Seastead Design - Scale Model & Full Scale Specifications

📐 Froude Scaling Rules (λ = 6)

Key Froude Scaling Relationships

For a geometric scale factor λ = 6 (full-scale / model-scale):

Parameter	Scaling Factor	Multiplier
Length, Beam, Draft	λ	× 6
Area	λ²	× 36
Volume / Displacement	λ³	× 216
Mass / Weight / Force	λ³	× 216
Velocity	λ^0.5	× 2.449
Time / Period	λ^0.5	× 2.449
Pressure	λ	× 6

📏 Dimensional Comparison

Component	1/6th Scale Model	Full Scale (× 6)
Triangle Platform — Side Length	10 ft	60 ft
Leg/Column Diameter	5 in (0.4167 ft)	30 in (2.5 ft)
Leg/Column Total Length	6 ft	36 ft
Leg Angle from Horizontal	45°	45° (angles preserved)
Leg — Submerged Length (~60%)	3.6 ft	21.6 ft
Leg — Above Water (~40%)	2.4 ft	14.4 ft
Horizontal Reach per Leg (6 ft × cos45°)	4.24 ft	25.46 ft
Vertical Drop per Leg (6 ft × sin45°)	4.24 ft	25.46 ft
Rope Length (each, approx.) See calculation below	~10.91 ft	~65.5 ft
Number of Ropes	6 (2 per leg)	6
Number of Legs/Columns	3	3

🌊 Displacement Calculations — Scale Model

Submerged Volume per Leg

Given:
Leg diameter: 5 in = 0.4167 ft, so radius = 0.2083 ft
Total leg length: 6 ft
Submerged fraction: 60% → Submerged length = 3.6 ft

Cross-sectional area of one leg:
A = π × r² = π × (0.2083)² = π × 0.04340 = 0.1364 ft²

Submerged volume per leg:
V = A × L = 0.1364 × 3.6 = 0.4909 ft³

Total submerged volume (3 legs):
V_total = 3 × 0.4909 = 1.4726 ft³

Mass of Water Displaced (Scale Model)

Using fresh water density: 62.4 lb/ft³
Using salt water density: 64.0 lb/ft³

Fresh water displaced:
1.4726 ft³ × 62.4 lb/ft³ = 91.9 lbs

Salt water displaced:
1.4726 ft³ × 64.0 lb/ft³ = 94.2 lbs

🔵 Scale Model — Water Displaced

Total submerged volume: 1.473 ft³ (2,544 in³)

Fresh Water:

91.9 lbs

Salt Water:

94.2 lbs

⚖️ Target Weight (Archimedes' Principle)

For the model to float with legs 60% submerged, the total weight of the model (platform + legs + ropes + payload) must equal the weight of water displaced.

🟢 Scale Model Target Weight

(Salt water)

~94 lbs

(Fresh water: ~92 lbs)

🟢 Full-Scale Target Weight

(Froude: × 216)

~20,347 lbs

≈ 10.2 tons (salt water)

(Fresh water: ~19,850 lbs ≈ 9.9 tons)

Froude mass scaling verification:
Full-scale weight = Model weight × λ³ = 94.2 × 216 = 20,347 lbs

Direct full-scale calculation check:
Full-scale leg diameter: 2.5 ft, radius: 1.25 ft
Full-scale submerged length per leg: 21.6 ft
Submerged volume per leg: π × 1.25² × 21.6 = 106.0 ft³
Total submerged volume (3 legs): 318.1 ft³
Salt water displaced: 318.1 × 64.0 = 20,358 lbs ✅ (matches Froude scaling)

🔗 Rope Geometry Detail

Configuration: Each leg extends from a triangle corner at 45° outward and downward. Two ropes connect the bottom of each leg back to the two adjacent corners of the triangle.

Leg tip position (model scale):
The leg goes outward from a corner along the angle bisector of that corner (pointing away from the triangle center), and downward at 45°.
Horizontal distance outward: 6 × cos(45°) = 4.243 ft
Vertical distance down: 6 × sin(45°) = 4.243 ft

Equilateral triangle side = 10 ft.
Distance from corner to adjacent corner = 10 ft.
Placing one corner at origin, the leg tip extends radially outward and down.

Approximate rope length (model):
The rope runs from the bottom of a leg back to an adjacent corner of the triangle. Using 3D geometry (horizontal separation ~10.9 ft accounting for the outward splay, plus 4.24 ft vertical drop):
Rope ≈ √(10.39² + 4.243²) ≈ √(107.9 + 18.0) ≈ √125.9 ≈ 10.91 ft

Note: Exact rope length depends on the precise outward direction of each leg. The above assumes each leg extends along the outward bisector of its triangle corner.

Rope Parameter	Scale Model	Full Scale
Approximate length per rope	~10.9 ft	~65.5 ft
Number of ropes per leg	2	2
Total ropes	6	6
Total rope length	~65.5 ft	~393 ft

📊 Complete Summary Table

Parameter	1/6 Scale Model	Full Scale	Scale Factor
Triangle side	10 ft	60 ft	×6
Leg diameter	5 in	30 in (2.5 ft)	×6
Leg length	6 ft	36 ft	×6
Submerged length per leg	3.6 ft	21.6 ft	×6
Leg angle	45°	45°	—
Draft (vertical depth of leg tip)	4.24 ft	25.46 ft	×6
Submerged volume (total)	1.473 ft³	318.1 ft³	×216
Rope length (each, approx.)	10.9 ft	65.5 ft	×6
TARGET WEIGHT (salt water)	~94 lbs	~20,350 lbs (10.2 tons)	×216
TARGET WEIGHT (fresh water)	~92 lbs	~19,850 lbs (9.9 tons)	×216

📝 Design Notes

⚠️ Important Considerations:

Target weights include everything: platform structure, legs, ropes, deck payload, equipment — the entire floating system.
If the model weighs less than ~94 lbs, legs will be less than 60% submerged (rides higher).
If it weighs more than ~94 lbs, legs will submerge more than 60% (rides lower / may sink).
Froude scaling preserves the ratio of inertial to gravitational forces — ideal for wave interaction studies.
Froude scaling does not preserve Reynolds number — viscous drag effects will differ at model scale.
The ropes must be designed to handle tension loads that scale as λ³ = 216× at full scale.
Stability analysis should verify the platform doesn't capsize; the 45° splayed legs provide good righting moment.

⚓ Seastead Design Specifications