# Seastead Trimaran - Froude Scale Model Calculations ```html Seastead Trimaran 1/10 Froude Scale Model Calculations

Seastead Trimaran — 1/10 Froude Scale Model

1. Scale Factor & Froude Scaling Rules

Linear scale ratio λ = 10 (full scale / model).

Quantity	Scale Factor (full / model)
Length	λ = 10
Area	λ² = 100
Volume / Weight / Displacement	λ³ = 1,000
Velocity	√λ = 3.1623
Time / Roll Period	√λ = 3.1623
Force (drag)	λ³ = 1,000
Power	λ^3.5 = 3,162.3

2. Dimensions

Item	Full Scale	1/10 Model (ft)	1/10 Model (in)
Triangle side (front-to-back)	80 ft	8.0 ft	96.0 in
Triangle back (side-to-side)	40 ft	4.0 ft	48.0 in
Leg total length (vertical)	19 ft	1.9 ft	22.8 in
Leg submerged length	9.5 ft	0.95 ft	11.4 in
Leg chord (NACA)	10 ft	1.0 ft	12.0 in
Leg width (thickness)	3 ft	0.3 ft	3.6 in

3. Foam per Model Leg (2 lb/ft³ expanded)

Approximate NACA airfoil cross-section area ≈ 0.685 × chord × thickness (typical for ~30% thick section).

Leg volume = 0.685 × 1.0 ft × 0.3 ft × 1.9 ft ≈ 0.390 ft³

Foam mass per leg = 0.390 ft³ × 2 lb/ft³ ≈ 0.781 lb

2-lb polyurethane pour foam is typically a 1:1 by volume mix of Part A (resin) and Part B (isocyanate). Liquid density ≈ 9.5 lb/gallon. Expansion ratio ≈ 1 volume liquid → ~25–30 volumes foam (use 25× to be safe).

Liquid volume needed = 0.390 ft³ / 25 = 0.0156 ft³ = 26.96 in³ ≈ 1.87 cups total

Mix Component	Per Leg (model)
Part A	~0.93 cups (~7.5 fl oz)
Part B	~0.93 cups (~7.5 fl oz)
Total mixed	~1.87 cups

Add ~15–20% extra to account for mold losses and variable rise. Always follow the specific A:B ratio on your product label.

4. Target Displacement / Weight (Caribbean Sea Water)

Caribbean seawater density ≈ 64.0 lb/ft³.

Submerged volume of all 3 legs (full scale):

V_full = 3 × 0.685 × 10 ft × 3 ft × 9.5 ft = 585.7 ft³

	Submerged Volume	Target Weight (buoyancy at 50% submersion)
Full Scale	585.7 ft³	~37,487 lb (~18.7 tons)
1/10 Model	0.5857 ft³	~37.49 lb

5. Tow Speed for Model (Simulating 5 knots full scale)

5 knots = 5 × 1.68781 ft/s = 8.439 ft/s

V_model = V_full / √λ = 8.439 / 3.1623

Tow the model at ~2.668 ft/s (~1.58 knots).

6. Model Drag (lbs) → Full-Scale Thruster Power (Watts)

Drag scales by λ³ = 1,000. Power = Force × Velocity.

Full-scale drag = F_model × 1,000 (lbf)
Full-scale velocity = 8.439 ft/s
Full-scale power (ft·lbf/s) = F_model × 1,000 × 8.439 = 8,439 × F_model
Convert ft·lbf/s → watts: × 1.35582

Watts_full = F_model (lb) × 8,439 × 1.35582

Constant ≈ 11,441 watts per lb of measured model drag.

Example: if the model drag sensor reads 0.5 lb, the full-scale thrust power required is ~5,720 W (~7.7 hp) at 5 knots. This is hydrodynamic (thrust) power — divide by thruster efficiency (typ. 0.5–0.7) to get electrical input.

7. Roll Period Scaling

Time scales with √λ.

T_full = T_model × √10

Multiply measured model roll period by ~3.162 to get full-scale roll period.

Summary of Key Constants

Conversion	Multiplier
Model tow speed (ft/s) for 5 knots full scale	2.668 ft/s
Model drag (lb) → Full-scale propulsion power (W) at 5 kt	× 11,441
Model roll period (s) → Full-scale roll period (s)	× 3.162
Model weight (lb) → Full-scale weight (lb)	× 1,000

``` ### Quick-reference summary - **Model leg dimensions:** 22.8 in long × 12 in chord × 3.6 in thick (NACA shape), 11.4 in submerged. - **Foam per leg:** ~0.93 cups Part A + ~0.93 cups Part B (1:1 mix, 2 lb/ft³ foam, ~25× expansion). Add ~15% waste factor. - **Target weight full scale:** ~37,500 lb in Caribbean seawater. - **Target weight model:** ~37.5 lb. - **Model tow speed:** 2.67 ft/s (simulates 5 kt full scale). - **Drag-to-power constant:** multiply model drag (lb) × **11,441** to get full-scale thrust power in watts. - **Roll period multiplier:** × **3.162** (=√10).