Seastead Leg Strength & Wave Force Analysis

Design Overview

The seastead features three hydrofoil-shaped legs, each 19 ft long with a NACA 0030 symmetric foil cross-section (10 ft chord, 3 ft max thickness). The legs are constructed from marine aluminum (6061-T6) with a wall thickness of 0.5 inches. They are cantilevered from the triangular frame at the top, with approximately half the length submerged (9.5 ft). Rim-drive thrusters are mounted on each leg.

Assumptions

Structural & Material

Hydrodynamic Loading

Structural Analysis

The leg is treated as a cantilever beam subjected to a uniformly distributed load w (lb/ft) over the submerged length. The maximum bending moment occurs at the fixed end:

M_max = w * (L_sub)^2 / 2 + w * L_above * L_sub

where L_above = 9.5 ft (unsubmerged part). Simplifying: M_max = w * 135.4 ft².

Cross-Section Properties

Approximating the thin-walled foil:

Note: A more refined analysis including arc-length effects yields I_x ≈ 980 in⁴ and S ≈ 54.4 in³, increasing strength by ~20%.

Failure Load

Using ultimate tensile strength:

M_max = σ_ult * S = 42,000 psi * 45.3 in³ = 1.90×10⁶ in-lb = 158,550 ft-lb.

Required distributed load on submerged portion:

w = M_max / 135.4 ft² = 158,550 / 135.4 ≈ 1,170 lb/ft.

Total lateral force on one leg:

F_total = w * L_sub = 1,170 lb/ft * 9.5 ft ≈ 11,100 lb (49.4 kN).

Wave Force Estimates

Using Morison's equation and integrating over depth (deep water, T = 10 s):

Component Formula Approximation
Maximum Drag Force F_drag = ½ ρ C_D D I₁ ≈ 2.92 H² lb
Maximum Inertia Force F_inertia = ρ C_M A ω I₂ ≈ 141 H lb

Where H is wave height in feet, D = 3 ft (thickness), A = 20.55 ft² (cross-sectional area), ω = 2π/T.

Wave Height for Failure

Equating wave force to the failure force (11,100 lb):

These are extreme wave heights, typical only in rogue waves or tsunamis. Breaking wave impact forces could be higher but are highly variable.

Conclusions

The aluminum leg can withstand a total lateral force of approximately 11,000 lb (49 kN) before failing in bending. This corresponds to a uniformly distributed load of about 1,170 lb/ft on the submerged portion.

Based on linear wave theory and Morison's equation, wave heights on the order of 60–80 ft would be required to generate such forces. These conditions are exceptionally rare in open ocean environments. However, localized effects such as breaking wave impacts, dynamic amplification, or corrosion could reduce the safety margin.

Recommendations: Consider higher-strength alloys, increased wall thickness, or internal stiffeners for enhanced safety. Detailed finite element analysis and model testing are advised for final design.

Disclaimer: This analysis is simplified and intended for preliminary assessment. Actual performance depends on many factors including fabrication quality, joint details, fatigue, and complex wave-structure interaction.

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