in any joints on the outside of the sphere then pump the water out that is in the inside, voilia you now have a floating 1/2 sphere.

Make rooms in the bottom with concrete walls all acting to brace the structure and a flat concrete deck and a hatch to go below.

Make the whole top a large greenhouse or shade area, pipe frame geodesic shell wrapped in plexiglasss, tarps or whatever.

Or continue to complete the whole concrete sphere with the bottom weighted much more than the top so it will always bob UP

I’m serious, What do ya all think?

my personal blog / forum – http://OutpostAlpha.com

[paulspainSubscriber]

If you want to be taken seriously, I suggest you express yourself clearly and use correct grammar, spelling and punctuation. I’m sure your idea is interesting but it’s very difficult to make heads or tails of what you’re saying.

[jtg423Subscriber]

I understand what you are trying to describe…a “prefab” sphere that will be constructed in much the same way as a geodesic dome home. It is not a bad idea but just imagine all the sealling you will have to do. Take a look at concrete domes http://www.monolithic.com/ , the air form and basalt construction ideas are amazing. Hard to transport (of course they did not design these to be moved) but amazing. Further more you will not have to make these 12-24 inches thick. One of the blog members, Ellmer, already has a company constructing concrete subs http://www.concretesubmarine.com/ and he has said 5-6 inches is fine.

Take everything said here with large grain of salt.

Welcome and continue with the Dream GeorgeBerz

Thank you

JTG

[Ellen-Re-GenerateSubscriber]

The benefit of using prefab concrete geodesic facets is that they can be cast in a controlled environment with a mix that’s precisely controlled. Include fly ash or other ultra-fine power amendments to fill every last airspace inside and it becomes high-performance concrete, impervious to water. But yeah, you’ll have to use some fierce adhesive to assemble them. They should use a spline to align them one to another. Once assembled, an epoxy coating should be added on the outside to improve hydrodynamic performance. (read: help prevent barnacle buildup.) Also, I would recomment using ample fiber reinforcement rather than steel rebar. Concrete fails most when the metal inside corrodes and expands. Since the sphere is going to be underwater for the most part, the compressive pressure should be ample to keep the thing in shape.

Think about how much water a concrete sphere would have to displace to get bouyant. I’m bettering most of the sphere would be under water. The dock/pier would be on the roof. Also think about orientation. A nice, round sphere doesn’t inherently have a preferred orientation. Without considerable engineering to place the heavy engineering equipment in the bottom of the sphere, it can get fun in a storm.

I’ve done some design work with freaquency 5 icosahedral spheres with an internal diameter of 20 meters, but I want to put mine underground rather than underwater.

–

I have a thorium reactor under the hood of my car. I get ∞ miles per gallon.

[georgeberzSubscriber]

Hey Paul, those that cant do nit pick. It seems others have been able to figur eout want my intentions were…

Thanks JTG, I was thiniking 12/24″ as you need allot of weight to displace seawater to sink the craft enough to make it stable (IMHO) see the math later and with a 3v dome the caulking lines would each be 13-15′ long not that many triangles in a sphere when the triaangles have 13-15 foot base sides.

I really love monolithics stuff but the problem remains is how to inexpensively manufacture and assemble on site, trying to make a sphere with a balloon, I cannto imagine how I would go about simply constructing it.

I will have a look at the subs soon… thanks.

Ellen, good comments thank you, yes prefab panels can be made of exacting specifications, agreed, no steel For structural reinforcement I like PVA fiber as it acutally bonds with concrete and can even let it flex some, this has been proven in bridge span sections, no rust issues at all. Actually makes a bond that is stronger than concrete for each fiber. I have bought some of their fiber to play with http://www.kuraray-am.com/pvaf/index.php Nothing like a good epoxy coating when done either.

My Math

Vol of 50 diam sphere 65416.667 cu’ Vol of 48 diam sphere 57876.48 cu’ Subtract to find volume of concrete in a 50′ outside diam concrete sphere and weight.

= 7540.187 cu’ /27 = 279.266 yards concrete approx 3500 lbs yard = 977,431 lbs

1 cu’ of regular water = 62.426 lbs and seawater weighs more.

The whole sphere would displace 65416.667 cu’ * 62.426 lbs = 4,083,700.854 over 4 million lbs of water and yet weigh around 1 million. So a full concrete sphere 1′ thick would only be submerged about 25% leaving 75% above the water line. Even if you made it 2′ thick it would still be less than ½ submerged.

This is why I say take the bottom ½ of a 50′ sphere for concrete compartments for storage, bedrooms, kitchen, office living rooms and the top ½ greenhouse and other open space with some natural lighting. This would make the lower ½ heavier and make it self righting… even put another 250k lbs of ballast in the bottom like sand/dirt/rocks.

As for linking the geodesic pannels, I was thinking a stainless pin / bolt latch. or somhow designing a keyway, grove or locking teeth of some sort.

No glueing of panels together, bolted, pinned, compression fittings. Just get them within 1/3 of an inch and fill the gap with a rubberized caulk, with the whole dome even fully submerged it would only need to stand up to 25 PSI from the surrounding water pressure at 50′ deep.

Concrete of the quality we are talking about is in the 4,000-5,000 PSI compression rating so 12″ is way overkill.

[Ellen-Re-GenerateSubscriber]

Not addressing your math regarding relative densities and volume of displacement, something struck me as hinky about your statement about 25% of the sphere below the waterline.

Volume of sphere.

V_sphere = 4/3 Pi r³

Volume of spherical cap.

V_cap = Pi h² (3r – h) / 3

At what value of h is exactly ¼ of the volume of the sphere in a spherical cap?

1/4 V_sphere = V_cap

1/4 (4/3 Pi r³) = Pi h² (3r – h) / 3

1//3 Pi r³ = Pi r h² – Pi h³/ 3

r³ = 3 r h² – h³

We can express the value of h in terms of r as h = pr, where p is a proportion on the interval (0, 1).

r³ = 3 r (p r)² – (p r)³

r³ = 3 p²r³ – p³r³

1 = 3p² – p³

3p² – p³ – 1 = 0

p³ – 3p²+ 1 = 0

Solving for p by way of Wolfram Alpha yields three possible solutions, only one of which is in the needed interval, p = 0.652704. So, a sphere that is bouyant when 25% of its volume displaces water will float with 65.2704% of its radius under water, or 32.6352% of its diameter. With your 50′ sphere, you would have a draft of 16.3176 feet or just under 16 feet, 3 13/16 inches. If only 25% of the diameter were below the waterline, the draft would be 12 feet, 6 inches, a difference of almost 3 feet, 10 inches. For an error of 30.6…67%.

–
I have a thorium reactor under the hood of my car. I get ∞ miles per gallon.

[Ellen-Re-GenerateSubscriber]

You mentioned your geodesic facets being 13-15 meters on a side. You realize you can’t transport that on a public thoroughfare, right? That’s why I chose a frequency 5 instead of a frequency 3 for my 20 meter spheres. Breaking the icosahedral facets up into smaller pieces means you can just fork-truck them onto a flatbed and haul `em from the factory to where ever you’re gonna assemble them.

I don’t see bow-tie splines being viable. Once you get any distance into the assembly process, it becomes impossible to slide the bow-tie into place laterally. A straight spline, on the other hand, will always be able to be inserted when putting any two triangular facets together… except the last one. But then, there’s no real use for a complete geodesic sphere. As you said, it’s gotta be able to be interlocked with other identical spheres, and there has to be entrances and egresses, windows, large windows for hydroponic green houses, etc., so there will always be a last facet that doesn’t need to be put in place. Several, actually.

As for your desire for an affirmative connection, you can always mould bolt flanges into the interior edges of the facets so that after they’re fitted together with the spline and sealant, you can shove some 1″ bolts through the holes and spinning a nut onto the other end. Torque them to spec and nothing on Heaven or Earth will be able to separate them.
–
I have a thorium reactor under the hood of my car. I get ∞ miles per gallon.

[jtg423Subscriber]

Because there will be superstructures.

Because there will be a need to link-up and move about between vessels. Think of connecting each individual structure together to form a community and all the anncillary structures that will be built in this community. Because no one will ever be able to do this alone and with only one “personal” living space.

Because there will be the need to produce, catch and store potable water. Think of reseviors. Think of reverse osmosis water makers. Think of large catch trays or condensation equipment. Because it would be unsustainable otherwise.

Because there will be a need to produce food stuff. Think of aquacultureal platforms. Think of growing plankton and mussels. Think of artificial upwells, produced on demand with “oceanic living equipment, of the nutrient rich waters from the bottom of the ocean to produce vast quantities of zoo and photoplankton to feed fish or lure them. Because it would be unsustainable, from a finacial and practical stand point, otherwise.

Because there will be a need to produce energy. Think of the weight of enough generators (alternative fuel, solar, wind, and wave) to create a high enough standard of living to induce people to abandon thier “natural” way of life (and do not kid yourselves, living on the water will be fairly unnatural until we have been doing if for quite awhile (psycologically and emotionally)). Think of the need provide reliable and strong methods of remote communication (not to mention all the anncillary structures that this will require), and to run compressors and such for filling scuba tanks to perform underwater work. Because it would be unsustainable, from a finacial and practical stand point, otherwise.

Because there will be a need to store alot extra equipment which will act as “balast” in quite a few number of forms. From batteries for back up, to food storage, to emergency equipment and spare parts. Because it would be unsustainable otherwise.

And a ton of other NEEDS that I have most likely forgotten or not thought of…

The methods of construction matter. The decision on these things is not something to be rushed. This is not an easy or cheap undertaking. If it were, it would be done already.

I have thought quite abit about this and have decided that I am not an engineer. Yall sound alot closer to it than me… but to really do this I think that it will take more than numbers on paper. It will take practical application. I would love to see a “prefab/modular” building method employeed for a number of practical reasons but I dont let this blind me to reality. If it is impossible, can you cope?

The oak stands tall and straight but in a strong wind can be broken. The willow can bend and bow to the wind and thus survives in more adverse conditions.

Thx

JTG

[georgeberzSubscriber]

I dont believe I ever said meters, I measure in the US format in inches feet and yards, there seems to have been a misunderstanding.

As for 25% being hinkey, according the the approximations I gave it is appropiate 25% of the volume will be displaces, not nesscerailly 25% of the structure, as we were talking about pounds.

What about the nearly 50% statement, that is better approximation, if the structure wall increased to 2 feet then the overall structure would come in just under 2 million pounds APPROX and if the structure had a total displacement of 4 million pounds then it would be phisically 1/2 submerged APPROX.

My numbers are and should be considered guesstimated until real architect or engineer has time to look things over, I am not an architect or an engineer, just a dreamer trying to dream up a way to make a virtually unsinkable ship / vessel etc…

I once read someplace that “Noah a common layperson gave us the Ark and engineers gave us the unsinkable titanic”

So can anyone offer positive help with an idea how to construct the system, like geodesic triangles or even a soccerball patchwork design I dont know what that is called.

Help me understand the dynamics involved

[SimianAngelSubscriber]

Just from looking at them the domes made with pentagons look more structurally sound to my eyes. It’s akin to the reason bricks in a brick wall are usually staggered. i don’t know how to describe it better than that.

You might want to check out your local library and see if Buckminster Fuller has written anything about the dynamics and construction of domes, which are what he was most famous for.

[SimianAngelSubscriber]

Welcome to the forum, Ellen Re-Generate!

[georgeberzSubscriber]

Hey Ellen thanks, you could have just said your about right the 50′ dome 2′ thick would be ABOUT 50% submerged.

When we are talking in millions of pounds I dont think a few feet either way makes much difference on the intitial idea.

On to more construction ideas

What about digging a making a lock type system doors closed pump out the water, make a sand mould in the shape of a 1/2 sphere then gunnite in the concrete just like a swimming pool, then flood the area with water to float it out the lock.

now you have a 1/2 structure ready to have the top added on

Making a concrete hull in a sphere and then conventional geodesic pipeframe over the top covered in white boat type shrinkwrap and clear windows strategically placed.

Back to a monolithic 1′ thickness and next to no weight on the top

can you tell me the draft? I admit I dont know how to even figure out all that.

Anothe rthing, I wonder how close to the ocean or beach you could dig a hole with an escavator, before it started filling up with water? if you put some gravel on the bottom and sand, you could bury a sump pump to keep it relatively dry, line the hole with plastic tarp and spray concrete away. When done flood the hole outside the structure with water it would float up, then dig a small canal to the ocean, beach, river. possibly even kinda roll it out of its hole with a bulldozer and wobble its way into the water.

I am serious, I have some $$ saved up and am tired of dealing with property zoning and planning people locally and there are NO regulations on building your own private boat in the USA other than having appropiate life vests and fire estinguishers. Id love to live in somehting like this in the sanfrancisco bay! put a 10 HP outboard on it and go slowly anywhere you want at displacement speeds, not planning speeds, a slow put put put… just thinking outloud.

Use mabye 150 cu yards of concrete, concrete here can come in a 8-9 yard truck, and a pump spray system goes pretty fast. 150 yards at $150 a yard $30k for a pretty impressive hull?

[Ellen-Re-GenerateSubscriber]

The problem I see with that is that there would really be no way to prevent the inclusion, into the gunnite mix, of sea salts. That would form voids as submersion in the ocean leeched them back out. Also, don’t forget, if you’re making your own drydock, to add in the costs of building it. If it’s going to have concrete walls, that’s $$$. And it will need oceanside locks holding back a height of water at high tide at least as tall as your draft plus clearances. Far better to find a commercial drydock and rent it for the time you need to construct it, fill it with clean sand to form into the lower hemisphere. Of course, commercial drydock time = $$$$$$$$$.

Also note that that calculation was for an empty shell. Add a bunch of internal structure for floors and walls and engines and appliances and batteries and furniture and food and water stores… that stuff adds up faster than you think, and pretty soon, you’re gonna be roughly where I said a couple of days ago, a concrete sphere ship mostly under water, with only about a floor’s worth above the surface, and in a good storm, expect to be more submarine than surface ship after all.

As for your design of concrete sphere on the bottom and plastic coated pipe-frame on top, you would have to figure for the weight of the frame and covering, which I have no references for how much of each a 50 ft. dome would take, and add that to the weight of just a hemisphere, and you would have to keep the finished product’s waterline well down from the hemisphere’s equator, p = [0,0.75).
–
I have a thorium reactor under the hood of my car. I get ∞ miles per gallon.

[Ellen-Re-GenerateSubscriber]

Volume of sphere: V_sphere = 4/3 Pi r³
Volume of spherical cap:V_cap = Pi h² (3r – h) / 3
Volume of spherical shell: V_shell = 4/3 Pi (o³- i³)

Density of High Performance Concrete: ρ_HPC ≈ 2250 kg/m³

< https://secure.wikimedia.org/wikipedia/en/wiki/Properties_of_concrete>
(Actually, not. I estimated 2250 from a research article. Proper value would be 2400 or higher.)

Density of air at sealevel: ρ_air ≈ 1.22521 kg/m³
< https://secure.wikimedia.org/wikipedia/en/wiki/Density_of_air>

Density of surface seawater: ρ_water ≈ 1024 kg/m³
< https://secure.wikimedia.org/wikipedia/en/wiki/Density_of_water#Density_of_saltwater_and_ice>

I’ve been considering a 20 meter interior diameter shell 15 cm thick.
r_shell = 10.15 m
t = 0.15 m

The shell will float in water when the weight of a volume of water displaced equals the over all weight of the shell.

W_shell = W_disp

W = Vρ
V_vphere ρ_sphere = V_cap ρ_water

But ρ_sphere is composed of many things, the shell itself, the air inside it, people, and ultimately any equipment installed. For the moment, let’s just assume a hollow shell. Not a huge leap, since these calculations are intended to apply to geodesic spheres, not true spheres.
V_shell ρ_HPC + V_interior ρ_air = V_cap ρ_water

4/3 Pi (o³ – i³) ρ_HPC + 4/3 Pi i³ ρ_air = Pi h² (3o – h) / 3 ρ_water

Solve for h.
4 (o³ – i³) ρ_HPC + 4 i³ ρ_air = h² (3o – h) ρ_water
4 ((o³ – i³) ρ_HPC + i³ ρ_air ) / ρ_water = 3o h² – h³
h³ – 3o h² + 4 ((o³ – i³) ρ_HPC + i³ ρ_air ) / ρ_water = 0

At this point, it’s beneficial to revert back to standard variables for (outer) radius, use the variable t for the thickness of the shell, and express h in terms of r as h = pr, where p is the proportion of radius underwater on the interval [0,2). p = 0 would mean the entire sphere is supported by a single mathematical point on the surface of the water. p = 1 means the sphere will float with its equator as the waterline. p = 2 means the sphere will be neutrally buoyant at the surface. p > 2 means the shell will be negatively buoyant and will sink.
o = r
i = r – t
h = pr

(pr)³ – 3r(pr)² + 4 ((r³ – (r – t)³) ρ_HPC + (r – t)³ ρ_air) / ρ_water = 0
p³r³ – 3p²r³ + 4 ((r³ – (r – t)³) ρ_HPC + (r – t)³ ρ_air) / ρ_water = 0
p³ – 3p² + 4 ((r³ – (r – t)³) ρ_HPC + (r – t)³ ρ_air) / (r³ ρ_water) = 0

Now, plugging in values for all known variables. For clarity, no units will be shown.
p³ – 3p² + 4 ((10.15³ – (10.15 – 0.15)³) 2250 + (10.15 – 0.15)³ 1.22521) / (10.15³ 1024) = 0
p³ – 3p² + 4 ((1046 – 10³) 2250 + 10³ 1.22521) / (1046 * 1024) = 0
p³ – 3p² + 4 (45.68 * 2250 + 1.225.21) /1071000 = 0
p³ – 3p² + 4 (102800 + 1.225.21) /1071000 = 0
p³ – 3p² + 4 (104000 /1071000) = 0
p³ – 3p² + 4 (0.0971) = 0
p³ – 3p² + 0.3885 = 0

Solving for p via Wolfram Alpha, yields three solutions, only one of which is in the expected interval, p = 0.3855. So, such a hollow shell will float in the ocean with 38.55% of its radius below the waterline, or 3.943 m.

I was once thinking of casting huge facets, 1.1 m thick to create my 20 m diameter geodesic concrete spheres. Quickly reworking the calculations for r_shell = 11.1 m, t = 1.1 m, finds p = 1.123, meaning such a thick walled sphere would float with its equator 1.361 m underwater, or 7.539 m above the water, with a draft of 12.46 m.

Doing the math for a 50 ft. outer diameter shell 2 ft. thick yields p = 0.98 or a draft of 7.49 m or about 24 ft 7 inches. The equator would be just 5 inches above the waterline. The shell would effectively be half in/half out.

These calculations are being done via this script, called waterline.bc, for the standard UNIX “binary calculator”, bc.

scale = 9 
r = 10.15   /* outer radius, meters */ 
t = 0.15    /* shell thickness, meters */ 
h = 2400    /* density of HPC, kg/m^3 */ 
a = 1.22521 /* density of air at sealevel, kg/m^3 */ 
w = 1024    /* density of seawater, kg/m^3 */ 
 
define c() { return 4*((r^3 - (r - t)^3)*h + (r - t)^3*a)/(r^3 * w) } 
define p() { print "solve for p: p^3 - 3 p^2 + ", c(), " = 0n" }

p()

It is invoked as `bc waterline.bc`, whereupon it’ll vomit up the results for the example I started with above. To rework the calculations, just enter new values for the variables you want to change and call p() again. The equation it spits out can be copy-pasted into WolframAlpha < http://www.WolframAlpha.com/>. One response is going to be negative, and another will be over 2. Ignore those. The third result is the value of p. Multiply p by the value you used for r, and that will tell you what your waterline is.

If anyone has better values for the densities, I’m happy to know them.

Of course, once you’re accounting for the interior structure, this equation and script will have to be completely reworked.

–
I have a thorium reactor under the hood of my car. I get ∞ miles per gallon.

[OCEANOPOLISSubscriber]

choose a geodesic dome for a hull? Nothing special about it,…And why build it 2 feet thick when even 5 inches is too much? I don’t get it.

[Author]

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