```html Seastead Scale Model Calculations

Seastead Tensegrity Semi-Submersible Scale Model

1. Froude Scaling and Scale Ratio

For Froude scaling, we preserve the Froude number: Fr = V/√(gL), where V is velocity, g is gravity, and L is length.

Given: Full-scale leg diameter = 4 ft = 48 inches, Model leg diameter = 5 inches

Scale ratio λ = L_full / L_model = 48 inches / 5 inches = 9.6

All dimensions scale by λ = 9.6, masses scale by λ³ = 9.6³ = 884.736.

2. Full-Scale Dimensions

Component	Full-Scale (feet)	Full-Scale (inches)
Body Length	60 ft	720 in
Body Width	14 ft	168 in
Body Height	8 ft	96 in
Leg Diameter	4 ft	48 in
Leg Length	35 ft	420 in

Leg Geometry: Each leg is at 45° in both front and side views, making a compound angle of approximately 54.7° from vertical. The vertical drop per leg is 35/√3 ≈ 20.21 ft, with horizontal displacements of the same amount.

3. Scale Model Dimensions (Using λ = 9.6)

Component	Model (inches)	Model (feet)
Body Length	75.0 in	6.25 ft
Body Width	17.5 in	1.46 ft
Body Height	10.0 in	0.83 ft
Leg Diameter	5.0 in	0.42 ft
Leg Length	43.75 in	3.65 ft
Leg Vertical Drop	25.26 in	2.11 ft

4. Scale Model Weights

Important: Actual weights depend on material density and construction details. These calculations assume uniform scaling of mass with λ³ and use typical material densities for estimation.

Mass Scaling: M_model = M_full / λ³ = M_full / 884.736

Volume Estimates:

Body volume (simplified as rectangular prism): 75 × 17.5 × 10 = 13,125 in³
Each leg volume (cylinder): π × (2.5)² × 43.75 ≈ 859 in³
Total leg volume (4 legs): ≈ 3,436 in³
Total model volume: ≈ 16,561 in³ (approx. 9.58 ft³)

Example Weight Estimates:

Material	Density (lb/in³)	Estimated Model Weight
Plastic (HDPE)	0.033	≈ 547 lb
Aluminum	0.098	≈ 1,623 lb
Fiberglass	0.065	≈ 1,077 lb

Full-Scale Weight Implication: If the model weighed 500 lb, the full-scale weight would be approximately 500 × 884.736 ≈ 442,368 lb (221 tons).

5. Using 55-Gallon Barrels for Model Body

Typical 55-Gallon Plastic Barrel Dimensions:

Diameter: ≈ 23 inches
Height: ≈ 35 inches
Volume: 55 gallons = 12,705 in³

Model Body Configuration: Two barrels connected end-to-end to form a long cylinder.

Parameter	Model (Two Barrels)	Full-Scale Equivalent (λ = 9.6)
Length	70 inches (5.83 ft)	672 inches = 56 feet
Diameter	23 inches (1.92 ft)	220.8 inches = 18.4 feet
Cross-sectional Area	415.5 in²	38,486 in² = 267.3 ft²
Volume	25,410 in³ (14.7 ft³)	22,481,664 in³ = 13,009 ft³

Comparison: The barrel-based model body represents a full-scale body 56 ft long and 18.4 ft in diameter, compared to the original design of 60 ft × 14 ft. The barrel version is shorter but wider.

6. Design Notes

The model should be built with attention to the 45° leg angles in both planes.
For proper Froude scaling, the model should be tested in the same gravitational field (earth) and fluid (water) as the full-scale version.
The cable connections between legs and body must be scaled appropriately to maintain the tensegrity structure's integrity.
Ballasting may be required to achieve the correct 60% submersion of legs in the model.
These calculations assume geometric similarity; actual hydrodynamic testing would require careful attention to Reynolds number effects as well.

Generated for seastead design analysis. All dimensions are approximate and should be verified with detailed engineering calculations.

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