Pressure Hull Shape, Thickness, and Size

We can figure out the shape, thickness, and size of our habitat pressure hull now that we’ve decided on an atmospheric composition and pressure. The shape will determine how thick the hull has to be. And the shape, thickness, and size of the habitat pressure hull will determine how much iron we need to extract and process for each habitat pressure hull. That will help us determine if iron is an acceptable construction material or if we need to alloy it or replace it completely.

I’ve been dragging my feet a bit on this section because it requires some engineering knowledge that I just don’t have. I’ve decided all I need is a rough estimate, not exact figures, right now. Eventually I’ll consult with someone who knows what they are doing (like a real engineer) when it’s time to actually build some prototypes.

Critical features for Lunar Homestead habitat pressure hulls:

• Standardization – This will make manufacturing, construction, operation, and repair of habitats much easier.
• Design simplicity – For the above reasons. Designing components that can be used for multiple purposes will help.
• Easily expandable – We want to easily link up habitats. Some shapes are more ideal than others.

 

Shape

The ideal shape of our habitat pressure hull would be something made from flat plates. Flat sheets of iron will be easier to manufacture than curved pieces. Flat pieces can be used in multiple configurations. Curved pieces will be a lot less versatile. So a dome or a cylinder will be less than ideal.

The problem is that square and rectangular pressure vessels require thicker material at the joints to counteract the increased atmospheric pressure focused there. The good news is that we’re only talking about 202.65 kPa internal pressure (before venting). We might need to have reinforcements at these points however.

I’m thinking octagonal cylinders would be a good compromise:

• Constructed of flat plates.
• The angles where the plates connect are more than 90º and may be able to handle the pressure better (that’s just a guess though).
• We would get more usable space than a round cylinder (try walking in a pipe).
• It should be easier to figure out how to link up habitat hulls using flat plates than curved cylinders.

The ceiling, floor, and sides will be composed of much wider plates than the corners. The effect would look something like this:

 

 

 

Hull thickness

I’m not a mechanical engineer. I’m not any type of engineer. So if I get this part wrong then let me know.

I’m only going to look into the properties of pure iron, not alloys. My previous research showed that only a certain percent of the iron our Homesteaders extract will be pure. The rest will be naturally alloyed with nickel and other metals. The concentration of theses alloying metals will vary by site and by sample. There’s just too much variability. So I’m going to stick with pure iron for now.

The data on pure iron (unalloyed):

• Tensile strength at yield (strain at 0.500%) = 50.0 MPa (50,000 KPa) (1) = Tensile strength is the capacity of a material to withstand loads that tend to elongate.
• Tensile strength at break = 540 MPa (540,000 KPa)(1)

OK, using Engineers Edge calculator for Pressure Vessel Wall Thickness (2) I have the following variables:

• Design pressure (internal)(psi) = 29.39 psi = 202.65 kPa
• Inside radius of shell under consideration (inches) = 160 inches = This is about 4 meters which would give us a nice 2-level habitat (each level is 4 meters high to allow for equipment. I don’t know, I’m just guessing here.
• Max allowable stress material (psi) = 5801 psi = I took the 50,000 KPa tensile strength at yield, removed 10,000 as a safety measure, and converted the rest to psi. Again, just guessing here.
• Joint efficiency = 0.8 = That’s the default. I have no idea if 80% confidence in the seam welds is good or bad.

Minimum wall thickness for shell (inches) = 1.0171 inches = 2.58 centimeters.

Yeah, the calculator is for cylinders and I’m interested in something octagonal-ish. It’s all I could find at the moment. It’s good enough for now and I don’t have to spend weeks (months?) trying to learn all the engineering.

Let’s say the hull needs to be 4 centimeters thick, just to add an additional safety factor. It’s probably excessive but what the heck.

 

Habitat size

Once again, this is all going to be pretty arbitrary at this point. But I have to start somewhere.

Here are the dimensions I’m using:

• 8 meters tall.
• 8 meters wide.
• The corners are cut off with a smaller plate. To make it simple, let’s say 1 meter from each corner is removed. We can figure out the width of the corner plate by calculating the hypotenuse of a right triangle (Pythagorean Theorem for my geometry nerds!). If legs a and b are 1 meter each then c²=a²+b². The width of the corner plates is  = 1.41 meters.
• Let’s say the habitats are 10 meters long. Why? Because it makes the math easier.
• Finally, we need to figure out the area of the end caps of our habitat. More geometry!
  • The shape of the endcap without the corners removed is a square. The area of this square is 8 meters x 8 meters = 64 m².
  • The shape of the removed corners is a right triangle. The formula to calculate the area of a right triangle is A=(ab)/2. The legs a and b are each 1 meter. So the area cut off each corner is 0.5 m².
  • Now we just subtract each removed corner area from the total area. 64 m² – 0.5 m² – 0.5 m² – 0.5 m² – 0.5 m² = 62 m² for each end cap.

So, total enclosed habitable space is 620 m³ with 120 m² (1291.67 ft²) of floor space.  Skylab had a habitable volume of 283.17 m³ (3). This should be plenty of space for a couple of Homesteaders and a bunch of equipment.

 

My thoughts

• The numbers I picked for most of the variables are, at best, pure SWAG (Scientific Wild Ass Guess). But I need to start from somewhere and this is my best guess. Actual results will certainly be different.
• The habitat is big by conventional aerospace standards. But people are going to have to live in these things for very long periods of time. At least until the Homesteads expand enough that they can enclose much larger areas.

 

Resources

1. MatWeb (www.matweb.com/search/DataSheet.aspx?MatGUID=654ca9c358264b5392d43315d8535b7d&ckck=1)
2. Engineers Edge (www.engineersedge.com/calculators/shell_internal_pres_pop.htm)
3. The Skylab Program (history.nasa.gov/apollo/skylab.html)