Seastead Scale Model Calculations

Part 1: Mold Volume and Foam Requirements

Geometry Assumptions

Length: 3.5 feet = 42 inches.
Cross-Section: A semicircle (PVC nose) attached to a triangle (plywood sides meeting at the tail).
Width (Thickness): The inside span of the PVC is 3.75 inches, giving a radius (R) of 1.875 inches.
Chord (Depth): The plywood is 16 inches wide. We assume this forms the side of the triangle from the PVC edge to the trailing point.

Volume Calculation

We calculate the cross-sectional area as the sum of the semicircle and the triangle formed by the plywood.

Area of Semicircle: 0.5 × π × R² ≈ 5.52 in²
Area of Triangle: 0.5 × Base × Height.
Using triangle geometry (Sides = 16", Base = 3.75"), Height ≈ 15.89".
Area ≈ 29.79 in²
Total Cross-Section Area: ≈ 35.31 in²

Total Volume: Area × Length = 35.31 in² × 42" = 1483 cubic inches.

Foam Mix Requirements

Total Volume: 0.86 ft³ (approx 6.4 gallons).

Using a standard 2 lb density foam:

Total Weight Needed: Volume (0.86 ft³) × Density (2 lb/ft³) ≈ 1.72 lbs.
Total Liquid Volume: Assuming a specific gravity of ~1.2 for liquid resin, the liquid volume is approx 2.75 cups.

Recommendation: Mix 1.5 cups of Part A and 1.5 cups of Part B (Total 3 cups). This provides a ~10% safety margin to ensure the mold fills completely despite any irregularities.

Part 2: Model Weight (Buoyancy)

We assume the model is ballasted to sit at 50% submergence.

Volume per leg: 1483 in³
Submerged Volume (per leg): 50% = 741.5 in³
Total Submerged Volume (3 legs): 2,224.5 in³ ≈ 1.29 ft³
Seawater Density: 64 lb/ft³

Total Model Weight:
1.29 ft³ × 64 lb/ft³ = 82.5 lbs.

Note: This includes the structure, living area, ballast, and the foam itself. The foam alone (3 legs × 1.7 lbs) weighs only ~5.1 lbs.

Part 3: Full Scale Specifications (1:6 Scale)

1. Full Scale Dimensions

Scaling Factor (λ) = 6.

Dimension	Model (1:6)	Full Scale
Height (Length)	3.5 ft (42")	21.0 ft
Chord (Width)	~16"	8.0 ft (approx)
Thickness	3.75"	1.9 ft (22.5")

2. Full Scale Displacement

Froude scaling laws state that displacement (weight) scales by the cube of the linear ratio (λ³).

Scale Factor Cubed: 6³ = 216
Model Displacement: 82.5 lbs

Full Scale Mass per Leg:
(82.5 lbs / 3 legs) × 216 = 5,940 lbs per leg.

Total Full Scale Mass:
82.5 lbs × 216 = 17,820 lbs.

3. Full Scale Thrust Requirements

Thrust scales by λ³ (same as displacement) if we are matching Froude number speeds, but here we are evaluating specific speeds (1, 2, 3 MPH). The drag is estimated using a streamlined strut formula including skin friction and form drag.

Speed (MPH)	Speed (ft/s)	Estimated Drag (lbs)
1 MPH	1.47 ft/s	~8 lbs
2 MPH	2.93 ft/s	~31 lbs
3 MPH	4.40 ft/s	~70 lbs

Note: Drag scales with velocity squared. At low speeds, skin friction dominates.

4. Full Scale Power Requirements

We calculate mechanical power needed (Drag × Velocity) and estimate electrical power assuming a propulsive efficiency of ~50% (standard for small motor/propeller setups).

Speed	Mechanical HP	Mechanical Watts	Est. Electrical Watts
1 MPH	0.02 HP	16 W	~32 W
2 MPH	0.17 HP	126 W	~250 W
3 MPH	0.56 HP	420 W	~840 W

Motor Sizing Summary:

For station-keeping (drifting or slow maneuvering): A single 500W (0.67 HP) motor would easily move the structure at 2-3 MPH.
For redundancy and efficiency, two 300W motors (like standard trolling motors) would be ideal for a structure of this scale.

Assumptions Notes

Shape: The "wing" cross-section is modeled as a semi-circle + triangle wedge. The "long way up and down" confirms the vertical strut orientation.
Density: Seawater is assumed to be 64 lbs/ft³ (1025 kg/m³).
Scaling: Froude number scaling is used for displacement. Drag forces are calculated directly for full-scale velocities, considering the wetted surface area of 3 submerged struts.

Seastead Scale Model & Full Scale Analysis