Four constituents, one wheel. Every height on this page is summed live from the harmonic series — nothing here is looked up.
The curve is drawn from the same four cosines that move the harbour above. Turn the wheel and the brass cursor tracks you — or take the register itself and drag: time follows your finger. High and low water are found by walking the curve's slope to zero.
A tide is not one wave but a chord. Each constituent is a cosine with a fixed speed, amplitude and phase lag — set once for this harbour, good for a century. Below, the four vectors are added tip-to-tail; the height of the chain's end above the datum line is the tide. Silence a voice and everything on this page recomputes.
When sun and moon pull in line — new moon or full — M2 and S2 arrive in step and the harbour swings hard: springs. At the quarters they argue, and the water goes quiet: neaps. The two constituents drift apart at 1.016° an hour, which works out to a cycle of 14.77 days — the fortnight engine. Here the biggest water lags the moon by about a day; harbourmasters call that lag the age of the tide. The disc above is drawn waxing-on-the-left, the way Tasmania actually sees it.
SLACKWATER began as a single sheet pinned to the harbourmaster's door at Bruny Harbour: tomorrow's highs and lows, worked by hand from Doodson's tables, initialled in pencil. One hundred and thirteen years later it is still the sheet the oyster leases, the ferry and the channel pilots set their days by — except this edition works itself out while you watch.
Four constituents are enough for this coast. M2 does the heavy lifting, S2 sets the fortnight, K1 and O1 lean on the two daily highs until one outgrows the other. The residual — weather, barometric surge, the odd shelf wave — is yours to judge from the sky.
Heights in metres above lowest astronomical tide. Times in harbour standard time, UTC+10. The water is indifferent to both.