```html Seastead Design: Scale Model vs. Full Scale

Seastead Design Analysis

Scale Ratio: 1:6 (Model to Full Scale)

Scaling Law: Froude Scaling (Geometric Similarity)

1. Dimensional Scaling

Using Froude scaling rules, linear dimensions scale by the factor $\lambda = 6$. Areas scale by $\lambda^2$ (36), and volumes/mass scale by $\lambda^3$ (216).

Component Scale Model Dimensions Full Scale Dimensions
Main Triangle Side Length 10 feet 60 feet
Leg/Column Diameter 5 inches 30 inches (2.5 feet)
Leg/Column Length 6 feet 36 feet
Leg Angle 45 degrees 45 degrees

2. Buoyancy and Displacement Calculation

Scale Model Calculation

Assumptions: Seawater density is approx. 64 lbs/ft³.

  1. Leg Volume (Single):
    Radius = 2.5 inches = 0.2083 ft. Length = 6 ft.
    Volume = $\pi \times r^2 \times L = \pi \times (0.2083)^2 \times 6 \approx 0.818$ ft³.
  2. Total Leg Volume (3 Legs):
    $0.818 \text{ ft}^3 \times 3 = 2.454$ ft³.
  3. Submerged Volume (60%):
    $2.454 \text{ ft}^3 \times 0.60 = 1.472$ ft³.
  4. Mass of Water Displaced:
    $1.472 \text{ ft}^3 \times 64 \text{ lbs/ft}^3 \approx \mathbf{94.2 \text{ lbs}}$.

Full Scale Calculation

Calculated directly from full-scale dimensions to ensure precision.

  1. Leg Volume (Single):
    Radius = 15 inches = 1.25 ft. Length = 36 ft.
    Volume = $\pi \times (1.25)^2 \times 36 \approx 176.71$ ft³.
  2. Total Leg Volume (3 Legs):
    $176.71 \text{ ft}^3 \times 3 = 530.14$ ft³.
  3. Submerged Volume (60%):
    $530.14 \text{ ft}^3 \times 0.60 = 318.09$ ft³.
  4. Mass of Water Displaced:
    $318.09 \text{ ft}^3 \times 64 \text{ lbs/ft}^3 \approx \mathbf{20,358 \text{ lbs}}$.

3. Target Weights

For the seastead to float at the designed waterline (60% submersion of the legs), the total weight of the structure must equal the mass of the water displaced.

Configuration Target Weight (lbs) Target Weight (Tons)
Scale Model (1/6th) ~94 lbs 0.05 tons
Full Scale (1:1) ~20,360 lbs 10.18 tons

*Note: The weight of the rigging (ropes) is negligible in this calculation but should be included in the final "Target Weight" budget during construction.

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