The fascinating conclusion
to the Coriolis effect
and Foucault's Pendulum

Tracing the development of the sciences from witchcraft and mysticism through the pages of astronomical history reveals a great many sacrifices, insights and necessary calculations that brought about today's recognised concepts describing the Earth and Solar System. Several degrees of relative rotation needed identification. The Earth rotates around its geocentric tilted (North-South) axis, while orbiting the Sun on an inclined plane, travelling with the Solar System at an obscure angle around a moving galaxy, drifting aimlessly in an immense Universe towards some super massive unseen hypothetical gravitational mass. The view of a spiralling filamentary orbital helix seems further complicated by ripples produced by the eccentric common gravitational axis of the Earth and Moon system weaving the orbit around the Sun.

To prove the Earth actually moves, one must gain certain keys and a level of understanding to appreciate and realise the truth. A great deal of evidence from many sources conclusively proves the spheroidal Earth moves under one's feet. Believe it or not, the Earth's magnetic field, tides, weather system and gravity all indicate a moving dynamic Earth. Some evidence remains hidden or put away on the back shelf because Nature deceives the ignorant, the arrogant, the unwary and the sophisticated. Realisation of Nature's simplicity only appears at the atomic level, where all actions and reactions occur process by process, one step at a time through various mechanisms involving different energy-forms throughout a period of activity. Complexity and confusion come when poorly conceived notions and beliefs use the wrong terms, definitions, or frames of reference. One reaction, one mechanism, one process, replicated trillions of times simultaneously taking place during a single event involving matter at the atomic level, confused by the need for an empirical blanket describing experimental observations in the terrestrial frame of reference. Some events historically carry erroneous and invalid descriptions.

In 1687, Newton proposed in his First Law that a body continues to travel in a straight line unless duly influenced by an external force. An atom that initially travels along a straight trajectory over the surface from pole to equator does so until the relative tip speeds of the primary body and its environ enter the calculations forcing the atom's trajectory to become geometric and vectorial, as mindless matter obeys the simple laws of geometry. The path curves either ahead of, or it falls behind the direction of rotation, giving rise to an apparent change in trajectory until such time as the direction of travel parallels the direction of rotation, perhaps perpendicular to the initial direction of impetus. Nature denies Newton's First Law of motion universal validity. Newton's law works in free space, but not on a rotating orbiting planet unless worded as "All things remain at a point of equilibrium, maintaining constant energy level until acted upon by an external force, to alter that energy or distribute that energy into the environment." Energy losses occur continually along the path of travel due to the viscosity or resistance in the medium.

One can only fear the relative obscurity noted in the pages of scientific history for the brilliant mid-nineteenth century mathematician Gaspard de Coriolis, who corrected several of Newton's fundamental mathematical blunders. Perhaps attitudes stem from Newton's scientific might after death. Learned gentlemen still honour the legend of the great Newton, falsely giving him credit for evolutionary corrections to the precious theory. Somehow, Newton retains the credit for inventing The Calculus, but the fact remains he used the wrong methods to obtain his results. This may sound like a joke, but most mathematics teachers today would fail the student Isaac Newton. Coriolis put the half into Newton's energy equation KE = mv². In the great competition between Newton and Leibnitz, Newton's answer to quality of motion was totally wrong, while Leibnitz was absolutely correct in giving the correct equation for momentum M = mv. To differentiate momentum once results in the Coriolis solution KE = ½ mv². One must not lose respect for Newton, rather one must applaud the man for what he got right, achievements that gave humanity the basic computation tools to allow complex calculations, to examine and grasp for the Universe as none before had done. In accepting a great deal of his education as true to Nature, Newton grew steadfast in his ways, maintaining some tragic historical mistakes. Some errors being realised only today, some 350 years later, only appear in causal scientific research applied to history through recently acquired knowledge and technology.

For higher commercial gains, in an attempt to determine the best routes for the great clipper ships to reach the Indies and Australia, Coriolis identified the Earth's primary weather cells as being; three cells per hemisphere (The Tropical, Temperate and Polar region). This, a direct consequence of the rotating planet and the relative tip speed of the planet at each latitude. Over the surface the relative speed of moving liquids to the spherical planet, creates the weather cells, the ocean currents and continental drift as the mantle flows. The flowing Coriolis cells in the mantle being directly responsible for the production of the Earth's magnetic field, (a provable fact).

Rotation supplies proof to support the existence of the Universal Stationary Frame of Reference in the Universe. Relative rotational motion occurs on the planet Earth, not linear motion. Nowhere on the Earth can linear motion be demonstrated, nor achieved. Evidence of this fact appears as functions of differential rotation and energy-forms associated with matter (ie. as differences in rotational forces from atom to atom.) Proof of this Stationary Frame of Reference denies Einstein's Special theory of relativity a great deal of credibility, especially concerning the affect and effects of matter and energy.

The use of the correct atomic model, with the correct definition of energy, with a more correct model of relativity, everything in Nature's Universe makes sense. Initially, the atomic model stores all energy as rotational energy. Given a fixed initial energy, any moving atom gains or loses energy to a relative environment. Any atom, given the impetus to travel uniformly over a stationary planet's spherical surface through an atmosphere, follows a basic curved trajectory. Rapidly, the atom loses velocity and motion as the stagnant environment absorbs all excess energy in presenting a resistive force against all degrees of stirring.

Consider this same atom given the impetus to travel uniformly over a rotating body's spherical surface. The geometry of a rotating sphere identifies the equator as travelling faster than the mid-latitudes and the stationary poles. Immediately, the geometry of the sphere creates differential energy needs, forcing the atom to travel at a different rate, (slower or faster than the rotation) in different directions from the original direction of impetus. This weird definite force without form, relates the Coriolis effects to the wondrous rotational devices of Foucault.

In the mind, form the image of a sphere made up of 90 latitude slices (in each hemisphere). Although the angular rate of rotation remains constant, each latitude slice experiences a different tip speed on the surrounding environment. The tip speed can be represented by a wheel rolling down a road with a certain velocity. Relative to the ground, the contact point tip speed remains stationary while wheel's centre moves down the road at that speed. If all the wheels rotate at one revolution per second, how fast would each wheel travel? The answer depends on the equation of a circle, where the length of the circumference travels a certain distance in a time frame. For such simple calculations use as the value of Pi (p) 3.14159

Rotational calculations do not involve the direction to the real centre of mass, rather in all cases the direction must be radiant from the axis to the circumference. Rarely, if at all, should calculations involving rotation consider the centre of mass because that center becomes apparent when the forces balance. Before that point, calculations only refer to the axis, radius and mass at that radius. Foucault's pendulum, flywheels and gyroscopes demand this concept be incorporated in the mathematics, excluding all gravitational references, else, one risks travelling on a tangent using the invalid physics of observational illusions. Many text books fall into the traps of relating gravity to rotation only because others have taken that invalid path to obtain some desired result.

Atoms situated along each parallel of latitude, with the same distance from the axis, share common energy needs, quite different to the atom's needs on other latitudes and radial positions. The greatest forces encountered occur when atoms with certain energy levels travel into regions with different energy needs. The greatest energy differential between the stationary poles and the equator occurs along the shortest North-South route, along the meridian over the rotating curved surface. Any change in latitude, or altitude that alters the radius, force major directional changes due to relative tip speed effects and the distribution of energy in the rotating environment.

If this atom happened to migrate across the surface from the equator towards the pole, progressively it travels faster than the tip speed of each higher latitude slice, racing ahead of the direction of rotation. In reverse, the atom would fall behind the increasing tip speed of each greater radius disks, travelling against the direction of rotation. This strange geometric phenomena forms the basis of the Coriolis effect where enormous energy seems derived from no where. Energy must be continually added to maintain a fixed direction of travel over the rotating curved surface, correcting for an apparent deviating force directed parallel to the direction of rotation, either with or opposing rotation. The spinning sphere drags some of the environment with it presenting another force that opposes motion to or from the equator. With the atom at a greater or lesser speed than the environment, the local environment experiences a force as a direct consequence of tip speed relativity.

Relative tip speed predictions use basic geometry. A close approximation obtained through the multiplication of the length of the sphere's circumference by the Cosine relationship to a particular latitude.

Unfortunately, the mathematical models applied to the Earth must be more of a squashed sphere, an oblate spheroid, with a shorter polar diameter than the equatorial diameter. Trivial as the Earth's oblateness appears at ¹/₂₉₆ to save on the difficult calculations, Clarke in 1866, formulated the basis of the next table. Without considering the Earth's other degrees of motion (Orbital, Galactic, and Universal), of interest, the tip speed velocities reveal some fascinating and frightening speeds. Using the sidereal day relative to the fixed stars, the true rate of rotation (23 hours 56 minutes) gives a constant rate of revolution per second for all latitude slices. The solar day adds other variants to any discussion concerning the atmosphere and weather.

At mid to high latitudes, recreational games involving projectile motion (such as archery, shooting and golf) demonstrate only too well the Coriolis effect over relatively short ranges. All basic unguided projectile motion, such as artillery shells and objects dropped from moving aircraft follow Coriolis affected paths. In certain situations, the golfer can blame the Earth's rotation for a poor hook or bad slice. The highly inclined face of the 7 Iron (or sand wedge) drives the golf ball 120 to 150 metres down the fairway on a high uninterrupted parabolic path. The 10 to 15 second duration of flight for the North-South fairways produce some amazing results, compared to the unaffected East-West fairways.

At both North-South fairway positions, the almost insignificant angular differences and tip speed differentials applied for 15 seconds, amounts to a considerable error in trajectory, giving rise to an apparent slice or hook. A golfer in the Southern hemisphere, facing the Southern Green drives the ball South and ahead of the Earth's rotation. To play the ball from where it lies, back towards the Tee without compensating for the theoretical position of the Tee, promotes a greater error due to over compensation in targeting the Tee. The theoretical tee position for ball that initially flew on a true South trajectory, must be right of due North, not to the apparent position of the Tee, a few degrees to the left of True North. The rotational parameters of the Southern location (down the fairway) serve to exasperate the golfer, for this region travels at a much slower tip speed and requires greater compensation for the duration of flight (when the same flight times are measured), the relative distances travelled during the period by each tip point differ by a considerable margin. The golfer must drive the ball to the right of true North, else the ball drops to the left of (behind) the tee-off point.

Explanation of the basic geometry merely involves drawing two triangles where the base of each represents the displacement of the relative tip points for the period of the flight. No way can the two triangles be identical. From the common time and adjacent side or direct path, the hypotenuse represents the total path travelled as a vectorial resultant.

At this moment Foucault's pendulum swings into view. The explanation being no more complex than butting these two very different triangles together, over and over again, back to back, thousands on thousands of times with the correct alignment. The relative difference in tip speed between North and South slowly forming a circle as the internal diameter remains shorter than the external diameter. The following table shows this to be absolutely true.

The hype behind Foucault's pendulum, painting it as a swinging time piece, something like a wondrous Sun dial, accurately prescribing 15^o of arc each hour wrongfully describes this device. The correct hourly timing observations being witnessed only near the Earth's axial poles. Irrespective of the pendulum's period, the observations confirm a trigonometric function relating tip speed of the Earth to the sinuous rotation of the pendulum. The time taken to produce a single 360^o rotation being dependent on the site's location, not to the gravitational effects. The sinuous path of the pendulum tells this graphic story as the gravity ball (the motor) prescribes figure '8' paths. The gravity motor that maintains the pendulum's motion does not affect the observations. The longer the period of the pendulum, the more evident the sinuous rotational deflection.

To degrade this amazing effect using the premature descriptive conclusion "proves the Earth rotates" denies science credibility because a far more important question was not answered, that being, "Relative to what and measured against what standard?" A fundamental question that if left unanswered would challenge the integrity of the scientific method and the sciences.

In this case, the standard must be any universal fixed position devoid of all motion, about which the laws of linear motion apply, ie. a Universal Stationary Frame of Reference, a standard position easily identified by the differential mechanical nature of the magneto-mechanical atomic model. A body moving away from the Universal stationary position travels in a straight line unless deviated by an external force. With respect to the ordinate of position in Nature's Universe, all non-linear motion (being relative to an absolutely NO motion condition) acts to maintain a curved trajectory around an apparent central point of equilibrium until such time as the differential energy equally distributes throughout that matter.

The ordinate of position has three coordinates of distance, (length, width and depth). The ordinate of matter exists as volume and quantity (mass). Energy being a function of matter, begins with an event in matter, being transferred by matter, through matter, to affect and cause effects in other matter, through magnetic means. The absolute measurement of duration between events marks Time as the ordinate representing the continual and on-going ageing process of the Universe.

The Road Traffic Authority sign above the highway asks a profound question "How fast are you going Now?" All terrestrial velocity measurements, being Earth Relative, result from and produce deluded observational illusions with respect to position, motion and time.

The Earth's rotational rate of just 0.000011606 rps seems slow by any standard, but great enough to produce tip speeds exceeding 1,642 Km/ hour at the equator. To apply Newton's laws of motion between two radial positions on the Earth's moving equator, of just one metre difference in height (say, from a radius/altitude of 6,378,000 metres to 6,378,000 and one metre) the tip speed for each point produces Momentum (M=mv) and Kinetic energy (KE= ½ mv²) levels that simply blow one through the roof, far greater than contemplated using the equation to determine the gravitation difference in potential energy (P_eD = mgh). Fear not, for only on striking a dead-stopped object would that potential energy (stored as rotational energy due to throughput) be liberated as unique energy-forms.

Both previous tables graphically illustrate a story of relative speeds in assisting the explanation of the sheer power behind the Earth's weather cells. They also pose the question as to why atoms remain attached to the Earth at all. Due to the high rotational speed, one would expect the atoms along the equator to be thrown off due to the high rotational speed. Although the equator travels at 1,642 Km/hour, faster than the speed of sound in air (1,193 Km/hour) all sound propagates on the equator because sound moves with the moving environment at the equator. In respect to an external stationary reference point, all equatorial produced sounds travel only in one direction around the Earth. At higher latitude angles (greater than 45 degrees) the reduced the tip speeds allow sound to travel in both directions with respect to an orbital relative universal stationary position. With motion being relative to the greater frame of reference, a gyroscope spins relative to a frame, about which other frames of reference define the local stationary frames. Nature's Universal Frame of Reference being the greatest frame of reference filling the entire universe.

With the magneto-mechanical atom, once rotation begins, common throughput, being greater than local throughput, a spinning object becomes an almost stand-alone-entity, presenting many observational illusions that serve to confuse. Needles to say, the central axis being stationary remains relative to the local environment.

Matter stores energy efficiently through rotation. The alignment and number of spinning sub-atomic particles (protons and neutrons) gives a body, mass, inertia and its protective magnetic field. The higher the rate of spin in one direction, the greater the directional inertia. Directional inertia is the v² component in the Kinetic energy equation. Equally, the more matter, the greater the standing state inertia as a consequence of m². as awkwardly defined in Newton's "Principia" (1687) but left out of most modern translations. Across a body each atom responds to and stores the prevailing level of magnetic throughput as sub-atomic particle rotation, transferred as throughput from atom to atom and differentially distributed throughout the material.

Every twenty years, misguided souls apply these illusions in futile attempts to build very dangerous anti-gravity or levitation machines. One must exercise extreme care near any rotating objects for they demand great respect. Rotating devices include tyres, pulleys, axels, gears, flywheels, propellers, impellors, turbines, gyroscopes, roller bearings, trolleys, carriages, locomotives, blenders and mixers, windmills, roller blades, scooters, bikes, trikes, the pendulum, levers, video heads, inertial guidance system, information storage systems, turntables, carousels, fans, lawn mowers, power tools, twist drills, motors and other motor vehicles, atoms and molecules. Beware the occasion when rotational forces tearing a device apart exceed those forces holding it together.

Evidence of Coriolis rotation can be observed from the coffee cup to the Quasar, as these convection cells hold tight spinning balls of matter together. With slow-down, galactic arms appear in the bubbles. The viscosity of the atmosphere, the oceans and the mantle all play important roles in transferring rotational energy from atom to atom, from the surface of a material to the centre of all matter in that material. When many atoms move on mass as a wind to travel uniformly from the equator to the Temperate zone, by the shortest possible path, expect trouble! The famous 'Jet Stream' effect becomes evident, as the atmosphere seemingly picks up speed, travelling faster than the Earth's rotation, swirling that pleasant tropical breeze into havoc creating monsoon winds and powerful eddying cyclones. Jet streams racing across the Northern hemisphere land masses, swirl thunderstorms into tornadoes, often the ground wind speeds approach 300 Km/hour. The Coriolis effect becomes Ferrel's law when geographer's describe the mindless motion of liquids flowing across a rotating spherical body.

In comparison, the Earth's fierce winds do not rank with the expected winds that circulate on the Sun and the planet Jupiter. Having an equatorial diameter near 1,390,600 Km, the mean solar rotation of 27 - 28 days makes for some fearful velocities. Jupiter (12 times greater in diameter than Earth) of 143,600 Km rotates in less than 10 hours. All atmospheric bodies (including galaxies, stars, planets and moons) exhibit different but common Coriolis structures. The forces experienced in any atmospheric circulation system with a change in latitude or altitude create massive directional changes. Venus portrays just 1 cell per hemisphere. Mars exhibits 2 cells per hemisphere while the Sun and Earth both carry three cells per hemisphere. With depth, the Earth's mantle and the Sun layer. This dual layer gives rise to an interesting magnetic field generator where the upper cells slip over the lower cells, producing periodic magnetic reversals. Fourier analysis on the 11 year Solar Sunspot cycle confirms a beating effect between the two levels. All these weather systems and rotating devices prove rotation as a Universal effect, relative to the Universal Stationary Frame of Reference, and most definitely not to any terrestrial frame of reference.

RLOK.

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