Tidal Lagoon Harmonic Scheduler

Generation Strategy

Tidal Forcing

Spring–neap strength (S2/M2) 0.45

Turbine capacity (K) 150

Time speed 0.15 h/s

Live Readout

Sea level

0.00 m

Lagoon level

0.00 m

Head Δh

0.00 m

Power

0.0 MW

Elapsed: 0.0 h · Energy: 0.00 MWh
Tidal phase:—

How it works

Real ocean tides are a sum of periodic gravitational forcing terms ("constituents"). The two dominant ones give this model its sea level:

h_sea(t) = A_M2 cos(ω_M2 t) + A_S2 cos(ω_S2 t)
ω_M2 = 2π / 12.42h  (principal lunar)
ω_S2 = 2π / 12.00h  (principal solar)

Because M2 and S2 drift in and out of phase, their sum beats with a ≈14.77-day period — the real spring–neap cycle. The "S2/M2" slider sets the solar constituent's relative strength; the phase tag reads the instantaneous envelope amplitude off that beat.

The lagoon exchanges water with the sea through a turbine/sluice, modelled as compressible-free orifice flow:

Q = K √|Δh| · sign(Δh)        (flow rate, m³/s)
P = ρ g Q Δh η                (hydro power, W)
dh_lagoon/dt = ∓Q / A_basin    (mass balance)

with ρ = 1025 kg/m³ (seawater), g = 9.81 m/s², η ≈ 0.87 (turbine efficiency). A minimum head (1 m) must build up before the turbine gates open — this is why the basin level "holds" flat for a while near each slack tide.

Ebb generation — gates stay shut while the sea rises, letting the basin fill for free; once the sea falls below the basin by more than the minimum head, the turbine opens and drains the basin, generating on the outflow only.
Flood generation — the mirror strategy: generate while the incoming tide fills the basin, then sluice it back out for free on the ebb.
Two-way — the turbine generates on both the fill and the drain, at the cost of a smaller average head per stroke (less power per unit flow, but power on every half-cycle).

Real-world relevance: this is the same head/flow/power accounting used to design and schedule actual tidal barrages — France's La Rance (240 MW, ebb-generating since 1966) and South Korea's Sihwa Lake (254 MW) both operate on exactly this logic.

Open sea level Lagoon level Turbine / gate

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