This analysis compares different cross-sectional shapes for tensegrity seastead legs, each 30 feet long with a fixed volume for buoyancy. The base volume is derived from a cylinder of diameter 3.9 ft (volume ≈ 358.14 ft³, cross-sectional area ≈ 11.938 ft²). All shapes are designed to have the same cross-sectional area. Costs and weights are estimated for two materials: Duplex Stainless Steel and Marine Aluminum. Drag and power requirements are calculated for half-submerged legs at speeds of 1, 1.5, and 2 MPH.
| Shape | Width/Thickness (ft) | Chord/Length (ft) | Perimeter (ft) | Characteristic Width (ft) 1 | Estimated Drag Coefficient (Cd) 2 | Container Fit (legs per 40' container) 3 |
|---|---|---|---|---|---|---|
| Cylinder | Diameter: 3.90 | N/A (axisymmetric) | 12.25 | 3.90 | 1.20 | 3–4 |
| Stadium 4 | Thickness: 2.70 | Overall: 5.00 | 13.08 | 2.70 | 0.80 | 4 |
| Ellipse | Width: 3.26 | Chord: 4.66 | 12.53 | 3.26 | 0.70 | 3 |
| Lenticular | Thickness: 2.76 | Chord: 5.51 | 13.35 | 2.76 | 0.60 | 3 |
| Ovate | Width: 3.29 | Chord: 4.62 | 12.51 | 3.29 | 0.70 | 3 |
| Kamm-Tail Teardrop | Width: 3.10 | Chord: 4.90 | 12.73 | 3.10 | 0.50 | 3 |
1 Characteristic width is the maximum dimension perpendicular to flow when the shape is oriented with its chord along the flow direction (for non-circular shapes). For the cylinder, it is the diameter.
2 Cd values are rough estimates for cross-flow (perpendicular to the long axis) based on shape bluffness.
3 Container interior dimensions: 40 ft long × 7.8 ft wide × 7.10 ft high. Legs are placed parallel to the length. Estimates assume optimal packing.
4 Stadium shape: rectangle (width T=2.70 ft, length C=2.30 ft) with semi-circles of diameter T on the ends, giving overall length C+T=5.00 ft.
Wall thickness assumed: 0.5 inches (0.04167 ft). Densities: Duplex Stainless Steel = 500 lb/ft³, Marine Aluminum = 170 lb/ft³. Cost estimates: Duplex = $2.50/lb, Marine Aluminum = $1.50/lb.
| Shape | Metal Volume (ft³) | Duplex Weight (lb) | Duplex Cost ($) | Marine Alu Weight (lb) | Marine Alu Cost ($) |
|---|---|---|---|---|---|
| Cylinder | 15.31 | 7,656 | 19,141 | 2,603 | 3,905 |
| Stadium | 16.35 | 8,176 | 20,440 | 2,780 | 4,170 |
| Ellipse | 15.66 | 7,830 | 19,575 | 2,662 | 3,993 |
| Lenticular | 16.69 | 8,345 | 20,863 | 2,837 | 4,256 |
| Ovate | 15.64 | 7,820 | 19,550 | 2,659 | 3,988 |
| Kamm-Tail Teardrop | 15.91 | 7,955 | 19,888 | 2,705 | 4,057 |
Assumptions: half of the 30 ft leg submerged (15 ft), seawater density = 1.99 slugs/ft³. Drag force: FD = 0.5 × ρ × v² × Cd × submerged length × characteristic width. Power: P = FD × v (converted to watts).
| Shape | Drag at 1 MPH (lb) | Drag at 1.5 MPH (lb) | Drag at 2 MPH (lb) | Power/leg at 1 MPH (W) | Power/leg at 1.5 MPH (W) | Power/leg at 2 MPH (W) |
|---|---|---|---|---|---|---|
| Cylinder | 150.2 | 338.1 | 600.9 | 299 | 1,009 | 2,389 |
| Stadium | 69.3 | 156.0 | 277.3 | 138 | 466 | 1,102 |
| Ellipse | 73.3 | 164.8 | 293.0 | 146 | 492 | 1,165 |
| Lenticular | 53.2 | 119.6 | 212.6 | 106 | 357 | 845 |
| Ovate | 73.9 | 166.3 | 295.5 | 147 | 496 | 1,175 |
| Kamm-Tail Teardrop | 49.8 | 112.0 | 199.0 | 99 | 334 | 791 |
| Shape | Total Power at 1 MPH (W) | Total Power at 1.5 MPH (W) | Total Power at 2 MPH (W) |
|---|---|---|---|
| Cylinder | 1,195 | 4,034 | 9,554 |
| Stadium | 552 | 1,862 | 4,410 |
| Ellipse | 582 | 1,966 | 4,659 |
| Lenticular | 423 | 1,427 | 3,380 |
| Ovate | 588 | 1,984 | 4,698 |
| Kamm-Tail Teardrop | 396 | 1,336 | 3,164 |
Applying a small internal pressure (e.g., 10 PSI) can enhance buckling resistance and facilitate leak detection. This approach is feasible for all shapes, provided the walls can withstand the pressure. For thin-walled vessels, hoop stress scales with radius and inversely with wall thickness. Shapes with continuous curvature (cylinder, ellipse, lenticular, ovate, Kamm-Tail) distribute pressure more evenly. The stadium shape, with its straight sections, may experience higher bending stresses but can still be designed to handle the pressure. Internal pressure introduces tensile stresses that counteract external compressive loads, improving buckling strength. Additionally, any leak would cause a pressure drop, allowing for easy detection.
The Kamm-Tail Teardrop shape offers the best hydrodynamic performance, with the lowest drag and power requirements, while maintaining similar weight and cost to other shapes. The stadium shape allows for the highest container packing density (4 legs per container). All shapes have comparable material costs, with Duplex Stainless Steel being approximately 5 times more expensive than Marine Aluminum for the same design. The cylinder, while simple to manufacture, has the highest drag. Internal pressure is a viable strategy for all shapes to improve buckling resistance and leak detection. The final choice should balance hydrodynamic efficiency, manufacturing complexity, and container logistics based on the project's priorities.