What Is the Coriolis Effect? Why Storms Spin, Winds Curve and Bath Water Does Not Care

Stand at the centre of a spinning roundabout and roll a ball to a friend at the edge. The ball travels in a straight line, but by the time it reaches the edge the friend has moved on, so from the roundabout's point of view the ball curved away. Nothing pushed it; the platform turned beneath it. The Earth is the roundabout, and anything moving across its surface for long enough, air, water, a shell, a plane, appears to curve, to the right in the northern hemisphere and to the left in the southern, because a point on the equator is moving east at 1,670 kilometres an hour with the Earth's spin while a point near the pole is barely moving at all. Air flowing from the equator towards the pole carries its eastward speed with it and outruns the ground beneath, so it drifts east; air flowing towards the equator lags and drifts west. The effect is proportional to the speed of the moving thing and to the sine of the latitude, so it is zero at the equator and strongest at the poles.

The deflection is small over a room and decisive over a continent:

• •Winds: air flowing from high pressure to low is bent until, in the large weather systems, it flows around the pressure centres rather than into them, anticlockwise around a low in the north and clockwise in the south, which is why cyclones and hurricanes spin the way they do and why they do not form within about five degrees of the equator, where there is no spin to start them
• •The trade winds and the westerlies: the global circulation, which would flow straight from equator to pole and back on a still Earth, is bent into the belts of east and west winds that sailing ships planned their voyages around
• •Ocean currents: the great gyres of the Atlantic and Pacific, the Gulf Stream and the Kuroshio, turn clockwise in the north and anticlockwise in the south, and the effect pushes surface water to the right of the wind, which is what makes cold water well up along the coasts of Peru and California
• •Artillery and aircraft: a shell fired 30 kilometres drifts a hundred metres or so, which gunners corrected for from the First World War, and a long flight is planned with it

The claim that water drains clockwise in one hemisphere and anticlockwise in the other, and straight down on the equator, is the most famous thing said about the effect and is false at that scale. The Coriolis acceleration on water moving a few centimetres a second across a basin is some ten million times weaker than the forces from the shape of the basin, the way the tap filled it, the residual swirl from the last person's hand and the tiniest draught, and the direction the plughole vortex turns is decided by those. In 1962 a physicist at MIT filled a two-metre tank, let it settle for a day, and drained it through a tiny hole: it turned anticlockwise, as the effect predicts, and the experiment has been repeated in the southern hemisphere with the opposite result, but it needs a large tank, hours of stillness and a very small drain, none of which a bath has. The roadside demonstrations at the equator, in which a basin drains differently on either side of a painted line a few metres apart, are done by the pouring.

Gaspard-Gustave de Coriolis was a mathematician and engineer at the Ecole Polytechnique who worked on the theory of machines and, in a paper of 1835 on the motion of bodies within a rotating frame such as a water wheel, derived the acceleration that carries his name; he never applied it to the weather and never mentioned the Earth. The deflection of winds by the Earth's rotation had been suggested by George Hadley in 1735 to explain the trade winds and worked out for the atmosphere by William Ferrel in 1856, and the term Coriolis force came into meteorology only around 1900. It is called a fictitious force because it exists only in the rotating frame: from space nothing is deflected, the air goes straight and the Earth turns.

In 1851 the French physicist Leon Foucault gave the first simple demonstration that the Earth rotates. He hung a heavy ball on a long wire from the dome of the Pantheon in Paris and set it swinging. A pendulum keeps swinging in the same plane in space, but over the hours the direction of its swing slowly turned relative to the floor, knocking over a ring of small markers one after another. Nothing was pushing the pendulum sideways; the building was turning underneath it, which is the same idea as the ball on the roundabout.

The rate depends on latitude in exactly the way the Coriolis effect does. At the North or South Pole a Foucault pendulum's swing would turn through a full circle in about a day, because the floor rotates directly beneath it. On the equator it would not turn at all. In between, the turning slows with the sine of the latitude, so in Paris a full circle takes a little over 31 hours. Many science museums have one. Seeing a pendulum track the rotation of the whole planet, with no telescope, is one of the most direct experiences of this physics you can have.

The explanation based on the ground moving faster at the equator covers motion north or south, but a wind or a train heading due east is deflected too, to the right in the northern hemisphere, which means towards the equator. Something travelling east is going round the Earth's axis slightly faster than the ground beneath it, so, like a passenger on a roundabout spun too fast, it tends to swing outward from the axis. Outward from the axis points partly towards the equator and partly upward, so the eastward traveller drifts towards the equator and is very slightly lifted. Westward travel does the reverse.

That upward part is called the Eotvos effect, after the Hungarian physicist Lorand Eotvos, who in the early twentieth century explained why measurements of gravity made aboard ships came out slightly lower when they sailed east than when they sailed west. A ship heading east weighs a little less than the same ship heading west at the same speed. The difference is well under a thousandth of its weight, far too small to feel on deck, but anyone measuring gravity from a moving ship or aircraft, as surveyors searching for oil and minerals do, must correct for both their speed and their heading.

The Coriolis effect is small over short distances, but for very long-range artillery it matters. In 1918 the German army bombarded Paris from more than a hundred kilometres away with a huge gun, often called the Paris Gun. Its shells climbed higher than any object made by humans before, spending about three minutes in flight.

Over that time and distance, the rotation of the Earth shifted where a shell would land enough that gunners had to correct for it, along with air density, the curvature of the Earth and the wear of the barrel. Modern long-range artillery and missile guidance include the same correction. For a bath or a sink, by contrast, the effect is far too weak to compete with the shape of the basin and the way the water was poured.

The Coriolis effect is the apparent curving of anything that moves across the rotating Earth, to the right in the northern hemisphere and the left in the southern, because the ground moves faster at the equator than near the poles; it is zero on the equator and strongest at the poles. It bends the winds into the trade winds and the westerlies, spins cyclones and ocean gyres, deflects shells and aircraft, and is far too weak at the scale of a bath to decide which way the water drains.