page twenty-five

The Tide

Twenty-four rooms, and not one of them has ever had to wait for anything. The Span holds its load the moment you draw it. The Lens forms its image the instant the glass is cut. Nothing on this site had ever been told it could not go yet. Today's number invents a small port, gives it thirteen harmonic constants, and then does the only honest thing you can do with a harbour: works out when there is enough water in it, and when there is not.

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Forty-eight hours of water

Every tide prediction ever printed is the same sum: a mean level, plus a cosine for each way the moon and the sun pull on this particular piece of coast, each with its own amplitude and its own lateness. Add the thirteen below and you get the curve. Drag it to move the clock; the harbour further down follows.

water level low water depth you need over the bar

Left and right arrow keys walk to other days. Every day is a different port.

Day
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Terms

What that does to a boat

The same numbers, seen from the side. The bar across the entrance is the shallowest thing between the sea and the berth, and it is the reason tide tables exist at all. Green hull means afloat. Red means you are sitting on the ground waiting, which in most of the harbours anybody has ever built is a perfectly normal way to spend six hours.

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Water now
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Next high water
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Next low water
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Type of tide
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Mean spring range
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Mean neap range
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Mean sea level
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Highest / lowest astronomical
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Age of the tide
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High water interval
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The bar
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EventTimeHeight above datumDepth over the bar

Springs and neaps

M2 goes round every 12 h 25 m and S2 every 12 h 00 m, so twice a month they line up and the range is the sum of the two, and twice a month they fight and the range is the difference. That beat is the only thing on this page nobody had to invent — it falls out of subtracting one number from another. Thirty days of daily range, with the day you are looking at picked out.

The harmonic constants

This is what a tidal authority actually publishes for a port: not a curve, but a short table. Give somebody these thirteen rows and they can rebuild every tide this harbour will ever have, forwards or backwards, for as long as they care to. A dot in the left margin means you have switched that term off above. 

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What is real here and what is not

The method is the genuine article. The harbour is a lie with a name on it.

  1. 01

    The speeds are real

    Every angular speed in the table — M2 at 28.9841042 degrees an hour, K1 at 15.0410686, the shallow-water quarter-diurnals up at 58 — is the published value, derived from the actual motions of the earth, moon and sun. Nothing about them depends on where you are. Only the amplitudes and the phases do, and those are what a port is.

  2. 02

    The classification is real

    The form factor, (K1 + O1) divided by (M2 + S2), is the standard way of saying what sort of tide a place has: under 0.25 and you get two clean tides a day, over 3 and you get one. The spring and neap ranges as twice the sum and twice the difference of M2 and S2 are the rules of thumb every harbourmaster uses. So is the age of the tide, which is why springs arrive a day or two after the full moon rather than on it.

  3. 03

    The amplitudes are invented

    The day's number picks a regime, then a principal lunar amplitude inside it, then derives the other twelve from the ratios real ports tend to show, with jitter. Shallow, muddy ports get a fatter M4, which is what makes a tide curve lopsided — a long slow ebb and a hurried flood. The phases are drawn at random except where physics ties them together.

  4. 04

    Nodal corrections are not here

    A real prediction multiplies every amplitude by a slowly varying factor and nudges every phase, on an 18.6-year cycle, because the moon's orbit tilts. Since these constants were never measured against a real epoch, correcting them would be correcting nothing. Weather is missing too: a deep low and a hard onshore wind can put a metre on top of everything here, and no astronomical table has ever predicted that.

  5. 05

    The chart datum is a convention, honoured

    Every height on this page is measured from chart datum, and chart datum is put at the lowest the water can astronomically get — the sum of all thirteen amplitudes below mean level. That is why the predictions are almost never negative, why charted depths add to the tide rather than subtract from it, and why a bar can be marked as drying and still be navigable for hours.

Twenty-five rooms and the number is still the only thing doing any work. Here it names a harbour, fixes its thirteen constants, and by doing so decides — for every day you can walk to with the arrow keys — exactly when a boat drawing what yours draws is allowed in.