Seastead Trimaran: 1/10 Scale Froude Model Calculations
Scale Factor (\u03bb): 10 (Model is 1/10th Linear Scale)
Seawater Density (\u03c1g): 64.0 lbs/ft\u00b3 (Caribbean)
Froude Scaling Laws Used: Length \u221d \u03bb, Area \u221d \u03bb\u00b2, Volume/Force \u221d \u03bb\u00b3, Time/Period \u221d \u221a\u03bb, Power \u221d \u03bb\u00b3\u2085.
1. Principal Dimensions
Full Scale (Prototype)
| Parameter | Value (ft) | Value (in) |
|---|
| Triangle Side Length (Front-Back) | 80.0 | 960 |
| Triangle Base Width (Side-Side) | 40.0 | 480 |
| Leg/Wing Length (Span) | 19.0 | 228 |
| Leg Chord | 10.0 | 120 |
| Leg Max Thickness (Width) | 3.0 | 36 |
| Submerged Leg Length (50%) | 9.5 | 114 |
1/10 Scale Model
| Parameter | Value (ft) | Value (in) |
|---|
| Triangle Side Length | 8.0 | 96.0 |
| Triangle Base Width | 4.0 | 48.0 |
| Leg/Wing Length (Span) | 1.9 | 22.8 |
| Leg Chord | 1.0 | 12.0 |
| Leg Max Thickness | 0.3 | 3.6 |
| Submerged Leg Length (50%) | 0.95 | 11.4 |
2. Foam Quantity for One Scale Leg (Batch Mix)
Assumptions: NACA Wing Volume approximated as Rectangular Box \u00d7 Form Factor (K=0.80). Standard 2-part pour foam (2 lbs/ft\u00b3 expanded). Mixed liquid density estimated at 65 lbs/ft\u00b3. Mix Ratio 1:1 by Volume (Part A : Part B).
Model Leg Volume = Length \u00d7 Chord \u00d7 Thickness \u00d7 K
= 1.9 ft \u00d7 1.0 ft \u00d7 0.3 ft \u00d7 0.80 = 0.456 ft\u00b3
Target Foam Weight = Volume \u00d7 Density = 0.456 ft\u00b3 \u00d7 2.0 lbs/ft\u00b3 = 0.912 lbs
Mixed Liquid Volume = Weight / Liquid Density = 0.912 lbs / 65 lbs/ft\u00b3 = 0.01403 ft\u00b3
Total Mixed Cups = 0.01403 ft\u00b3 \u00d7 119.69 cups/ft\u00b3 = 1.679 cups (Total Mix)
Per Batch (One Leg):
Part A (Resin/ISO): 0.84 cups (approx 6.7 fl oz / 198 ml)
Part B (Polyol/RES): 0.84 cups (approx 6.7 fl oz / 198 ml)
Total Mixed Volume: ~1.68 cups (13.4 fl oz)
Critical: Verify your specific foam system's mixed liquid density (SDS/TDS) and mix ratio (weight vs volume). Weigh components if possible for accuracy. Mix slightly extra (5-10%) for waste/headspace.
3. Target Weight (Displacement / Buoyancy)
Full Scale
Submerged Vol / Leg = SubLength \u00d7 Chord \u00d7 Thickness \u00d7 K = 9.5 \u00d7 10 \u00d7 3 \u00d7 0.8 = 228 ft\u00b3
Total Submerged Vol (3 Legs) = 684 ft\u00b3
Displacement = 684 ft\u00b3 \u00d7 64 lbs/ft\u00b3 = 43,776 lbs
Full Scale Target Weight (Displacement): 43,776 lbs (~19.5 Long Tons)
1/10 Scale Model
Model Sub Vol / Leg = 228 ft\u00b3 / 1000 (\u03bb\u00b3) = 0.228 ft\u00b3
Total Model Sub Vol = 0.684 ft\u00b3
Model Displacement = 0.684 ft\u00b3 \u00d7 64 lbs/ft\u00b3 = 43.78 lbs
Model Target Weight (Displacement): 43.78 lbs
Model Weight Budget:
3 Legs Foam Weight: 3 \u00d7 0.912 lbs = 2.74 lbs
Allowable Weight for Frame, Deck, Ballast, Sensors: 43.78 - 2.74 = ~41.0 lbs
4. Towing Speed for 5 Knots Full Scale (Froude Scaling)
Vfull = 5 kts = 5 \u00d7 1.68781 = 8