Seastead Design - Buoyancy & Scaling Analysis

🌊 Seastead Design Analysis

Froude Scaling Analysis | Scale Factor λ = 1/6 | Volume Factor λ³ = 1/216

Executive Summary: For the seastead to float at the designed 60% submergence, the total weight of the structure (platform + legs + hardware) must equal the weight of the displaced water. Based on the leg geometry, this target weight is approximately 94 lbs for the model and 20,400 lbs for the full-scale version.

📐 Dimensional Scaling (Froude Rules)

Linear dimensions scale by factor λ = 6. All lengths multiplied by 6 for full scale.

Component	Model (1:6)	Full Scale (6:1)	Scaling Method
Triangle Platform (side)	10.0 ft	60.0 ft	× 6
Leg Length	6.0 ft	36.0 ft	× 6
Leg Diameter	5.0 in (0.417 ft)	30.0 in (2.5 ft)	× 6
Submerged Length (60%)	3.6 ft	21.6 ft	× 6
Leg Angle	45°	45°	Angle (no change)

Component

Model (1:6)

Full Scale (6:1)

Scaling Method

Triangle Platform (side)

10.0 ft

60.0 ft

× 6

Leg Length

6.0 ft

36.0 ft

× 6

Leg Diameter

5.0 in (0.417 ft)

30.0 in (2.5 ft)

× 6

Submerged Length (60%)

3.6 ft

21.6 ft

× 6

Leg Angle

45°

Angle (no change)

⚖️ Buoyancy Calculations

Model Scale (1:6)

Parameter	Value	Calculation
Leg Radius	0.2083 ft (2.5 in)	2.5/12 ft
Cross-sectional Area	0.1364 ft²	π × (0.2083)²
Submerged Volume (per leg)	0.491 ft³	0.1364 ft² × 3.6 ft
Total Displaced Volume (3 legs)	1.473 ft³	3 × 0.491 ft³
Mass of Water Displaced	2.93 slugs	94.25 lbs ÷ 32.174 ft/s²
Weight of Water Displaced	94.3 lbs	1.473 ft³ × 64 lbs/ft³

Parameter

Value

Calculation

Leg Radius

0.2083 ft (2.5 in)

2.5/12 ft

Cross-sectional Area

0.1364 ft²

π × (0.2083)²

Submerged Volume (per leg)

0.491 ft³

0.1364 ft² × 3.6 ft

Total Displaced Volume (3 legs)

1.473 ft³

3 × 0.491 ft³

Mass of Water Displaced

2.93 slugs

94.25 lbs ÷ 32.174 ft/s²

Weight of Water Displaced

94.3 lbs

1.473 ft³ × 64 lbs/ft³

Full Scale (6:1)

Values derived via Froude scaling (Weight × 216, Volume × 216) or direct calculation.

Parameter	Value	Calculation
Leg Radius	1.25 ft (15 in)	π × (1.25)²
Total Displaced Volume	318.1 ft³	3 × π × (1.25)² × 21.6
Mass of Water Displaced	632.7 slugs	20,358 lbs ÷ 32.174 ft/s²
Weight of Water Displaced	20,358 lbs	318.1 ft³ × 64 lbs/ft³
Metric Equivalent	~9,234 kg / 9.2 tonnes	20,358 × 0.4536

Parameter

Value

Calculation

Leg Radius

1.25 ft (15 in)

π × (1.25)²

Total Displaced Volume

318.1 ft³

3 × π × (1.25)² × 21.6

Mass of Water Displaced

632.7 slugs

20,358 lbs ÷ 32.174 ft/s²

Weight of Water Displaced

20,358 lbs

318.1 ft³ × 64 lbs/ft³

Metric Equivalent

~9,234 kg / 9.2 tonnes

20,358 × 0.4536

🎯 Target Weights (Design Buoyancy)

To maintain the designed 60% submergence line, the total structure weight must equal the displaced water weight:

Weight includes: Platform triangle + 3 legs + connection hardware + ropes + payload
Maximum payload capacity = Target Weight - Structure Self-Weight

⚠️ Important Assumptions:

Ropes: Guy wires/tethers connecting leg bottoms to adjacent triangle corners are excluded from buoyancy calculations due to unspecified diameters. If submerged, their additional buoyancy is negligible for steel/ synthetic ropes, but their weight must be included in the total weight budget.
Platform: Assumes the 10ft/60ft triangle platform is entirely above water and provides no buoyancy.
Leg Uniformity: Assumes legs are uniform cylinders with 60% of their total volume submerged.
Water Type: Calculations use seawater at 64 lbs/ft³. Fresh water (62.4 lbs/ft³) would reduce capacity by ~2.5%.

📊 Scaling Relationships Reference

Quantity	Scale Factor	Model → Full Scale
Length	λ	× 6
Area	λ²	× 36
Volume / Displacement	λ³	× 216
Time / Period	λ^(1/2)	× 2.45
Velocity	λ^(1/2)	× 2.45
Weight / Force	λ³	× 216

Quantity

Scale Factor

Model → Full Scale

Length

× 6

Area

λ²

× 36

Volume / Displacement

λ³

× 216

Time / Period

λ^(1/2)

× 2.45

Velocity

λ^(1/2)

× 2.45

Weight / Force

λ³

× 216

Seastead Engineering Analysis | Froude Scaling Applied | 1:6 Scale Model