Active Stabilization Analysis

Executive Summary

Bottom line: Yes — three 7,000 N submersible mixers used as vertical thrusters are a physically credible and well-matched stabilization system for this platform in the conditions you say you'll choose. The limiting factor is not the idea, it's actuator authority above H_s ≈ 0.8 m and thruster response speed. The dual-use (propulsion + stabilization) concept is sound; the submerged curved track is the risky part — a fixed 45° mount or an above-water tilt bracket achieves the same thing far more reliably.

75–90%

motion reduction in protected lees (H_s 0.3–0.6 m)

2–13 cm

residual significant heave in those conditions — near "tied to a dock"

60–75%

reduction in open roadstead (H_s ≈ 1 m), actuators saturating

3–18 kW

typical average electrical draw — compatible with your solar + battery budget

Heave authority: 3 × 7 kN = 21 kN vs. a wave excitation of ≈ 50 kN per metre of wave amplitude → full cancellation possible up to wave amplitude ≈ 0.42 m, i.e. H_s ≈ 0.8 m (mixers vertical). Mounted at 45°, that drops to H_s ≈ 0.55–0.6 m.
Pitch authority: ≈ 81 kN·m available vs. ≈ 150–180 kN·m of wave moment per metre of amplitude — full pitch control to H_s ≈ 1 m on its own; in practice heave demand saturates first when both are controlled together.
Important design note: with heave plates fitted, your heave and pitch natural periods land around 6–7 s — right in the Caribbean trade-wind sea band (4–8 s). Passive response is therefore amplified near 6 s. Heave plates (damping), the tension-leg mooring (when in shallow water), and the active mixers (deep water / unmoored) are the three mitigations, and they complement each other well.
Energy: damping-style control is cheap (3–8 kW); full cancellation in bigger seas is expensive (18–35 kW). Run modes scheduled by battery state-of-charge.

1. What 3 × 7,000 N Can Command

The wave pushes on the platform almost entirely through the three waterplanes (the horizontal foil sections). For a small-waterplane craft the wave-frequency heave force is approximately the hydrostatic stiffness times the wave elevation, with a small reduction for pressure decay over the 2.2 m draft:

F_heave ≈ ρ g A_wp × a × 0.89 ≈ 50 kN per metre of wave amplitude a
M_pitch ≈ ρ g A_leg Σx⊂i; sin(kx⊂i;) ≈ 150–180 kN·m per metre (6 s waves, head seas)

Axis	Wave excitation (per m amplitude)	Authority — mixers vertical	Full-cancel limit (vertical)	Authority — mixers at 45°	Full-cancel limit (45°)
Heave	≈ 50 kN/m	21 kN	a ≈ 0.42 m → H_s ≈ 0.8 m	14.8 kN	a ≈ 0.30 m → H_s ≈ 0.55–0.6 m
Pitch	≈ 150–180 kN·m/m	≈ 81 kN·m	a ≈ 0.5 m → H_s ≈ 1.0 m	≈ 57 kN·m	a ≈ 0.33 m → H_s ≈ 0.65 m

"Full-cancel limit" means the actuator can oppose the significant wave excitation; occasional larger individual waves (≈ 1.5–2× H_s) will clip. When heave and pitch are controlled together they share the same three actuators, so the practical full-control ceiling is roughly H_s 0.5–0.8 m vertical, 0.35–0.5 m at 45°. Beyond the ceiling the system degrades gracefully into "active damping + partial cancellation," which is still very valuable because uncontrolled response near resonance is amplification, not just following.

Asymmetry to design for: when a mixer jets water upward against the foil's underside, impingement/suction effects deduct roughly 10–25% of the useful force. The downward jet is clean. The allocation algorithm should command ~15% more in the "pull-down" direction to compensate.

2. Passive Motion (No Active Control)

Waterplane: 3 foils × ≈ 17–20 ft² ≈ 52–61 ft² (4.8–5.7 m²). Heave stiffness ≈ 50–57 kN/m — consistent with your "1 ft ≈ 1/7 of buoyancy" figure.
Heave added mass is large because the 8.5 ft chord foils are flat plates moving vertically: ≈ ρπ(c/2)² ≈ 5.4 t per metre of draft, ≈ 30–36 t for the three legs. Heave plates add roughly 15–25 t more.
Heave natural period T_n ≈ 5.5 s (foils only) to 6.5–7.5 s (with generous heave plates). Pitch T_n ≈ 6–7 s. Damping ratio ζ ≈ 0.15 without plates, 0.25–0.35 with plates.
Consequence: response amplification at resonance of 1.7–3× wave amplitude, and the resonance sits at 5.5–7.5 s — exactly where trade-wind seas live. This is the single most important passive-dynamics fact about this design.
Silver lining: short lagoon chop (3–4.5 s) is already well attenuated (RAO ≈ 0.3–0.5). The problem band is 5.5–8 s seas and wrap-around swell. Consider sizing heave plates to push T_n toward ≥ 7.5 s so the everyday chop case is further off resonance.
In H_s ≈ 1.5 m, relative motion at the bow vertex can approach the ≈ 2.2 m clearance to the underside of the platform — occasional underside slap becomes possible. One more reason Row 4 of the table below is "moor or move" territory.

3. Predicted Motion — Baseline vs. Actively Stabilized

Head seas, heave plates fitted (T_n ≈ 6.5 s, ζ ≈ 0.25), mixers vertical. "Controlled" assumes skyhook-damping feedback + feedforward from leg pressure sensors, with a realistic 70–90% realization efficiency after thruster lag (≈ 1 s thrust reversal) and saturation. Significant heave = 2σ. Accel = vertical RMS acceleration at deck level.

Condition	H_s	T_p	Passive sig. heave	Passive RMS accel	Stabilized sig. heave	Stabilized RMS accel	Reduction	Comfort (stabilized)
Sheltered lagoon / island lee	0.3 m	3.5–4.5 s	≈ 0.08 m	≈ 0.010 g	0.01–0.02 m	0.001–0.002 g	80–90%	Imperceptible
Protected anchorage, wrap-around swell	0.6 m	5.5–6.5 s	≈ 0.5 m + 2–3° pitch	0.015–0.025 g	0.05–0.13 m, <0.5° pitch	0.002–0.005 g	75–90%	Very comfortable
Open roadstead / moderate trades	1.0 m	6–7 s	≈ 1.0 m + ≈5° pitch	0.025–0.035 g	0.25–0.4 m, 1–1.5° pitch	0.008–0.012 g	60–75%	Comfortable
Rough for this concept	1.5 m	6.5–7.5 s	≈ 1.5 m + 6–8° pitch	0.03–0.05 g	0.7–0.9 m	0.015–0.02 g	40–55%	Tolerable — moor or move

The system earns its keep most in the 5.5–8 s band where the platform is resonant; short chop is already handled passively by the small waterplane + heave plates.
Protect pitch first when saturated: with a 25 ft lever arm from centroid to each vertex, pitch produces the largest vertical accelerations out in the living spaces. At H_s = 1 m uncontrolled, pitch contributes as much perimeter acceleration as heave does.
Roll is not excited in pure head seas; in quartering seas the same actuators provide roll authority comparable to pitch.

4. How Comfortable Is That?

RMS vertical accel	Subjective (habitability practice / ISO 2631 family)
< 0.005 g	Imperceptible to almost everyone
0.005–0.015 g	Noticeable if you look for it — fine for sleep, cooking, desk work
0.015–0.03 g	Clearly noticeable — most people unbothered; sensitive sleepers aware of it
0.03–0.06 g	Annoying over hours — fine-motor tasks degrade; mild seasickness risk for susceptible people (0.1–0.25 Hz is the nauseogenic band and you live in it)
> 0.06 g	Uncomfortable — significant seasickness risk with prolonged exposure

Mapping the performance table onto these thresholds: in your stated operating scenario (protected Caribbean lees), the stabilized seastead sits at or below the perception threshold — it should feel essentially stationary. Uncontrolled, the same conditions are "clearly noticeable." In an open roadstead at H_s ≈ 1 m the system turns a "lively, annoying over hours" platform into a "comfortable" one. That is a genuinely large quality-of-life difference.

5. Power & Energy Budget

A 2.5 m propeller making 7,000 N has an ideal (momentum-theory) power of only ≈ 5.8 kW; with real propulsor and drive losses (η ≈ 0.5 overall) budget ≈ 12 kW electric per mixer at full thrust. Stabilization, however, uses oscillating partial thrust, so averages matter:

Control mode	Typical sea state	Mean thrust per mixer	Total electric draw
Eco — active damping only	H_s < 0.5 m	1–2 kN	3–8 kW
Comfort — damping + partial feedforward	H_s 0.5–1 m	2–4 kN	8–18 kW
Max — full cancellation attempt	H_s > 1 m	4–7 kN bursts	18–35 kW

Your roof (≈ 78 m² of array) gives ≈ 15–17 kW peak, ≈ 70–90 kWh/day in the Caribbean.
25% of displacement in LiFePO4 ≈ 3.1 t ≈ 320–400 kWh of storage. Overnight "Comfort" mode (10 kW × 12 h ≈ 120 kWh) uses about a third of the usable bank. Very workable.
Implement gain scheduling by state of charge, exactly as you intuited: full cancellation when the sun is out, damping-only (the energy-cheap mode that still kills the resonant amplification) when the battery is low.
Spec the mixer drives for 4-quadrant operation with braking resistors: a 2.5 m prop needs on the order of 1–2.5 s for a full thrust reversal. The controller must be designed around this lag (see §7).

6. The 90° Curved Track — Practical?

Verdict: The dual-use idea is good and the thrust budget supports it — the platform needs only ≈ 1–5 kN horizontally (cruise at 3–4 kt, or hold station against 20–25 kt trades) and ≤ 21 kN vertically, both well under the 3 × 7 kN installed. The submerged curved track with wheels and a winch is the weak link in warm Caribbean water: biofouling in weeks, grit and corrosion in the track, 7 kN thrust plus wave-slap and gyroscopic loads carried by wheel contact points, and a jam loses both functions at once. Recommended alternatives below.

Option A — Fixed 45° mount (your fallback idea) — recommended

Zero moving parts below the waterline. Each mixer delivers 4.95 kN vertical + 4.95 kN horizontal simultaneously; totals 14.8 kN each axis.
Still covers: full stabilization to H_s ≈ 0.55–0.6 m, cruise at 3–4 kt (needs < 2 kN), station-keeping against ~25 kt wind.
Bonus: the vertical component gives underway ride control — active damping of heave/pitch while moving, like interceptors on a fast ferry.
Differential use of the three mixers gives heave, pitch, surge and yaw allocation even though each unit's axis is fixed.

Option B — Above-water tilt bracket (outboard-style power tilt)

Pivot on the trailing edge near the waterline, electric actuator in a dry housing above; only the (already submersible-rated) mixer swings. Proven technology — every outboard does this. Far more maintainable than a subsea track.
Bracket must react 7 kN at a ~1 m moment arm plus gyroscopic moments of the 2.5 m prop; expect 50–100 kg of bracket per leg on top of 200–400 kg mixers.

Option C — Mixers fixed vertical, RIM drives keep the propulsion job (status quo)

Simplest and most redundant. The mixers only earn their keep when stationary in deep water (where your helical screws can't reach) — which is exactly when propulsion is not needed.

If you build the track anyway

Put the winch at the top of the leg in a dry well; route the cable alongside the same trailing-edge conduit you already plan for power (preserves the "no through-hulls" rule).
Hard stops with over-center locks at both ends; design so a jam mid-track fails at ~45° (still partially useful for both jobs); sacrificial anodes; galvanic isolation of the stainless mixer from the aluminum leg; a monthly exercise cycle against fouling.
Watch the geometry: a 2.5 m prop swinging through 90° competes for space with the heave plates at the leg bottom.

Two operational issues regardless of mount

Draft: a 2.5 m prop under the leg bottom takes total draft to ≈ 4.5–4.8 m (from 2.2 m). Many prime Caribbean anchorages are 3–6 m. Make the mixer modules bolt-on/removable like the heave plates — they ship inside the container anyway — and remove them for shallow cruising seasons or haul-outs.
Safety & lines: interlock to stop props during swimmer/dinghy operations, fit guard rings, and route the tension-leg mooring lines clear of the mixer jets/intakes.

7. Control & Sensing Notes

Sensors: one IMU + one pressure sensor per leg at known depth (gives local wave elevation through the e^−kz correction). Cheap and robust. A wave radar is optional.
Start with skyhook damping (control force proportional to measured platform velocity). It needs no wave prediction, is robust to thruster lag, and directly attacks the resonant amplification that dominates your discomfort. Add feedforward/MPC later for the extra 20–30%.
Thruster lag is the key engineering risk: ~1–2.5 s full reversal of a 2.5 m prop is a 60–120° phase error at wave frequencies if unmanaged. Mitigate with: 4-quadrant VFD + braking resistor, model-predictive control using wave preview, and operating around a bias RPM so reversals through zero are less frequent.
Free wave preview: heading into the waves, the bow leg's pressure sensor sees each wave 1–2 s before the stern legs. And when two seasteads raft bow-to-stern, the leader is a free wave probe for the follower — the follower can get 5–10 s of preview over your existing inter-seastead network. That is enough preview to hide most of the thruster lag.
When on tension legs, schedule the mixers to handle only wave-frequency loads; let the mooring carry the mean (don't fight your own mooring).
Noise: large slow props at these loadings (≈ 1.4 kN/m² disk loading, minimal cavitation) are quiet — a low hum through the legs. Resilient mounts recommended; not a habitability concern.

8. Key Assumptions & Formulas

Displacement Δ = 27,500 lb ≈ 12.5 t | draft d = 7.25 ft = 2.21 m | chord c = 8.5 ft = 2.59 m
Foil area/leg ≈ 0.685·c·t ≈ 17.3 ft² → A_wp ≈ 52–61 ft² (4.8–5.7 m²)
K_heave = ρgA_wp ≈ 50–57 kN/m (your "1 ft ≈ 1/7 of buoyancy")
Heave added mass/leg ≈ ρπ(c/2)²·d ≈ 10–12 t → total 30–36 t + heave plates 15–25 t
T_n,heave ≈ 5.5 s (no plates) → 6.5–7.5 s (with plates) | T_n,pitch ≈ 6–7 s | ζ ≈ 0.15–0.35
Wave excitation: F ≈ ρgA_wp·a·(1−e^−kd)/(kd) ≈ 50 kN per m amplitude @ 6 s
Pitch excitation ≈ 150–180 kN·m per m @ 6 s | actuator pitch authority ≈ 81 kN·m
Mixer power: P = T^3/2/(√(2ρA)·η) → 7 kN thrust ≈ 5.8 kW ideal ≈ 12 kW electric
Leg positions: (7.74, 0), (−3.87, ±6.7) m from centroid | Σx² ≈ 90 m²

Estimates are first-order (linear potential-flow, head seas, narrow-band spectra, ±30–50%). Diffraction neglected (leg thickness ≪ wavelength — valid). Real directional seas will add roll excitation in quartering conditions. Before committing hardware: run a proper seakeeping model (strip theory / WAMIT-class + thruster dynamics), bench-test mixer reversal response, and fatigue-check the leg structure for ≈ 10&sup6;–10&sup7; thrust cycles per year of continuous stabilization duty.