Tides: reading tide times, the French coefficient and the rule of twelfths

High water, low water, tidal range: the vocabulary

One port, and a whole coastline that relies on it. France’s tidal coefficient is calculated for Brest alone; it is the precision of that one figure that allows it to be used on every coast of mainland France, provided you take account of the time difference between high water at Brest and high water at the port you are interested in [1]. Before you read it, a few words are all you need.

High water is the moment the sea reaches its highest level, low water its lowest. The difference in height between the two is the tidal rangeThe difference in height between high water and the low water that follows or precedes it.. When the tide is rising, it is the flood; when it is falling, the ebb [1]. Heights in tide tables are measured from chart datum, the common reference for nautical charts and tide tables, which in France is set close to the level of the lowest tides, a level the sea drops below only very exceptionally [1].

On France’s Channel and Atlantic coasts, the tide is semi-diurnal: two high waters and two low waters a day [2]. By tidal range, the SHOM, the French Navy’s hydrographic and oceanographic service, classifies tides as microtidal, under 2 m, mesotidal, from 2 to 4 m, and macrotidal, above 4 m [1].

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The coefficient: Laplace’s idea, calculated for Brest

The tidal coefficient is a French way of describing the tide, and if you think in spring and neap tides, you already have the idea: it grades each tide on a single scale, from the smallest neaps to the biggest springs. It was the mathematician Laplace who devised it, to characterise each port by a unit of height, taken from the biggest tide that follows shortly after the full or new moon around the equinoxes. By convention, a coefficient of 100 is given to the average range of equinoctial spring tides; the accepted extremes today run from 20 to 120 [1].

So a high coefficient means a big tide: the sea rises higher, falls lower and uncovers more of the foreshore. The coefficient does not give a height in metres; it is calculated from the semi-diurnal constituents alone [2], and the SHOM points out that it is hardly used outside France [1]. For a height, you need the tide table for the port.

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The rule of twelfths, step by step

Good news: you don’t need a calculator to know how much water there will be in an hour’s time. Sailors use the rule of twelfths, which even comes up in France’s professional maritime exams [3] [4]. You divide the duration of the tide, between high water and low water, into six ‘tidal hours’. Over those six intervals, the sea rises or falls by 1, 2, 3, 3, 2 and then 1 twelfth of the tidal range [4].

Take a high water at 6.12am, at 5.20 m, and the following low water at 12.24pm, at 1.10 m. The tide runs for 6 hours 12 minutes, so each tidal hour lasts 1 hour 2 minutes. The tidal range is 4.10 m, and one twelfth is about 34 cm.

The rule is an approximation: it swaps the cosine curve the tide follows for straight segments. Before calculators, it was a remarkable tool, and it is still excellent for a rough estimate in your head [4]. It assumes a regular tide; in ports where the curve is distorted, the tide table and its curves are the better bet.

Where to find official tide times

In France, the SHOM publishes tide times for its ports free of charge on a dedicated website [6]. Its predictions are based on the analysis of long series of measurements and are accurate to within a few centimetres; but the weather can shift sea level by a few tens of centimetres, which cannot be forecast in the medium or long term [1]. In its prediction service, the coefficient option is only offered for mainland French ports on the Channel and the Atlantic [7].

Outside France, each country has its own official service. In the UK, the UK Hydrographic Office publishes ADMIRALTY EasyTide [8]; in Germany, the federal maritime and hydrographic agency, the BSH, publishes its tide predictions [9]; in the United States, NOAA publishes its own on Tides and Currents [10]. These services give no coefficient: you read the times and heights of high and low water directly.

Before a sea fishing trip or a swim in cool water, in the right wetsuit thickness, checking the tide times is part of the same habit as checking the weather.

So, with a big spring tide on the way (a three-figure coefficient, in France), the tide table in your pocket and your return time worked out, all that is left is to head down onto the foreshore, where the sea has just left its treasures behind.

Worth watching

A tide diagram works through the rule of twelfths hour by hour, turning tide times and the tidal range into a water height at any time between high and low water.

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Nolwenn Bastide

Trail running, snow, water, nature and destinations

Nolwenn covers trail running, snow, water, nature and destinations for Outfarer. Curious about everything, from meteor showers to night-train timetables, she has a knack for unearthing the one detail that changes everything, and putting it in a single sentence.

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