The equilibrium tide, live: Moon and Sun each raise two opposing bulges (H ∝ cos²θ), Earth rotates beneath them, and the 24h50m lunar day makes the tide arrive 50 minutes later every day. Set the lunar calendar, perigee, solar distance and coastal amplification — then read spring/neap, range and high-tide times.
Equilibrium tide: H = A_m·cos²(θ_m) + A_s·cos²(θ_s), fundamental equilibrium amplitudes 0.268 m (Moon) and 0.124 m (Sun). Distances scale amplitude by (d̄/d)³. Earth's rotation gives each body a 12h25m semi-diurnal period; the lunar day is 24h50m, so highs are ~50 minutes later each day. Spring tides at new & full Moon (bulges aligned), neap at the quarters. Perigean springs occur when a spring tide coincides with lunar perigee — flagged automatically.