Seastead Wing/Float Leg Analysis
Scale: 1:6 (Model : Full Scale) | Foam: 2 lb/ft³ Two-Part Pour Foam | Fluid: Seawater (64 lb/ft³, ν ≈ 1.28×10⁻⁵ ft²/s)
Geometry Definitions (Model Scale)
| Parameter | Value | Notes |
|---|
| Leg Length (Span / Draft) | 42 in (3.5 ft) | Vertical dimension |
| Leading Edge Radius (PVC ID/2) | 1.875 in | From 3.75" inside span of 4" PVC halved |
| Plywood Side Width | 16 in | Flat side panels hinged to PVC edges |
| Total Chord Length | 17.875 in | Radius (1.875) + Plywood (16) |
| Max Thickness | 3.75 in | PVC Diameter |
| Thickness/Chord Ratio (t/c) | 0.21 | Thick foil section (NACA 0021 class) |
| Number of Legs | 3 | |
1. Mold Volume & Foam Requirements (Model)
Cross-Sectional Area Calculation
- Leading Edge (Semi-circle):
0.5 × π × 1.875² = 5.526 in²
- Two Side Triangles:
2 × (0.5 × 16 × 1.875) = 30.000 in²
- Total X-Section Area = 35.526 in²
| Item | Volume (in³) | Volume (ft³) | Weight (lbs @ 2 lb/ft³) |
|---|
| Single Leg Volume | 1,492.1 | 0.8635 | 1.73 |
| Total (3 Legs) | 4,476.3 | 2.590 | 5.18 |
Two-Part Foam Mixing (1:1 Volume Ratio Assumed)
| Component | Volume (ft³) | Volume (Gallons) | Volume (Cups) |
|---|
| Part A (per leg) | 0.4318 | 3.23 | 51.7 cups |
| Part B (per leg) | 0.4318 | 3.23 | 51.7 cups |
| Total Mixed (per leg) | 0.8635 | 6.46 | 103.4 cups |
| Total Mixed (3 legs) | 2.590 | 19.4 | 310 cups |
Practical Tip: Mix in batches (e.g., 5-gal buckets). 0.86 ft³ ≈ 6.5 gallons per leg. Account for ~5-10% waste/expansion overflow. Pour immediately after mixing; 2lb foam rises fast.
2. Model Target Weight (Static Floating Condition)
Condition: 3 Legs, 50% Submerged (Draft = 21 in = 1.75 ft) in Seawater (64 lb/ft³).
| Calculation Step | Value |
|---|
| Volume per Leg (Full) | 0.8635 ft³ |
| Submerged Volume per Leg (50%) | 0.43175 ft³ |
| Total Displaced Volume (3 Legs) | 1.29525 ft³ |
| Buoyant Force (Target Weight) | 82.9 lbs |
Ballast Required: The foam itself weighs ~5.2 lbs (3 legs). You need ~77.7 lbs of ballast (lead, steel, batteries, structure) distributed in the model to achieve the 50% draft waterline. The living area structure above water must be included in this 82.9 lbs total.
3. Full Scale Dimensions (1:6 Scale / Froude Scaling)
Length Scale Factor λ = 6. Area scales by λ² = 36. Volume/Mass scales by λ³ = 216.
| Parameter | Model | Full Scale (×6) |
|---|
| Leg Length (Draft) | 3.5 ft | 21.0 ft |
| Chord Length | 1.49 ft (17.875 in) | 8.94 ft |
| Max Thickness | 0.3125 ft (3.75 in) | 1.875 ft |
| Leading Edge Radius | 0.156 ft (1.875 in) | 0.9375 ft |
| Wetted Area (1 Leg) | 10.32 ft² | 400 ft² |
| Volume (1 Leg) | 0.8635 ft³ | 186.5 ft³ |
4. Full Scale Displaced Weight (Buoyancy)
Condition: 3 Legs, 50% Submerged (Draft = 10.5 ft).
| Parameter | Value |
|---|
| Full Scale Leg Volume | 186.5 ft³ |
| Submerged Volume per Leg (50%) | 93.25 ft³ |
| Total Displaced Volume (3 Legs) | 279.75 ft³ |
| Displaced Seawater Weight (Buoyancy) | 17,904 lbs |
| Equivalent Mass (Long Tons) | 8.0 long tons |
| Equivalent Mass (Metric Tonnes) | 8.12 tonnes |
This is the maximum payload + structure weight the 3 legs can support at half submergence. The legs themselves (foam/concrete/steel) weigh a fraction of this.
5. Drag Force to Move 3 Full Scale Legs (Aligned, Low Cd)
Hydrodynamic Assumptions
- Reference Area: Total Wetted Area (3 Legs) = 1,200 ft² (Perimeter × Span × 3).
- Reynolds Numbers: 1.0×10⁶ (1 mph) → 3.1×10⁶ (3 mph). Turbulent flow regime.
- Skin Friction (ITTC 1957):
Cf = 0.075 / (log₁₀ Re - 2)² → 0.0047 → 0.0038.
- Form Factor (1+k): Estimated 2.8 for t/c = 0.21 (Hoerner, Streamlined Bodies).
- Total Cd (Wetted Area Basis):
Cd = Cf × (1+k) ≈ 0.011 – 0.013. Used 0.012 average.
- Seawater Density (ρ): 1.99 slugs/ft³ (64 lb/ft³ / 32.2 ft/s²).
| Speed | Velocity (ft/s) | Reynolds # | Cd (Wet) | Drag Force (3 Legs) |
|---|
| 1 MPH | 1.467 | 1.02 × 10⁶ | 0.013 | 31 lbs |
| 2 MPH | 2.933 | 2.04 × 10⁶ | 0.012 | 123 lbs |
| 3 MPH | 4.400 | 3.06 × 10⁶ | 0.011 | 277 lbs |
Drag scales roughly with V². Forces are surprisingly low due to streamlined orientation. If legs are yawed (cross-flow), Cd jumps to ~1.0 (Frontal Area basis) and forces increase 10x-15x.
6. Required Propulsion Power (Full Scale)
Efficiency Chain Assumptions
- Propulsive Efficiency (ηₚ): 0.60 (Open propeller, low speed, large diameter ideal).
- Motor/ESC Efficiency (ηₘ): 0.90 (Brushless DC / PMAC).
- Total System Efficiency (η): 0.54.
- Formula:
Watts = (Drag_lbs × Velocity_ft/s) / (η × 0.7376)
| Speed | Drag (lbs) | Effective Power (HP) | Shaft Power (HP) | Electrical Input (Watts) |
|---|
| 1 MPH | 31 | 0.082 | 0.14 | 113 W |
| 2 MPH | 123 | 0.66 | 1.10 | 908 W |
| 3 MPH | 277 | 2.22 | 3.70 | 3,065 W |
Motor/Propeller Sizing Guidance (Full Scale)
- 1 MPH (Station Keeping / Slow Maneuver): ~150W electrical per leg (3 × 50W motors). Small trolling motors or large ROV thrusters (e.g., Blue Robotics T200 × 3) are sufficient.
- 2 MPH (Transit): ~300W electrical per leg (3 × 300W motors). Requires ~1.5 kW total battery power. Standard 48V electric outboard or 3× 1kW pod drives.
- 3 MPH (Max Cruise): ~1 kW electrical per leg (3 × 1kW+ motors). Total ~3.1 kW. Requires ~10-15 kWh battery for 3-5 hour range. Look at 4-6 kW electric outboards (e.g., Torqeedo Cruise 4.0, ePropulsion Navy 3.0/6.0) or custom large diameter (24-30") props on 48V motors for best ηₚ.
Froude Scaling Note for Model Testing: To simulate full scale 1, 2, 3 mph at 1:6 scale, tow model at 0.41, 0.82, 1.22 mph (0.6, 1.2, 1.8 ft/s). Model drag forces will be ~0.14, 0.57, 1.28 lbs total. Measure tow force to validate Cd assumptions.
Summary: Key Numbers for Website/Design Doc
| Category | Model Scale (1:6) | Full Scale (1:1) |
|---|
| Leg Length | 3.5 ft | 21 ft |
| Leg Chord | 1.49 ft | 8.94 ft |
| Foam Volume (1 Leg) | 0.86 ft³ (103 cups mixed) | 186.5 ft³ |
| Foam Weight (3 Legs) | 5.2 lbs | ~373 lbs (if solid foam) |
| Target Displacement (50% Sub) | 83 lbs | 17,900 lbs |
| Drag @ 2 mph (3 Legs) | 0.57 lbs (at 0.82 mph) | 123 lbs |
| Power @ 2 mph (3 Legs) | ~0.02 W | 908 Watts |
Calculations assume ideal streamlined flow (0° yaw), turbulent boundary layer, ITTC 1957 friction line, form factor 2.8 for t/c=0.21.
Real world Cd may be higher due to surface roughness, hinge gaps, biofouling, and strut/fairing interference.
Always add 25-50% margin to motor sizing for waves, windage on superstructure, and maneuvering.