A cylindrical tank with hemispherical end caps under internal pressure P carries a hoop (circumferential) stress in its cylindrical wall given by the thin-wall pressure-vessel equation:
σ_hoop = P·r / t
Design rule: t = P·r·SF / σ_yield
where r is the inner radius, t the wall thickness, and SF the target safety factor against the material's yield strength. Solving for t gives the minimum wall thickness the material needs to carry the load — thicker walls cost mass, thinner walls erode the safety margin. Total mass is the tank's surface area (cylinder side + two hemispherical caps, treated as one sphere) times thickness times material density.
Because life-support tanks are pressurized and depressurized repeatedly (fill cycles, EVA prebreathe draws, resupply), the wall also sees cyclic stress. Fatigue life is estimated with the Basquin strain-life relation for a 0→P→0 cycle (stress amplitude σa ≈ σ_hoop / 2):
σ_a = σ_f' · (2N)^b
N = 0.5 · (σ_f' / σ_a)^(1/b)
σf′ is the material's fatigue strength coefficient and b its Basquin exponent (both negative-slope material constants). Because the design rule always sizes t to hit the chosen safety factor exactly, the operating hoop stress — and therefore the fatigue life — depends only on the material and the safety-factor slider, while pressure and radius drive thickness and mass. This is the same trade every real ECLSS tank designer makes: titanium and Inconel buy strength and fatigue life at a mass and cost premium, aluminum is light but needs thicker walls, and carbon-fibre overwrap gives the best strength-to-mass ratio but the least forgiving failure mode.
Controls: pick a material, then move pressure, radius and safety-factor sliders to see wall thickness, mass and cycle life respond in real time on the cutaway drawing.