Seastead Leg (NACA Foil Float) — Lateral Load & Wave Analysis

This is a first-order engineering estimate of how much sideways (beam-on) force one leg of your triangular seastead can take before the marine-aluminum skin fails, and the size of breaking wave that could produce that force.

1. Leg Geometry & Assumed Properties

Parameter	Value
Overall leg length	19 ft (5.79 m)
Chord (fore–aft, strong axis)	10 ft (3.05 m)
Thickness (beam, weak axis)	3 ft (0.914 m)
Wall thickness (marine Al, e.g. 5083-H116)	0.5 in (0.0127 m)
Yield strength F_y	≈ 215 MPa (31 ksi)
Ultimate strength F_u	≈ 305 MPa (44 ksi)
Submerged length	9.5 ft (2.90 m)
Cantilever length (attach at top of triangle to submerged bottom)	~19 ft (5.79 m)

2. Section Properties (thin-walled hollow NACA airfoil)

A NACA 4-digit symmetric section with 10 ft chord × 3 ft max thickness has these approximate properties for a 0.5″ thick wall:

Perimeter ≈ 2.04 × chord ≈ 20.4 ft = 6.22 m
Wall cross-section area A ≈ 0.0127 m × 6.22 m ≈ 0.079 m²
Enclosed section area ≈ 0.685 × c × t ≈ 0.685·3.05·0.914 ≈ 1.91 m²

For bending about the weak axis (sideways / beam-on loading — the bad case you asked about):

I_weak ≈ (wall t)·(perimeter)·(half-thickness)² × shape factor. Using a thin-wall ellipse/airfoil approximation:
I_weak ≈ π · (t_wall) · a · b² where a = c/2 = 1.524 m, b = thk/2 = 0.457 m
I_weak ≈ π · 0.0127 · 1.524 · 0.457² ≈ 0.0127 m⁴
Section modulus S_weak = I / b ≈ 0.0127 / 0.457 ≈ 0.0278 m³

3. Bending-Strength Limited Lateral Load

Treat the leg as a cantilever fixed to the triangle frame. A load uniformly distributed along its full 19 ft length produces a maximum moment at the root of:

M_max = w · L² / 2 = F_total · L / 2

Setting bending stress equal to yield:

F_total = 2 · F_y · S / L

Limit	Total Uniform Lateral Force
Yield (first permanent damage)	F = 2 · 215e6 · 0.0278 / 5.79 ≈ 2.06 MN ≈ 464,000 lbf ≈ 232 tons
Ultimate (skin tears/buckles, "break")	F ≈ 2 · 305e6 · 0.0278 / 5.79 ≈ 2.93 MN ≈ 659,000 lbf ≈ 330 tons

Reality check — local buckling. A 0.5″ aluminum skin spanning a 3 ft-wide airfoil with no internal stiffeners will locally buckle long before the material yields. With ring frames / bulkheads every 2–3 ft, you can approach the numbers above. Without internal structure, realistic capacity is closer to 30–50% of the yield number, i.e. roughly 70–100 tons. The numbers below assume a properly stiffened leg.

4. What Wave Height Produces That Force?

Only the submerged portion (9.5 ft ≈ 2.90 m) sees direct wave force. Wave loading on a slender body comes from the Morison equation:

F = 0.5·ρ·Cd·A·u² + ρ·Cm·V·(du/dt)

For a NACA foil presented broadside (flow on the 3 ft side), drag coefficient C_d ≈ 1.0 (similar to a flat plate / thick bluff body). Projected beam-on area:

A = 3.05 m (chord seen sideways) × 2.9 m (submerged depth) ≈ 8.85 m²
Wait — sideways the projected width is the chord (10 ft), so A = 10 ft × 9.5 ft = 95 ft² = 8.83 m². ✓

Peak horizontal water particle velocity under a wave of height H and period T in deep water at the surface ≈ u ≈ π·H/T.

Typical ocean wave: H = wave height, T ≈ 4·√H (seconds, H in meters — reasonable for wind seas).

Wave Height H	Period T	Peak u (m/s)	Drag Force on one leg	Fraction of 2.06 MN yield
1 m (3.3 ft)	4.0 s	0.79	≈ 3.2 kN (720 lbf)	0.2%
2 m (6.6 ft)	5.7 s	1.10	≈ 6.2 kN (1,400 lbf)	0.3%
4 m (13 ft)	8.0 s	1.57	≈ 12.6 kN (2,800 lbf)	0.6%
8 m (26 ft)	11.3 s	2.22	≈ 25 kN (5,700 lbf)	1.2%
15 m (49 ft) storm	15.5 s	3.04	≈ 47 kN (10,600 lbf)	2.3%
Breaking wave / slam H≈10 m, u ≈ √(gH)	—	~10 m/s	≈ 500 kN (112,000 lbf)	24%

How big would the wave have to be to actually break a leg?

Inverting the Morison drag equation for the force that equals ultimate strength (2.93 MN):

u = √(2·F / (ρ·Cd·A)) = √(2·2.93e6 / (1025·1.0·8.85)) ≈ 25 m/s

That water-particle speed corresponds to a fully-developed plunging/breaking wave slam with crest velocity on the order of 25 m/s — roughly an H ≈ 60 m (200 ft) non-breaking wave, or the equivalent slam load from a breaking wave of about H ≈ 25–30 m (80–100 ft) hitting the leg directly with its crest.

5. Summary & Design Take-aways

Ultimate lateral capacity per leg: ~2.9 MN (≈ 330 tons / 660,000 lbf) if the leg is internally stiffened (ring frames & bulkheads). Without stiffeners, plan on roughly 1/3 of that.

Normal seas (up to 8 m / 26 ft wind waves): lateral drag on each leg stays under 2% of yield — completely negligible for structure; the design driver is fatigue and motions, not ultimate strength.

Storm / breaking wave slam: Even a severe breaking wave (~10 m) produces only ~25% of yield. You'd need a genuine rogue/breaking wave taller than the leg's submerged draft (9.5 ft) hitting broadside with crest velocity ~25 m/s to threaten a properly built leg.

Caveats

Inertia (added-mass) term can equal or exceed drag in steep waves; for a 3-ft-thick body in a 10-m wave it roughly doubles the peak force. Even so, safety margins remain large (>5×).
The controlling load case is almost never beam-on drag on one leg — it is (a) differential heave between legs (the triangle tries to twist), and (b) wave slam on the underside of the deck if freeboard is lost. Those should be checked separately.
Fatigue from millions of wave cycles on aluminum welds is usually the real lifetime limit, not ultimate strength.
Local plate buckling of the 0.5″ skin between frames must be checked; add longitudinal stiffeners or a foam/honeycomb core if frame spacing exceeds ~30 inches.