Elon Musk: glass geodesic domes

[Lar]

And I take it that there aren't any practical processes for getting SiO2 out of silicates?

Its more like nobody bothers because there is ample SiO2 in the wild. We have already seen hydrothermal SiO2 on mars. We will probably find the felsic minerals (granites etc). Probably need to dig a little. Mechanical separation is easier if these sources exist.

There appears to be a significant dispute about this. I want to believe. But Dalhousie is convinced that SiO2 that isn't contaminated with impurities (alloyed in) is very low abundance on Mars.

Ground truth is needed I think.

[Slarty1080]

I've been thinking about this for a while now, but I believe we're going about glass domes all wrong. Glass is good in compression, as Paul451 has mentioned several times, but not good in tension. And domes are good for compression under passive Earth weight, but are fiddly when you try and pressurise them (they want to be spheres). So, perhaps domes should be inverted.

This doesn't solve either issue. The glass is still under the exact same tension in the frame. The frame is under compression, but making a tensile frame was never my objection. And you still have 75 tonnes of force per linear metre of rim, trying to rip the rest of that roof off.

If you have a structure capable of holding that force, and the glass can handle the air-pressure, then the structure in that image can also have an upward dome.

I just like to remind people of the forces involved whenever they plonk a dome on the surface, with no apparent sub-structure. I don't think it's an unsolvable problem, I just think people either don't know or really want to forget that it even exists as a problem. It's not a little house. It's a pressure vessel.

a 30m diameter dome.

What keeps the ~14,000 tonnes of pressure in. (Half of it straight up. About 75 tonnes of force per linear metre around the rim.)

If you don't mind me asking, how did you get that number?

It's just air pressure. At approximately sea-level pressure, you've got 100,000 Pa pushing outwards on the dome. That's creates a force equivalent to 10 tonnes per square metre. Force = Pressure X Area. (Using equivalent-mass-on-Earth as a pseudo-unit for force to make it easier to visualise. Since Force = Mass X Acceleration, we let Acc=1g.)

All of the force that isn't vertically aligned is taken up by the frame. So as long as the frame is strong enough... But the vertical component is unopposed, it's trying to lift the dome off the ground. Thankfully, working that out is simply the cross-sectional area of the dome (a circle radius 15m). The dome is, presumably, only attached at the rim (otherwise why bother with a dome shape), and so you divide the total unopposed force by the circumference (circle radius 15m) to work out the upward force pushing on every linear metre of rim.

(You can try to drop the pressure, but that opens up other issue.)

Imagine the dome has 10m of water in it (Olympic diving pool depth x2) and you have to secure it upside down to some sort of huge ceiling. Not quite the right analogy but it conveys the magnitude of the forces involved. That will take some major engineering - hard but doable.

[Oersted]

In "envisioning amazing habitats" we already went through the dome discussion around 60 pages and three years back. Yup, glass domes are actually no good on Mars.

For those who are new to this forum and to discussing bases on Mars that thread is a good long read.

It will also explain to you why so many oldtimers in here seem to fancy tunnels (as does Musk).

[lamontagne]

Divide and conquer.  If glass is too weak for wide spans, make smaller spans.  And add steel.

With the smaller glass panes, I'm pretty confident 2 cm thick would be OK

But when does it become too much steel?

[Cinder]

What about additional layers ? D&C'ing further.  It's been mentioned upthread but I'm not sure I understand if it's ruled out for this specific case too.

[Jcc]

I am thinking geodesic domes are not really a good idea on Mars. Arched glass roof over a rectangular building would work, and be easier to design to hold in the pressure.

[Robotbeat]

In "envisioning amazing habitats" we already went through the dome discussion around 60 pages and three years back. Yup, glass domes are actually no good on Mars.

For those who are new to this forum and to discussing bases on Mars that thread is a good long read.

It will also explain to you why so many oldtimers in here seem to fancy tunnels (as does Musk).

That wasn’t actually a consensus opinion.

[Paul451]

I just like to remind people of the forces involved whenever they plonk a dome on the surface, with no apparent sub-structure.

Imagine the dome has 10m of water in it (Olympic diving pool depth x2) and you have to secure it upside down to some sort of huge ceiling. Not quite the right analogy but it conveys the magnitude of the forces involved.

(Or 26m of water on Mars.) Not sure the analogy helps, I don't think people actually have a good grasp of how much water weighs. It's a common building cock-up you hear about, where people add hot-tubs, waterbeds, aquariums, and don't realise how much weight they are adding to the floor, frame, deck, etc.

[Paul451]

So I made a little test for the glass, spreadsheet joined.

I haven't gone through all of it, I was looking at the anchoring part. (Spot the obsessive.) And there's some oddities there.

Eg, you calculate the weight (MxA) of the dome (row 32), you have the cross-sectional force from air-pressure (row 29),
then at row 34 you have the anchoring force required, which is calculated by row 29 minus row 32. Okay. But then you calculate the "Mars regolith required to keep the dome down", where you subtract the dome weight again, before converting to kg-equivalent. The latter seems wrong, unless I'm missing another assumption in another formula.

Similarly, the formulas for depth of anchoring seem... weird. Eg, you seem to be treating the entire volume under the dome as one anchor. But there's something else going on, given that the first three cases (5m, 15m, 30m) all end up with an identical 56m anchor depth.

[Lampyridae]

So I made a little test for the glass, spreadsheet joined.

I haven't gone through all of it, I was looking at the anchoring part. (Spot the obsessive.) And there's some oddities there.

Eg, you calculate the weight (MxA) of the dome (row 32), you have the cross-sectional force from air-pressure (row 29),
-snip-

I also had a look at it, and here's what I think.

Looking at the bending moment, this is true if you have to actually place a load on the surface, like 1.5 fully grown African elephants or 10m of water. But this isn't really representative of hoop stress.

The ability to resist the African elephant's weight comes from the tangent of the curvature of the pressure vessel, which is where the stress is carried. Which is part of the reason why we like curved pressure vessels. You can only resist the outward pressure with the outward component of the tension "vector."



Pressure vessels are less walls holding back force and more like strings holding up a weight. The longer your string has to be, the more you have to pull on the string to bring the weight upwards.

[lamontagne]

So I made a little test for the glass, spreadsheet joined.

I haven't gone through all of it, I was looking at the anchoring part. (Spot the obsessive.) And there's some oddities there.

Eg, you calculate the weight (MxA) of the dome (row 32), you have the cross-sectional force from air-pressure (row 29),
then at row 34 you have the anchoring force required, which is calculated by row 29 minus row 32. Okay. But then you calculate the "Mars regolith required to keep the dome down", where you subtract the dome weight again, before converting to kg-equivalent. The latter seems wrong, unless I'm missing another assumption in another formula.

Similarly, the formulas for depth of anchoring seem... weird. Eg, you seem to be treating the entire volume under the dome as one anchor. But there's something else going on, given that the first three cases (5m, 15m, 30m) all end up with an identical 56m anchor depth.

Really appreciate your checking the spreadsheet!
Yes there were mistakes at the end.  Corrected, I hope. 
Reduced the strength of the steel to common construction steel.
I also clarified the mass of the dome by putting in a glass thickness parameter.
The final column is for a plastic bag used as a aquarium for algae, as it is continuous, it doesn't need to be anchored.
It's clear that the larger the dome, the deeper the anchors, since the force from the pressure goes up to the square of the radius, while the anchoring circumference goes up linearly.   Eventually, the mass of the dome starts playing a significant part and you end up getting negative forces, i.e the dome keeps itself in place.
Anchoring requirements are sever in all cases.  I think it is more practical to build a continuous pressure vessel, i.e. have a spherical dome or have a structural floor.

Anyway, it's clear to me that you have to really really want a dome to bother building one of significant size.

[Rocket Surgeon]

So I made a little test for the glass, spreadsheet joined.

I haven't gone through all of it, I was looking at the anchoring part. (Spot the obsessive.) And there's some oddities there.

Eg, you calculate the weight (MxA) of the dome (row 32), you have the cross-sectional force from air-pressure (row 29),
then at row 34 you have the anchoring force required, which is calculated by row 29 minus row 32. Okay. But then you calculate the "Mars regolith required to keep the dome down", where you subtract the dome weight again, before converting to kg-equivalent. The latter seems wrong, unless I'm missing another assumption in another formula.

Similarly, the formulas for depth of anchoring seem... weird. Eg, you seem to be treating the entire volume under the dome as one anchor. But there's something else going on, given that the first three cases (5m, 15m, 30m) all end up with an identical 56m anchor depth.

Really appreciate your checking the spreadsheet!
Yes there were mistakes at the end.  Corrected, I hope. 
Reduced the strength of the steel to common construction steel.
I also clarified the mass of the dome by putting in a glass thickness parameter.
The final column is for a plastic bag used as a aquarium for algae, as it is continuous, it doesn't need to be anchored.
It's clear that the larger the dome, the deeper the anchors, since the force from the pressure goes up to the square of the radius, while the anchoring circumference goes up linearly.   Eventually, the mass of the dome starts playing a significant part and you end up getting negative forces, i.e the dome keeps itself in place.
Anchoring requirements are sever in all cases.  I think it is more practical to build a continuous pressure vessel, i.e. have a spherical dome or have a structural floor.

Anyway, it's clear to me that you have to really really want a dome to bother building one of significant size.

Has there been any discussion about building a sphere instead of a dome? I know the general consensus is that burying half a sphere would involve moving too much dirty, but what if you build it above ground?
 
Support it at the "South Pole" and have Support struts running from the ground up to the Equator. Could make it mostly out of steel with small windows at various locations.

[lamontagne]

So I made a little test for the glass, spreadsheet joined.

I haven't gone through all of it, I was looking at the anchoring part. (Spot the obsessive.) And there's some oddities there.

Eg, you calculate the weight (MxA) of the dome (row 32), you have the cross-sectional force from air-pressure (row 29),
then at row 34 you have the anchoring force required, which is calculated by row 29 minus row 32. Okay. But then you calculate the "Mars regolith required to keep the dome down", where you subtract the dome weight again, before converting to kg-equivalent. The latter seems wrong, unless I'm missing another assumption in another formula.

Similarly, the formulas for depth of anchoring seem... weird. Eg, you seem to be treating the entire volume under the dome as one anchor. But there's something else going on, given that the first three cases (5m, 15m, 30m) all end up with an identical 56m anchor depth.

Really appreciate your checking the spreadsheet!
Yes there were mistakes at the end.  Corrected, I hope. 
Reduced the strength of the steel to common construction steel.
I also clarified the mass of the dome by putting in a glass thickness parameter.
The final column is for a plastic bag used as a aquarium for algae, as it is continuous, it doesn't need to be anchored.
It's clear that the larger the dome, the deeper the anchors, since the force from the pressure goes up to the square of the radius, while the anchoring circumference goes up linearly.   Eventually, the mass of the dome starts playing a significant part and you end up getting negative forces, i.e the dome keeps itself in place.
Anchoring requirements are sever in all cases.  I think it is more practical to build a continuous pressure vessel, i.e. have a spherical dome or have a structural floor.

Anyway, it's clear to me that you have to really really want a dome to bother building one of significant size.

Has there been any discussion about building a sphere instead of a dome? I know the general consensus is that burying half a sphere would involve moving too much dirty, but what if you build it above ground?
 
Support it at the "South Pole" and have Support struts running from the ground up to the Equator. Could make it mostly out of steel with small windows at various locations.

I have a few variations done.  It's a fun idea.  What's your favorite of the three?

[Paul451]

Has there been any discussion about building a sphere instead of a dome? I know the general consensus is that burying half a sphere would involve moving too much dirty, but what if you build it above ground?

Bunch of variations in the Envisioning Amazing Habitats thread.

It doesn't have to be a sphere, per se, it just needs to be a complete pressure vessel. The further you go from an ideal shape, the higher the forces at the sharpest angles/curves.

In the case of half-burial to create a "dome", it particularly doesn't have to have a sphere because the pressure of the regolith will be countering the side-pressure of the atmosphere. As long as it has a foundation sufficient to anchor the dome. It's just that the forces are substantial enough that by the time you've anchored it down, and sealed the floor against air loss, IMO you might as well have built the "anchor" as part of the floor foundation and just fully enclosed the structure.

[Rocket Surgeon]

So I made a little test for the glass, spreadsheet joined.  Turns out that for a span of 500mm you would need glass about 50mm thick (2 inches).  So glass slabs, not glass sheets.

This is for a glass beam.  Continuously supported plates would be under considerably less strain, but nevertheless, that's thick glass.
Polycarbonate is twice as strong as soda glass, so it would be about 35 mm thick.

There are formula for supported plates
https://en.wikipedia.org/wiki/Bending_of_plates#Simply-supported_plate_with_uniformly-distributed_load

Too much work for me but if someone want to tackle it would love to see the results!

So although the mass of steel remains the same the mass of glass goes up to 140 tonnes, so an overall mass of 170 tonnes.
I guess we should include the anchor mass,that should be at least as much as the dome, so the mass requirements for a dome are about 200 tonnes, plus the concrete for the slab.

Really need to want to look outside  :-)

So I didn't do the support plate calculations...I just went straight to FEMAP

The below images are of glass with a Young's Modulus of 50 GPa, of varying thicknesses (10mm, 30mm and 50mm) and different net pressures (50 kPa and 25 kPa). Modelled as a plate, 1000mm long each side.

https://www.engineeringtoolbox.com/young-modulus-d_417.html

50 kPa may be doable with higher oxygen content (somthing like 8psi, 32% Oxygen...or 8/32), 25 kPa would have to be done by having a second layer, pressurised with atmospheric CO2 to partially counteract the internal pressure.

Results are:
- 50 kPa, 10mm, the highest stress is 49.25 MPa
- 50 kPa, 30mm, the highest stress is 5.448 MPa
- 50 kPa, 50mm, the highest stress is 1.943 MPa

- 25 kPa, 10mm, the highest stress is 24.62 MPa
- 25 kPa, 30mm, the highest stress is 2.724 MPa
- 25 kPa, 50mm, the highest stress is 0.971 MPa

With all cases, the peak stress is half way along the edges. Tensile yield stress of basic glass is 7 MPa, so 10mm of glass fails under both situations. Thickening rapidly makes it stronger. Bare in mind that these results are actually an over estimate as the plates are Constrained by fixing along their edges, which is an over estimation, increasing the stress.

https://en.wikipedia.org/wiki/Strength_of_glass

Lamontage, what where you using as your Yield Stress for the Glass? and what would be an advisable Safety Factor?

[lamontagne]

So I made a little test for the glass, spreadsheet joined.  Turns out that for a span of 500mm you would need glass about 50mm thick (2 inches).  So glass slabs, not glass sheets.

This is for a glass beam.  Continuously supported plates would be under considerably less strain, but nevertheless, that's thick glass.
Polycarbonate is twice as strong as soda glass, so it would be about 35 mm thick.

There are formula for supported plates
https://en.wikipedia.org/wiki/Bending_of_plates#Simply-supported_plate_with_uniformly-distributed_load

Too much work for me but if someone want to tackle it would love to see the results!

So although the mass of steel remains the same the mass of glass goes up to 140 tonnes, so an overall mass of 170 tonnes.
I guess we should include the anchor mass,that should be at least as much as the dome, so the mass requirements for a dome are about 200 tonnes, plus the concrete for the slab.

Really need to want to look outside  :-)

So I didn't do the support plate calculations...I just went straight to FEMAP

The below images are of glass with a Young's Modulus of 50 GPa, of varying thicknesses (10mm, 30mm and 50mm) and different net pressures (50 kPa and 25 kPa). Modelled as a plate, 1000mm long each side.

https://www.engineeringtoolbox.com/young-modulus-d_417.html

50 kPa may be doable with higher oxygen content (somthing like 8psi, 32% Oxygen...or 8/32), 25 kPa would have to be done by having a second layer, pressurised with atmospheric CO2 to partially counteract the internal pressure.

Results are:
- 50 kPa, 10mm, the highest stress is 49.25 MPa
- 50 kPa, 30mm, the highest stress is 5.448 MPa
- 50 kPa, 50mm, the highest stress is 1.943 MPa

- 25 kPa, 10mm, the highest stress is 24.62 MPa
- 25 kPa, 30mm, the highest stress is 2.724 MPa
- 25 kPa, 50mm, the highest stress is 0.971 MPa

With all cases, the peak stress is half way along the edges. Tensile yield stress of basic glass is 7 MPa, so 10mm of glass fails under both situations. Thickening rapidly makes it stronger. Bare in mind that these results are actually an over estimate as the plates are Constrained by fixing along their edges, which is an over estimation, increasing the stress.

https://en.wikipedia.org/wiki/Strength_of_glass

Lamontagne, what where you using as your Yield Stress for the Glass? and what would be an advisable Safety Factor?

Wow, great to see up to date tools being used. Thanks a lot!
I used 30 MPa yield for the glass with a factor of safety of 2, that comes out to about 15 MPa.  So likely optimistic.
I think the 7 MPa may be for a limit state design, so you wouldn't really add much of a factor of safety?  Musn't mix two methods :-)

I expect the most likely means of breaking the glass is a sharp punch that breaks the glass no matter what the safety factor is. That might be countered with a safety film, although I'm not certain the film could survive the tension once the glass was broken.

Yeah, fixing the edges would be a recipe for disaster.  Dome explodes on the first morning/night cycle!  I do wonder of the high strain at the edges might be a calculation artifact, due to the constraints.  Would have thought that the highest stress would have been in the center.  Ah, unless it's shear along the supports. That would work.

I think the best solution is to use smaller glass panes.  You could fit much smaller glass panes into a larger triangular frame and still have a lot of light.  More steel required, but much thinner glass.  The steel is so much safer than the glass!

The problem with the small glass panes is that the total length of joints to seal go up tremendously, so all that many more leak possibilities.  We need a long lasting sealant that can survive low temperatures. 

We also need to design a glass arrangement that keeps the sealant as warm as possible, that's why I think a second, or even third non structural glass layer will be required to carry low e film, so the interior glass surface temperature doesn't get too low.  We'll need something of the kind to prevent condensation anyway, as that seems to be bad structurally for Soda glass.  Plus it rusts the steel.  And you can't see out, defeating the initial purpose!

Joined is a nice little text on glass structural properties.  Too bad we can't make perfect glass!

Thanks again!  If you can find the time to do some tests with smaller glass panes would love to see the results.

[Semmel]

There are plenty different glass types that have all kinds of expansion coefficients. ZERODUR for example has a zero expansion coefficient, hence the name. You also might  find some with the same coefficient as steel. Not sure about the price though. And these glasses are usually made for optical elements, they probably are not easily available in planes.

[Paul451]

50 kPa may be doable with higher oxygen content (somthing like 8psi, 32% Oxygen...or 8/32),

That would drastically increase your fire risk.

[Nice FEA though. I'm curious how much difference it would make if the glass wasn't flat but was domed. For eg, doming it inwards (towards the pressure) would put some of the force in compression. AIUI, glass has a compressive strength better than two orders of magnitude higher than its tensile strength.]

[Rocket Surgeon]

50 kPa may be doable with higher oxygen content (somthing like 8psi, 32% Oxygen...or 8/32),

That would drastically increase your fire risk.

[Nice FEA though. I'm curious how much difference it would make if the glass wasn't flat but was domed. For eg, doming it inwards (towards the pressure) would put some of the force in compression. AIUI, glass has a compressive strength better than two orders of magnitude higher than its tensile strength.]

Will look into, the above was REALLY easy to run as it's a basic static load. I'll do a few extra Sims tomorrow. I also need to reconsider my constraints. WAY too over constrained right now.

As for atmosphere, I'll check my source but my understanding was 8/32 had the right balance of increase percentage and decreased pressure to maintain a similar flammability.

I know it's much more dependant on concerntration than pressure, but I thought the above mix walked that line. I'll double check.

[Paul451]

50 kPa may be doable with higher oxygen content (somthing like 8psi, 32% Oxygen...or 8/32),

That would drastically increase your fire risk.

As for atmosphere, I'll check my source but my understanding was 8/32 had the right balance of increase percentage and decreased pressure to maintain a similar flammability.

Looking at what I have at hand, something which is on the just self-extinguishing at 14.7psi & 21% Oxygen will self-extinguish at 12/23 and 7/28. Therefore 8/32 is well over the line.

That's at 1g. At Mars gravity, flammability is even higher.