Seastead Tensegrity Model Scaling Report
This document outlines the Froude scaling calculations for a semi-submersible seastead model based on a 5-inch diameter leg constraint.
1. Scale Ratio Determination
The scale ratio is derived from the leg diameter, as this is the fixed constraint for the model materials.
- Full Scale Leg Diameter: 4 feet = 48 inches
- Model Leg Diameter: 5 inches
- Scale Ratio (λ): 48 / 5 = 9.6
Result: 1 Inch on the Model = 9.6 Inches on the Full Scale Vessel.
2. Model Dimensions (Geometric Scaling)
All linear dimensions are divided by the scale ratio (9.6). Angles (45°) remain unchanged.
| Component |
Full Scale (ft/in) |
Model Scale (inches) |
| Body Length |
60 ft (720 in) |
75.0 in |
| Body Width |
14 ft (168 in) |
17.5 in |
| Body Height |
8 ft (96 in) |
10.0 in |
| Leg Diameter |
4 ft (48 in) |
5.0 in (Fixed) |
| Leg Length |
35 ft (420 in) |
43.75 in |
| Leg Submergence |
60% (21 ft) |
60% (26.25 in) |
3. 55-Gallon Barrel Body Analysis
You proposed using two 55-gallon plastic barrels connected end-to-end for the model body. Below is the analysis of what this represents in Full Scale and the weight implications.
Barrel Specifications (Nominal)
- Single Barrel Length: ~34.5 inches
- Single Barrel Diameter: ~22.5 inches
- Two Barrels (End-to-End) Length: ~69.0 inches
Full Scale Equivalents
Using the scale ratio of 9.6, here is what the barrel body represents in the real-world design:
| Dimension |
Model (Barrels) |
Represented Full Scale |
Original Design Goal |
| Length |
69.0 in |
55.2 ft |
60.0 ft |
| Width/Height |
22.5 in |
18.0 ft |
14.0 ft / 8.0 ft |
Design Note: The barrels represent a full-scale body that is slightly shorter (55' vs 60') but significantly wider/taller (18' vs 14') than your original design. This increases windage and weight in the model relative to the scaled leg design.
4. Weight and Buoyancy (Froude Scaling)
For Froude scaling to be valid for hydrostatics and wave interaction, mass must scale by the cube of the length ratio (λ³).
- Scale Factor for Weight: 9.6³ = 884.7
Estimated Displacement
Based on the submerged volume of the 4 legs at 60% submergence (assuming the body stays dry):
- Full Scale Leg Buoyancy: ~67,500 lbs (Saltwater)
- Target Model Total Weight: 67,500 / 884.7 ≈ 76.3 lbs
Model Weight Budget
To achieve the correct 60% leg submergence, your model must weigh approximately 76 lbs.
| Component |
Estimated Weight |
Notes |
| 2 Plastic Barrels |
~45 - 50 lbs |
Empty standard drums |
| 4 Leg Cylinders |
~15 - 20 lbs |
Assuming 5" PVC, sealed ends |
| Cables & Hardware |
~5 lbs |
Steel cable, turnbuckles |
| Current Total |
~65 - 75 lbs |
Very close to target! |
| Required Ballast |
~1 - 10 lbs |
Add inside body to tune waterline |
Good News: The weight of two empty 55-gallon barrels plus PVC legs happens to align very well with the Froude scaled weight requirement of 76 lbs. You will likely only need minor ballast adjustments.
5. Cable Geometry for Model
The cables maintain the tensegrity structure. Their lengths must be scaled linearly.
- Bottom Triangle Cables (Front & Back):
- Full Scale Span: The legs angle out at 45°. Horizontal spread per leg = 35ft × sin(45°) ≈ 24.75 ft.
- Distance between leg tips (Front or Back): Depends on body width + spread. Approx 50 ft Full Scale.
- Model Cable Length: Approx 62 inches (Verify during assembly based on exact attachment points).
- Vertical Tension Cables (Leg Tip to Body Center):
- Full Scale Length: Approx 35 ft (vertical component).
- Model Cable Length: Approx 43.75 inches.
6. Dynamic Testing Note (Velocity)
If you plan to tow this model to test wave resistance or stability under motion, Froude scaling applies to speed as well.
- Velocity Scale: &sqrt;λ = &sqrt;9.6 ≈ 3.1
- Rule: 1 knot in the Model = 3.1 knots in Full Scale.
- Time: 1 second in the Model = 3.1 seconds in Full Scale.