Funny Trimaran Seastead — 1/10 Froude Scale Model

Scale factor λ = 10 (every full-scale length ÷ 10). Seawater (Caribbean, ≈1025 kg/m³) = 64.0 lb/ft³ for both model and full scale.

Key results at a glance

Model tow speed: 2.67 ft/s (simulates 5 kn full scale)
Drag → power constant: Watts_hydro = 11,440 × (lbs on model). Electrical watts = 11,440 × lbs ÷ η_drive
Target all-up weight: ≈ 37,500 lb full scale; 37.5 lb model (add ~35 lb ballast to model)
Foam per leg batch: ≈ 0.7 cups Part A + 0.7 cups Part B (test-pour to confirm)
Roll period: T_full = 3.162 × T_model

1 · Dimensions

Item	Full scale (ft)	Model (ft)	Model (inches)
Triangle side (front-to-back), each of 2	80	8.0	96
Triangle base (back, side-to-side)	40	4.0	48
Triangle height (apex-to-base centerline)	77.5	7.75	93
Leg length	19	1.9	22.8
Leg chord (NACA section)	10	1.0	12
Leg thickness / width (NACA section)	3	0.3	3.6
Draft (submerged half of leg)	9.5	0.95	11.4

2 · Buoyancy & Target Weight

Cross-sectional area of a NACA 4-digit symmetric section ≈ 0.685 × chord × max thickness.

Leg volume (full scale) = 0.685 × 10 ft × 3 ft × 19 ft = 390.45 ft³ per leg Submerged (50%) per leg = 195.2 ft³ Total submerged, 3 legs = 585.7 ft³ Target weight = 585.7 ft³ × 64.0 lb/ft³ = 37,483 lb ≈ 37,500 lb Model (÷1000 in volume): 0.586 ft³ × 64.0 = 37.5 lb

	Full scale	Model (1/10)
Displaced volume (3 legs @ 50%)	585.7 ft³	0.586 ft³
Target all-up weight (floats at 50% draft)	≈ 37,500 lb	37.5 lb
Contributed by foam legs (model)	—	2.34 lb
Ballast + structure still needed (model)	—	≈ 35.1 lb

The 37,500 lb figure is the total allowable weight (frame, deck, systems, ballast) for the full-scale boat to sit with legs half-submerged. Likewise the model needs ~35 lb of added ballast beyond the foam.

3 · Foam Batches (one batch = one leg, same mold ×3)

Finished foam per leg = 0.390 ft³ (≈ 46.7 cups of expanded foam) Finished foam mass = 0.390 ft³ × 2 lb/ft³ = 0.78 lb per leg (2.34 lb for all 3) Mass is conserved through expansion → weigh 0.78 lb of mixed liquid per batch. Typical 2-lb PU foam expands ~30–36×; at 1:1 by volume that is:

Component (per batch / per leg)	Nominal	Practical range
Part A	0.7 cups (5.6 fl oz)	0.6 – 0.8 cups
Part B	0.7 cups (5.6 fl oz)	0.6 – 0.8 cups
Total mixed liquid (all 3 legs)	≈ 2.1 cups each part	1.8 – 2.4 cups each

Do one test pour first. Expansion varies with temperature, mix ratio, and mold confinement. The reliable target is 0.78 lb of mixed liquid per batch; adjust cup counts until the finished leg comes out full and ≈0.78 lb. If your foam's datasheet states a yield (e.g., "1 qt makes X ft³"), scale from that instead.

4 · Tow Speed (Froude scaling: speed ÷ √λ)

V(full) = 5 kn = 8.439 ft/s V(model) = 8.439 ÷ √10 = 2.67 ft/s ( = 1.58 kn = 0.81 m/s = 1.82 mph )

5 · Model Drag (lbs) → Full-Scale Thruster Power (watts)

Froude force scaling: F(full) = λ³ × F(model) = 1000 × F(model) P(full) = F(full) × V(full) × 1.3558 W/(ft·lbf/s) = 1000 × 8.439 × 1.3558 × F(model) ➜ P(hydro) [W] = 11,440 × F(model) [lbf] Electrical input to thrusters: ➜ P(elec) [W] = 11,440 × F(model) ÷ η(drive)

Drive/train efficiency η	Constant (W per model-lbf)
0.50	22,900
0.55	20,800
0.60 (typical thruster)	19,100
0.65	17,600
0.70	16,300

Example: model tows at 2.67 ft/s and the load cell reads 0.50 lbf → full-scale resistance = 500 lbf → hydrodynamic power = 5,720 W (7.7 hp) → at 60% drive efficiency, ≈ 9,530 W electrical.

Rule of thumb: every 0.1 lbf on the model ≈ 1,144 W hydrodynamic ≈ 1,900 W electrical at 60% efficiency.

6 · Roll Period Scaling

T(full) = √10 × T(model) = 3.162 × T(model) Example: model rolls at 1.2 s → full scale ≈ 3.8 s

7 · Assumptions & Practical Notes

Legs treated as prismatic NACA 4-digit symmetric sections: area = 0.685 × chord × thickness. If your molded shape differs, recompute leg volume and everything downstream scales with it.
Even keel, 50% of each leg submerged at rest; the above-water triangle frame adds no buoyancy.
Seawater taken as 64.0 lb/ft³ (≈1025 kg/m³) for both model and full scale.
Froude laws used: length λ, speed λ^½, force/displacement λ³, power λ^3.5, periods λ^½.
The 11,440 constant ignores viscous scale effects (model Reynolds number is ~31.6× smaller, so the model's skin friction is proportionally larger). Your measured lbs will read slightly high, making the predicted full-scale power mildly conservative — fine for sizing thrusters.
For cleaner flow separation behavior, trip the model legs with a thin wire or grit strip near the leading edge.