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The science
A buoy as a driven oscillator
A heaving buoy of waterplane area Aw obeys (m + ma) x'' + (Brad + Bpto) x' + ρ g Aw x = Fe cos(ωt). The restoring term is hydrostatic, ma is the added mass (about ρ D³/3 for a disc), Brad is the damping caused by the waves the buoy itself radiates and Bpto is the power take-off. The power absorbed is P = ½ Bpto ω² X².
The limit that matters
A regular deep-water wave carries J = ρ g² a² T / 8π watts per metre of crest. A small axisymmetric heaving buoy can at best absorb J λ / 2π, i.e. it can capture the power of a stretch of crest as wide as λ/2π (the Budal-Falnes limit), which is much wider than the buoy itself. Here Brad is taken from the Haskind relation so that this limit is reached exactly at resonance with Bpto = Brad; away from resonance the best damping is √(Brad² + (ωM - K/ω)²). Power is highest when the wave period matches the buoy period and falls quickly otherwise.
Honest simplifications: regular deep-water waves, not a real sea state; a single heave mode with frequency-dependent hydrodynamic coefficients replaced by the constants above; no wave interaction between buoys, so the farm total is simply N times one buoy, capped by the power passing through the farm frontage (J times width), which is a real energy limit; no PTO losses, end stops, mooring or storm survival.
What to try
- Start with Tuned buoy: the buoy period matches the wave period and the yellow point sits on the peak of the power curve.
- Choose Detuned (short waves): the same buoy absorbs a fraction of the power.
- Move the PTO damping slider on the second graph: the best value is near 1 only at resonance.
- Choose Crowded farm and see the farm output hit the frontage limit, so extra buoys add nothing.