Rough Estimate: Active Pitch Reduction Using Forward Thruster Modulation

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.

Key result: If the six thrusters can provide about ±3,000 lbf total sinusoidal thrust modulation around the cruise thrust, active pitch control might reduce pitch by roughly 25% to 35%. Putting the thrusters at the very bottom of the legs instead of 2 ft above the bottom improves pitch authority by roughly 15% to 20%, but the improvement in actual pitch angle is more modest.

Assumptions Used

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.

Estimated Pitch Reduction

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.

Important Thrust Authority Issue

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

Will People Notice the Thrust Modulation?

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.

Practical Conclusion

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.