Seastead Design Calculations
This report details the dimensions, displaced volume, and target weight for a Top-level Triangle Seastead design, comparing the 1/6th scale model to the full-scale build using Froude scaling conventions.
1. Assumptions & Scaling Laws
- Scale Factor (λ): 6 (1/6th scale model)
- Geometric Scaling: Linear dimensions scale by a factor of λ. Volumes scale by a factor of λ³ (216). Angles do not scale.
- Fluid Densities: It is assumed the scale model is tested in Freshwater (62.4 lbs/ft³) and the full-scale seastead will be deployed in Seawater (64.0 lbs/ft³).
- Rope Volume: The volume of the stabilization ropes going from the legs to the triangle is considered negligible for the hydrostatic calculations.
2. Data & Calculations
Scale Model (1/6) Calculations:
- Leg Diameter: 5 inches = 0.4167 ft
- Leg Cross-Sectional Area: π × (radius)² = 3.14159 × (0.2083 ft)² = 0.1364 ft²
- Submerged Length: 6 ft × 60% = 3.6 ft per leg
- Submerged Volume per Leg: 0.1364 ft² × 3.6 ft = 0.491 ft³
- Total Submerged Volume (3 Legs): 0.491 ft³ × 3 = 1.473 ft³
- Target Model Weight: 1.473 ft³ × 62.4 lbs/ft³ (freshwater) = 91.9 lbs
Full Scale (1/1) Calculations:
- Froude Volume Scaling Factor: λ³ = 6³ = 216
- Total Submerged Volume: 1.473 ft³ (model vol) × 216 = 318.17 ft³
- Target Full Scale Weight: 318.17 ft³ × 64.0 lbs/ft³ (seawater) = 20,363 lbs (Approx 9.09 Long Tons)
3. Specifications Table
| Parameter |
1/6th Scale Model |
Full Scale Design |
| Main Triangle Side Length |
10 ft |
60 ft |
| Leg Length (Total) |
6 ft |
36 ft |
| Leg Diameter |
5 inches (0.417 ft) |
30 inches (2.5 ft) |
| Leg Angle (Out and Down) |
45 degrees |
45 degrees |
| Leg Submerged Length (60%) |
3.6 ft |
21.6 ft |
| Total Displaced Volume of Water |
1.47 ft³ |
318.1 ft³ |
| Target Weight (Displacement) |
91.9 lbs (in freshwater) |
20,363 lbs (in saltwater) |
Designer Note: The "Target Weight" refers to the maximum weight of the seastead (including structure, rigging, payloads, and living loads) required to push the legs down to exactly 60% submergence. To achieve the 60% waterline, the total mass of your 1/6 scale model must be exactly 91.9 pounds once placed in a freshwater testing pool.
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