This is an engineering estimate of how much lateral (side-on) force one of the NACA-foil buoyancy legs can take before it breaks, and roughly what wave height could produce that force. A real design would need a qualified naval architect and FEA — these numbers are order-of-magnitude sanity checks.
| Parameter | Value |
|---|---|
| Leg length (total) | 19 ft (5.79 m) |
| Submerged length | 9.5 ft (2.90 m) |
| Chord (fore–aft) | 10 ft (3.05 m) |
| Thickness (max width across foil) | 3 ft (0.914 m) |
| Wall thickness | 0.5 in (0.0127 m) |
| Material | Marine Al (5083-H116) |
| Yield strength σy | ~215 MPa (31 ksi) |
| Ultimate strength σu | ~305 MPa (44 ksi) |
The leg is fixed to the triangle frame at the top and acts as a cantilever sticking down into the water. Side loads bend it about its weak axis (the 3-ft thickness direction). We model it as a hollow rectangular tube, 3.05 m (chord) × 0.914 m (thickness) with 12.7 mm walls. For side loads, the bending is about the chord-line axis, so the relevant depth is the 0.914 m thickness.
Second moment of area (hollow rectangle, bending about chord axis):
I = (B·H³ − b·h³) / 12
where B = 3.05 m, H = 0.914 m, b = 3.025 m, h = 0.889 m.
I ≈ (3.05 × 0.764 − 3.025 × 0.702) / 12 ≈ 0.017 m⁴
Section modulus:
S = I / (H/2) = 0.017 / 0.457 ≈ 0.0372 m³
Myield = σy · S = 215 × 10⁶ × 0.0372 ≈ 8.0 × 10⁶ N·m
Multimate = σu · S ≈ 1.14 × 10⁷ N·m
A uniformly distributed load w (N/m) over the full 5.79 m leg, cantilevered at the top, gives max moment at the root:
M = w · L² / 2 → w = 2M / L²
| Limit | w (N/m) | Total force F = w·L | Total force (lbf) |
|---|---|---|---|
| Yield | ≈ 477,000 N/m | ≈ 2.76 MN | ≈ 621,000 lbf |
| Ultimate (break) | ≈ 677,000 N/m | ≈ 3.92 MN | ≈ 881,000 lbf |
Only the submerged portion (2.9 m) actually sees wave loading. Two main effects:
Fd = ½ ρ Cd A u²Fi = ρ Cm V aUsing ρ = 1025 kg/m³, submerged projected side area A = 2.9 m × 3.05 m ≈ 8.85 m², Cd ≈ 1.2 (side-on to a foil is a bluff face), Cm ≈ 2.0, submerged volume ≈ 6 m³.
For a deep-water wave, the horizontal orbital velocity at the surface is roughly u ≈ π H / T, where H is wave height and T is period. For a typical ocean wave of given height, T ≈ 3–5 s for short seas, longer for swell.
| Wave height H | Period T (typical) | Orbital vel. u | Drag force | Inertia force | Total peak side load |
|---|---|---|---|---|---|
| 1 m (3 ft) | 4 s | 0.79 m/s | ~3,400 N | ~15,000 N | ≈ 18 kN (4,000 lbf) |
| 2 m (6.5 ft) | 5 s | 1.26 m/s | ~8,600 N | ~19,000 N | ≈ 28 kN (6,300 lbf) |
| 4 m (13 ft) | 7 s | 1.80 m/s | ~17,700 N | ~19,000 N | ≈ 37 kN (8,300 lbf) |
| 8 m (26 ft) | 10 s | 2.51 m/s | ~34,400 N | ~19,000 N | ≈ 54 kN (12,000 lbf) |
| 15 m (49 ft) — extreme | 14 s | 3.37 m/s | ~62,000 N | ~19,000 N | ≈ 81 kN (18,000 lbf) |
Even in a 15 m rogue wave, the direct hydrodynamic side load on one leg is on the order of 80 kN, which is roughly 1% of the leg's breaking strength. So pure wave drag/inertia is nowhere near enough to break the leg.
What actually loads these small-waterplane legs near failure is wave slamming — a plunging breaker hitting the side of the leg. Slamming pressures are typically:
Pslam = ½ ρ Cs v², with Cs = 3 to 6
If a breaking wave crest hits the leg at ~10 m/s with Cs ≈ 5:
P ≈ 0.5 × 1025 × 5 × 100 ≈ 260 kPa
Over a patch of, say, 1 m × 3 m = 3 m² of the leg, that's about 780 kN concentrated load — within striking distance of the yield envelope if it hits high on the leg (large moment arm). Slamming from a breaking wave of roughly 8–12 m (25–40 ft) hitting squarely on the side is the scenario that could realistically approach leg failure.
Estimates only. Local plate buckling, weld fatigue, corrosion, and combined axial + bending loads (the leg also carries the seastead's weight in compression) must be checked in a full design.
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