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Seastead Scale Model Calculations
Seastead Trimaran 1/10th Scale Model Specs
1. Scale Model Dimensions (1/10th Scale)
Applying a 1/10th scale factor (Scale = 0.1) to the full-scale dimensions.
| Component |
Full Scale (ft) |
Scale Model (ft) |
Scale Model (inches) |
| Big Triangle Frame |
| Side Length |
80 |
8.0 |
96.0 |
| Back (Base) Width |
40 |
4.0 |
48.0 |
| Buoyancy Legs (NACA Wing Shape) |
| Length |
19 |
1.9 |
22.8 |
| Chord |
10 |
1.0 |
12.0 |
| Width (Max Thickness) |
3 |
0.3 |
3.6 |
2. Foam Mix Volume per Leg
Calculating the volume of one scale model leg. For a standard symmetric NACA 4-digit airfoil, the cross-sectional area is approximately 0.685 × chord × width.
- Cross-sectional area (model) = 0.685 × 1.0 ft × 0.3 ft = 0.2055 sq ft
- Volume (model) = Area × Length = 0.2055 sq ft × 1.9 ft = 0.39045 cubic ft
- Expanded volume in cups: 0.39045 cu ft × 7.48 gal/cu ft × 16 cups/gal = 46.7 cups
- Mass of foam needed (2 lbs/cu ft): 0.39045 cu ft × 2 lbs/cu ft = 0.78 lbs
⚠️ Crucial Note on Pouring Volume: Two-part pour foams expand significantly. You do NOT pour 46 cups of liquid into the mold. The required amount of liquid mix depends entirely on your specific foam's expansion ratio (often listed as "yield" on the technical data sheet). A typical 2 lb density foam yields roughly 4 to 5 cubic feet per mixed gallon. Assuming a yield of 4.5 cu ft per gallon, to get 0.39 cu ft of expanded foam, you need roughly 0.78 cups of Part A and 0.78 cups of Part B (assuming a 1:1 volume mix ratio). Always consult your specific manufacturer's yield data and do a small test pour first!
3. Target Weights (Caribbean Sea Water)
Target weight equals the weight of displaced water (buoyancy). Since 50% of the leg is submerged, the total displaced volume is half the total volume of the 3 legs. Caribbean seawater density is approximated at 64.0 lbs/cubic-ft.
- Full-scale total leg volume (3 legs) = 3 × (0.685 × 10 × 3) × 19 = 1171.35 cu ft
- Full-scale submerged volume (50%) = 585.675 cu ft
- Scale model submerged volume = 585.675 / 1000 = 0.585675 cu ft
| Scale |
Displaced Volume |
Target Weight |
| Full Scale |
585.675 cu ft |
37,483 lbs |
| 1/10th Model |
0.585675 cu ft |
37.5 lbs |
To ensure proper hydrostatic behavior, configure your scale model's ballast so that it weighs exactly 37.5 lbs when placed in the water.
4. Towing Speed for 5 Knots
Speed scales by the square root of the scale factor (Froude number scaling). Full scale speed is 5 knots, which is 5 × 1.6878 = 8.439 ft/s.
Scale Model Towing Speed = 8.439 ft/s × √0.1 = 2.67 feet/second (or ~1.58 knots)
5. Drag-to-Watts Conversion Constant
To convert the drag force measured on the model (in lbs) to the electrical wattage required for the full-scale thrusters, we must scale the drag, calculate mechanical power, and convert to electrical power.
- Drag Scaling: At equivalent Froude numbers, drag scales by the cube of the scale factor. Drag_full = Drag_model × (1/0.1)³ = Drag_model × 1000
- Mechanical Power: Power_mech (Watts) = Force (lbs) × Speed (ft/s) × 1.3558
- Full-scale mechanical power = (Drag_model × 1000) × 8.439 × 1.3558 = Drag_model × 11,445.8
Therefore, the mechanical power constant is 11,446. To get electrical watts, you must divide by the thruster system's efficiency (η). Assuming a typical combined propeller/motor/controller efficiency of 50% (0.50):
Electrical Watts = Sensor Reading (lbs) × 11,446 ÷ Efficiency
Assuming 50% efficiency: Multiply lbs by 22,892
If your full-scale thrusters are highly efficient (e.g., 65%), your constant would be 11,446 / 0.65 = 17,609. Adjust the efficiency variable based on your actual hardware specs.
6. Roll Period Scaling
Natural roll period scales with the square root of the scale factor, just like speed and time in Froude scaling.
Full-scale roll period = Model roll period × 3.162 (which is 1 / √0.1)
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