This is a first-order estimate, not a seakeeping simulation. The numbers below assume the seastead is in 4 ft wave height Caribbean chop, moving at 4 mph, with waves either directly ahead or directly astern.
| Item | Assumed value |
|---|---|
| Operating displacement | 27,500 lb |
| Wave height | 4 ft, so wave amplitude ≈ 2 ft |
| Representative chop period | 5 seconds |
| Deep-water wavelength for 5 sec wave | ≈ 128 ft |
| Seastead speed | 4 mph = 5.9 ft/s |
| Encounter period, heading into waves | ≈ 4.1 sec |
| Encounter period, going away from waves | ≈ 6.5 sec, assuming waves overtake from astern |
| Estimated pitch natural period | Roughly 3.5 to 4.5 sec, depending heavily on added mass and heave-plate damping |
| Estimated vertical lever arm from CG to thrusters |
Thrusters 2 ft above bottom: ≈ 11 ft Thrusters at bottom: ≈ 13 ft |
| Assumed active thrust modulation case | Six thrusters together provide ±3,000 lbf total sinusoidal modulation. This is about ±500 lbf per thruster. |
Pitch values below are approximate peak pitch amplitudes. Peak-to-peak pitch would be about twice these values. The uncertainty is large; real values could easily vary by ±50% depending on wave period, actual mass distribution, heave plates, control tuning, and added mass.
| Case | Wave direction relative to travel | Encounter period | Thruster vertical location | Estimated peak pitch | Estimated peak-to-peak pitch | Approx. reduction vs. no modulation | Comments |
|---|---|---|---|---|---|---|---|
| Base case | Heading directly into waves | ≈ 4.1 sec | No modulated thrust | ≈ 8.0° | ≈ 16° | — | This is the more difficult case because the encounter period may be close to the pitch natural period. |
| Active pitch control | Heading directly into waves | ≈ 4.1 sec | Thrusters 2 ft above bottom | ≈ 5.6° | ≈ 11° | ≈ 30% | Assumes ±3,000 lbf total thrust modulation. This is a noticeable improvement, but not cancellation. |
| Active pitch control | Heading directly into waves | ≈ 4.1 sec | Thrusters at bottom of legs | ≈ 5.2° | ≈ 10° | ≈ 35% | Bottom placement gives a larger moment arm, so the same thrust gives more pitch-control moment. |
| Base case | Going directly away from waves | ≈ 6.5 sec | No modulated thrust | ≈ 5.5° | ≈ 11° | — | The waves overtake the seastead from astern. Encounter frequency is lower, so pitch is usually less aggressive. |
| Active pitch control | Going directly away from waves | ≈ 6.5 sec | Thrusters 2 ft above bottom | ≈ 4.2° | ≈ 8.4° | ≈ 24% | Still helpful, but the lower-frequency thrust changes may be more noticeable to people onboard. |
| Active pitch control | Going directly away from waves | ≈ 6.5 sec | Thrusters at bottom of legs | ≈ 3.9° | ≈ 7.8° | ≈ 29% | Best of these cases, but still not a complete elimination of pitch. |
The above reduction assumes the thrusters can actually create a roughly sinusoidal thrust variation of ±3,000 lbf total. That may require either:
At only 4 mph, the normal cruise drag of this seastead may be much less than 3,000 lbf. If the thrusters cannot reverse while underway and can only reduce thrust down to zero, then the usable zero-mean modulation may be limited to roughly the normal cruise thrust. In that case, the pitch reduction could be much smaller.
| Total thrust modulation available | Pitch-control moment, thrusters 2 ft above bottom | Pitch-control moment, thrusters at bottom | Likely usefulness |
|---|---|---|---|
| ±500 lbf total | ≈ 5,500 ft-lbf | ≈ 6,500 ft-lbf | Small effect; perhaps 5% pitch reduction |
| ±1,500 lbf total | ≈ 16,500 ft-lbf | ≈ 19,500 ft-lbf | Noticeable but modest; perhaps 10% to 20% pitch reduction |
| ±3,000 lbf total | ≈ 33,000 ft-lbf | ≈ 39,000 ft-lbf | Useful; roughly 25% to 35% pitch reduction |
| ±6,000 lbf total | ≈ 66,000 ft-lbf | ≈ 78,000 ft-lbf | Strong effect, but likely very noticeable and power-hungry |
Yes, if the modulation is strong enough to reduce pitch substantially, people will probably notice it. For the assumed ±3,000 lbf total modulation, the fore-aft acceleration could be on the order of 0.05 g to 0.10 g, depending on added mass and drag. That is not dangerous by itself, but it is noticeable.
| Effect | Heading into waves | Going away from waves |
|---|---|---|
| Pitch improvement | Likely clearly noticeable and appreciated | Noticeable, but base pitch is already somewhat lower |
| Fore-aft thrust sensation | Felt as a repeated push/pull about every 4 seconds. Less objectionable because it coincides with the faster wave motion. | Felt as a slower surge about every 6.5 seconds. This may be more noticeable or annoying to some people. |
| Thruster noise / vibration | Likely noticeable unless the RIM drives are very quiet and control is smoothed | Likely noticeable, especially because the modulation is slower |
| Passenger comfort outcome | Probably positive if pitch reduction is around 30% and acceleration is smoothly controlled. | Mixed: some people may prefer the reduced pitch, while others may notice the slow surge. |
The low-mounted forward thrusters can help reduce pitch, but they probably cannot eliminate it unless the installed thruster power is large and reversible. With about ±3,000 lbf total modulation, a realistic expectation is:
For best comfort, the control system should probably not try to maximize pitch cancellation. A better strategy would be to use moderate active damping, limit jerk, avoid abrupt thrust reversals, and accept a partial pitch reduction that does not create an unpleasant fore-aft surging sensation.