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Seastead Scale Model & Full Scale Calculations
Seastead Wing-Float Calculations
Scale model: 1:6 Froude scaling | Material: 2 lb/ft³ polyurethane foam | Seawater density: 64 lbs/ft³
1. Model Specifications (1:6 Scale)
Mold Geometry
- Leading edge: 3.5 ft (42 in) of 4" PVC pipe cut lengthwise (ID = 3.75")
- Radius of leading edge: 1.875 inches
- Plywood sides: 3.5 ft × 16 inches, hinged to PVC edges
- Shape: Semi-circular leading edge with flat tapering sides meeting at trailing edge (assumed)
Volume Calculation
Cross-sectional Area = (π × r²)/2 + 2 × (0.5 × base × height)
= (π × 1.875²)/2 + 2 × (0.5 × 16 × 1.875)
= 5.53 in² + 30 in² = 35.53 in²
Volume = 35.53 in² × 42 in = 1,492 in³ (0.863 ft³)
| Unit | Value |
|---|
| Cubic inches | 1,492 in³ |
| Cubic feet | 0.863 ft³ |
| Gallons | 6.46 gal |
| Liters | 24.5 L |
Foam Mixing Requirements (2-Part 2 lb/ft³ Foam)
Assuming 1:1 volume ratio (Parts A & B):
Total volume: 6.46 gallons = 103.4 cups
Each part: ~52 cups (3.25 gallons)
Note: Add 10-15% extra to account for waste and expansion tolerance. Recommended: 58-60 cups of each part.
Model Buoyancy (3 Legs, 50% Submerged)
Displacement per leg = 0.863 ft³ × 0.5 × 64 lbs/ft³ = 27.6 lbs
Total weight for neutral buoyancy = 27.6 × 3 = 82.8 lbs
2. Full Scale Dimensions (Froude 1:6 Scaling)
Scale factor λ = 6. Linear dimensions multiply by 6.
| Dimension |
Model |
Full Scale |
| Length (Vertical/Span) |
3.5 ft (42 in) |
21 ft |
| Chord (Lengthwise) |
~17.9 in (16 + 1.875) |
8.94 ft (107 in) |
| Max Thickness (Width) |
3.75 in |
1.88 ft (22.5 in) |
| Volume per leg |
0.863 ft³ |
186.4 ft³ |
3. Full Scale Displacement & Mass
With each leg 50% submerged in seawater (64 lbs/ft³):
Submerged volume per leg = 186.4 ft³ / 2 = 93.2 ft³
Displaced water per leg = 93.2 ft³ × 64 lbs/ft³ = 5,965 lbs
Total for 3 legs = 5,965 × 3 = 17,895 lbs
Note: This represents the required weight of the full-scale structure (legs + living area) to achieve 50% submergence. This is approximately 8.1 metric tonnes or 8.9 US tons.
4. Drag Force at Full Scale
Assumptions:
- Movement along chord direction (low Cd orientation)
- Drag coefficient Cd ≈ 0.15 (streamlined wing/float at low Froude number)
- Reference area: 50% of frontal area (submerged portion) = 0.5 × (Span × Thickness)
- Submerged frontal area per leg = 0.5 × (21 ft × 1.875 ft) = 19.69 ft²
- Total for 3 legs: 59.1 ft²
- Seawater density (ρ): 1.99 slugs/ft³
Drag Force = ½ × ρ × v² × Cd × A
Where v is in ft/s (1 MPH = 1.467 ft/s)
| Speed |
Velocity (ft/s) |
Drag Force |
| 1 MPH |
1.47 |
19 lbs |
| 2 MPH |
2.93 |
76 lbs |
| 3 MPH |
4.40 |
170 lbs |
Drag increases with the square of velocity. These values assume calm water and do not account for wave drag (which is minimal at these low Froude numbers) or barnacle fouling.
5. Electrical Power Requirements
Assumptions:
- Propeller efficiency: 70%
- Electric motor efficiency: 85%
- Combined efficiency: ~60%
- Power (watts) = (Force × Velocity) / Efficiency × 1.356 (conversion factor)
| Speed |
Drag Force |
Propulsive Power |
Electrical Power
(approximate) |
| 1 MPH |
19 lbs |
38 W |
60-70 W |
| 2 MPH |
76 lbs |
300 W |
500-550 W |
| 3 MPH |
170 lbs |
1,015 W |
1.7 kW |
Motor Selection Guidance:
- 1 MPH: Small trolling motor (~80-100W) or electric outboard
- 2 MPH: 1 hp electric outboard (~750W rated)
- 3 MPH: 2-3 hp electric outboard (~1.5-2.2 kW rated)
Given the high displacement (18,000 lbs), these power levels represent excellent hydrodynamic efficiency typical of wing-shaped hulls. For comparison, a conventional barge of similar displacement might require 3-5× more power.
Summary Table
| Parameter |
Model Scale |
Full Scale |
| Leg Dimensions |
3.5' × 1.5' × 0.3' |
21' × 8.9' × 1.9' |
| Foam Needed (per leg) |
0.86 ft³ |
186 ft³ |
Total Structure Weight
(for 50% submergence) |
83 lbs |
17,900 lbs |
| Power to move @ 2 MPH |
N/A |
~500 Watts |
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