```html Tensegrity Seastead Leg Shape Trade Study (Rough Order Estimates)

30 ft Tensegrity Seastead Legs — Shape/Cost/Drag Estimates (Duplex SS vs Marine Aluminum)

Important: This is a concept-level / rough-order-of-magnitude estimate using generic hydrodynamic coefficients and simplified structural assumptions. It is not a design you can build from without a naval architect + structural engineer, welding procedure specs (WPS), fatigue design, and (if applicable) class rules (DNV/ABS/etc.).

1) Baseline inputs & assumptions

Geometry & buoyancy basis

Leg length: 30 ft (9.144 m)
Baseline cylinder diameter: 3.9 ft (1.189 m)
All alternative shapes assumed to have the same internal displaced volume as the baseline cylinder.
Cross-sectional area (constant across shapes):
Acs = π (D/2)^2 = 11.94 ft² = 1.109 m²
Total displacement volume per leg:
V = Acs · L = 358 ft³ = 10.15 m³ (≈ 10.4 t buoyancy in seawater if fully submerged)
Drag calcs assume half the leg is submerged: submerged length 15 ft (4.572 m)

Hydrodynamics model (simplified)

Seawater density: ρ = 1025 kg/m³
Speeds: 1.0 / 1.5 / 2.0 mph = 0.447 / 0.671 / 0.894 m/s
Drag equation (per leg): F = 0.5 ρ V² Cd Aproj
Reference/projected area used: Aproj = (submerged length) × (max thickness/width)
Cd values are representative of clean sections at Re ~ 5e5–1e6, aligned to minimize drag (i.e., “streamlined axis” facing into flow where applicable). Fouling and yaw misalignment can increase drag substantially.

Power model (legs only): Mechanical towing power Pmech = F · V. Estimated electrical input for propulsion to overcome leg drag only: Pelec ≈ Pmech / η with overall efficiency η = 0.55 (illustrative: propulsor ~0.6 × motor/controller ~0.9).

Structure/weight/cost model (very approximate)

Assumed shell thickness baseline:
- Duplex SS (e.g., 2205): t = 4 mm
- Marine aluminum (e.g., 5083/5086): t = 6 mm
These are placeholders; real thickness will be driven by dents, fatigue, hardpoint loads, handling, and global bending.
Includes end closures + local stiffening allowance: +10% mass
Densities: duplex ~8000 kg/m³, aluminum ~2700 kg/m³
Fabricated cost basis (Asia, rough): includes plate/extrusion, forming, welding, NDT, basic coatings/finish, but excludes freight/duties/QA oversight on your side.
- Duplex fabricated: $11.5/kg (typical band $9–$14/kg)
- Marine aluminum fabricated: $9/kg (typical band $7–$11/kg)
Shape complexity multipliers applied to account for extra forming, jigs, weld seams, and QC.

2) Candidate shapes & assumed bounding dimensions (same volume)

Dimensions below are chosen to keep the same cross-sectional area as the 3.9 ft cylinder, while being more streamlined. “Width” = thickness normal to flow (used for projected area). “Chord/length” = streamlined dimension.

Shape	Assumed cross-section dimensions (ft)	Max width (ft)	Projected area Aproj (m²) (15 ft submerged)	Relative perimeter (≈ weight scaling)	Assumed Cd (aligned, clean)	Notes
1) Cylinder	D = 3.9	3.90	5.43	1.00	1.10	Bluff body in crossflow.
2) “Airfoil-like” streamlined section	Bounding box ≈ 5.0 (chord) × 3.04 (thickness)	3.04	4.24	1.10	0.08	Represents a thick symmetric foil; actual Cd depends strongly on nose radius, tail thickness, and yaw.
3) Stadium (capsule)	Chord ≈ 4.62 × width 3.00	3.00	4.18	1.03	0.25	Simple to fabricate from rolled plate + flats; still fairly bluff at the “rear” unless tapered.
4) Ellipse	Major axis 5.0 × minor axis 3.04	3.04	4.24	1.05	0.15	Good compromise; ends are rounded both sides (not a sharp tail).
5) Lenticular (biconvex lens)	Approx bounding 5.2 × 2.92	2.92	4.07	1.05	0.10	More streamlined than ellipse; harder to form consistently without dedicated tooling.
6) Ovate (egg-ish)	Approx 4.75 (length) × 3.20 (width)	3.20	4.46	1.06	0.18	Asymmetric; Cd depends on which way it faces.
7) Kamm-tail teardrop	Approx 4.90 (chord) × 3.10 (width)	3.10	4.32	1.08	0.12	Good drag/length trade; truncated tail adds base drag but still far better than cylinder.
8) “Other”: tapered stadium (capsule + mild tail taper)	Approx 5.0 × 3.04 (as ellipse bbox)	3.04	4.24	1.06	0.14	Often buildable with developable surfaces + a few weld seams; less tooling than true lens/foil.

3) Estimated leg weight (per leg) & fabricated cost (per leg)

Weights include +10% allowance for end caps, hardpoint doublers, and light internal stiffening. If you add heavy frames/bulkheads, weights go up quickly. Costs shown are mid-estimates with a suggested uncertainty band.

Shape	Estimated mass (kg)		Mid fabricated cost per leg (USD)		Cost uncertainty	Fabrication complexity driver (qualitative)
Shape	Duplex SS (t=4mm)	Marine Al (t=6mm)	Duplex SS	Marine Al	Cost uncertainty	Fabrication complexity driver (qualitative)
1) Cylinder	1,275	648	$14.7k	$5.8k	±30–40%	Single roll + one long seam, simplest fixturing
2) Airfoil-like	1,403	713	$32.3k	$12.8k	±35–50%	More complex forming + tighter shape control, more weld length
3) Stadium	1,313	667	$18.1k	$7.2k	±30–45%	Roll + flats; moderate fixturing
4) Ellipse	1,339	680	$21.6k	$8.6k	±35–50%	Non-cylindrical forming; more jigs/QC
5) Lenticular	1,339	680	$27.7k	$11.0k	±40–55%	Harder curvature control; likely multi-piece shells
6) Ovate	1,351	687	$23.3k	$9.3k	±35–55%	Asymmetric; jigs + orientation management
7) Kamm-tail teardrop	1,377	700	$25.3k	$11.2k	±35–55%	Streamlined nose + truncated tail; still tooling-heavy vs cylinder
8) Tapered stadium (“other”)	1,339	680	$20.0k	$8.0k	±35–50%	Can be done with developable panels + limited compound curvature

Interpreting costs: The cylinder stays cheap because yards can do it with standard rolling machines and long straight welds. Anything “airfoil/lens-like” tends to require more segments, more seams, and more shape verification. If you can accept a tapered-capsule built from mostly-developable surfaces, you often get much of the drag benefit without “true foil” tooling.

4) Drag force per leg (half submerged) at 1 / 1.5 / 2 mph

Shape	1.0 mph		1.5 mph		2.0 mph
Shape	F (N)	F (lbf)	F (N)	F (lbf)	F (N)	F (lbf)
1) Cylinder	613	138	1,380	310	2,448	550
2) Airfoil-like	35	7.8	78	17.6	139	31.3
3) Stadium	107	24.1	241	54.1	428	96.2
4) Ellipse	65	14.7	147	33.0	260	58.5
5) Lenticular	42	9.4	94	21.1	167	37.6
6) Ovate	82	18.5	185	41.6	329	74.0
7) Kamm-tail teardrop	53	11.9	119	26.8	212	47.7
8) Tapered stadium (“other”)	61	13.7	137	30.8	243	54.6

5) Power to overcome leg drag (4 legs), and estimated electrical input

This is only the power to overcome the legs’ drag (not the rest of the structure, wave-making, appendages, thruster losses beyond η, etc.).

Shape	1.0 mph		1.5 mph		2.0 mph
Shape	Pmech (kW)	Pelec (kW)	Pmech (kW)	Pelec (kW)	Pmech (kW)	Pelec (kW)
1) Cylinder	1.10	2.00	3.70	6.73	8.75	15.9
2) Airfoil-like	0.062	0.11	0.208	0.38	0.496	0.90
3) Stadium	0.192	0.35	0.648	1.18	1.53	2.78
4) Ellipse	0.116	0.21	0.396	0.72	0.93	1.69
5) Lenticular	0.074	0.13	0.252	0.46	0.596	1.08
6) Ovate	0.147	0.27	0.496	0.90	1.18	2.15
7) Kamm-tail teardrop	0.095	0.17	0.320	0.58	0.756	1.38
8) Tapered stadium (“other”)	0.108	0.20	0.372	0.68	0.868	1.58

6) 40 ft container fit estimate (30 ft long pieces)

Assumed container: 40 ft High-Cube (internal ~39.5 ft L × 7.7 ft W × 7.85 ft H). Real packing depends on cradles, tie-downs, and whether over-height/flat-rack is allowed.

Shape	Max width (ft)	Conservative count in 40' HC	Comment
1) Cylinder (3.9 ft dia)	3.90	2	Likely 1 across × 2 high (tight). Getting 3–4 generally needs open-top/flat-rack or special nesting/diagonal packing.
2) Airfoil-like	3.04	4	2 across × 2 high typically feasible.
3) Stadium	3.00	4	2 across × 2 high.
4) Ellipse	3.04	4	2 across × 2 high.
5) Lenticular	2.92	4	2 across × 2 high, with more clearance.
6) Ovate	3.20	4	Still typically 2×2, but less lateral clearance.
7) Kamm-tail teardrop	3.10	4 (maybe 5 with custom nesting)	Your “alternating front/back” stacking idea can help; count depends on cradle design and allowable contact points.
8) Tapered stadium (“other”)	3.04	4	2×2.

7) “Must handle being pushed at 4 mph without buckling” — what the drag implies

You asked for “when held at the ends” and pushed through water at 4 mph in any direction without buckling. That is primarily a global bending and local dent/buckling problem, depending on how the hardpoints load the shell. Below are drag-only lateral forces at 4 mph (half submerged) to give magnitude.

Shape	Drag at 4 mph (N)	Drag at 4 mph (lbf)	Design implication (very high-level)
1) Cylinder	9,800	2,200	Large lateral load; bending moments can become dominant. Likely needs thicker shell and/or internal frames.
2) Airfoil-like	556	125	Much lower. Structural design becomes more about hardpoint load introduction & fatigue than pure drag.
3) Stadium	1,711	385	Moderate lateral load; still far less than cylinder.
4) Ellipse	1,041	234	Moderate.
5) Lenticular	666	150	Lower.
6) Ovate	1,315	296	Moderate; also asymmetric.
7) Kamm-tail teardrop	849	191	Lower.
8) Tapered stadium (“other”)	973	219	Moderate-low.

Structural caveat: “Held at the ends” is ambiguous. If the leg is a simply-supported beam with a distributed lateral load on the submerged half, peak bending moment can be large at/near the supports and/or waterline, and fatigue from wave/current oscillation may govern. The shell thicknesses assumed above (4 mm duplex / 6 mm aluminum) may be insufficient without rings/bulkheads, especially for handling impacts and hardpoint load introduction.

8) Internal pressure (~10 psi) to improve buckling resistance & leak detection

Do I agree that a small internal pressure helps? Yes, with important caveats.

Leak detection: Mild overpressure makes leaks obvious (pressure decay) and can be instrumented.
Dent resistance / local stability: Internal pressure can improve resistance to local panel “oil-canning” and dent-induced buckling, especially for thin shells.
Global bending strength: Internal pressure usually does not dramatically increase global bending stiffness; it helps more with local buckling/denting than with beam bending stress.
Non-circular sections (ellipse/lens): Overpressure tends to “round out” flexible sections unless the shape is well-stiffened; you generally need internal frames/bulkheads or thicker plating to hold the intended profile.
Practicalities: Temperature swings change pressure; add a relief valve and define a safe pressure envelope. Also consider corrosion/crevice issues at internal stiffeners.

In short: 10 psi can be a useful part of the design (especially for leak detection and dent resistance), but you should not rely on it as the primary means to prevent global buckling under end loads.

9) What shapes look best for your stated goals?

If you want largest drag reduction per manufacturing pain: Kamm-tail, ellipse, or a tapered stadium are usually strong contenders.
If you want minimum drag and are willing to pay: thick airfoil-like or lenticular—but expect tooling/jig/QC costs.
If you want lowest cost: cylinder, but it is dramatically worse in drag (and thus power at speed) and higher 4-mph lateral loads.

10) If you want, I can tighten these numbers with a few inputs

Are legs allowed to weathervane/rotate so the streamlined axis stays aligned with motion/current?
What is your target wall thickness or allowable mass per leg?
What is the hardpoint concept (end ring frames? central tie rod? internal bulkheads?)
Is the container a standard 40' HC, or are flat racks / open top acceptable?
Expected biofouling interval and coating plan (Cd can double with fouling).

Prepared as an approximate trade-study summary for early design exploration. Validate with CFD/towing-tank data and structural FEA before committing to tooling.

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