Habitat pressure shell: what breathable air does to the structure

Question

What load does breathable air put on a Mars habitat?

Assumptions

• Cabin pressure101, 70.3 or 56.5 kPa (BVAD Rev 2, Table 4-1)
• OutsideMars mean surface pressure 0.636 kPa, so Δp ≈ cabin pressure; g = 3.71 m/s²
• Shapecylinder, radius 3 m (our assumption)
• Coverfrom Study 003
• Materialallowable stress and safety factor left as variables; no alloy strength is quoted

The numbers

Hoop stress          σ_h = p r / t   → wall  t = p r / σ_allow
Longitudinal stress  σ_l = p r / (2t)

Line load p r:  101,325 Pa × 3 m ≈ 0.30 MN/m   (70.3 kPa → 0.21;  56.5 kPa → 0.17 MN/m)

Illustrative wall, p = 101.3 kPa, r = 3 m (σ_allow values are placeholders, not material data):
  50 MPa → 6.1 mm    100 MPa → 3.0 mm    200 MPa → 1.5 mm   (before safety factor)

End-cap force:  101,325 × π × 3² ≈ 2.9 MN

Can soil hold the air in?  overburden = ρ g h
  2 m loose soil   1,500 × 3.71 × 2 ≈ 11 kPa
  575 g/cm² cover  5,740 kg/m² × 3.71 ≈ 21 kPa
  soil depth to balance 101.3 kPa ≈ 18 m  (56.5 kPa → 10 m)

Net uplift, 160 m² habitat at 101.3 kPa under 575 g/cm²:
  (101.3 − 21.3) kPa × 160 m² ≈ 12.8 MN

Result

Modeled: the shell is a pressure vessel in tension, carrying about 0.30 MN per metre of wall at 101 kPa. Regolith is radiation shielding, not structure: a buried habitat at sea-level pressure pushes up about 13 MN through its anchors or floor.

Trade-offs

Atmosphere pairs from BVAD Rev 2 §4.1, citing Norcross et al. 2013.

Open problems

• Material choice and fatigue over thousands of pressure cycles (airlocks).
• Leak rate (BVAD nominal 0.02 kg/day per module).
• Thermal cycling around a −60 °C mean outside.
• Anchoring for about 13 MN of uplift.

What would change the answer

• Lower cabin pressure cuts structural load almost in proportion, at the cost of fire risk from the richer oxygen mix.

Sources

1. Ewert, Chen, Powell, Life Support Baseline Values and Assumptions Document (BVAD), NASA/TP-2015-218570/REV2 (2022)
2. NASA NSSDC, Mars Fact Sheet (solar irradiance 586.2 W/m²)