Storm Station

The Field Book/Vol. I, The Engine/FB-ENG-008

Coriolis as geometry

The Earth turns under the air that moves over it. Seen from the ground, anything that travels far and long enough seems to curve: to the right in the Northern Hemisphere, to the left in the Southern. The Coriolis effect is that curve, and it is geometry, the ground turning beneath a straight path, not a push.

Plate FB-ENG-008DynamicsRevision 1, 2026-09-25Status draftAlso called Coriolis effect, Coriolis force, Coriolis parameter, inertial circle, inertial oscillation, Rossby number, Foucault pendulum, deflection to the right

Two plans of a round table turning counterclockwise, as the Earth turns seen from above the North Pole, while a ball rolls from its centre to its rim in six equal steps of time and the table turns 60 degrees: seen from above, standing still, the ball runs in a straight line and the table's painted mark turns beneath it; seen from the table, the same roll curves steadily to the right of the way it set off.1122334455667788AABBCCDDEE© 2026 STORM STATION 247THE FIELD BOOKPLATE FB-ENG-008-AA BALL ROLLED STRAIGHT ACROSS A TABLE TURNING COUNTERCLOCKWISE, DRAWN AS SEEN STANDING STILL AND AS SEEN FROM THE TABLE, SIX EQUAL STEPS OF TIMEFIG. A A BALL ON A TURNING TABLESEEN FROM ABOVE, STANDING STILL0123456SEEN FROM THE TABLE0123456DASHED: THE TABLE’S PAINTED MARK, TURNINGTHE SAME ROLL CURVES TO THE RIGHTTHE TABLE TURNS 60° WHILE THE BALL CROSSES, IN SIX EQUAL STEPS OF TIME1234TITLECoriolis as geometry, a ball on a turning tableVOL. I THE ENGINE · DYNAMICSTYPEPLANSCALENOT TO SCALEREVREV 1 DRAFT SHEET 1 of 3DATE2026-09-25IDFB-ENG-008-ADRAWN AS linework on paperSOURCES AMS, Wallace
Fig. A A ball on a turning table. A ball rolled straight across a table turning counterclockwise, drawn as seen standing still and as seen from the table, six equal steps of time NOT TO SCALEMaximizeThe sheet, SVG, 11 by 17
  1. The ball's straight path, seen standing still
  2. The table's painted mark, turning beneath it
  3. The same path seen from the table, curving right
  4. The table's turn, counterclockwise from above

What it is

The Earth turns, and everything on it turns with it: the ground, the buildings, the observer. Air that moves over the ground for a long time travels in a nearly straight line through space while the ground turns beneath it. Seen from the ground, its path curves: to the right in the Northern Hemisphere, to the left in the Southern. That curve is the Coriolis effect.

Fig. A shows it on a turning table. A ball rolled straight across a table turning counterclockwise runs straight as seen by someone standing beside it. Seen from the table, the same roll curves to the right, because the table has turned beneath the ball while it crossed. Nothing pushed the ball sideways. The curve is geometry: a straight path drawn on a turning floor.

What it is not

It is not a real push. No force acts on the air sideways; the deflection comes entirely from watching from a turning Earth. The weather equations still carry it as a force, because the weather is measured from the ground.

It is not why a sink drains one way or the other. Its effect on anything small and quick is far too weak, as the second equation below shows.

Lookalikes

The swirl of a draining sink
Its Rossby number is in the thousands: the basin's shape and the way it was filled decide the swirl, not the Earth.
A tornado's spin
Most turn counterclockwise because the storm that makes them does, and the storm's turn comes from the wind shear; a few turn clockwise.
A real force
Nothing pushes the air sideways; the ground turns beneath a straight path, so the path curves as seen from the ground.

The machine

How much of the spin counts

The Earth turns once against the stars every 23 hours 56 minutes. How much of that turn a place feels depends on its latitude. Fig. B splits the spin at 40° N into two parts: a turn about the local vertical and a turn about the local horizontal. Only the turn about the vertical swings horizontal motion sideways. At the poles all of the spin is about the vertical; at the equator none of it is, and the Coriolis effect on horizontal winds vanishes there. That is why hurricanes do not form within a few degrees of the equator, Hurricane FB-EVT-043.

The first equation below measures it with the Coriolis parameter, f: twice the spin times the sine of the latitude. At 40° N, f is 9.37 × 10⁻⁵ per second.

The inertial circle

Set air moving at 20 mph (8.9 m/s) at 40° N and let nothing act on it but the Earth's turn. It curves steadily right and runs round a circle 59 mi (95 km) in radius, back where it started after 18.6 hours. Fig. C draws the circle to scale. The period is half a pendulum day: 18.6 hours at 40°, 12.0 hours at the pole, and endless at the equator. Winds on real days carry the same swing, and it shows as a nighttime wind maximum over the Plains, the low level jet.

When it matters

The second equation, the Rossby number, compares a motion's own turning with the Earth's. At 40° N a winter low, 20 mph (8.9 m/s) across 600 mi (970 km), has a Rossby number of 0.1: the Earth's turn rules it. The wind cannot blow straight from high pressure into low; it is swung sideways until it blows round the low instead, counterclockwise in the Northern Hemisphere, Geostrophic and thermal wind FB-ENG-009. A supercell's mesocyclone is near 44, a tornado near 1,200 and a draining sink near 3,600: for each of those the Earth's turn is too slow to matter, Tornado FB-EVT-009.

Section through the Earth with its spin along the axis; at a place at 40 degrees north the spin is drawn again and split into a turn about the local vertical, the spin times the sine of the latitude, and a turn about the local horizontal; all of it about the vertical at the pole and none at the equator; beside it a table of the Coriolis parameter and the inertial period at 0, 20, 40, 60 and 90 degrees, 18.6 hours at 40 degrees.1122334455667788AABBCCDDEE© 2026 STORM STATION 247THE FIELD BOOKPLATE FB-ENG-008-BTHE EARTH IN SECTION, ITS SPIN AT 40° N SPLIT INTO A TURN ABOUT THE LOCAL VERTICAL AND ONE ABOUT THE LOCAL HORIZONTALFIG. B THE SPIN ABOUT THE LOCAL VERTICALEQUATORTHE EARTH’S SPIN40°ABOUT THE LOCAL VERTICAL:Ω SIN 40°LATITUDEf, PER SECONDINERTIAL PERIOD0°0NONE20°4.99 × 10⁻⁵35.0 HOURS40°9.37 × 10⁻⁵18.6 HOURS60°1.26 × 10⁻⁴13.8 HOURS90°1.46 × 10⁻⁴12.0 HOURS12345TITLECoriolis as geometry, the spin about the local verticalVOL. I THE ENGINE · DYNAMICSTYPESECTIONSCALENOT TO SCALEREVREV 1 DRAFT SHEET 2 of 3DATE2026-09-25IDFB-ENG-008-BDRAWN AS linework on paperSOURCES AMS, Wallace
Fig. B The spin about the local vertical. The Earth in section, its spin at 40° N split into a turn about the local vertical and one about the local horizontal NOT TO SCALEMaximizeThe sheet, SVG, 11 by 17
  1. The Earth's spin
  2. A place at 40° N
  3. The turn about the local vertical, Ω sin 40°
  4. The turn about the local horizontal
  5. The Coriolis parameter and inertial period by latitude
Plan, north at the top and to scale, of air set moving east at 20 miles an hour (8.9 metres a second) at 40 degrees north with nothing but the Earth's turn acting on it: it curves to the right round a circle 59 miles (95 kilometres) in radius, clockwise, marked every 3 hours, and is back at the start after 18.6 hours and 372 miles.1122334455667788AABBCCDDEE© 2026 STORM STATION 247THE FIELD BOOKPLATE FB-ENG-008-CPLAN OF AIR SET MOVING EAST AT 20 MPH AT 40° N WITH NOTHING BUT THE EARTH'S TURN ACTING ON IT, NORTH AT THE TOPFIG. C THE INERTIAL CIRCLE59 MI (95 KM)0 H3 H6 H9 H12 H15 H18 HSETS OFF EAST AT 20 MPH (8.9 M/S)BACK AT THE START AFTER 18.6 HOURS, 372 MILES LATERN050 miles(80.5 km)LATITUDE 40° N; NOTHING BUT THE EARTH’S TURN ACTING1234TITLECoriolis as geometry, the inertial circleVOL. I THE ENGINE · DYNAMICSTYPEPLANSCALETO SCALEREVREV 1 DRAFT SHEET 3 of 3DATE2026-09-25IDFB-ENG-008-CDRAWN AS linework on paperSOURCES AMS, Wallace
Fig. C The inertial circle. Plan of air set moving east at 20 mph at 40° N with nothing but the Earth's turn acting on it, north at the top TO SCALEMaximizeThe sheet, SVG, 11 by 17
  1. Where it sets off, moving east
  2. It curves to the right
  3. The radius, 59 mi (95 km)
  4. Every 3 hours round the circle

Ingredients

  • The Earth's spin, one turn against the stars every 23 hours 56 minutes
  • Latitude, which sets how much of that spin is a turn about the local vertical: all at the poles, none at the equator
  • Motion over the ground lasting long enough, and travelling far enough, for the turn beneath it to matter

Scales

time
it matters for motions lasting hours or longer; the air's inertial circle at 40° N takes 18.6 hours
horizontal
it matters for motions hundreds of miles (hundreds of km) across; it is negligible in a tornado or a sink
vertical
the whole atmosphere; it acts on horizontal motion at every height
orlanski
synoptic

Equations

The Coriolis parameter

f=2Ωsin⁡φ,aCo=f Vf = 2\Omega \sin\varphi, \qquad a_{Co} = f\,V
ff
the Coriolis parameter, per second
Ω\Omega
the Earth's rate of spin against the stars, 7.29 × 10⁻⁵ per second
φ\varphi
the latitude
aCoa_{Co}
the sideways acceleration of air moving at speed V, at right angles to its motion
VV
the speed of the air over the ground

Assumes The horizontal part only; the Earth's spin about the local horizontal, the Ω cos φ part, bends vertical motion very slightly and is left out, as the weather equations leave it out.

Working form At 40° N, f is 9.37 × 10⁻⁵ per second. Air set moving at 20 mph (8.9 m/s) with nothing else acting runs round a circle 59 mi (95 km) in radius, clockwise, and is back where it started 18.6 hours later.

The Rossby number

Ro=Vf LRo = \frac{V}{f\,L}
RoRo
the ratio of a motion's own turning to the Earth's turn beneath it
VV
the motion's speed, m s⁻¹
LL
its size, m
ff
the Coriolis parameter, per second

Assumes A scale comparison, good to a factor of a few. Where Ro is much larger than 1 the Earth's turn does not matter; near 1 or smaller, it rules.

Working form At 40° N a draining sink, water moving 4 in (0.1 m) a second across 1 ft (0.3 m), has Ro near 3,600; a tornado, 100 mph (45 m/s) across a quarter mile (400 m), near 1,200; a supercell's mesocyclone, 45 mph (20 m/s) across 3 mi (4.8 km), near 44; a winter low, 20 mph (8.9 m/s) across 600 mi (970 km), 0.1.

Signatures

sounding
surface
the wind blowing round lows and highs rather than straight into them; counterclockwise round lows and clockwise round highs in the Northern Hemisphere
satellite
the comma of a low and the spiral of a hurricane; turning counterclockwise in the Northern Hemisphere and clockwise in the Southern
radar

The numbers

QuantityValue, and the kind of number it is
Coriolis effectThe apparent deflection of a moving object seen from a rotating frame; on the Earth, to the right of the motion in the Northern Hemisphere and to the left in the SouthernStandard, Glossary of Meteorology
The Earth's spin7.2921 × 10⁻⁵ radians a second, one turn against the stars in 23 hours 56 minutesStandard, Glossary of Meteorology
The inertial periodHalf a pendulum day, 12 hours ÷ sin φ very nearly: 35.0 hours at 20°, 18.6 hours at 40°, 13.8 hours at 60°, 12.0 hours at the pole; none at the equatorThis site, Glossary of Meteorology
A Foucault pendulumTurns once in 23.93 hours ÷ sin φ: 37.2 hours at 40°Standard, Glossary of Meteorology
Rossby numberThe ratio of the inertial force to the Coriolis force in a flow; small for motions the Earth's turn controlsStandard, Glossary of Meteorology

How the station sees it

An airport station records the wind's direction every minute. Near the ground, friction slows the wind and the Coriolis effect weakens with it, so the wind blows partly across the isobars, inward toward the low. A few thousand feet up, with less friction, it blows nearly along them. Stations across a whole map show the pattern: counterclockwise round each low and clockwise round each high, the hand of the Earth's turn on every weather chart, Midlatitude cyclone life cycle FB-EVT-060.

  • Airport weather stations: the wind's direction and speed, which blow across the isobars near the ground and along them higher up

How it is warned

The Coriolis effect is not warned. It sets the direction every large storm turns and the track it takes. Every forecast of where a low or a hurricane will go carries it.

See also

Sources

  1. American Meteorological Society. Glossary of Meteorology.
  2. Wallace, J. M. and P. V. Hobbs. Atmospheric Science, An Introductory Survey, 2nd ed. (2006).

Definition after the Glossary of Meteorology. Plate FB-ENG-008, revision 1, 2026-09-25. The number is permanent; cite it.