Submersible Hull Collapse Depth

Descent

Descent rate 40 m/s

Pressure Hull

Hull radius R 1.00 m

Wall thickness t 60 mm

Hull material

Live Readout

Depth

0 m

Hydrostatic P

0.10 MPa

Safety Factor (P_cr / P)

—

How it works

Hydrostatic pressure grows linearly with depth h:

P(h) = P_atm + ρ·g·h
ρ (seawater) ≈ 1025 kg/m³, g = 9.81 m/s²
→ roughly +1 atm (0.101 MPa) every 10 m

A submersible's spherical pressure hull resists this by pure compressive hoop stress until it buckles elastically. For a thin spherical shell under uniform external pressure, the classical critical buckling pressure (Zoelly's formula) is:

P_cr = [2·E / √(3·(1−ν²))] · (t/R)²
E = Young's modulus, ν = Poisson's ratio
t = wall thickness, R = mid-surface radius

Real hulls never reach the idealised value — small manufacturing imperfections trigger buckling earlier, so naval-architecture practice applies a knockdown factor of roughly 0.3–0.5 to the classical result; this simulator uses 0.4, which is why the on-screen collapse depth sits below the "perfect sphere" number you'd get by hand.

Descent rate — how fast simulated depth increases once you press Start (compressed relative to a real ~30–40 m/min dive, so the outcome is visible in seconds).
Hull radius / wall thickness — the two geometric levers: P_cr scales with (t/R)², so doubling thickness quadruples strength, while doubling radius quarters it — the reason deep-rated hulls stay small and thick-walled.
Material — titanium alloy (used on Alvin, Shinkai 6500) and HY-100 steel are real hull materials; acrylic stands in for a viewport/observation-dome material, which buckles at far shallower depths.
Safety factor — P_cr ÷ current P(h). It falls as you descend; when it crosses 1 the hull passes its buckling threshold and the sphere collapses inward, exactly as the elastic-stability formula predicts.

DEPTH0 m

Pressure hull Marine snow (depth cue)

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