# Seastead Leg Optimization Calculator
I'll create an interactive HTML calculator that models the tradeoffs between leg geometry, stability, speed, and stabilizer effectiveness.
```html
Seastead Leg Optimization Calculator
Seastead Leg / Stabilizer Trade Study
Inputs
Leg Profile Comparison (3 legs per seastead)
Leg Profile
Chord (ft)
Width/Thick (ft)
Draft (ft)
Waterplane Area (Total Sq Ft, 3 legs)
Restoring Force (lbs/ft heave)
Speed @ Power (knots)
Heave w/o Stab (ft)
Stab Force Total (lbs, 3 stabs)
Stab Influence (ft equiv)
Net Heave w/ Stab (ft)
Wt / Leg (lbs Al)
Cost / Leg + Stab (USD)
Modeling Notes:
Waterplane area for a NACA 00xx foil is approximated as area ≈ 0.685 × chord × thickness (integral of NACA 4-digit thickness equation), per leg, × 3 legs.
Volume of a leg = waterplane area × total length. Different NACA profiles adjust thickness to keep the same volume (same buoyancy) as the NACA 0030 baseline (10 ft chord × 3 ft thick × 19.5 ft draft).
Restoring force = waterplane area × 64 lb/ft³ (seawater).
Drag: form drag coefficient scales with thickness ratio. Using Cd ≈ 0.0085 + 0.1·(t/c)² referenced to frontal area; thinner foils are faster. Speed found where thrust from (P·η)/V = drag.
Heave w/o stab: assumes rise of water surface ≈ (wave height)/2 over ~¼ of the wave period (peak of a sinusoidal wave). We model heave as water-following damped by inertia & waterplane area response time; for this small-waterplane design the leg partially follows the wave. Approximation: heave ≈ (wave rise) × response_factor, where response_factor decreases with smaller waterplane area (less coupling to surface).
Stabilizer force: L = ½·ρ·V²·S·CL, with ρ_seawater = 1.99 slug/ft³. Force per stabilizer × 3.
Stab influence in ft = (stab force) / (restoring force). This is how many feet of heave the stabilizer can counteract in steady state.
Marine aluminum estimated at density 169 lb/ft³, wall thickness 0.375 in ≈ 0.03125 ft. Weight ≈ surface area × thickness × density.
```
## How the Model Works
**Key calculations:**
1. **Waterplane area** per NACA foil ≈ 0.6854 × chord × thickness (true integration of NACA 4-digit profile)
2. **Same volume constraint**: When changing thickness, length is scaled inversely (thinner foils = longer legs) to preserve buoyancy
3. **Speed**: Solved from `P·η = ½ρV³·Cd·A`, where Cd depends on thickness ratio
4. **Wave response**: Uses base-excitation transmissibility `1/√(1+(ω_wave/ω_natural)⁴)` — small waterplane = low natural frequency = platform decouples from waves
5. **Stabilizer force**: `L = ½ρV²·S·CL` × 3 stabilizers — grows with speed²
6. **Stabilizer "feet equivalent"** = stabilizer force ÷ restoring force — directly comparable to heave
**The trade-offs you'll see:**
- **NACA 0040** (thicker, shorter): more waterplane area, stiffer in waves, more drag, slower, less stabilizer force → follows waves more
- **NACA 0025** (thinner, longer): less waterplane, softer ride (decouples from waves), less drag, faster, stronger stabilizer → better motion reduction overall but heavier structure
- **Baseline 0030** sits in the middle
Save this as an `.html` file and open in any browser. Adjust the input fields and click **Recalculate** to explore the design space.