```html Active Hydrofoil Stabilizer Analysis - Seastead Design

Active Hydrofoil Stabilizer Analysis for Tri-Maran Seastead

Note: All calculations are first-order engineering estimates based on strip-theory hydrodynamics, standard marine aluminum properties, and preliminary mass/force balances. Final design requires CFD, FEM stress analysis, and sea-state load testing.

1. Buoyancy Force Added per Foot of Submersion (Per Leg)

Calculation:
• Leg cross-section = NACA symmetric foil, 10 ft chord × 4 ft max thickness
• Approximate area fraction for NACA 40% thickness ≈ 0.55 → Area ≈ 0.55 × 10 × 4 = 22 ft²
• Seawater displacement ≈ 64 lb/ft³
• Buoyancy added per vertical foot = 22 ft² × 64 lb/ft³ ≈ 1,400 lbs/ft

When the seastead rides down into a trough an extra foot, each leg picks up ~1,400 lbs of restoring buoyancy. This directly dictates the lift force the active foils must counter to maintain target heave reduction.

2. Wave Reduction: 4 ft vs. 3 ft

Yes. If the passive wave-driven heave creates a 4 ft peak-to-trough vertical excursion, successfully suppressing 6 inches at the peak + 6 inches in the trough reduces the total excursion to 3 feet. However, human comfort is more dependent on vertical acceleration and frequency than pure amplitude. The stabilizer primarily improves ride quality by damping resonant pitch/heave coupling and smoothing acceleration spikes.

3. Foil/Wing Size Required to Cut 6 Inches at 3 Knots

To offset a 6-inch heave deviation, each stabilizer must generate lift equal to half the buoyancy change:

Target Lift per stabilizer ≈ 1,400 lb/ft × 0.5 ft × (1/2 shared per side) ≈ 700 lbs
Lift Equation: L = 0.5 × ρ × V² × A × CL
• ρ = 1.99 slugs/ft³ (seawater) | V = 3 kn = 5.06 ft/s | V² ≈ 25.6
• Max efficient CL ≈ 0.8 (symmetric hydrofoil, non-stalling)
• A = L ÷ (0.5 × 1.99 × 25.6 × 0.8) ≈ 700 ÷ 20.4 ≈ 34 ft² planform area per foil

Example geometry: 6.5 ft span × 5.2 ft chord (or ~6 ft span wrapping the trailing edge). Three units (one per leg) are optimal.

4. Added Draft at 3 Knots with Stabilizers

Induced drag ≈ Lift / (L/D ratio). Marine foils achieve L/D ≈ 20–30 at low Cl.
D ≈ 700 ÷ 25 ≈ 28 lbs/foil × 3 = 84 lbs total induced drag
Parasite drag (foil skin + fairings) ≈ 0.05 hp (35 W) baseline ```