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Coriolis effect 1 Coriolis effect In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right. Although recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology. Newton's laws of motion govern the motion of an object in a (non-accelerating) inertial frame of reference. When Newton's laws are transformed to a uniformly rotating frame of reference, the Coriolis and centrifugal forces appear. Both forces are proportional to the mass of the object. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to its square. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces or pseudo forces.[1] They allow the application of Newton's laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame. In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. However, the observer (red dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame. Perhaps the most commonly encountered rotating reference frame is the Earth. The Coriolis effect is caused by the rotation of the Earth and the inertia of the mass experiencing the effect. Because the Earth completes only one rotation per day, the Coriolis force is quite small, and its effects generally become noticeable only for motions occurring over large distances and long periods of time, such as large-scale movement of air in the atmosphere or water in the ocean. Such motions are constrained by the surface of the earth, so only the horizontal component of the Coriolis force is generally important. This force causes moving objects on the surface of the Earth to be deflected in a clockwise sense (with respect to the direction of travel) in the northern hemisphere, and in a counter-clockwise sense in the southern hemisphere. Rather than flowing directly from areas of high pressure to low pressure, as they would in a non-rotating system, winds and currents tend to flow to the right of this direction north of the equator, and to the left of this direction south of it. This effect is responsible for the rotation of large cyclones (see Coriolis effects in meteorology). Coriolis effect 2 History Italian scientists Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi described the effect in connection with artillery in the 1651 Almagestum Novum, writing that rotation of the Earth should cause a cannon ball fired to the north to deflect to the east.[2] The effect was described in the tidal equations of Pierre-Simon Laplace in 1778. Gaspard-Gustave Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as waterwheels.[3] That paper considered the supplementary forces that are detected in a rotating frame of reference. Coriolis divided these supplementary forces into two categories. The second category contained a force that arises from the cross product of the angular velocity of a coordinate system and the projection of a particle's velocity into a plane perpendicular to the system's axis of rotation. Coriolis referred to this force as the "compound centrifugal force" due to its analogies with the centrifugal force already considered in category one.[4][5] The effect was known in the early 20th century as the "acceleration of Coriolis",[6] and by 1920 as "Coriolis force".[7] In 1856, William Ferrel proposed the existence of a circulation cell in the mid-latitudes with air being deflected by the Coriolis force to create the prevailing westerly winds.[8] Understanding the kinematics of how exactly the rotation of the Earth affects airflow was partial at first.[9] Late in the 19th century, the full extent of the large scale interaction of pressure gradient force and deflecting force that in the end causes air masses to move 'along' isobars was understood. Formula In non-vector terms: at a given rate of rotation of the observer, the magnitude of the Coriolis acceleration of the object is proportional to the velocity of the object and also to the sine of the angle between the direction of movement of the object and the axis of rotation. The vector formula for the magnitude and direction of the Coriolis acceleration [10] is where (here and below) is the acceleration of the particle in the rotating system, is the velocity of the particle in the rotating system, and Ω is the angular velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator. The equation may be multiplied by the mass of the relevant object to produce the Coriolis force: . See fictitious force for a derivation. The Coriolis effect is the behavior added by the Coriolis acceleration. The formula implies that the Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the frame's rotation axis. So in particular: • • • • • if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero. if the velocity is straight inward to the axis, the acceleration is in the direction of local rotation. if the velocity is straight outward from the axis, the acceleration is against the direction of local rotation. if the velocity is in the direction of local rotation, the acceleration is outward from the axis. if the velocity is against the direction of local rotation, the acceleration is inward to the axis. The vector cross product can be evaluated as the determinant of a matrix: Coriolis effect where the vectors i, j, k are unit vectors in the x, y and z directions. Causes The Coriolis effect exists only when one uses a rotating reference frame. In the rotating frame it behaves exactly like a real force (that is to say, it causes acceleration and has real effects). However, Coriolis force is a consequence of inertia, and is not attributable to an identifiable originating body, as is the case for electromagnetic or nuclear forces, for example. From an analytical viewpoint, to use Newton's second law in a rotating system, Coriolis force is mathematically necessary, but it disappears in a non-accelerating, inertial frame of reference. For example, consider two children on opposite sides of a spinning roundabout (carousel), who are throwing a ball to each other (see diagram). From the children's point of view, this ball's path is curved sideways by the Coriolis effect. Suppose the roundabout spins counter-clockwise when viewed from above. From the thrower's perspective, the deflection is to the right.[11] From the non-thrower's perspective, deflection is to left. For a mathematical formulation see Mathematical derivation of fictitious forces. An observer in a rotating frame, such as an astronaut in a rotating space station, very probably will find the interpretation of everyday life in terms of the Coriolis force accords more simply with intuition and experience than a cerebral reinterpretation of events from an inertial standpoint. For example, nausea due to an experienced push may be more instinctively explained by Coriolis force than by the law of inertia.[12][13] See also Coriolis effect (perception). In meteorology, a rotating frame (the Earth) with its Coriolis force proves a more natural framework for explanation of air movements than a non-rotating, inertial frame without Coriolis forces.[14] In long-range gunnery, sight corrections for the Earth's rotation are based upon Coriolis force.[15] These examples are described in more detail below. The acceleration entering the Coriolis force arises from two sources of change in velocity that result from rotation: the first is the change of the velocity of an object in time. The same velocity (in an inertial frame of reference where the normal laws of physics apply) will be seen as different velocities at different times in a rotating frame of reference. The apparent acceleration is proportional to the angular velocity of the reference frame (the rate at which the coordinate axes change direction), and to the component of velocity of the object in a plane perpendicular to the axis of rotation. This gives a term . The minus sign arises from the traditional definition of the cross product (right hand rule), and from the sign convention for angular velocity vectors. The second is the change of velocity in space. Different positions in a rotating frame of reference have different velocities (as seen from an inertial frame of reference). In order for an object to move in a straight line it must therefore be accelerated so that its velocity changes from point to point by the same amount as the velocities of the frame of reference. The effect is proportional to the angular velocity (which determines the relative speed of two different points in the rotating frame of reference), and to the component of the velocity of the object in a plane perpendicular to the axis of rotation (which determines how quickly it moves between those points). This also gives a term . Length scales and the Rossby number The time, space and velocity scales are important in determining the importance of the Coriolis effect. Whether rotation is important in a system can be determined by its Rossby number, which is the ratio of the velocity, U, of a system to the product of the Coriolis parameter, , and the length scale, L, of the motion: The Rossby number is the ratio of inertial to Coriolis forces. A small Rossby number signifies a system which is strongly affected by Coriolis forces, and a large Rossby number signifies a system in which inertial forces dominate. For example, in tornadoes, the Rossby number is large, in low-pressure systems it is low and in oceanic systems it is 3 Coriolis effect 4 around 1. As a result, in tornadoes the Coriolis force is negligible, and balance is between pressure and centrifugal forces. In low-pressure systems, centrifugal force is negligible and balance is between Coriolis and pressure forces. In the oceans all three forces are comparable.[16] An atmospheric system moving at U = 10 m/s (22 mph) occupying a spatial distance of L = 1,000 km (621 mi), has a Rossby number of approximately 0.1. A baseball pitcher may throw the ball at U = 45 m/s (100 mph) for a distance of L = 18.3 m (60 ft). The Rossby number in this case would be 32,000. Needless to say, one does not worry about which hemisphere one is in when playing baseball. However, an unguided missile obeys exactly the same physics as a baseball, but may travel far enough and be in the air long enough to notice the effect of Coriolis. Long-range shells in the Northern Hemisphere landed close to, but to the right of, where they were aimed until this was noted. (Those fired in the southern hemisphere landed to the left.) In fact, it was this effect that first got the attention of Coriolis himself.[17][18][19] Applied to Earth An important case where the Coriolis force is observed is the rotating Earth. Intuitive explanation As the Earth turns around its axis, everything attached to it turns with it (imperceptibly to our senses). An object that is moving without being dragged along with this rotation travels in a straight motion over the turning Earth. From our rotating perspective on the planet, its direction of motion changes as it moves, bending in the opposite direction to our actual motion. When viewed from a stationary point in space above, any land feature in the Northern Hemisphere turns counter-clockwise, and, fixing our gaze on that location, any other location in that hemisphere will rotate around it the same way. The traced ground-path of a freely moving body traveling from one point to another will therefore bend the opposite way, clockwise, which is conventionally labeled as "right," where it will be if the direction of motion is considered "ahead" and "down" is defined naturally. Rotating sphere Consider a location with latitude φ on a sphere that is rotating around the north-south axis.[20] A local coordinate system is set up with the x axis horizontally due east, the y axis horizontally due north and the z axis vertically upwards. The rotation vector, velocity of movement and Coriolis acceleration expressed in this local coordinate system (listing components in the order East (e), North (n) and Upward (u)) are: Coordinate system at latitude φ with x-axis east, y-axis north and z-axis upward (that is, radially outward from center of sphere). Coriolis effect 5 When considering atmospheric or oceanic dynamics, the vertical velocity is small and the vertical component of the Coriolis acceleration is small compared to gravity. For such cases, only the horizontal (East and North) components matter. The restriction of the above to the horizontal plane is (setting vu = 0): where is called the Coriolis parameter. By setting vn = 0, it can be seen immediately that (for positive φ and ω) a movement due east results in an acceleration due south. Similarly, setting ve = 0, it is seen that a movement due north results in an acceleration due east. In general, observed horizontally, looking along the direction of the movement causing the acceleration, the acceleration always is turned 90° to the right and of the same size regardless of the horizontal orientation. That is:[21][22] On a merry-go-round in the night Coriolis was shaken with fright Despite how he walked 'Twas like he was stalked By some fiend always pushing him right — David Morin, Eric Zaslow, E'beth Haley, John Golden, and Nathan Salwen As a different case, consider equatorial motion setting φ = 0°. In this case, Ω is parallel to the North or n-axis, and: Accordingly, an eastward motion (that is, in the same direction as the rotation of the sphere) provides an upward acceleration known as the Eötvös effect, and an upward motion produces an acceleration due west. Distant stars The apparent motion of a distant star as seen from Earth is dominated by the Coriolis and centrifugal forces. Consider such a star (with mass m) located at position r, with declination δ, so Ω · r = |r| Ω sin(δ), where Ω is the Earth's rotation vector. The star is observed to rotate about the Earth's axis with a period of one sidereal day in the opposite direction to that of the Earth's rotation, making its velocity v = –Ω × r. The fictitious force, consisting of Coriolis and centrifugal forces, is: where uΩ = Ω−1Ω is a unit vector in the direction of Ω. The fictitious force Ff is thus a vector of magnitude m Ω2|r| cos(δ), perpendicular to Ω, and directed towards the center of the star's rotation on the Earth's axis, and therefore recognisable as the centripetal force that will keep the star in a circular movement around that axis. Coriolis effect 6 Meteorology Perhaps the most important impact of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology and oceanography, it is convenient to postulate a rotating frame of reference wherein the Earth is stationary. In accommodation of that provisional postulation, the centrifugal and Coriolis forces are introduced. Their relative importance is determined by the applicable Rossby numbers. Tornadoes have high Rossby numbers, so, while tornado-associated centrifugal forces are quite substantial, Coriolis forces associated with tornados are for practical purposes negligible.[23] High pressure systems rotate in a direction such that the Coriolis force will be directed radially inwards, and nearly balanced by the outwardly radial pressure gradient. This direction is clockwise in the northern hemisphere and counter-clockwise in the southern hemisphere. Low pressure systems rotate in the opposite direction, so that the Coriolis force is directed radially outward and nearly balances an inwardly radial pressure gradient. In each case a slight imbalance between the Coriolis force and the pressure gradient accounts for the radially inward acceleration of the system's circular motion. This low pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force. Flow around a low-pressure area If a low-pressure area forms in the atmosphere, air will tend to flow in towards it, but will be deflected perpendicular to its velocity by the Coriolis force. A system of equilibrium can then establish itself creating circular movement, or a cyclonic flow. Because the Rossby number is low, the force balance is largely between the pressure gradient force acting towards the low-pressure area and the Coriolis force acting away from the center of the low pressure. Schematic representation of flow around a low-pressure area in the Northern hemisphere. The Rossby number is low, so the centrifugal force is virtually negligible. The pressure-gradient force is represented by blue arrows, the Coriolis acceleration (always perpendicular to the velocity) by red arrows Instead of flowing down the gradient, large scale motions in the atmosphere and ocean tend to occur perpendicular to the pressure gradient. This is known as geostrophic flow.[24] On a non-rotating planet, fluid would flow along the straightest possible line, quickly eliminating pressure gradients. Note that the geostrophic balance is thus very different from the case of "inertial motions" (see below) which explains why mid-latitude cyclones are larger by an order of magnitude than inertial circle flow would be. This pattern of deflection, and the direction of movement, is called Buys-Ballot's law. In the atmosphere, the pattern of flow is called a cyclone. In the Northern Hemisphere the direction of movement around a low-pressure area is counter-clockwise. In the Southern Hemisphere, the direction of movement is clockwise because the rotational dynamics is a mirror image there. At high altitudes, Coriolis effect 7 outward-spreading air rotates in the opposite direction.[25] Cyclones rarely form along the equator due to the weak Coriolis effect present in this region. Inertial circles An air or water mass moving with speed subject only to the Coriolis force travels in a circular trajectory called an 'inertial circle'. Since the force is directed at right angles to the motion of the particle, it will move with a constant speed around a circle whose radius is given by: where is the Coriolis parameter (where is the latitude). The time taken for the mass to complete a full circle is therefore , introduced above Schematic representation of inertial circles of air masses in the absence of other forces, calculated for a wind speed of approximately 50 to 70 m/s (110 to 160 mph). . The Coriolis parameter typically has a mid-latitude value of about 10−4 s−1; hence for a typical atmospheric speed of 10 m/s (22 mph) the radius is 100 km (62 mi), with a period of about 17 hours. For an ocean current with a typical speed of 10 cm/s (0.22 mph), the radius of an inertial circle is 1 km (0.6 mi). These inertial circles are clockwise in the northern hemisphere (where trajectories are bent to the right) and counter-clockwise in the southern hemisphere. If the rotating system is a parabolic turntable, then planet, is constant and the trajectories are exact circles. On a rotating varies with latitude and the paths of particles do not form exact circles. Since the parameter varies as the sine of the latitude, the radius of the oscillations associated with a given speed are smallest at the poles (latitude = ±90°), and increase toward the equator.[26] Other terrestrial effects The Coriolis effect strongly affects the large-scale oceanic and atmospheric circulation, leading to the formation of robust features like jet streams and western boundary currents. Such features are in geostrophic balance, meaning that the Coriolis and pressure gradient forces balance each other. Coriolis acceleration is also responsible for the propagation of many types of waves in the ocean and atmosphere, including Rossby waves and Kelvin waves. It is also instrumental in the so-called Ekman dynamics in the ocean, and in the establishment of the large-scale ocean flow pattern called the Sverdrup balance. Eötvös effect The practical impact of the Coriolis effect is mostly caused by the horizontal acceleration component produced by horizontal motion. There are other components of the Coriolis effect. Eastward-traveling objects will be deflected upwards (feel lighter), while westward-traveling objects will be deflected downwards (feel heavier). This is known as the Eötvös effect. This aspect of the Coriolis effect is greatest near the equator. The force produced by this effect is similar to the horizontal component, but the much larger vertical forces due to gravity and pressure mean that it is generally unimportant dynamically. In addition, objects traveling upwards or downwards will be deflected to the west or east respectively. This effect is also the greatest near the equator. Since vertical movement is usually of limited extent and duration, the size of the effect is smaller and requires precise instruments to detect. Coriolis effect Draining in bathtubs and toilets Water rotation in home bathrooms under normal circumstances is not related to the Coriolis effect or to the rotation of the earth, and no consistent difference in rotation direction between toilets in the northern and southern hemispheres can be observed. The formation of a vortex over the plug hole may be explained by the conservation of angular momentum: The radius of rotation decreases as water approaches the plug hole so the rate of rotation increases, for the same reason that an ice skater's rate of spin increases as they pull their arms in. Any rotation around the plug hole that is initially present accelerates as water moves inward. Only if the water is so still that the effective rotation rate of the earth (once per day at the poles, once every 2 days at 30 degrees of latitude) is faster than that of the water relative to its container, and if externally applied torques (such as might be caused by flow over an uneven bottom surface) are small enough, the Coriolis effect may determine the direction of the vortex. Without such careful preparation, the Coriolis effect may be much smaller than various other influences on drain direction,[27] such as any residual rotation of the water[28] and the geometry of the container.[29] Despite this, the idea that toilets and bathtubs drain differently in the Northern and Southern Hemispheres has been popularized by several television programs, including The Simpsons episode "Bart vs. Australia" and The X-Files episode "Die Hand Die Verletzt".[30] Several science broadcasts and publications, including at least one college-level physics textbook, have also stated this.[31][32] In 1908, the Austrian physicist Ottokar Tumlirz described careful and effective experiments which demonstrated the effect of the rotation of the Earth on the outflow of water through a central aperture.[33] The subject was later popularized in a famous article in the journal Nature, which described an experiment in which all other forces to the system were removed by filling a 6 ft (1.8 m) tank with 300 US gal (1,100 L) of water and allowing it to settle for 24 hours (to allow any movement due to filling the tank to die away), in a room where the temperature had stabilized. The drain plug was then very slowly removed, and tiny pieces of floating wood were used to observe rotation. During the first 12 to 15 minutes, no rotation was observed. Then, a vortex appeared and consistently began to rotate in a counter-clockwise direction (the experiment was performed in Boston, Massachusetts, in the Northern hemisphere). This was repeated and the results averaged to make sure the effect was real. The report noted that the vortex rotated, "about 30,000 times faster than the effective rotation of the earth in 42° North (the experiment's location)". This shows that the small initial rotation due to the earth is amplified by gravitational draining and conservation of angular momentum to become a rapid vortex and may be observed under carefully controlled laboratory conditions.[34][35] Ballistic missiles and satellites Ballistic missiles and satellites appear to follow curved paths when plotted on common world maps mainly because the Earth is spherical and the shortest distance between two points on the Earth's surface (called a great circle) is usually not a straight line on those maps. Every two-dimensional (flat) map necessarily distorts the Earth's curved (three-dimensional) surface. Typically (as in the commonly used Mercator projection, for example), this distortion increases with proximity to the poles. In the northern hemisphere for example, a ballistic missile fired toward a distant target using the shortest possible route (a great circle) will appear on such maps to follow a path north of the straight line from target to destination, and then curve back toward the equator. This occurs because the latitudes, which are projected as straight horizontal lines on most world maps, are in fact circles on the surface of a sphere, which get smaller as they get closer to the pole. Being simply a consequence of the sphericity of the Earth, this would be true even if the Earth didn't rotate. The Coriolis effect is of course also present, but its effect on the plotted path is much smaller. The Coriolis effects became important in external ballistics for calculating the trajectories of very long-range artillery shells. The most famous historical example was the Paris gun, used by the Germans during World War I to bombard Paris from a range of about 120 km (75 mi). 8 Coriolis effect 9 Special cases Cannon on turntable The animation at the top of this article is a classic illustration of Coriolis force. Another visualization of the Coriolis and centrifugal forces is this animation clip [36]. Given the radius R of the turntable in that animation, the rate of angular rotation ω, and the speed of the cannonball (assumed constant) v, the correct angle θ to aim so as to hit the target at the edge of the turntable can be calculated. The inertial frame of reference provides one way to handle the question: calculate the time to interception, which is tf = R / v . Then, the turntable revolves an angle ω tf in this time. If the cannon is pointed an angle θ = ω tf = ω R / v, then the cannonball arrives at the periphery at position number 3 at the same time as the target. Cannon at the centre of a rotating turntable. To hit the target located at position 1 on the perimeter at time t = 0s, the cannon must be aimed ahead of the target at angle θ. That way, by the time the cannonball reaches position 3 on the periphery, the target also will be at that position. In an inertial frame of reference, the cannonball travels a straight radial path to the target (curve yA). However, in the frame of the turntable, the path is arched (curve yB), as also shown in the figure. No discussion of Coriolis force can arrive at this solution as simply, so the reason to treat this problem is to demonstrate Coriolis formalism in an easily visualized situation. The trajectory in the inertial frame (denoted A) is a straight line radial path at angle θ. The position of the cannonball in (x, y) coordinates at time t is: In the turntable frame (denoted B), the x- y axes rotate at angular rate ω, so the trajectory becomes: and three examples of this result are plotted in the figure. Successful trajectory of cannonball as seen from the turntable for three angles of launch θ. Plotted points are for the same equally spaced times steps on each curve. Cannonball speed v is held constant and angular rate of rotation ω is varied to achieve a successful "hit" for selected θ. For example, for a radius of 1 m and a cannonball speed of 1 m/s, the time of flight tf = 1 s, and ωtf = θ → ω and θ have the same numerical value if θ is expressed in radians. The wider spacing of the plotted points as the target is approached show the speed of the cannonball is accelerating as seen on the turntable, due to fictitious Coriolis and centrifugal forces. To determine the components of acceleration, a general expression is used from the article fictitious force: Coriolis effect 10 in which the term in Ω × vB is the Coriolis acceleration and the term in Ω × ( Ω × rB) is the centrifugal acceleration. The results are (let α = θ − ωt): Acceleration components at an earlier time (top) and at arrival time at the target (bottom) Coriolis acceleration, centrifugal acceleration and net acceleration vectors at three selected points on the trajectory as seen on the turntable. producing a centrifugal acceleration: Also: Coriolis effect producing a Coriolis acceleration: These accelerations are shown in the diagrams for a particular example. It is seen that the Coriolis acceleration not only cancels the centrifugal acceleration, but together they provide a net "centripetal", radially inward component of acceleration (that is, directed toward the centre of rotation):[37] and an additional component of acceleration perpendicular to rB (t): The "centripetal" component of acceleration resembles that for circular motion at radius rB, while the perpendicular component is velocity dependent, increasing with the radial velocity v and directed to the right of the velocity. The situation could be described as a circular motion combined with an "apparent Coriolis acceleration" of 2ωv. However, this is a rough labelling: a careful designation of the true centripetal force refers to a local reference frame that employs the directions normal and tangential to the path, not coordinates referred to the axis of rotation. These results also can be obtained directly by two time differentiations of rB (t). Agreement of the two approaches demonstrates that one could start from the general expression for fictitious acceleration above and derive the trajectories shown here. However, working from the acceleration to the trajectory is more complicated than the reverse procedure used here, which, of course, is made possible in this example by knowing the answer in advance. As a result of this analysis an important point appears: all the fictitious accelerations must be included to obtain the correct trajectory. In particular, besides the Coriolis acceleration, the centrifugal force plays an essential role. It is easy to get the impression from verbal discussions of the cannonball problem, which are focussed on displaying the Coriolis effect particularly, that the Coriolis force is the only factor that must be considered;[38] emphatically, that is not so.[39] A turntable for which the Coriolis force is the only factor is the parabolic turntable. A somewhat more complex situation is the idealized example of flight routes over long distances, where the centrifugal force of the path and aeronautical lift are countered by gravitational attraction.[40][41] 11 Coriolis effect 12 Tossed ball on a rotating carousel The figure illustrates a ball tossed from 12:00 o'clock toward the centre of an counter-clockwise rotating carousel. On the left, the ball is seen by a stationary observer above the carousel, and the ball travels in a straight line to the centre, while the ball-thrower rotates counter-clockwise with the carousel. On the right the ball is seen by an observer rotating with the carousel, so the ball-thrower appears to stay at 12:00 o'clock. The figure shows how the trajectory of the ball as seen by the rotating observer can be constructed. A carousel is rotating counter-clockwise. Left panel: a ball is tossed by a thrower at 12:00 o'clock and travels in a straight line to the centre of the carousel. While it travels, the thrower circles in an counter-clockwise direction. Right panel: The ball's motion as seen by the thrower, who now remains at 12:00 o'clock, because there is no rotation from their viewpoint. On the left, two arrows locate the ball relative to the ball-thrower. One of these arrows is from the thrower to the centre of the carousel (providing the ball-thrower's line of sight), and the other points from the centre of the carousel to the ball.(This arrow gets shorter as the ball approaches the centre.) A shifted version of the two arrows is shown dotted. On the right is shown this same dotted pair of arrows, but now the pair are rigidly rotated so the arrow corresponding to the line of sight of the ball-thrower toward the centre of the carousel is aligned with 12:00 o'clock. The other arrow of the pair locates the ball relative to the centre of the carousel, providing the position of the ball as seen by the rotating observer. By following this procedure for several positions, the trajectory in the rotating frame of reference is established as shown by the curved path in the right-hand panel. The ball travels in the air, and there is no net force upon it. To the stationary observer the ball follows a straight-line path, so there is no problem squaring this trajectory with zero net force. However, the rotating observer sees a curved path. Kinematics insists that a force (pushing to the right of the instantaneous direction of travel for an counter-clockwise rotation) must be present to cause this curvature, so the rotating observer is forced to invoke a combination of centrifugal and Coriolis forces to provide the net force required to cause the curved trajectory. Coriolis effect Bounced ball The figure describes a more complex situation where the tossed ball on a turntable bounces off the edge of the carousel and then returns to the tosser, who catches the ball. The effect of Coriolis force on its trajectory is shown again as seen by two observers: an observer (referred to as the "camera") that rotates with the carousel, and an inertial observer. The figure shows a bird's-eye view based upon the same ball speed on forward and return paths. Within Bird's-eye view of carousel. The carousel rotates clockwise. Two viewpoints are each circle, plotted dots show the same time illustrated: that of the camera at the center of rotation rotating with the carousel points. In the left panel, from the camera's (left panel) and that of the inertial (stationary) observer (right panel). Both viewpoint at the center of rotation, the tosser observers agree at any given time just how far the ball is from the center of the (smiley face) and the rail both are at fixed carousel, but not on its orientation. Time intervals are 1/10 of time from launch to bounce. locations, and the ball makes a very considerable arc on its travel toward the rail, and takes a more direct route on the way back. From the ball tosser's viewpoint, the ball seems to return more quickly than it went (because the tosser is rotating toward the ball on the return flight). On the carousel, instead of tossing the ball straight at a rail to bounce back, the tosser must throw the ball toward the right of the target and the ball then seems to the camera to bear continuously to the left of its direction of travel to hit the rail (left because the carousel is turning clockwise). The ball appears to bear to the left from direction of travel on both inward and return trajectories. The curved path demands this observer to recognize a leftward net force on the ball. (This force is "fictitious" because it disappears for a stationary observer, as is discussed shortly.) For some angles of launch, a path has portions where the trajectory is approximately radial, and Coriolis force is primarily responsible for the apparent deflection of the ball (centrifugal force is radial from the center of rotation, and causes little deflection on these segments). When a path curves away from radial, however, centrifugal force contributes significantly to deflection. The ball's path through the air is straight when viewed by observers standing on the ground (right panel). In the right panel (stationary observer), the ball tosser (smiley face) is at 12 o'clock and the rail the ball bounces from is at position one (1). From the inertial viewer's standpoint, positions one (1), two (2), three (3) are occupied in sequence. At position 2 the ball strikes the rail, and at position 3 the ball returns to the tosser. Straight-line paths are followed because the ball is in free flight, so this observer requires that no net force is applied. 13 Coriolis effect 14 Bullets at high velocity through the atmosphere Because of the rotation of the earth in relationship to ballistics, the bullet does not fly straight although it may seem like it from the shooter's perspective. The Coriolis effect changes the trajectory of the bullet slightly to give the path of the projectile a more arched shape. This situation only occurs at extremely long distances and therefore, is used to calculate a perfect shot by today's trained snipers. Visualization of the Coriolis effect To demonstrate the Coriolis effect, a parabolic turntable can be used. On a flat turntable, the inertia of a co-rotating object would force it off the edge. But if the surface of the turntable has the correct paraboloid (parabolic bowl) shape (see the figure) and is rotated at the corresponding rate, the force components shown in the figure are such that the component of gravity tangential to the bowl surface will exactly equal the centripetal force necessary to keep the object rotating at its velocity and radius of curvature (assuming no friction). (See banked turn.) This carefully contoured surface allows the Coriolis force to be displayed in isolation.[42][43] A fluid assuming a parabolic shape as it is rotating Discs cut from cylinders of dry ice can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable, with results as shown in the figure. In the left panel of the figure, which is the viewpoint of a stationary observer, the gravitational force in the inertial frame pulling the object toward the center (bottom ) of the dish is proportional to the distance of the object from the center. A centripetal force of this form The forces at play in the case of a curved surface. causes the elliptical motion. In the right panel, which shows the Red: gravity viewpoint of the rotating frame, the inward gravitational force in the Green: the normal force Blue: the resultant centripetal force. rotating frame (the same force as in the inertial frame) is balanced by the outward centrifugal force (present only in the rotating frame). With these two forces balanced, in the rotating frame the only unbalanced force is Coriolis (also present only in the rotating frame), and the motion is an inertial circle. Analysis and observation of circular motion in the rotating frame is a simplification compared to analysis or observation of elliptical motion in the inertial frame. Because this reference frame rotates several times a minute rather than only once a day like the Earth, the Coriolis acceleration produced is many times larger and so easier to observe on small time and spatial scales than is the Coriolis acceleration caused by the rotation of the Earth. In a manner of speaking, the Earth is analogous to such a turntable.[44] The rotation has caused the planet to settle on a spheroid shape, such that the normal force, the gravitational force and the centrifugal force exactly balance each other on a "horizontal" surface. (See equatorial bulge.) The Coriolis effect caused by the rotation of the Earth can be seen indirectly through the motion of a Foucault pendulum. Coriolis effect 15 Coriolis effects in other areas Coriolis flow meter A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate and density of a fluid flowing through a tube. The operating principle involves inducing a vibration of the tube through which the fluid passes. The vibration, though it is not completely circular, provides the rotating reference frame which gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed represent the mass flow rate and density of the fluid.[45] Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory. Left: The inertial point of view. Right: The co-rotating point of view. Molecular physics In polyatomic molecules, the molecule motion can be described by a rigid body rotation and internal vibration of atoms about their equilibrium position. As a result of the vibrations of the atoms, the atoms are in motion relative to the rotating coordinate system of the molecule. Coriolis effects will therefore be present and will cause the atoms to move in a direction perpendicular to the original oscillations. This leads to a mixing in molecular spectra between the rotational and vibrational levels from which Coriolis coupling constants can be determined.[46] Insect flight Flies (Diptera) and moths (Lepidoptera) utilize the Coriolis effect when flying: their halteres, or antennae in the case of moths, oscillate rapidly and are used as vibrational gyroscopes.[47] See Coriolis effect in insect stability.[48] In this context, the Coriolis effect has nothing to do with the rotation of the Earth. References [1] Bhatia, V.B. (1997). Classical Mechanics: With introduction to Nonlinear Oscillations and Chaos. Narosa Publishing House. p. 201. ISBN 81-7319-105-0. [2] Graney, Christopher M. (2011). "Coriolis effect, two centuries before Coriolis". Physics Today 64: 8. Bibcode 2011PhT....64h...8G. doi:10.1063/PT.3.1195. [3] G-G Coriolis (1835). "Sur les équations du mouvement relatif des systèmes de corps". J. de l'Ecole royale polytechnique 15: 144–154. [4] Dugas, René and J. R. Maddox (1988). A History of Mechanics (http:/ / books. google. com/ books?id=vPT-JubW-7QC& pg=PA374). Courier Dover Publications: p. 374. ISBN 0-486-65632-2 [5] Bartholomew Price (1862). A Treatise on Infinitesimal Calculus : Vol. IV. The dynamics of material systems (http:/ / books. google. com/ ?id=qrMA0R_0TPEC& pg=PA420). Oxford : University Press. pp. 418–420. . [6] Arthur Gordon Webster (1912). The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies (http:/ / books. google. com/ ?id=zXkRAAAAYAAJ& pg=PA320). B. G. Teubner. p. 320. ISBN 1-113-14861-6. . [7] Edwin b. Wilson (1920). James McKeen Cattell. ed. "Space, Time, and Gravitation" (http:/ / books. google. com/ ?id=xYUZAAAAYAAJ& pg=PA226). The Scientific Monthly (American Association for the Advancement of Science) 10: 226. . [8] William Ferrel (November 1856). "An Essay on the Winds and the Currents of the Ocean" (http:/ / www. aos. princeton. edu/ WWWPUBLIC/ gkv/ history/ ferrel-nashville56. pdf). Nashville Journal of Medicine and Surgery xi (4): 7–19. . Retrieved on 1 January 2009. [9] Anders O. Persson. The Coriolis Effect:Four centuries of conflict between common sense and mathematics, Part I: A history to 1885 (http:/ / www. aos. princeton. edu/ WWWPUBLIC/ gkv/ history/ persson_on_coriolis05. pdf). . [10] Hestenes, David (1990). New Foundations for Classical Mechanics. The Netherlands: Kluwer Academic Publishers. pp. 312. ISBN ISBN=90-277-2526-8 (pbk). Coriolis effect [11] John M. Wallace and Peter V. Hobbs (1977). Atmospheric Science: An Introductory Survey. Academic Press, Inc.. pp. 368–371. ISBN 0-12-732950-1. [12] Sheldon M. Ebenholtz (2001). Oculomotor Systems and Perception (http:/ / books. google. com/ ?id=1W7ePrvrRyYC& pg=PA151). Cambridge University Press. ISBN 0-521-80459-0. . [13] George Mather (2006). Foundations of perception (http:/ / books. google. com/ ?id=LYA9faq3lt4C& pg=PA73). Taylor & Francis. ISBN 0-86377-835-6. . [14] Roger Graham Barry, Richard J. Chorley (2003). Atmosphere, Weather and Climate (http:/ / books. google. com/ ?id=MUQOAAAAQAAJ& pg=PA115). Routledge. p. 113. ISBN 0-415-27171-1. . [15] The claim is made that in the Falklands in WW I, the British failed to correct their sights for the southern hemisphere, and so missed their targets. John Edensor Littlewood (1953). A Mathematician's Miscellany (http:/ / www. archive. org/ details/ mathematiciansmi033496mbp). Methuen And Company Limited. p. 51. . John Robert Taylor (2005). Classical Mechanics (http:/ / books. google. com/ ?id=P1kCtNr-pJsC& pg=PA364). University Science Books. p. 364; Problem 9.28. ISBN 1-891389-22-X. . For set up of the calculations, seeDonald E. Carlucci, Sidney S. Jacobson (2007). Ballistics (http:/ / books. google. com/ ?id=pX9Tzs7VuSoC& pg=PA225). CRC Press. p. 225. ISBN 1-4200-6618-8. . [16] Lakshmi H. Kantha & Carol Anne Clayson (2000). Numerical Models of Oceans and Oceanic Processes (http:/ / books. google. com/ ?id=Gps9JXtd3owC& pg=PA103). Academic Press. p. 103. ISBN 0-12-434068-7. . [17] Stephen D. Butz (2002). Science of Earth Systems (http:/ / books. google. com/ ?id=JB4ArbvXXDEC& pg=PA304). Thomson Delmar Learning. p. 305. ISBN 0-7668-3391-7. . [18] James R. Holton (2004). An Introduction to Dynamic Meteorology (http:/ / books. google. com/ ?id=fhW5oDv3EPsC& pg=PA18). Academic Press. p. 18. ISBN 0-12-354015-1. . [19] Donald E. Carlucci & Sidney S. Jacobson (2007). Ballistics: Theory and Design of Guns and Ammunition (http:/ / books. google. com/ ?id=pX9Tzs7VuSoC& pg=PA224). CRC Press. pp. 224–226. ISBN 1-4200-6618-8. . [20] William Menke & Dallas Abbott (1990). Geophysical Theory (http:/ / books. google. com/ ?id=XP3R_pVnOoEC& pg=PA120). Columbia University Press. pp. 124–126. ISBN 0-231-06792-5. . [21] David Morin, Eric Zaslow, Elizabeth Haley, John Goldne, and Natan Salwen (2 December 2005). "Limerick – May the Force Be With You" (http:/ / www. phys. canterbury. ac. nz/ newsletter/ 2005/ nl20051202. pdf). Weekly Newsletter Volume 22, No 47. Department of Physics and Astronomy, University of Canterbury. . Retrieved 1 January 2009. [22] David Morin (2008). Introduction to classical mechanics: with problems and solutions (http:/ / books. google. com/ ?id=Ni6CD7K2X4MC& pg=PA466). Cambridge University Press. p. 466. ISBN 0-521-87622-2. . [23] James R. Holton (2004). An Introduction to Dynamic Meteorology (http:/ / books. google. com/ ?id=fhW5oDv3EPsC& pg=PA64). Burlington, MA: Elsevier Academic Press. p. 64. ISBN 0-12-354015-1. . [24] Roger Graham Barry & Richard J. Chorley (2003). Atmosphere, Weather and Climate (http:/ / books. google. com/ ?id=MUQOAAAAQAAJ& pg=PA115). Routledge. p. 115. ISBN 0-415-27171-1. . [25] Cloud Spirals and Outflow in Tropical Storm Katrina (http:/ / earthobservatory. nasa. gov/ Newsroom/ NewImages/ images. php3?img_id=17026) from Earth Observatory (NASA) [26] John Marshall & R. Alan Plumb (2007). p. 98 (http:/ / books. google. com/ ?id=aTGYbmVaA_gC& pg=PA98). Amsterdam: Elsevier Academic Press. ISBN 0-12-558691-4. . [27] Larry D. Kirkpatrick and Gregory E. Francis (2006). Physics: A World View (http:/ / books. google. com/ books?id=8hOLs-bmiYYC& pg=PA168& f=false). Cengage Learning. pp. 168–9. ISBN 978-0-495-01088-3. . Retrieved 1 April 2011. [28] Y. A. Stepanyants and G. H. Yeoh (2008). "Stationary bathtub vortices and a critical regime of liquid discharge" (http:/ / journals. cambridge. org/ action/ displayAbstract?fromPage=online& aid=1878300). Journal of Fluid Mechanics 604 (1): 77–98. Bibcode 2008JFM...604...77S. doi:10.1017/S0022112008001080. . [29] Creative Media Applications (2004). A Student's Guide to Earth Science: Words and terms (http:/ / books. google. com/ books?id=fF0TTZVQuZoC& pg=PA22). Greenwood Publishing Group. p. 22. ISBN 978-0-313-32902-9. . [30] "X-Files coriolis error leaves viewers wondering" (http:/ / web. archive. org/ web/ 20080105055918/ http:/ / www. encyclopedia. com/ doc/ 1G1-16836639. html) from Skeptical Inquirer [31] Fraser, Alistair. "Bad Coriolis" (http:/ / www. ems. psu. edu/ ~fraser/ Bad/ BadCoriolis. html). Bad Meteorology. Pennsylvania State College of Earth and Mineral Science. . Retrieved 17 January 2011. [32] Tipler, Paul (1998). Physics for Engineers and Scientists (4th ed.). W.H.Freeman, Worth Publishers. p. 128. ISBN 978-1-57259-616-0. "...on a smaller scale, the coriolis effect causes water draining out a bathtub to rotate counter clockwise in the northern hemisphere..." [33] Tumlirz, Ottokar (1908). "Ein neuer physikalischer Beweis für die Achsendrehung der Erde". Sitzungsberichte der math.-nat. Klasse der kaiserlichen Akademie der Wissenschaften IIa 117: 819–841. [34] Shapiro, Ascher H. (1962). "Bath-Tub Vortex". Nature 196 (4859): 1080. Bibcode 1962Natur.196.1080S. doi:10.1038/1961080b0. [35] (Vorticity, Part 1) (http:/ / web. mit. edu/ fluids/ www/ Shapiro/ ncfmf. html). Web.mit.edu. Retrieved on 8 November 2011. [36] http:/ / www. youtube. com/ watch?v=49JwbrXcPjc [37] Here the description "radially inward" means "toward the axis of rotation". That direction is not toward the center of curvature of the path, however, which is the direction of the true centripetal force. Hence, the quotation marks on "centripetal". [38] George E. Owen (2003). Fundamentals of Scientific Mathematics (http:/ / books. google. com/ ?id=9dRxGCktg7QC& pg=PA22) (original edition published by Harper & Row, New York, 1964 ed.). Courier Dover Publications. p. 23. ISBN 0-486-42808-7. . 16 Coriolis effect [39] Morton Tavel (2002). Contemporary Physics and the Limits of Knowledge (http:/ / books. google. com/ ?id=SELS0HbIhjYC& pg=PA88). Rutgers University Press. p. 88. ISBN 0-8135-3077-6. . [40] James R Ogden & M Fogiel (1995). High School Earth Science Tutor (http:/ / books. google. com/ ?id=fFmqhNXixLUC& pg=PA167). Research & Education Assoc.. p. 167. ISBN 0-87891-975-9. . [41] James Greig McCully (2006). Beyond the moon: A Conversational, Common Sense Guide to Understanding the Tides (http:/ / books. google. com/ ?id=RijQELAGnEIC& pg=PA76). World Scientific. pp. 74–76. ISBN 981-256-643-0. . [42] When a container of fluid is rotating on a turntable, the surface of the fluid naturally assumes the correct parabolic shape. This fact may be exploited to make a parabolic turntable by using a fluid that sets after several hours, such as a synthetic resin. For a video of the Coriolis effect on such a parabolic surface, see Geophysical fluid dynamics lab demonstration (http:/ / www-paoc. mit. edu/ labweb/ lab5/ gfd_v. htm) John Marshall, Massachusetts Institute of Technology. [43] For a java applet of the Coriolis effect on such a parabolic surface, see Brian Fiedler (http:/ / mensch. org/ physlets/ inosc. html) School of Meteorology at the University of Oklahoma. [44] John Marshall & R. Alan Plumb (2007). Atmosphere, Ocean, and Climate Dynamics: An Introductory Text (http:/ / books. google. com/ ?id=aTGYbmVaA_gC& pg=PA101). Academic Press. p. 101. ISBN 0-12-558691-4. . [45] Omega Engineering. Mass Flowmeters (http:/ / www. omega. com/ literature/ transactions/ volume4/ t9904-10-mass. html). . [46] califano, S (1976). Vibrational states. Wiley. pp. 226–227. ISBN 0471129968. [47] "Antennae as Gyroscopes", Science, Vol. 315, 9 February 2007, p. 771 [48] Wu, W.C.; Wood, R.J.; Fearing, R.S. (2002). "Halteres for the micromechanical flying insect". IEEE International Conference on Robotics and Automation, 2002. Proceedings. ICRA '02. 1: 60–65. doi:10.1109/ROBOT.2002.1013339. ISBN 0-7803-7272-7. Further reading: physics and meteorology • Riccioli, G.B., 1651: Almagestum Novum, Bologna, pp. 425–427 ( Original book (http://www.e-rara.ch/zut/content/pageview/141486) [in Latin], scanned images of complete pages.) • Coriolis, G.G., 1832: Mémoire sur le principe des forces vives dans les mouvements relatifs des machines. Journal de l'école Polytechnique, Vol 13, 268–302. ( Original article (http://www.aos.princeton.edu/WWWPUBLIC/gkv/history/Coriolis-1831.pdf) [in French], PDF-file, 1.6 MB, scanned images of complete pages.) • Coriolis, G.G., 1835: Mémoire sur les équations du mouvement relatif des systèmes de corps. Journal de l'école Polytechnique, Vol 15, 142–154 ( Original article (http://www.aos.princeton.edu/WWWPUBLIC/gkv/history/Coriolis-1835.pdf) [in French] PDF-file, 400 KB, scanned images of complete pages.) • Gill, AE Atmosphere-Ocean dynamics, Academic Press, 1982. • Robert Ehrlich (1990). Turning the World Inside Out and 174 Other Simple Physics Demonstrations (http:// books.google.com/?id=ehSTsNS9qB4C&pg=PA80). Princeton University Press. p. Rolling a ball on a rotating turntable; p. 80 ff. ISBN 0-691-02395-6. • Durran, D. R. (http://www.atmos.washington.edu/~durrand/), 1993: Is the Coriolis force really responsible for the inertial oscillation? (http://www.atmos.washington.edu/~durrand/pdfs/Coriolis_BAMS.pdf), Bull. Amer. Meteor. Soc., 74, 2179–2184; Corrigenda. Bulletin of the American Meteorological Society, 75, 261 • Durran, D. R., and S. K. Domonkos, 1996: An apparatus for demonstrating the inertial oscillation (http://www. atmos.washington.edu/~durrand/pdfs/inertial_osc.pdf), Bulletin of the American Meteorological Society, 77, 557–559. • Marion, Jerry B. 1970, Classical Dynamics of Particles and Systems, Academic Press. • Persson, A., 1998 (http://www.aos.princeton.edu/WWWPUBLIC/gkv/history/Persson98.pdf) How do we Understand the Coriolis Force? Bulletin of the American Meteorological Society 79, 1373–1385. • Symon, Keith. 1971, Mechanics, Addison–Wesley • Akira Kageyama & Mamoru Hyodo: Eulerian derivation of the Coriolis force (http://arxiv.org/abs/physics/ 0509004v2) • James F. Price: A Coriolis tutorial (http://www.whoi.edu/science/PO/people/jprice/class/aCt.pdf) Woods Hole Oceanographic Institute (2003) 17 Coriolis effect Further reading: historical • Grattan-Guinness, I., Ed., 1994: Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vols. I and II. Routledge, 1840 pp. 1997: The Fontana History of the Mathematical Sciences. Fontana, 817 pp. 710 pp. • Khrgian, A., 1970: Meteorology — A Historical Survey. Vol. 1. Keter Press, 387 pp. • Kuhn, T. S., 1977: Energy conservation as an example of simultaneous discovery. The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, 66–104. • Kutzbach, G., 1979: The Thermal Theory of Cyclones. A History of Meteorological Thought in the Nineteenth Century. Amer. Meteor. Soc., 254 pp. External links • The definition of the Coriolis effect from the Glossary of Meteorology (http://amsglossary.allenpress.com/ glossary/search?id=coriolis-force1) • Anders Persson The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885 (http://www.meteohistory.org/2005historyofmeteorology2/01persson.pdf) History of Meteorology 2 (2005) • 10 Coriolis Effect Videos and Games (http://weather.about.com/od/weathertutorials/tp/coriolisvideos.htm)from the About.com Weather Page • Coriolis Force (http://scienceworld.wolfram.com/physics/CoriolisForce.html) – from ScienceWorld • Coriolis Effect and Drains (http://www.newton.dep.anl.gov/askasci/phy00/phy00733.htm) An article from the NEWTON web site hosted by the Argonne National Laboratory. • Catalog of Coriolis videos (http://www.imaginascience.com/articles/sciencesphysiques/mecanique/coriolis/ coriolis4.php) • Do bathtubs drain counterclockwise in the Northern Hemisphere? (http://www.straightdope.com/classics/ a1_161.html) by Cecil Adams. • Bad Coriolis. (http://www.ems.psu.edu/~fraser/Bad/BadCoriolis.html) An article uncovering misinformation about the Coriolis effect. By Alistair B. Fraser, Emeritus Professor of Meteorology at Pennsylvania State University • The Coriolis Effect: A (Fairly) Simple Explanation (http://stratus.ssec.wisc.edu/courses/gg101/coriolis/ coriolis.html), an explanation for the layperson • Coriolis Effect: A graphical animation (http://www.youtube.com/watch?v=mcPs_OdQOYU), a visual earth animation with precise explanation • Observe an animation of the Coriolis effect over Earth's surface (http://www.classzone.com/books/ earth_science/terc/content/visualizations/es1904/es1904page01.cfm?chapter_no=visualization) • Animation clip (http://www.youtube.com/watch?v=49JwbrXcPjc) showing scenes as viewed from both an inertial frame and a rotating frame of reference, visualizing the Coriolis and centrifugal forces. • Vincent Mallette The Coriolis Force @ INWIT (http://www.inwit.com/inwit/writings/coriolisforce.html) • NASA notes (http://pwg.gsfc.nasa.gov/stargaze/Srotfram.htm) • Interactive Coriolis Fountain (http://andygiger.com/science/e-coriolis/index.html) lets you control rotation speed, droplet speed and frame of reference to explore the Coriolis effect. 18 Article Sources and Contributors Article Sources and Contributors Coriolis effect Source: http://en.wikipedia.org/w/index.php?oldid=535318699 Contributors: 100110100, 1exec1, 213.253.40.xxx, 2over0, @modi, A. di M., A4, Aaron McDaid, Addshore, AdjustShift, Afogarty, Ahoerstemeier, Ajm81, Ajraddatz, Alabastair, AlexD, Amorymeltzer, Amosslee, Ancheta Wis, Andrewjlockley, Andrewlp1991, Andycjp, Ann Stouter, Antandrus, Ante Aikio, Army1987, Ashhley!, Ask123, Asknine, AstroNomer, Atkinson 291, Attilios, Avanu, Aviast, Awickert, AxelBoldt, AySz88, Azcolvin429, BW95, Ball of pain, Bantosh, Bazonka, Benbest, Benua, Berkut, Bigbluefish, BillFlis, Birdhombre, Blahm, Blake-, Bob.v.R, Bobblewik, Bobelehman, Bobo192, Boccobrock, Bongwarrior, Bowfee, Brews ohare, Brighterorange, Brockert, Bryan Derksen, Bsodmike, Buster2058, Bwilkins, CPColin, CWY2190, Calvin 1998, Can't sleep, clown will eat me, CanadianLinuxUser, Canthusus, Capecodeph, CarbonCopy, CardinalDan, Carrionluggage, Cbdorsett, Cfullmer, Chanerdar, Charles Benham, Chetvorno, Chowbok, Chrishmt0423, Christian75, Chuck Carroll, Citrab121, Cjolly92, Cleonis, Climatedragon, Cmapm, Colin Angus Mackay, CommonsDelinker, Conscious, Conversion script, Corinne68, Cornflake pirate, Correogsk, CurlyGirl93, D.M. from Ukraine, DHN, Dan Gluck, Dan100, Dancter, Dankelley, Davehi1, David J Wilson, DavidH, DavidWBrooks, Davidhorman, Deeptrivia, Denni, DerHexer, Deundre, DewiMorgan, Dgroseth, Diablod666, Diannaa, Dicklyon, Dirac66, Dna26, Dolphin51, Dr Smith, Dreadstar, Drphysics, EKindig, EWS23, EagerToddler39, Echidna, Eddiehimself, Eejey, Eequor, Ehines1, Eisnel, El C, Elektron, Elg26, Ellywa, Elpaw, Enviroboy, Eog1916, Epbr123, Epipelagic, Esperant, Eteq, Eug, Evil saltine, Excirial, FDT, Facts707, Faithlessthewonderboy, Falcon8765, Fang Aili, Farbror Erik, Fenderbenderstrat, Firsfron, Flowirin, ForestDim, FrancoGG, Frecklefoot, Frogital, Funandtrvl, FyzixFighter, Gabriel Kielland, Gaius Cornelius, GangofOne, Gareth Owen, Gark, Gavintlgold, Gbuffett, Gelo71, Gene Nygaard, Getztashida, Gfoley4, Ghirlandajo, Giftlite, Gilliam, Gioto, Glenn, Glennd83, Gnowor, Gob Lofa, Gogo Dodo, Golgofrinchian, GorillaWarfare, Gustavesarkozy, Gwernol, Gyrobo, Hadal, Haham hanuka, Hairy Dude, HalfShadow, Harry, Headbomb, Herbert Dingle, Heron, Heycobber15, Hoo man, HowardMorland, Howcheng, Hpfeil, Hropod, Hugh24, Hydrox, ILike2BeAnonymous, Ian Strachan, IceKarma, Ilario, Ilikemen123456789, IllicitDolmar, Immunize, Introgressive, Iridescent, Irishguy, IronGargoyle, Itub, Itwilltakeoff, J. 'mach' wust, J.delanoy, JForget, JKeck, Jahon whahite, Jake roman, James599, Jarvi006, Javalenok, Jbuford39, Jdchamp31, Jeepday, JerryFriedman, Jh51681, Jimfbleak, Jimp, Jmcc150, John of Reading, John254, Johndarrington, Johngorno, Jonathan Hall, Joseph Solis in Australia, Jowan2005, Jptate, Jrobinjapan, Jrockley, Julesd, Juliancolton, Jxg, KGasso, Kanonkas, Karl Palmen, Karol Langner, Kaszeta, Kb*babe128, Kbk, Kenyon, KevinDM84, Kingpin13, KiwiKittyBoy, Kjkolb, Krea, Kuru, Kurykh, Kvng, Kzollman, L fle, La goutte de pluie, Lajsikonik, LapoLuchini, Laserpointergenius, Laurascudder, Leon00, Lestrade, Ligand, Lighthead, Lights, Linas, Ling.Nut, Livajo, Lo2u, Logan, Logicus, Looxix, LordHarris, LostAccount, Lou1986, Lozeldafan, MC10, MCTales, Maddogbrgs1, Magic.dominic, Magioladitis, MagneticFlux, Makewa, Maniac18, MarcM1098, Marnanel, Martin Hogbin, Masiano, Maskedskulker, Materialscientist, Mav, Maximillion Pegasus, Mdoc7, Melchoir, Menschenfresser, Mhs5392, Michael Hardy, Midway, Mikez, Mild Bill Hiccup, Mimihitam, Mooquackwooftweetmeow, Morn, Mr Minchin, Mrniceguy85020, Mrtomh, Mschlindwein, Myrtone86, Mysid, NCS2004, NHRHS2010, Nanju.murthy, Nashpur, Nathan Johnson, NerdyScienceDude, Netkinetic, Nfutvol, Nick.hardman, Nikai, Nilfanion, Nimbus1947, Nimur, NineEighteen, Nvaccaro, Obradovic Goran, Ohnoitsjamie, OlEnglish, Old Moonraker, Oleg Alexandrov, Oliballz, OrbitOne, Oreo Priest, Orphan Wiki, Oxymoron83, PIrish, ParticleMan, Pavel Vozenilek, Pbn, PeR, Pearle, Perceval, Perspeculum, Petergans, Pflatau, Philip Trueman, Philippe, Philosophus, Piano non troppo, Pinethicket, Pishogue, Plasticup, Pleasantville, Plswinford, Plvekamp, Polatrite, Pparazorback, Procellarum, Psb777, PseudoSudo, Pt, Quadrius, RA0808, Rakesh Dhanireddy, Raylopez99, Rehman, RexNL, Riana, Rich Farmbrough, Richard, Richard B, Ridernyc, Rjstott, Rjwilmsi, Rmotz, Robinh, RockMagnetist, RodC, Rodrigob, Roflcopter123abc, Ronhjones, Ross Fraser, Rossami, Rracecarr, Rrburke, Rror, Rune.welsh, Runningonbrains, RupertMillard, Ruy Pugliesi, Ruyn, SWAdair, Sanpaz, Saperaud, Saulpwanson, SchfiftyThree, Scientific29, Scientus, Seaphoto, Semperf, Sf222, Shadowjams, Shadowlynk, Shantavira, SidP, Sigma 7, Sj, Skankboy, Skizzik, Smalljim, Spellcast, Spencer62, Splatt, Spoon!, Starpine, Stephenchou0722, Steverapaport, Strider01, StuRat, Suisui, Svance, Svick, Swamp Ig, Szopen, TakuyaMurata, Tamfang, Targaryen, Tavilis, Tcsetattr, Teapeat, Techman224, That CS Guy, The Albino Alligator, The Anome, The Thing That Should Not Be, The2dayslate, Thegreatdr, Theresa knott, Thick as a Planck, Thrapper, Tide rolls, Tideflat, Timbercat, Tinus, Titoxd, Tom, Tom is short, Tomtheman5, Tomytalker, Tonderai, Toxicity², Trappist the monk, Trelvis, Tripodian, Tyler, Udirock, Urineography, User A1, Utcursch, V35b, Valley2city, Vandymorgan, VectorField, Vectornaut, Vectro, Vildricianus, Viscious81, Vishnava, Vitaleyes, Vsmith, Vyznev Xnebara, WFPM, Warren oO, Watchwolf49z, Watjen, Wavelength, White 720, Widr, Wikfr, Wiki9-2-11, WikiDao, William M. Connolley, Willking1979, WilyD, Windatheels, WitchDrSmith, Wolf grey, Wolfkeeper, Woodshed, Woodstone, Wperdue, Wwoods, XJamRastafire, Xaariz, Xanzzibar, Xaos, Xiner, Xxhopingtearsxx, Yurivict, Zachlipton, Zaheen, Zalgo, Zazou25, Zelda Simpson, Zvn, Σ, 1049 anonymous edits Image Sources, Licenses and Contributors File:Corioliskraftanimation.gif Source: http://en.wikipedia.org/w/index.php?title=File:Corioliskraftanimation.gif License: GNU Free Documentation License Contributors: Hubi File:Earth coordinates.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Earth_coordinates.PNG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Low pressure system over Iceland.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Low_pressure_system_over_Iceland.jpg License: Public Domain Contributors: NASA File:Coriolis effect10.svg Source: http://en.wikipedia.org/w/index.php?title=File:Coriolis_effect10.svg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Of this SVG version, Roland Geider (Ogre), of the original PNG, (Cleontuni) File:Coriolis effect14.png Source: http://en.wikipedia.org/w/index.php?title=File:Coriolis_effect14.png License: GNU Free Documentation License Contributors: Cleontuni, Saperaud File:Target on turntable.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Target_on_turntable.PNG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Trajectory for three angles of launch.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Trajectory_for_three_angles_of_launch.PNG License: Creative Commons Attribution-Share Alike Contributors: Brews_ohare File:Vector relationships.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Vector_relationships.PNG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Cannon force components.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Cannon_force_components.PNG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Coriolis construction.JPG Source: http://en.wikipedia.org/w/index.php?title=File:Coriolis_construction.JPG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Points of view.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Points_of_view.PNG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Coriolis effect11.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Coriolis_effect11.jpg License: GNU Free Documentation License Contributors: Matthew Trump File:Forces parabolic dish.png Source: http://en.wikipedia.org/w/index.php?title=File:Forces_parabolic_dish.png License: Creative Commons Attribution-Sharealike 3.0 Contributors: en:User:Cleonis File:Parabolic dish ellipse oscill.gif Source: http://en.wikipedia.org/w/index.php?title=File:Parabolic_dish_ellipse_oscill.gif License: Creative Commons Attribution-Sharealike 2.5 Contributors: IngerAlHaosului, Tomatejc, 2 anonymous edits License Creative Commons Attribution-Share Alike 3.0 Unported //creativecommons.org/licenses/by-sa/3.0/ 19


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White Chocolate Cookies-n-Cream Popcorn: Flame-popped Popcorn seasoned with Corn Oil and Salt. Oreo Cookies: Unbleached Enriched Flour (wheat flour, niacin, reduced iron, thiamine mononitrate, riboflavin, folic acid) Sugar, Palm and/or Canola Oil, Cocoa (processed with alkali), High Fructose Corn Syrup, Baking Soda and/or Calcium Phosphate, Salt, Soy Lecithin, Chocolate, Artificial Flavor. Coating: Sugar, Palm Kernel and Palm Oils, Whey, Nonfat Milk, Titanium Dioxide color, Sunflower Lecithin, Natural Flavor and Vanilla.
Cheese Corn: Flame-popped Popcorn, Vegetable Oils (soybean oil, palm oil), Dried Cheddar Cheese (milk, cheese culture, salt, enzymes, and artificial color), Cream, Salt, Sodium Phosphate (preservative), Yellow #5, Lactic Acid, Soy Lecithin, and Yellow #6.
Caramel Corn: Flame-popped Popcorn, Pure Cane Brown Sugar, Glucose, Water, Salted Butter, Baking Soda.
Snowflake Pretzels: White coating: sugar, vegetable oil, whey powder, non-fat milk, soy lecithin, vanillin, non pareil seeds. Pretzels: wheat flour, corn syrup and salt.
Jelly Belly's Jingle Bell Jells: Sugar, corn syrup, corn starch, Kosher gelatin, pectin, citric acid, tartaric acid, sodium citrate, sodium potassium, sodium polyphosphate, natural and artificial colors and flavors and carnauba wax.

subset: commoncrawl


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What a difference a few hours make. The fog burned off, and the temps are about 30 degrees warmer than this morning. I headed over to a nub of Broomfield County that extends north of Flatirons Mall towards highway 36. I had wanted to check it out for a while, ever since I spotted a pair of golden eagles in one of the trees on the way into work.
It is a spot that I believe will produce some good birding results over time. There is a stretch of undeveloped land that the mall developers must have had to throw some cash at while they were bidding.
Now by parking at the remote end of the parking lot I find myself looking down over a terraced layout of habitats. First there is a retention pond with some landscaped trees and shrubs. Next, a footbridge crossing the "enhanced" section of creek. It features some extra rock work and staged drops which I believe will attract some attention over time. Finally, there is a last section of undeveloped creek bed cut deep and covered by cottonwoods. The only drawback to the site is that it is close to the highway, and therefore a bit noisy to locate birds by sound. On the other hand, it doesn't look like many people head down that way too often. So I guess I will see how that site pans out. At least it is close and has potential.
2009 Count: 46
Lifetime: 84


text: Zombies Deadly Target is the most horrible and breathtaking zombie survival shooting game with a lot of thrilling action and ultimate commando shooting adventure in mid of zombie city. Zombies Deadly Target with extreme sniper shooting skills so that you can survive longer in the zombie apocalypse. Although you have already experienced many zombie shooting games, this time, explore some deadly zombie escape missions in most realistic virtual reality. As a spy sniper commando shooter, slay all the deadly zombies and bloody monsters which are roaming here and there causing heavy bloodshed. You have to stop these merciless zombies from attacking the innocent citizens by using killer headshots. Just take out all your tactical weapons and get ready for the brutal zombies shooting games missions in Zombies Deadly Target FEATURES: - Challenging and adventurous zombie missions - Realistic and natural horrifying Apocalypse climate - Nonstop Front line zombie Hero Action - Interesting Sound Effects and compatible user interface - A game of death fight between evils hunter vs zombies


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Tim Reynolds
Dave Matthews cohort Tim Reynolds is a small, vaguely impish man, and his fretboard moves are entirely inhuman -- nimble, mischievous, and just a little magical.
For Tim Reynolds, playing in his former hometown at a venue that didn't exist during his residency must be something of a surreal experience. Five years ago, he performed at an ancient and astonishingly greasy bar a few blocks northeast of the Satellite Ballroom -- it was his first homecoming show in years. Enthused by Reynolds' 1999 double-disc with Dave Matthews, Live at Luther College, area college students turned out for the occasion slightly drunk, fully bekhakied, and ready for an evening of frat-tastic acoustic tunes. But Reynolds hit the stage wearing a gas mask and started heaving industrial metal without so much as a word. Watching the look of horror gradually wash over the unsuspecting Pi Kappa Alpha lads like a plague of locusts was quite a spectacle, and by the end of the night, the packed house had dwindled to two rows of converts. The poor guy actually thanked them for staying. Thanks to a string of regional appearances over the course of the last year, there were no such misfires this time around. Reynolds' current tour does indeed lean to the acoustic side, but almost nobody from the DMB fan base turned out; instead, the audience consisted mostly of grungy young males, most of whom seemed to be guitarists themselves and thus knew the perfect superlatives to heap upon him. Reynolds is a small, vaguely impish man, so his fretboard moves, though entirely inhuman, still seemed in character -- nimble and mischievous, that is, and just a little magical. The raw speed and unmatched precision he displays on an electric guitar were unchanged on the acoustic, despite its reputation as a slower instrument, and his sharp melodic runs disappeared into the night just as readily. What little space remained between notes was soon filled by their disembodied auras: growling volume swells, ringing harmonics, and throbbing quarter-note echoes. The tunes with lyrics, however, seem like they should be the work of a singer-songwriter type, and that's one thing Reynolds definitely isn't. Wizard? Sure. Musical miracle? Quite possibly. But can he play credible reggae? Not a chance. Still, you'd think that the opportunity to see a master up close as he works his instrument in the raw would be a transcendental experience. With all due respect to Reynolds' spacey wobbles and echo-laden swirls, that wasn't really the case; he seemed to do best when he wasn't saddled with duties of pulse, rhythm, or harmony. When he put his fingers on autopilot and let them free-associate on the fretboard, it made for a stupefying display, but his talents were ultimately wasted on rhythm guitar. Sometimes he was able to set himself up through the use of loops and delays, but he'd probably have done better with someone else providing a context -- or, rather, a launch pad. That finally came about at the very end of his set. For the finale, Reynolds jammed his way through "In a Silent Way" with opener Mike Sokolowski -- offering the song as a tribute to recently departed Weather Report keyboardist Joe Zawinul. For the first time, his fingers could do as they pleased, as Sokolowski eased through the chord progression on a rickety old upright. Sparkling natural harmonics, knuckle-rapping percussion, and short bursts of melody combined to form a subtle wash of sound, and after ramming it all through a ring modulator, Reynolds called it a night. Once again, the room was sparsely populated. "Thank you for coming out tonight," he said. "And you, and you, and you..." He rattled them off very quickly and with a lighthearted smirk, but he came dangerously close to squeezing one out for everybody in the room. Aside from a traumatized class of Pi Kaps, not much has changed in the last few years; nearly a decade after Luther College, Tim Reynolds is still a sleeper hit.


text: FADE IN:INT. THE CRUMBLED RUINS OF A ONCE GREAT GREEK TEMPLE Juniper(whispers)Jaune…just who are youJaune uncurls his fists and looks up slowly at JuniperJauneI think you already know.fireflies flitter and swarm around Jaune's bodyfirefliesprince…prince…princeJUNIPERYes…maybe I've always knownJuniper laughs bitterly, looks around at the ruins of the city around. Columns of dark smoke rise from the rubble.JUNIPERPrince of the netherworld. A look of defeat comes across Juniper's face. Juniper That's where we are isn't it. Jaune looks down again. Juniper's face crumples even more.JUNIPERI've always known there was something different between us. I tried to deny it. I tried to ignore it.. but the falling of the cities just confirmed it even more. The netherworld is suffering isn't it. With you neglecting your duties on Earth. Juniper takes a step closer to Jaune. A tear escapes from his right eye. JUNIPER(whispers)Am I a ghost? Am I dead? Am I… real?Jaune brings his left hand up and closes it around a single firefly. When he opens his fist, it is gone. JAUNEYou're not a ghost. This universe…exists in a separate place. JUNIPERIs it real?JAUNEIt is not the plane on which the living inhabits, but that doesn't make it any less real. Jaune takes a step closer until there is only inches between their faces. He grips Juniper's shoulder hard. Juniper flinches.JAUNEThis is real. I am touching you. Even if we are different, we are both real Juniper. JUNIPERFor as long as I'd been conscious enough to wonder, I've wondered. I've found many answers, but they were all wrong because they never fit the question. Juniper takes a breath and rasps it out, trembling all over. JUNIPERCan you still really call me your friend when I'm already dead? Jaune closes the distance between them and presses his forehead to Jaune's and closes his eyes. JAUNEYou're so stupid. Watch me, because I'm going to bend every rule and bring you back with me.


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One of the seven most ancient religious cities of India, Dwarka, Gujarat, is also known as the 'Gateway to Heaven'. Thousands of devotees visit this destination to explore the birthplace of Lord Krishna who also had his kingdom here. While planning a visit to the famous Dwarkadhish Temple and Sudama Setu, one can stay at Regenta Inn Dwarka, which is situated in a 2 km radius from the city's prominent temples, holy shrines and railway station.
Regenta Inn provides a comfortable stay at pocket-friendly prices. It also has a multi-cuisine vegetarian restaurant; Prasad and a coffee shop, which serves throughout the day. With 2 banqueting spaces, it is one of those hotels in Dwarka that is best suitable to host private, social and business gatherings.
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I am happy to be your Spanish instructor this year. I am a native Spanish speaker from Colombia and have been teaching Spanish for over ten years to students from K to 8th grade. I enjoy sharing my language and my culture with my students and am looking forward to a great school year.
Contact me at: firstname.lastname@example.com
Spanish 1, 1A, and 1B:
We will be learning about stereotypes, cognates, Spanish alphabet, punctuation marks, greetings and farewells, useful classroom vocabulary, definite and indefinite articles, time, class schedules, Spanish speaking countries, subject pronouns, verbs ser and estar & other regular verbs, numbers, colors, days of the week, months of the year, places in the school & in the community, seasons, adjectives, and family relationships, places in the school/places in the community, and means of transportation. Students will be able to hold a simple conversation where they can greet, introduce themselves, give and ask for personal and contact information, talk about themselves, their family, and what they do in the School and in the community. Please review your notes and practice every day. Do not fall behind.
In Unit 2 the students will learn adjectives, school subjects, places around the school, time and schedules so students can talk about life at school, events after school including at what time and where they occur.
In Unit 3 the students will learn about family, family relationships, likes & dislikes, describing physical and personality traits, leisure time activities, extend, accept, & decline an invitation.
In Unit 4 the students will learn about places in the city, means of transportation, identify & describe foods & drinks, order a simple meal & ask for the bill, identify & describe clothing.


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16 revealing stories about the human brain
Ever wondered how Scandinavians cope with 24-hour darkness, why we feel pain - or whether smartphones really make children stupid?
Have you heard about the US army's research into supercharging minds?
You need some Brainology. Written for Wellcome, the health charity, these stories follow doctors as they solve the puzzle of our emotions, nerves and behaviour.
Aimed at the general reader, they fascinate and intrigue. Sample the start of the first chapter.
EXCERPT: Ouch! The science of pain
John Walsh
One night in May, my wife sat up in bed and said, 'I ve got this awful pain just here.' She prodded her abdomen and made a face. 'It feels like something's really wrong.' Woozily noting that it was 2am, I asked what kind of pain it was. 'Like something s biting into me and won t stop,' she said.
'Hold on,' I said blearily, 'help is at hand.' I brought her a couple of ibuprofen with some water, which she downed, clutching my hand and waiting for the ache to subside.
An hour later, she was sitting up in bed again, in real distress. 'It s worse now,' she said, 'really nasty. Can you phone thedoctor?' Miraculously, the family doctor answered the phone at 3am, listened to her recital of symptoms and concluded, 'It might be your appendix. Have you had yours taken out?' No, she hadn't. 'It could be appendicitis,' he surmised, 'but if it was dangerous you'd be in much worse pain than you re in. Go to the hospital in the morning, but for now, take some paracetamol and try to sleep.'
Barely half an hour later, the balloon went up. She was awakened for the third time, but now with a pain so savage and uncontainable it made her howl like a tortured witch face down on a bonfire. The time for murmured assurances and spousal procrastination was over. I rang a local minicab, struggled into my clothes, bundled her into a dressing gown, and we sped to St Mary's Paddington at just before 4am.
The flurry of action made the pain subside, if only through distraction, and we sat for hours while doctors brought forms to be filled, took her blood pressure and ran tests. A registrar poked a needle into my wife's wrist and said, 'Does that hurt? Does that? How about that?' before concluding: 'Impressive. You have a very high pain threshold.'
The pain was from pancreatitis, brought on by rogue gallstones that had escaped from her gall bladder and made their way, like fleeing convicts, to a refuge in her pancreas, causing agony. She was given a course of antibiotics and, a month later, had an operation to remove her gall bladder.
'It's keyhole surgery,' said the surgeon breezily, 'so you ll be back to normal very soon. Some people feel well enough to take the bus home after the operation.' His optimism was misplaced. My lovely wife, she of the admirably high pain threshold, had to stay overnight, and came home the following day filled with painkillers; when they wore off, she writhed with suffering. After three days she rang the specialist, only to be told: 'It s not the operation that s causing discomfort it's the air that was pumped inside you to separate the organs before surgery.' Like all too many surgeons, they had lost interest in the fallout once the operation had proved a success.
During that period of convalescence, as I watched her grimace and clench her teeth and let slip little cries of anguish until a long regimen of combined ibuprofen and codeine finally conquered the pain, several questions came into my head. Chief among them was: Can anyone in the medical profession talk about pain with any authority? From the family doctor to the surgeon, their remarks and suggestions seemed tentative, generalised, unknowing..
Buy the book and carry on reading
• Ouch! The science of pain - John Walsh
• Why doctors are reclaiming LSD and ecstasy - Sam Wong
• Inside the mind of an interpreter - Geoff Watts
• How should we deal with dark winters? - Linda Geddes
• Smartphones won't* make your kids dumb (*Probably) - Olivia Solon
• You can train your mind into 'receiving' medicine - Jo Marchant
• Charting the phenomenon of deep grief - Andrea Volpe
• The mirror cure for phantom limb pain - Srinath Perur
• Can you think yourself into a different person? - Will Storr
• How to survive a troubled childhood - Lucy Maddox
• What tail-chasing dogs reveal about humans - Shayla Love
• A central nervous solution to arthritis - Gaia Vince
• Could virtual reality headsets relieve pain? - Jo Marchant
• What it means to be homesick in the 21st Century - John Osborne
• Lighting up brain tumours with Project Violet - Alex O'Brien
• The US military plan to supercharge brains - Emma Young
A companion to Bodyology, Brainology consists of articles originally published on the Mosaic Science website and funded by medical charity Wellcome. These are well-written, professional articles: if you hit on a topic that interest you, it's very easy to be sucked in.
Because I'm not a great fan of medical journalism, I was less interested by topics such as 'the nerve cure for arthritis' and 'you can train your body to receive medicine.' However, some of the other articles really rewarded my read: for example, 'How should we deal with dark winters' and (despite the 'doctor' word) 'How doctors are reclaiming LSD', which was genuinely interesting on the history of attempts to use LSD and MDMA for medical purposes (though perhaps a little light on the deaths allegedly caused by the latter).
For me, though, the standout article was 'What tail-chasing dogs reveal about humans', which uses studies of the compulsive behaviour of dogs to try to get insights into OCD. If I'm honest, I wasn't very interested in the human side, but the idea that dogs could have such behaviour - one dog, for example, apparently had to put seven pieces of food into recesses in a couch before eating - was fascinating.
In reviewing Bodyology, I complained about the over-heavy use of 'true life stories'. This is also the case with Brainology, though more of them here are first person, which tend to have less of the over-dramatised wording. Perhaps because of limiting the book to a single organ - even one as interesting as the brain - though, I found there were fewer stories that really grabbed me. However, the ones that did were superb.
As with Bodyology, it's a great collection to dip into for a single item as a quick read - though it's very tempting then to read just one more. And another. Makes a potentially heavy topic approachable and fascinating.
Goodreads Reviews+
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Component maker GrapeCity today announced that it is acquiring spreadsheet component vendor FarPoint Technologies. Details about the deal, expected to be completed by October 1st, were not disclosed. FarPoint's Spread family of products includes Spread for .NET Bundle, Spread for Windows Forms and Spread for ASP.NET, among other products.
FarPoint CEO Rick Williamson said the purchase will enable FarPoint to extend its product development efforts and reach a considerably larger audience than it has in the past. He said FarPoint, based in Morrisville, NC, will gain access to a large pool of offshore developers, as well as to a dedicated QA team.
"It became clear that we did not have the resources to go where we wanted to. With GrapeCity's help we felt we would be able to do that," Williamson said. "Our customers should be a lot happier because now we have a lot more resources behind us. This is a win-win for the customers."
GrapeCity, based in Sendai, Japan, and with U.S. offices in Seattle, Wash., employed 850 people before the FarPoint acquisition. The company has had a business relationship with FarPoint for over a decade, distributing and supporting FarPoint's spreadsheet components in Japan.
"We've always been impressed with the high quality of FarPoint products—in fact, their Spread product is one of the top components used by Microsoft Visual Studio developers in Japan," said Naoyuki Baba, GrapeCity President, in a statement."With our 25-plus years of experience in bringing world-class software solutions to a global client base, we're in a great position to further extend FarPoint's market reach. And their outstanding developer components will help us expand our developer tools offerings across a broader range of vertical markets."
The acquisition of FarPoint is the second significant purchase by GrapeCity in a year. In October 2008, GrapeCity acquired data analysis and reporting component maker Data Dynamics. Like FarPoint, DataDynamics was a long-time business partner of GrapeCity, which distributed DataDynamics products in Japan. In both cases, GrapeCity has said it expects to expand the market reach of the acquired companies.
"Yes, we recognize the obvious synergy in terms of both product lines being very complimentary," said Sanjeev Jagtap, director of product management at GrapeCity. "Reporting/BI and spreadsheets together pretty much make up bulk of the heavy lifting that today's business users need to do in terms of rapid data processing and business reporting/intelligence. So it is an easy fit between the two product lines."
Julian Bucknall, chief technology officer of component maker Developer Express, said the GrapeCity acquisition doesn't portend a consolidation in the .NET component marketplace.
"It's more of a strategic decision by GrapeCity to take over a product they were already marketing in Japan and, as I understand, had a hand in developing," Bucknall said. "At a stretch you could make the argument that these two acquisitions, DataDynamics and FarPoint, were about carving a niche in the business intelligence component market."
FarPoint's Williamson said he expects the GrapeCity acquisition to energize initiatives in the FarPoint product family. In addition to providing resources for FarPoint to support Microsoft's expanding platform reach -- including emerging WPF, Silverlight and mobile platforms -- FarPoint is working to debut a common code base for its components. The first example of this effort, said Williamson, is present in the charting component in Spread for Windows Forms Version 5, currently in beta.
About the Author
Michael Desmond is an editor and writer for 1105 Media's Enterprise Computing Group.
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Aston Martin Vanquish 6.0L V12 2+2
Vehicle Information
- Odometer 38,000 Miles
- Fuel Type Petrol
- Transmission Semi-Automatic
- Road Tax £178.75 / £330
- Year 2003 (03)
- Body Coupe
- Engine Size 6.0L
- Colour
- Doors 2
About this Aston Martin Vanquish
Finished in Special Order Seal Grey Metallic with Contrasting Full Two-Tone Grey Leather, 2+2 configuration, Satellite Navigation, Rear Parking Sensor, Powerfold Mirrors, Body Coloured Door Handles, Electric Seats, Memory Seats, Climate Control, Heated Seats, Paddle Shift, Red Brake Calipers, Aluminium Dash,this car has a great service history and has been maintained irrelevant of cost. There are bills and receipts for the past 2 years of over £20,000.00 of works carried out, the vehicle has just been serviced and comes with 6 months warranty. Viewing by appointment only.
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Technical Specification
Cost and Efficiency
Urban 25.7 mpg
Extra Urban 11.5 mpg
Combined 16.7 mpg
Engine and Performance
0 - 62mph 4s
Top Speed 190mph
Max Power 460bhp
Max Torque 400lb-ft
Weights and Measures
Dimensions (mm)kght. 2690mmWidth 1981mmLength 4665mm
- Max Gross Weight 2175kg
- Towing Weight (Braked)
- Towing Weight (Unbraked)
- Seats 4
Safety (NCAP)
- Adult
- Child
- Pedestrian
- Safety Assist
- Overall
Note: These figures show the typical specification for this vehicle, actual figures may vary.
Disclaimer: Please note, the vehicles registered on/after April 1st 2017 and with an original retail price of £40,000 and over will incur an additional tax charge of £310 per year from the second year for 5 years. After 5 years the RFL will revert back to the normal rate.
Slades Garage is authorised and regulated by the Financial Conduct Authority. Indemnities may be required in certain circumstances. Finance is only available to persons aged 18 or over, subject to status. We work with a number of carefully selected lenders who may be able to offer you finance for your vehicle. We are only able to offer finance from these providers. Postal Address: Church Road, Penn, Buckinghamshire, HP10 8LY