When heading directly into 5-second waves at 4 mph, the encounter frequency (1.54 rad/s) nearly coincides with the vessel's pitch natural frequency (1.55 rad/s). This near-resonance condition is the worst case and is inherent to the geometry: the pitch period (~4 s) falls in the range of common Caribbean chop.
The thrusters create a pitch moment because they apply forward thrust below the center of gravity. A force F at depth d below CG produces pitch moment M = F × d. By modulating thrust harder when the bow pitches up (creating more bow-down moment) and easing off when the bow pitches down, you add active damping.
The fundamental limitation: The pitch moment arm (7–9 ft from CG to thruster) is smaller than the distance from CG to where people stand (~10–20 ft toward the triangle edges). This means the fore-aft surge acceleration you introduce will generally feel larger than the pitch acceleration you cancel for people not seated near the center.
Encounter period ≈ 4.1 s — near pitch resonance. This is the worst-case condition.
| Configuration | Pitch Amplitude (±) | Pitch Reduction | Fore-Aft Surge Added | Speed Fluctuation (±) | Net Comfort Assessment |
|---|---|---|---|---|---|
| Base Case (no modulation) |
9.7° | — | None | None | Uncomfortable. Vertical motion at edges ≈ ±2.5 ft. |
| Thrusters 2 ft from bottom (±200 lbs/motor modulation) |
8.9° | 8.4% | ±0.6 ft displacement (1.4 ft/s² accel) |
±0.9 ft/s (±0.6 mph) |
Marginal improvement. Surge noticeable every 4 s. |
| Thrusters AT bottom (±200 lbs/motor modulation) |
8.7° | 10.8% | ±0.6 ft displacement (1.4 ft/s² accel) |
±0.9 ft/s (±0.6 mph) |
Best realistic option. Noticeable but modest improvement. |
Encounter period ≈ 6.5 s — below resonance. Waves pass the vessel more slowly from behind.
| Configuration | Pitch Amplitude (±) | Pitch Reduction | Fore-Aft Surge Added | Speed Fluctuation (±) | Net Comfort Assessment |
|---|---|---|---|---|---|
| Base Case (no modulation) |
7.0° | — | None | None | Moderate motion. Less bad than head-on case. |
| Thrusters 2 ft from bottom (±200 lbs/motor modulation) |
6.4° | 8.4% | ±1.5 ft displacement (1.1 ft/s² accel) |
±0.6 ft/s (±0.4 mph) |
Trade-off questionable. Large excursion over long period. |
| Thrusters AT bottom (±200 lbs/motor modulation) |
6.2° | 10.8% | ±1.5 ft displacement (1.1 ft/s² accel) |
±0.6 ft/s (±0.4 mph) |
Modest benefit. Surge at 6.5 s period feels like slow lurching. |
Key insight: Humans are more susceptible to vertical angular motion (pitch) for seasickness than to horizontal translation (surge). So even though the surge acceleration may be comparable in magnitude, replacing some pitch with surge is a slight net positive for nausea prevention — but passengers will still be annoyed by the surging.
| Factor | Value | Impact |
|---|---|---|
| Wave pitch moment (4 ft / 5 s chop) | ~103,000 lb·ft | This is what you're fighting against |
| Max thruster pitch moment (6 motors × 200 lbs × 9.25 ft arm) | ~11,100 lb·ft | Only 10.8% of wave moment available |
| Thruster moment arm (9.25 ft) | Less than person-distance from CG (~15 ft) | Surge accel will exceed pitch accel saved for most people |
| All thrusters at same depth | Cannot use differential fore/aft thrust for pitch | Must modulate total thrust → always causes surge |
The fundamental constraint: with all six thrusters mounted at the same height on the legs, any change in total forward thrust creates the same pitch moment regardless of which leg it comes from. You cannot independently control pitch and surge — they are coupled. The only way to break this coupling would be thrusters at different heights on the same leg (one high, one low), creating a differential moment without changing net thrust.
Moving from 2 ft to 0 ft from the bottom gains you ~28% more pitch authority for the same surge penalty. This is a free improvement — do it if structurally feasible.
Instead of continuous sinusoidal modulation, only activate thrust correction when pitch angle exceeds a threshold (e.g., |θ| > 4°). This reduces average surge annoyance by ~50% while still catching the worst oscillations.
The bolt-on heave plates on the lower legs are actually your primary pitch-reduction mechanism. They increase hydrodynamic damping dramatically by creating drag proportional to velocity². With 25-35% damping ratio from heave plates, pitch near resonance drops from ~16° (undamped) to ~7-10° even without thrusters. The thrusters are a fine supplement but shouldn't be the main strategy.
Since near-resonance occurs at 4 mph in 5 s waves (encounter period ≈ 4 s = pitch period), slightly changing speed shifts the encounter frequency away from resonance. At 6 mph, encounter period drops to ~3.6 s (above resonance, response falls off). At 2 mph, it rises to ~4.5 s (below resonance). Small speed changes can reduce pitch more than thruster modulation.
If each leg had one thruster near the bottom and one near the waterline (or above), differential operation would create pitch moment without surge — breaking the coupling that limits the current design. This could achieve 30-50% pitch reduction with negligible surge penalty.
The helical mooring screw + tension leg system will eliminate nearly all pitch when stationary. The thruster modulation discussion only matters during transit. For community living (connected walkways between seasteads), the tension-leg mode is far superior to any active system.
This analysis uses linear strip-theory-style calculations for a three-body semi-submersible with small waterplane area. The pitch RAO was computed from:
|θ| = M_wave / √[(C55 − Iyy·ωe²)² + (B55·ωe)²]
where C55 is hydrostatic pitch restoring from the three waterplane areas at their respective distances from CG, Iyy includes estimated structural mass distribution plus added mass (~50%), and B55 uses a modal damping ratio of 25% (heave plates assumed). The wave excitation moment was computed from the phase differences of wave elevation at the three leg positions (equilateral triangle geometry, 25.4 ft forward / 12.7 ft aft of CG). Thruster authority was computed as pure moment couples below CG with no hydrodynamic interaction effects. Speed was assumed constant (no feedback between thrust modulation and forward resistance). Results are order-of-magnitude engineering estimates ±30%.