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Active Stabilizer Analysis — Tri-Leg Foil Seastead

Preliminary engineering estimate • Rev A • All figures approximate; validate with tow tests / CFD before fabrication.

Bottom line: With a 20 ft² active fin per leg, each fin can impose roughly 630–2,540 lbf of vertical force between 4 and 8 knots — equivalent to shifting that leg's waterline by ±7″ to ±28″. Averaged over real seas expect roughly ⅔ of that. Your “4-ft wave feels like 3-ft” intuition is correct, and the acceleration reduction is even better than the height reduction. Expect active fins to consume roughly 0.7–5.4 kW (all three legs) depending on speed, partially offset by reduced plunging-drag on the legs. In a 12-ft/12-s head swell the fins can hold the deck nearly level above ~5.5 knots. Estimated manufactured cost (batch of 20, China): ≈ $3,500/stabilizer; suggested installed option price $9k–12k per boat; expected customer take-rate 40–60%.

1. Basis & Assumptions

Item	Value used	Note
Strut cross-section	NACA 0035, chord 8.5 ft (TE trimmed)	Section area ≈ 17.0 ft²
Draft (half of 14.5 ft)	7.25 ft	Strut bottoms 7.25 ft below WL
Displacement at WL	27,500 lb (target)	Struts alone ≈ 23,500 lb; heave plates/brackets make up the rest
Seawater	64 lb/ft³, ρ = 1.99 slug/ft³
Stabilizer fin (assumed)	Span 8.0 ft × chord 2.5 ft, S = 20 ft², NACA 0015, pivot at ¼-chord	⚠ Size was not specified — tell me your actual fin and I will re-run every number.
Operational C_L	≤ 0.70 (peak), 0.35 (rms, active in seas)	Comfortable margin from stall; no cavitation risk at ≤8 kt
Fin drag coefficients	C_D0=0.012, span efficiency e=0.80	Includes pivot fairing

2. Buoyancy Gradient — “Additional Foot of Water”

The waterplane area of one strut equals its foil section area (≈17.0 ft²), so each extra foot of immersion displaces 17.0 ft³:

Per leg: ≈ 1,090 lbf per foot of extra immersion ≈ 91 lbf per inch.
All three legs: ≈ 3,270 lbf/ft (272 lbf/in).
Check vs. your “1 ft = 1/7 of buoyancy”: 3,270 / 27,500 ≈ 1/8.4 — same ballpark; bolt-on heave plates add waterplane and push the true figure toward your 1/7 estimate.

Metric: ≈ 15.9 kN per meter of immersion per leg.

3. Fin Authority vs. Speed (one stabilizer, one leg)

Lift: L = ½ρV² · S · C_L, with S = 20 ft², C_L,max = 0.70

Speed	V (ft/s)	q = ½ρV² (psf)	Peak force (lbf)	= waterline shift (in)	Total crest+trough authority (in, theoretical)	Realistic in irregular seas*
4 kt	6.75	45.4	635	±7	14	~8–10
5 kt	8.44	70.9	992	±11	22	~13–16
6 kt	10.13	102.1	1,429	±16	32	~19–23
7 kt	11.81	138.9	1,944	±21	43	~26–31
8 kt	13.50	181.4	2,540	±28	56	~34–40

*Irregular seas require phase lead, actuators saturate occasionally, and force falls when the fin nears the surface in a trough. ~65% of theoretical is a fair planning number. Below ~3.5 kt authority drops fast (force ∝ V²): at 3 kt only ≈ ±4″.

Your 4-ft-wave example: confirmed. Removing 6″ of crest and 6″ of trough turns a 48″ heave into a 36″ heave — a 4-ft wave rides like a 3-footer. Bonus: for a sinusoidal motion at the same period, vertical accelerations scale with amplitude, so they drop by (¾)² ≈ 44%. Comfort improves even more than the height numbers suggest.

4. Drag & Power Budget

4.1 Baseline propulsion (calm water, fins locked at 0°)

Rough estimate for 27,500 lb displacement, ~450 ft² wetted surface, rim drives at ~65% overall efficiency:

Speed	Est. electric propulsion power
4 kt	~2.0 kW
5 kt	~3.2 kW
6 kt	~5.5 kW
7 kt	~10 kW
8 kt	~15 kW

4.2 Fin drag — off/locked vs. active

Speed	Fins OFF (locked, 0° AoA)		Fins ACTIVE (rms C_L=0.35)
Speed	Drag/fin (lbf)	Fleet power (kW)	Total drag/fin (lbf)	Fleet power (kW)	% of baseline propulsion
4 kt	11	0.30	25	0.68	~34%
5 kt	17	0.59	39	1.33	~42%
6 kt	25	1.01	56	2.29	~42%
7 kt	33	1.60	76	3.63	~36%
8 kt	43	2.39	99	5.42	~36%

4.3 Savings from level legs — your instinct is right

When a leg plunges, its drag spikes from extra immersion, wave slap on the walkway, heave-plate separation drag, and added wetted area; when it rises, the system loses balanced flow. Keeping all three struts at mean immersion claws back a meaningful share. In seas rough enough to warrant the stabilizers, estimate a 30–60% recovery of the active-fin drag:

Speed	Active fin fleet power (kW)	Est. recovery from calmer legs (kW)	Net extra power, stabilizers ON (kW)
4 kt	0.68	0.2 – 0.4	~0.3 – 0.5
5 kt	1.33	0.4 – 0.8	~0.5 – 0.9
6 kt	2.29	0.7 – 1.4	~0.9 – 1.6
7 kt	3.63	1.1 – 2.2	~1.5 – 2.5
8 kt	5.42	1.6 – 3.3	~2.1 – 3.8

In calm water the stabilizers save nothing, so treat the “OFF-fleet power” column as the pure penalty there (and consider switching to FREE/LOCKED mode in calm conditions). Actuator electricity itself is minor: ~50–150 W average, ≤1 kW peak per fin.

5. Head Sea — 12-ft Swell, 12-s Period

5.1 Wavelength

λ = gT²/2π = 32.2 × 12² / 6.283 ≈ 740 ft (deep water — satisfied nearly everywhere in the Caribbean except banks)

Wave celerity ≈ 61.5 ft/s ≈ 36 kt; encounter period head-on at 6 kt ≈ 10.3 s.

5.2 How much higher is the water at one end?

Max slope = πH/λ = π(12)/740 = 0.051 rad ≈ 2.9°
Δη across a spacing d: Δη = H·sin(πd/λ)

Bow apex to stern line (d = 38.1 ft): ≈ 1.9 ft height difference.
Across the 44-ft after beam (beam sea): ≈ 2.2 ft.

5.3 Can the fins hold the deck level?

Nice geometric property of your triangle: all three corners sit 25.4 ft from the CG. Front fin down + two aft fins up gives a couple with arm 50.8 ft. Pitch stiffness from waterplane inertia ≈ 18,300 ft·lbf/deg.

Speed	Fin force (lbf)	Pitch couple (ft·lbf)	Counter-tilt authority	vs. 2.9° swell slope
4 kt	635	32,200	1.8°	~60% — helps, not full
5 kt	992	50,400	2.8°	~95% — nearly full
6 kt	1,429	72,600	4.0°	Full leveling with margin
7 kt	1,944	98,800	5.4°	Full
8 kt	2,540	129,000	7.1°	Full

Dynamic (inertial) torque demand is small at 12-s period (~3,000 ft·lbf), so quasi-static balance governs — this mode genuinely works. Verdict: above ~5.5 kt the seastead can climb these swells deck-level; at 4–5 kt expect partial leveling (~60–95%).

Depth check (important): with a 6-ft amplitude, a strut's local immersion cycles between ~1 ft and ~13 ft. A fin centered 5.5 ft below the WL will break the surface in troughs (your rim drives at 5.25 ft depth have the same issue in big swells). Mount stabilizers deep (~7 ft below WL, just above strut bottom), and program instant load-shed when a fin ventilates.

5.4 Beam sea

Yes — potentially even better. Any 2-versus-1 fin pairing produces a roll couple (arm 44 ft, ~3.4° authority at 6 kt) against the same 2.9° max slope, and in beam seas there's no Doppler shift, so the controller sees a clean 12-s signal. Critically, if the vessel's natural roll/heave period sits near 12 s (very plausible given the small waterplane), this is exactly the resonant-growth case you flagged — active fins at speed are the direct cure. At anchor the tension-leg mooring takes over that job.

6. Zero-Speed Behavior & Locking Mechanism

You've identified a real problem: with the pivot at ¼-chord, a bob