Seastead 1/6th Scale Model - Froude Scaling Analysis

Seastead 1/6th1>

Scaling Parameters

Parameter	Value
Scale Ratio (Model : Full)	1 : 6 (λ = 6)
Length Scale Factor	L_r = 1/6
Area Scale Factor	A_r = 1/36
Volume / Mass / Force Scale Factor (Froude)	V_r = M_r = F_r = λ³ = 216
Time Scale Factor	T_r = √λ = √6 ≈ 2.449
Velocity Scale Factor	V_r = √λ = √6 ≈ 2.449
Fluid Density (Seawater)	64.0 lb_f/ft³ (1025 kg/m³)

Model Geometry (1/6th Scale)

Component	Dimension	Details
Main Triangle Side Length	10.0 ft	Equilateral triangle above water
Leg Count	3	One per corner
Leg Diameter	5.0 in (0.4167 ft)	Cylindrical floats/columns
Leg Length (Total)	6.0 ft	Along 45° angle
Leg Angle	45°	Out and Down from corners
Submerged Fraction	60%	Draft condition
Submerged Length per Leg	3.6 ft	0.60 × 6.0 ft
Rope Bracing	2 per leg	Bottom of leg to adjacent triangle corners

Full Scale Geometry (Froude Scaled ×6)

Component	Dimension	Calculation
Main Triangle Side Length	60.0 ft	10 ft × 6
Leg Diameter	30.0 in (2.50 ft)	5 in × 6
Leg Length (Total)	36.0 ft	6 ft × 6
Leg Angle	45°	Geometrically similar
Submerged Length per Leg	21.6 ft	3.6 ft × 6 (60% of 36 ft)
Horizontal Leg Projection (Total)	~25.46 ft	36 ft × cos(45°)
Vertical Leg Drop)	~25.46 ft	36 ft × sin(45°)
Submerged Drop	~25.46 ft	21.6 ft × sin/cos(45°)

Hydrostatics & Displacement Calculations

Model Displaced Volume

Volume of one submerged leg cylinder: V = π × (D/2)² × L_sub

Radius r = 5/24 ft ≈ 0.2083 ft
Submerged Length V_leg = π × (5/24)² × 3.6 = 5π/32 ≈ 0.4909 ft³
Total Volume (3 legs): V_model = 15π/32 ≈ 1.4726 ft³

Weight of Displaced Seawater (Buoyant Force = Target Weight)

Using Seawater Density γ = 64 lb_f/ft³

Model Displaced Weight: 94.25 lbs (≈ 42.75 kg)

Calculation: 1.4726 ft³ × 64 lb/ft³ = 30π ≈ 94.248 lbs

Full Scale Displaced Weight: 20,358 lbs (≈ 9,234 kg / 9.23 Metric Tonnes)

Calculation: 94.248 lbs × 216 (λ³) = 6,480π ≈ 20,357.5 lbs

Full Scale Displacement in Common Marine Units

Unit	Value
Pounds (lb_f)	20,358 lbs
Short Tons (2,000 lbs)	10.18 tons
Long Tons (2,240 lbs)	9.09 tons
Metric Tonnes (1,000 kg / 2,204.62 lbs)	9.23 tonnes
Kilograms (mass)	9,234 kg
Cubic Meters Displacement (Seawater)	9.01 m³

Target Weights Summary

Scale	Target Weight (Displacement)	Mass Equivalent
1/6th Scale Model	94.3 lbs (42.8 kg)	42.8 kg
Full Scale Seastead	20,360 lbs (9.23 Metric Tonnes)	9,230 kg

Design Note: The target weights above represent the total allowable weight (Structure + Deckhouse + Ballast + Payload + Consumables) for the vessel to float at the specified 60% leg submergence (waterline). The model must be ballasted to exactly ~94.3 lbs total weight to correctly simulate the full-scale hydrostatics and stability.

Froude Scaling Implications for Testing

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Quantity	Scale Factor (Model:Full)	Implication for Model Testing
Length / Draft	1 : 6	Model dimensions are 1/6th full size.
Mass / Displacement / Weight	1 : 216	Model weight must be 1/216th of full scale target (94.3 lbs).
Time (Periods: Roll, Pitch, Heave, Waves)	1 : √6 ≈ 1 : 2.45	Model motions are 2.45x faster. A 10s full scale roll period = 4.08s model period.
Velocity / Wave Celerity	1 : √6 ≈ 1 : 2.45	Tow speed / Wave speed must be 1/2.45th of full scale knots.
Acceleration (g)	1 : 1	Gravitational acceleration is identical (Froude similarity).
Force (Mooring, Wave Loads)	1 : 216	Measured model forces × 216 = Full scale forces.
Power	1 : 529 (λ^3.5)	Model power × 529 = Full scale power.
Stiffness (Mooring/Spring)	1 : 216	Spring constants must scale with Force/Length (216/6 = 36? No, Force/Length = 216/6 = λ). Stiffness = Force/Length. Scale Stiffnessratio is 1:216. => 1:216 λ36. : 1 16

Seastead 1/6th1>Seastead