Presets
Playback
Port
Latitude of the port and the local resonance gain.
Sky
Moon phase at the start, season, orbit tilt and distance.
Layers
Model checks
The science
Equilibrium tide
A body of mass M at distance d raises a tidal bulge on both the near and far side of the Earth. The tide-generating acceleration scales as M/d3, and the equilibrium surface height at an angle ψ from the body's zenith is ζ(ψ) = (M/ME) (R/d)3 R · (3 cos2ψ − 1)/2. This gives about 0.36 m for the Moon and 0.16 m for the Sun, a ratio of 0.46.
Rotating Earth and two bodies
For a port at latitude φ the zenith angle follows cos ψ = n · u, with n the port's direction (rotating once per sidereal day) and u the unit vector to the Moon or the Sun, found from their ecliptic longitudes, the 23.44 degree obliquity, the 5.14 degree lunar orbit inclination and each orbit's eccentricity. The Moon lags the Sun by about 50 minutes per day, so high tides are spaced 12.42 h apart, and the Sun's part adds to or subtracts from the Moon's every 14.77 days: spring and neap tides.
Harbour gain
Real coasts amplify the open-ocean tide through resonance. The harbour gain slider multiplies the equilibrium tide by a constant factor to show this, as in resonant bays that reach several times the equilibrium height.
Honest simplifications: equilibrium theory has no ocean inertia, friction, continents or amphidromic systems, so real tides differ in height and timing. The lunar node does not regress, there are no other constituents (K1, O1, N2 and so on), and the gain is a single number. Do not use for predicting real tides.
What to try
- Start at new moon and step through the quarters: the daily range peaks at new and full moon and drops at the quarters.
- Choose the perigee preset: a closer Moon gives bigger ranges (cube of the distance).
- Move the port to 60 degrees latitude and see the two daily highs become unequal (diurnal inequality) when the Moon has declination.
- Increase the harbour gain to model a resonant bay.