Coriolis effect

The Coriolis force [ kɔrjoli skraft ː ] is among the sham or inertial forces. It occurs in rotating frames of reference in addition to the centrifugal force when mass does not rest within the rotating reference frame (ie if they do not just " co-rotates "), but moves relative to the reference system. It is named after Gaspard Gustave de Coriolis, who in 1835 first time herleitete mathematically.

The magnitude of the Coriolis force is proportional to the mass of the moving body, the angular velocity of the reference system and to the amount of the orthogonal projection of the velocity vector of the body on a plane perpendicular to the axis of rotation level. Condition of the Coriolis force is so that the velocity of the body is not parallel to the rotation axis of the reference system. Of no importance, however, is the component of the speed at which the body moves parallel to the axis of rotation. The direction of the Coriolis force is perpendicular to the rotation axis and to the velocity vector. Therefore, the Coriolis force always acts in the sense of lateral deflection of the current direction of movement.

In the field of meteorology and physical oceanographic the Coriolis force also plays an important role. Due to the rotation of the earth, the air and water masses moving in a rotating frame of reference. This causes the northern hemisphere a deflection to the right, to the left in the southern hemisphere, which determines the direction of high and low pressure areas.

  • 4.1 Horizontal movements
  • 4.2 Vertical movements
  • 4.3 overall consideration of the Corioliskomponenten on a rotating sphere

Introduction - The Coriolis force on a turntable

A person (such as a carousel ) rests on a rotating disc, receives an outward centrifugal force. Moving the person on the wheel, it undergoes addition, a force directed towards the side (perpendicular to the current direction of movement of the person). This is the Coriolis force.

It is a common misperception that the Coriolis force only in radial movements, ie in those which are directed away from the center or to him either way, am working. In fact, they act in any movements in the horizontal plane relative to the turntable, is in each case perpendicular to the direction of movement and has in each case the same amount. Rotates the wheel - as in the picture - Right, and the Coriolis force acts to the left relative to the direction of movement of the red body.

A displacement parallel to the axis of rotation, perpendicular to the hub, gives rise to no Coriolis force.

Coriolis force due to the Earth's rotation

On each moving object on earth affects a Coriolis force, which goes back to the Earth's rotation. The influence of the earth's rotation on the motion of bodies was first studied by Isaac Newton.

Vertical movements

Vertical movement (perpendicular to the surface) can be parallel to the axis of rotation and a break down perpendicular to the axis of rotation in a share. Only the latter generates a Coriolis force, which is directed to the west to the east in a downward movement, in an upward movement. Due to the positioning of the body in the polar coordinate system also occurs Scheinkraft in North / South direction, which has nothing to do with the Coriolis force.

If you drop an object, it is deflected due to the Coriolis force to the east. Early measurements of this effect comes from Giovanni Battista Guglielmini (1791 in Bologna ), Johann Friedrich Benz Berg ( 1802 in Hamburg) and Ferdinand Reich (1832 in Freiberg ), see case experiments to demonstrate the Earth's rotation.

Marin Mersenne wrote to you, to have raised the question of where - a vertical shot up cannon ball falls to the ground - without consideration of air movement and air resistance. By the Coriolis force it is accelerated during the upward movement to the west and during the downward movement towards the east. The increasing apparent speed during the ascent to the west takes the descent alike again, so that the velocity vector is directed to the west during the entire flight and reaches its maximum at the turning point. As a result, it is therefore deflected to the west. At an initial speed of 100 m / s and a latitude of 50 °, the West distraction is for example 65 cm.

Horizontal movements

Horizontal movements, so movement in a tangential plane of the surface of the earth, require, in addition to the two components of movement, the vertical movement can be decomposed, a third component that it is directed opposite to the direction of the rotation or. This component also generates no Coriolis force, but increases the centrifugal force and weakens them so that, for example, at the equator with a speed of sound to the east flying plane by approximately one-thousandth of its weight is lighter - it flies to the west, it is correspondingly heavier. This apparent force plays in practice only as a correction term in precision measurements of the Earth's gravity a role.

On Earth, we therefore usually denotes the horizontal component as " Coriolis force ". The horizontal component pulls the moving observer in the northern hemisphere to the right and to the left in the southern hemisphere, and that the stronger the closer it is located at the poles. During movements of the equator is the horizontal component of the Coriolis force to zero. The magnitude of the horizontal component does not depend on the direction of movement. In a north-south movement is exactly the same horizontal component of the Coriolis force as with an east -west movement.

The Coriolis force has a significant influence on the shapes of the large-scale motions in the atmosphere and in the ocean. Considered theoretically it was the first time in this regard in the Laplace ( 1778) established tidal theory. The modified by the Coriolis effect of the wind on ocean currents, which leads to the northern hemisphere to a legal distraction, was declared in 1905 by Vagn Walfrid Ekman and is determined by the Ekman transport (see also corkscrew flow ) described. The influence of the Coriolis force on movement as in the sea and the atmosphere is characterized by the dimensionless Rossby number. The smaller this is, the more influence the Coriolis force on the motion.

Influence of the Coriolis force on the weather

The Coriolis force is responsible for ensuring that the air masses to large-scale high-pressure areas of the northern hemisphere, clockwise to low pressure areas move counterclockwise. In a low pressure area, the air flows due to the pressure gradient inside. This flow is diverted to the northern hemisphere by the Coriolis force to the right and it results in an anti -clockwise rotation. The resulting flow pattern can be explained by the geostrophic balance between the horizontal pressure gradient and the Coriolis force: In a vortex, which rotates counterclockwise, the Coriolis force acts outwards and compensates the inward force of the pressure gradient. In general, the air always turns to the northern hemisphere to low pressure areas counterclockwise and clockwise around high pressure areas. In the southern hemisphere this is reversed. The geostrophic equilibrium forms only the large-scale weather patterns. At the direction of rotation, for example, of tornadoes the Coriolis force has no direct influence. Furthermore, the Coriolis force also plays an important role in the formation of the Rossby and Yanai waves.

Coriolis force and railway

In rail transport, the Coriolis force leads to the northern hemisphere theoretically mean that on straight stretches of track that which is right in the direction, is charged slightly more than the left rail. Both tracks would have to lie exactly on the same level, which can never be the case in practice. This effect is so small that it has no technical relevance.

A train (for example, an ICE 3 400 t mass ), which runs at a latitude of 51 degrees (Cologne) with a speed of 250 km / h experiences a force of 3.200 N to the right. This corresponds to about a thousandth of the gravitational force. Has the train eight cars, each with four axes, each right wheel is pressed with a Coriolis force of 100 N to the right against the rail. In comparison, results at this speed for a curve radius of 3,000 m on each wheel lateral force of 20,000 N, ie, 200 times as much as the Coriolis force.

Inertial circles

Due to the Coriolis force describes an air or water mass moving in a co-rotating with the Earth reference system with the speed without influence of other forces " of inertia circles" with radii of In mid-latitudes with values ​​of Coriolisparameters (see below) and from a typical sea - flow rate of yields a radius of. The movement takes place in the northern hemisphere clockwise in the Southern Hemisphere counterclockwise. The period of the orbital motion, for example, at 60 degrees latitude around 15 hours. They have been observed eg in free-floating buoys in the Baltic Sea, which initially followed a fanned by strong winds surface flow, after the wind abates but orbits or cycloid ( as was superimposed on a flow of gyration ) described. For the course of marine and air currents, the Coriolis force plays an important role, in addition to other forces that deal with her to balance or even dominate ( geostrophy ).

Coriolis force and Foucault 's Pendulum

The term of the Coriolis force allows an easy understanding of Foucault's pendulum. Since the pendulum is drawn ( in the northern hemisphere ) by the Coriolis force to the right, its oscillation plane rotates. The speed of rotation decreases with increasing distance from the pole.

Erosion of river banks

The Coriolis force also means that are eroded in the northern hemisphere those riverside which are in flow direction right in the middle more than the left leads. This phenomenon was first described in 1763 by Mikhail Lomonosov. First observations were from PA Slowzow (1827 ) and Karl Ernst von Baer ( 1856). Although these researchers believed the effect kick in only on rivers that flow from south to north, the effect today is called Baersches law. The correct view that the effect of the direction of flow is independent, formulated first time in 1859, Jacques Babinet and later Albert Einstein ( 1926).

Influence of the Coriolis force on the water runoff in a basin

A frequently encountered opinion regarding the Coriolis force refers to the rotational behavior of a water vortex, for example, in a bathtub. If the drain is opened, the resulting vortex to move to the northern hemisphere compared to the southern hemisphere clockwise - similar to the low pressure of the atmosphere. In fact, the Coriolis force in such small dimensions plays no practical role. In comparison with other factors, such as pre-existing flows, the influence of the Coriolis force is negligible.

Coriolis force in the art

Coriolis forces in the art are of importance, when a rotational motion from a second motion " superposed " is. This is the case, rotating simultaneously and extends its gripper arm, for example, in a robot.

  • When a load is on the jib of a crane moves inward or outward, while the crane rotates, it depends on the basis of the Coriolis force is not straight down but is deflected sideways. If the load is retracted along the boom inside, she is ahead of the crane.
  • In the transmission technique ( linkage ) and in robotics, the Coriolis forces also play an important role, since here also take place simultaneous movements along several degrees of freedom. If one uses to simplify the description rotating coordinate systems are effective for motion in this rotating reference systems, Coriolis forces.
  • To measure the mass flow through flowing liquids or gases are used the Coriolis mass flowmeter. The measuring tube to vibrate. These are measured in the inlet and outlet and compared. In Corioliswaage especially bulk material is measured by measuring the change in the required torque of a rotor disc.
  • In centrifugal pumps, the medium is displaced from the generally axially located suction passage through the impeller in rotation, and ejected to the exit by the centrifugal force. The medium exerts Coriolis forces on the impeller, thereby providing a braking torque to the drive. The effective energy expended the pump is thus approximately proportional to the radial mass flow, the radius of the impeller and the rotational speed ( turbulence, backflow and friction disregarded ).
  • Some gyroscopes to measure rotational velocities using the Coriolis force in the form of so-called " tuning fork " principle, which is explained in the picture. Due to the rotational movement of the tines of the tuning fork to move not only to each other, but they also cause lateral movements from each other, which are caused by the Coriolis force. The lateral displacement is approximately proportional to the rotational speed, and may, for example be detected by a capacitive or inductive measurement.

Formulas

The Coriolis force acting on a body which moves in a rotating reference frame.

Generally

In which

  • The mass of the moving body,
  • The angular velocity of the reference system and
  • The velocity vector of the movement of the body relative to the rotating reference system,.

With a known angle between the rotation axis and the direction of movement can be expected with the scalar quantities. The reference frame rotates clockwise, the Coriolis force acts in relation to the left to the direction of movement. With a turn to the left it looks right.

  • Angle between the velocity and angular velocity vector
  • Velocity component parallel to the plane of rotation and perpendicular to the angular velocity

In the following animation, the vector of the Coriolis force for a radial and a tangential moving sphere is located on a turntable ( viewed from mitrotiertem reference system ). The Coriolis force corresponds with Upside Down sign exactly the constraint force, which would have to be expended by the drawn ball to force the trajectories shown ( where the centrifugal force is not taken into account).

Tangential motion to the rotating disc, which leads to a radial Coriolis force

Horizontal movements

Considering the Coriolis force due to the rotation of the earth, we are interested mostly only for horizontal movements, and only for the horizontal component of the Coriolis force.

In this economy:

Or

It is

  • The component of the Coriolis force in a northerly direction,
  • The component of the Coriolis force in an easterly direction,
  • The latitude,
  • The component of the velocity vector in an easterly direction and
  • The component of the velocity vector in the northerly direction.

The Earth's rotation (one revolution in 23 hours 56 minutes 4.09 seconds = 1 Sidereal Day = 86164.09 s ) here has the angular velocity

Vertical movements

For pure upward movements, the Coriolis force acts to the west, the vertical free fall it acts to the east. Your amount is

An over the length L of freely falling body experiences due to the Coriolis force a Ostablenkung of

One with the initial velocity perpendicular shot upward ball is first deflected westward by the amount

Once it has reached the height of rise, so it has a speed of West. Dropping the ball, therefore, one must in addition to the above formula, the contribution to Ostablenkung consider:

The total offset arises from the difference of the two expressions according to according to simplifications of the laws for the rise and fall times to an effective deviation to the west to

G is the gravitational acceleration, respectively.

At the equator, the offset is greatest (). Because results showed no difference between northern and southern hemispheres.

Overall consideration of the Corioliskomponenten on a rotating sphere

Consider a place on the width of a ball that rotates around the North-South axis. Then there is a local Cartesian coordinate system with the horizontal axis shows the east, which axis horizontally to the north and the axis vertically upward (upward, perpendicular to the spherical surface ). The vectors of the angular velocity, the velocity and the Coriolis force can be described in this local coordinate system as:

With the following indices are:

  • East: o
  • North: n
  • Up: a

Related terms

The Coriolis acceleration is belonging to the Coriolis acceleration. The amount referred to applies. For the sign is to be noted that the textbooks of physics (for example ) and engineering mechanics (for example ) follow different conventions:

The different conceptualization of the same word " Coriolis acceleration " has its basis in the fact that in physics, the inertial forces on the consideration of the be introduced by an accelerated reference system from observed movements of a body usually while the Engineering Mechanics usually from the standpoint of the rest in the inertial observer starts looking at the accelerated reference system and in the relative movement of the body. At the end of both considerations in concrete results again agree.

With the Coriolis parameter can represent simple formulas for the horizontal component of the Coriolis force due to the Earth's rotation. The magnitude of the Coriolis force is then easy Typical magnitude at mid-latitudes are values ​​of around

As Coriolis effect is called every phenomenon that comes into existence by the Coriolis force.

Swell

  • JF Benzenberg: Essays on the law of the case, the resistance of the air and the earth's rotation. Dortmund 1804, 2nd edition 1824 Hamburg
  • F. Reich: case experiments on the rotation of the earth: the brothers employed in shafts at Freiberge.Freiberg 1832
  • G. Coriolis: Memoire sur les equations du mouvement relatifs of the system de corps. In: J. Ec. Polytech .. No. 15, 1835, pp. 142-154 ( http://www.aos.princeton.edu/WWWPUBLIC/gkv/history/Coriolis-1835.pdf ).
  • PS Laplace: Recherches sur plusieurs points you système du monde. In: Mém. Acad. Roy. d Sci .. 88, 1775, pp. 75-182 ( http://mathdoc.emath.fr/cgi-bin/oetoc?id=OE_LAPLACE__9 ). At this source should be the footnote 12 in: note "The Coriolis Effect Four centuries of conflict in between common sense and mathematics"
  • KE von Baer: About a universal law in the design of river beds. In: Caspian Studies. No. VIII, 1860, pp. 1-6.
Oceanography Pressure-gradient force Pierre-Simon Laplace Ekman-Transport Equatorial waves Mass flow meter Jearl Walker Integrated Authority File
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