Propulsion Concept Analysis for 30,000 lb Seastead

1. The Physics: You Are Entirely Correct

Your understanding of marine propulsion physics is spot on. Applying Actuator Disk Theory and the principles of conservation of momentum and kinetic energy, the most efficient way to generate thrust is exactly as you described: pushing a massive amount of water very slowly. The power required scales with the cube of the water velocity, while thrust scales with the square. Therefore, for a heavy, high-drag vessel (like a tiny oil platform) moving slowly (1 MPH), sweeping the largest possible area of water is incredibly energy efficient.

                The Core Idea: A transverse oscillating foil (wing) riding on a cable track between the aft floats, flipping its angle of attack at each end, and providing both forward thrust and biased directional steering.
            

2. Advantages of the Oscillating Wing Concept

Massive Swept Area: The distance between your back floats is roughly 44 feet. If a foil travels back and forth across a large portion of this span, the effective "swept area" (and thus the mass of water moved) absolutely dwarfs what two 2.5-meter propellers can achieve. The theoretical efficiency is stellar.
Biomimetic Efficiency: This mimics how aquatic animals (fish, whales) swim. Oscillating foils can achieve propulsive efficiencies exceeding 80%, compared to 40-50% for standard propellers at low speeds.
Integrated Steering: Your idea of shifting the centerline of the oscillation (e.g., making it sweep only the right side) to create differential thrust is brilliant. It acts as an integrated rudder with no additional drag from actual rudder surfaces.
Shallow Draft / Protection: A horizontal sweep keeps the moving parts tucked up between the floats, protected from deep subsurface obstructions compared to massive hanging propellers.

3. The Engineering Reality Check (Challenges)

While the physics and hydrodynamics are excellent, the mechanical execution of a cable-driven underwater wing presents severe real-world engineering hurdles:

Cable Deflection (The Bowstring Effect): When the wing pushes water backward to move the seastead forward, the water pushes the wing forward. If the wing is mounted on 44-foot long cables, that thrust will bow the cables outward. Keeping cables pulled tight enough over a ~44-foot span to prevent massive sagging and derailment of the wheel carriage will require immense structural tensioning, which puts enormous strain on your floats and columns.
Biofouling: The ocean is alive. Within weeks, your cables will be coated in slime, algae, and barnacles. If the wing's carriage uses pulleys or wheels to grip the cables, barnacles will jam or derail the mechanisms instantly. Enclosing the wheels inside the wing protects them from direct water flow, but the cable itself must still pass through the wheels, inviting fouling into the mechanism.
The "End-of-Stroke" Flip: To be efficient, the wing cannot simply slam to a halt and violently snap to a new angle. It must decelerate, smoothly rotate its angle of attack (pitch), and accelerate in the opposite direction. Passive flipping (relying on water pressure to snap it to a hard stop) is jarring, causes mechanical fatigue, and loses significant energy. Active pitch control requires underwater servos.
Drive Mechanism: Pushing the wing back and forth requires a drive system—likely a secondary looping cable driven by an onboard motor. This adds more moving parts, belts, and tensioners to the harsh marine environment.

4. Comparison: Wing vs. Submersible Mixers

Submersible Mixers (The Safe Bet):
Low-speed, large-diameter agricultural/industrial mixers are rugged, off-the-shelf, and designed to run continuously in terrible environments (like manure pits). While two 2.5m props sweep less area than the wing, they are vastly more reliable. They have one moving part (a sealed shaft). The 1 MPH target is easily achievable with them.

The Oscillating Wing (The High-Tech R&D Project):
The wing will undoubtedly use less solar power to achieve 1 MPH if it runs perfectly. However, the maintenance overhead, risk of jamming, and complexity of building it make it a major mechanical risk.

5. Conclusion and Recommendations

Your oscillating wing concept is a highly sound hydrodynamic theory, but a mechanical nightmare if implemented on flexible cables underwater.

If you want to pursue the biomimetic wing, consider these modifications:

Use a Rigid Track: Connect the bottom of the two aft columns with a rigid, lightweight truss (aluminum or fiberglass) instead of cables. A carriage with Delrin sliders (not wheels) sliding on a rigid rail will tolerate thrust forces and biofouling much better.
The Pendulum Alternative: Instead of a linear sliding track, hang a large vertical arm down from the living deck to the water with a foil at the bottom. Oscillate the arm back and forth like a sculling oar. This moves all mechanical linkages, motors, and bearings above the water line, entirely eliminating the underwater jamming and cable tension problems.

Final Verdict: For a prototype seastead where survival and basic functionality are priority #1, go with the low-speed submersible mixers. They are a proven technology. The oscillating wing is an amazing concept for a phase-two upgrade, provided you replace the cable track with a rigid rail or a pendulum sculling system.