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Seastead Scale Model & Full-Scale Analysis
Seastead Wing/Leg Model & Full-Scale Analysis
The following calculations are based on the geometric approximation of your mold, standard hydrodynamic principles, and Froude/linear scaling rules. All imperial units assume standard sea-level conditions and seawater density of 64 lb/ft³ (1.99 slugs/ft³).
1. Model Mold Volume & Foam Requirements
Cross-Section & Volume Assumption
The mold cross-section is modeled as a semi-circular nose (from the 4" PVC) joined to two flat plywood surfaces meeting at a trailing edge (triangular aft body).
• Semi-circle radius: 3.75" ÷ 2 = 1.875"
• Semi-circle area: π × (1.875)² ÷ 2 ≈ 5.52 in²
• Triangular aft base: 3.75" | Height: 16"
• Triangle area: 0.5 × 3.75 × 16 = 30.00 in²
• Total cross-section: 35.52 in²
• Length: 3.5 ft = 42"
• Volume: 35.52 in² × 42" = 1,491.8 in³ ≈ 0.863 ft³ (24.4 L)
Foam Mixing Requirements (2 lb/ft³ Density)
Standard 2 lb expansion foam weighs 2 lbs per cured cubic foot.
• Cured foam weight: 0.863 ft³ × 2 lb/ft³ = 1.73 lbs
• Liquid volume to pour (1:1 mix ratio assumed): 0.863 ft³ × 119.69 cups/ft³ ≈ 103.3 cups total
• Each component: ~51.6 cups (recommend 10% overpour → ~57 cups per part)
⚠️ Check Manufacturer Datasheet: Mixing ratios vary (1:1 volume, 1:1 weight, or 1:0.92). Always verify the specific brand's ratio and account for mold expansion/venting.
2. Required Model Weight for 50% Submersion
Buoyancy equilibrium requires total model weight = weight of displaced seawater.
• Submerged volume per leg: 0.863 ft³ × 0.50 = 0.4315 ft³
• Buoyancy per leg: 0.4315 ft³ × 64 lb/ft³ = 27.62 lbs
• 3 legs total: 27.62 × 3 = 82.9 lbs
Total model weight should be ~83 lbs to float with exactly half of each leg submerged. (Subtract ~5.2 lbs for the cured foam itself; remaining payload/structure capacity ≈ 78 pts)
Froude & Geometric Scaling (1:6 Model → Full Scale)
Note: Dimensions scale linearly (1:6). Dynamic wave speeds scale by √6 ≈ 2.45, but static displacement and drag are calculated below per your requested full-scale speeds.
1. Full-Scale Dimensions
| Parameter | 1:6 Model | Full Scale |
|---|
| Length (longway) | 3.5 ft | 21.0 ft |
| Nose Diameter (PVC) | 3.75 in | 22.5 in (1.875 ft) |
| Flat Panel Length (Chord) | 16 in | 96 in (8.0 ft) |
| Total Cross-Section Area | 35.5 in² | 1,279 in² (8.88 ft²) |
| Volume per Leg | 0.863 ft³ | 186.5 ft³ |
2. Displaced Seawater Mass (50% Submerged)
At full scale, half of each leg in seawater:
| Condition | Volume Displaced | Mass Displaced (Weight) |
|---|
| Per Leg | 93.25 ft³ | 5,968 lbs |
| 3 Legs Combined | 279.75 ft³ | 17,904 lbs (~8.12 metric tonnes) |
3. Hydrodynamic Drag Force (1, 2, 3 MPH)
Calculated using the drag equation: Fd = 0.5 × ρ × v² × Cd × A
• ρ (seawater) = 1.99 slugs/ft³
• A (effective frontal area, 50% submerged) = 8.88 ft² × 0.50 × 3 legs = 13.32 ft²
• Cd = 0.07 (streamlined hydrofoil/strut aligned with flow, standard marine estimate)
• Formula simplifies to: Fd (lbs) ≈ 0.928 × v² (v in ft/s)
| Speed | Velocity (ft/s) | Drag Force (lbs) |
|---|
| 1 MPH | 1.467 | ~2.0 lbs |
| 2 MPH | 2.933 | ~8.0 lbs |
| 3 MPH | 4.000 | ~14.8 lbs |
4. Electrical Power Requirements
Mechanical power to overcome drag: Pmech = F × v. System efficiency (η) assumed at 0.55 (covers motor, ESC, gearbox, and propeller losses typical in low-speed marine thrusters).
| Speed | Mech Power (W) | Electrical Power (W) | Practical Motor Sizing |
|---|
| 1 MPH | 4.0 W | 7.2 W | ≥ 50 W |
| 2 MPH | 31.8 W | 57.8 W | ≥ 100 W |
| 3 MPH | 80.5 W | 146 W | ≥ 200-250 W |
💡 Propulsion Note: These figures only cover hydrodynamic drag on the submerged struts. Real seasteads require significantly more power for station-keeping against wind, surface waves, platform parasitic drag, and control margins. Size thrusters at 2-3× calculated base load for operational reliability.
Engineering Assumptions & Limitations:
• Cross-section assumes flat plywood panels meeting at a sharp trailing edge. If panels are angled or faired, volume and drag will change ~5-15%.
• Drag coefficient (0.07) assumes smooth surface finish, streamlined alignment, and negligible wave-making resistance at these low speeds (Fr < 0.2).
• Imperial "lbs" for displacement refers to force (lbf) in standard US engineering practice.
• Always validate with physical model testing and consult marine structural/hydrodynamic engineers before full-scale fabrication.
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