Seastead Leg Shape Comparison

Tensegrity Seastead – Leg Shape Trade‑off

Assumptions (all figures are order‑of‑magnitude estimates):

Leg length = 30 ft (≈ 9.1 m). Half of the leg (15 ft) is submerged when the platform is at the waterline.
Required buoyancy ≈ 358 ft³ (≈ 22 900 lb) per leg – i.e. the same volume as the original 3.9 ft‑diameter cylinder.
Shell thickness = 5 mm (≈ 0.016 ft) for both stainless steel and marine‑grade aluminium. Adding the “hard‑point” end caps adds ≈ 10 % to the weight.
Density: stainless‑steel (duplex) ≈ 490 lb/ft³, marine‑aluminium (5083) ≈ 168 lb/ft³.
Material cost in the Far East: ≈ $2.5 /lb for duplex stainless, ≈ $1.2 /lb for aluminium. Fabrication + labour ≈ $500 (steel) or $400 (Al), plus $200 for end‑hardware.
Drag coefficients (Cd) are approximate for a smooth surface at the low Reynolds numbers encountered (1–2 mph). Skin‑friction coefficient Cf ≈ 0.003.
Power = total drag × velocity, assuming 100 % propulsion efficiency (real world you would need 1.5–2× more).

1. Geometry, Weight & Cost (per leg)

Shape	Width (flow direction) W (ft)	Thickness (ft)	Perimeter P (ft)	Weight – Duplex SS (lb)	Weight – Al 5083 (lb)	Cost – Duplex SS (US$)	Cost – Al 5083 (US$)	Legs per 40 ft container*
Cylinder (baseline)	3.90	3.90	12.25	3 170	1 090	≈ $8 600	≈ $1 900	4
Airfoil (thick wing)	5.00	3.70	13.70	3 540	1 220	≈ $9 600	≈ $2 100	2
Stadium (rectangle + semicircles)	4.62	3.00	12.66	3 280	1 120	≈ $8 900	≈ $1 950	4
Ellipse	5.07	3.00	12.90	3 340	1 140	≈ $9 000	≈ $1 970	2
Lenticular (lens)	6.50	3.00	≈ 14.0	3 620	1 240	≈ $9 800	≈ $2 100	2
Ovate (egg‑shaped)	5.00	3.00	≈ 13.0	3 360	1 150	≈ $9 100	≈ $2 000	2
Kamm‑Tail Teardrop	5.39	3.41	≈ 14.0	3 620	1 240	≈ $9 800	≈ $2 100	2
Streamlined “other” (very thin)	4.50	2.80	≈ 13.0	3 360	1 150	≈ $9 100	≈ $2 000	2

Shape
Width (flow direction) W (ft)
Thickness (ft)
Perimeter P (ft)
Weight – Duplex SS (lb)
Weight – Al 5083 (lb)
Cost – Duplex SS (US$)
Cost – Al 5083 (US$)
Legs per 40 ft container*

Cylinder (baseline)
3.90
3.90
12.25
3 170
1 090
≈ $8 600
≈ $1 900
4

Airfoil (thick wing)
5.00
3.70
13.70
3 540
1 220
≈ $9 600
≈ $2 100
2

Stadium (rectangle + semicircles)
4.62
3.00
12.66
3 280
1 120
≈ $8 900
≈ $1 950
4

Ellipse
5.07
3.00
12.90
3 340
1 140
≈ $9 000
≈ $1 970
2

Lenticular (lens)
6.50
3.00
≈ 14.0
3 620
1 240
≈ $9 800
≈ $2 100
2

Ovate (egg‑shaped)
5.00
3.00
≈ 13.0
3 360
1 150
≈ $9 100
≈ $2 000
2

Kamm‑Tail Teardrop
5.39
3.41
≈ 14.0
3 620
1 240
≈ $9 800
≈ $2 100
2

Streamlined “other” (very thin)
4.50
2.80
≈ 13.0
3 360
1 150
≈ $9 100
≈ $2 000
2

*Number that can be shipped in a standard 40 ft (12.2 m) container – assumes legs are laid horizontally, width ≤ 4.5 ft can be packed 2 across the container width and 2 high (4 total); wider shapes are limited to 1‑across and 2‑high (2 total). Exact packing will depend on the final orientation you choose.

2. Hydrodynamic Drag (half‑submerged leg, 15 ft underwater)

Drag per leg = V² · L_sub · (Cd·W + Cf·P) with L_sub=15 ft, Cf≈0.003, ρ≈2 slug ft⁻³ (seawater). V in ft s⁻¹ (1 mph ≈ 1.467 ft s⁻¹). Values are rounded.

2.1 Speed = 1 mph (1.47 ft s⁻¹)

Shape	Drag / leg (lb)	Drag 4 legs (lb)	Required elec. power (W)
Cylinder	115	458	≈ 910 W
Airfoil	34	134	≈ 270 W
Stadium	53	214	≈ 425 W
Ellipse	34	136	≈ 270 W
Lenticular	43	173	≈ 345 W
Ovate	42	166	≈ 330 W
Kamm‑Tail	40	158	≈ 315 W
Other	23	92	≈ 185 W

Shape
Drag / leg (lb)
Drag 4 legs (lb)
Required elec. power (W)
Cylinder115458≈ 910 W
Airfoil34134≈ 270 W
Stadium53214≈ 425 W
Ellipse34136≈ 270 W
Lenticular43173≈ 345 W
Ovate42166≈ 330 W
Kamm‑Tail40158≈ 315 W
Other2392≈ 185 W

2.2 Speed = 1.5 mph (2.20 ft s⁻¹)

Shape	Drag / leg (lb)	Drag 4 legs (lb)	Required elec. power (W)
Cylinder	258	1 030	≈ 3 070 W
Airfoil	76	302	≈ 900 W
Stadium	120	481	≈ 1 430 W
Ellipse	77	306	≈ 910 W
Lenticular	97	390	≈ 1 160 W
Ovate	94	374	≈ 1 115 W
Kamm‑Tail	89	357	≈ 1 060 W
Other	52	207	≈ 620 W

Shape
Drag / leg (lb)
Drag 4 legs (lb)
Required elec. power (W)
Cylinder2581 030≈ 3 070 W
Airfoil76302≈ 900 W
Stadium120481≈ 1 430 W
Ellipse77306≈ 910 W
Lenticular97390≈ 1 160 W
Ovate94374≈ 1 115 W
Kamm‑Tail89357≈ 1 060 W
Other52207≈ 620 W

2.3 Speed = 2 mph (2.93 ft s⁻¹)

Shape	Drag / leg (lb)	Drag 4 legs (lb)	Required elec. power (W)
Cylinder	458	1 832	≈ 7 300 W
Airfoil	134	538	≈ 2 140 W
Stadium	214	854	≈ 3 400 W
Ellipse	136	544	≈ 2 160 W
Lenticular	173	693	≈ 2 750 W
Ovate	167	666	≈ 2 650 W
Kamm‑Tail	159	634	≈ 2 520 W
Other	92	368	≈ 1 470 W

Shape
Drag / leg (lb)
Drag 4 legs (lb)
Required elec. power (W)
Cylinder4581 832≈ 7 300 W
Airfoil134538≈ 2 140 W
Stadium214854≈ 3 400 W
Ellipse136544≈ 2 160 W
Lenticular173693≈ 2 750 W
Ovate167666≈ 2 650 W
Kamm‑Tail159634≈ 2 520 W
Other92368≈ 1 470 W

3. Internal Pressure (≈ 10 psi)

Applying a modest internal pressure (≈ 10 psi) to a thin‑walled leg raises the hoop stress σ_hoop=p·r/t. With a radius ≈ 2 ft and a 5 mm wall (t ≈ 0.016 ft) the hoop stress is only about 1 250 psi – far below the yield of both duplex stainless (≈ 50 ksi) and marine‑aluminium (≈ 30 ksi). The pressure therefore helps resist buckling and also provides a simple leak‑detection method. The same principle works for any closed‑section shape (cylinder, ellipse, lenticular, etc.). Sharp‑edged profiles (e.g., a very thin airfoil) can have stress concentrations at the leading/trailing edge, but a modest pressure is still tolerable; just ensure the wall thickness is uniform.

4. Summary & Recommendations

Use the tables above to pick the shape that best balances hydrodynamic efficiency, manufacturing cost, weight, and shipping constraints for your specific seastead design.

Tensegrity Seastead – Leg Shape Trade‑off

1. Geometry, Weight & Cost (per leg)

2. Hydrodynamic Drag (half‑submerged leg, 15 ft underwater)

2.1 Speed = 1 mph (1.47 ft s⁻¹)

2.2 Speed = 1.5 mph (2.20 ft s⁻¹)