The Coriolis effect Paper
Galileus corrected this view by explaining the path of such a projectile as a parabola, where a continual downward motion acts on the object, that being the pull of gravity. Newton furthered Galileus’ argument in showing mathematically, that the impetus was not used up, rather gravity restricted the cannon’s range by altering the shape to that of a parabola. Newton would argue that when sufficient force is given to the shell, the projectile would fall all the way around the Earth, never touching the ground, prescribing an elliptical orbit.
But here is a contradiction. The trajectory of a projectile must follow the arc of an ellipse, not that of a parabola. The curve of a parabola is totally different to an ellipse, so, why then, does Science maintain such a basic false belief? Newton did not realise that he copied an error. It is obvious he did not understand the effects of atmospheric drag, cross-winds, tail winds, chemical behaviour, supersonic melting, and the rotation of the Earth, (the Coriolis effect) because these effects were scientific mysteries at that time.
Since Newton’s time, much has been discovered and alterations made to Newton’s theory. But these changes were at great cost. Although new words and definitions clarified Newton’s laws, the nineteenth century scientists and mathematicians who resolved Newton’s initial mistakes and omissions, feared scientific outrage, for Newton, the legend, grew more powerful in death. Many who although correct and for the correct reasons, attacked The Great Newton, became ostracised by the scientific community. Credit was rarely bestowed on them, leaving them in history’s void.
One can pick up virtually any Physics book (this one included) to discover unique translations and understandings of Newton’s laws by each author. In Newton’s “Principia” (1726) , the three laws of motion are written as; Law 1. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by force impressed thereon. Law 11. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
Law 111. To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. The second law is perhaps the most changed through translation. There are so many interpretations of this law that the situation becomes rather confusing. The following are three common variations on Newton’s theme.
“The force required to accelerate a body is proportional to the product of its mass and its acceleration. ” (Various authors)”that if an unbalanced force acts upon a body, the body will be accelerated; the magnitude of the acceleration is proportional to the magnitude of the unbalanced force, and in the direction of the acceleration is in the direction of the unbalanced force. ” (H. Semat) “The acceleration caused by one or many forces acting on a body is proportional in magnitude to the resultant of the forces, and parallel to its direction, and is inversely proportional to the mass of the body. ” (Resnick & Halliday) But these translations seem to have different meanings.
In the “Principia”, Newton’s words describe this second law with “If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.
” Newton’s second law seems to be in contradiction to his third law, though there is something in the third law which many fail to see. Again, from Newton’s “Principia”, the description of the third law is ” If a body impinges upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. The changes made by these actions are equal, not in the velocities but in the motion of bodies; that is to say, if the bodies are not hindered by any other impediments.
For, because the motions are equally changed, the changes of the velocities made towards contrary parts are reciprocally proportional to the bodies. ” Both Newton and Galileus noticed that the outcome bore an inverse proportionality to the body (the mass) of the object. Yet, none of the equations involve the square root of the mass, or the mass squared. In mathematics, when two or more variables are proportional, then the mathematics reflects that concern by the use of the symbol ? . Normally, Newton calls equal proportions, equal, but here he does not and none of the translations do.
Universally, they must use the word proportional, not equal. The equation written as F = m a, does not state any proportionality, rather the emphatic is bluntly stated using the operand equals. This equation fails to imply proportionality or that the force is directly proportional, or for that matter, that there is a reciprocity in proportions between the components. Should not the equation be written as F ? m a or perhaps, F = m2 a If F = m2 a happens to be true, it would create a disaster in many areas, for it does not answer (at this moment) any questions, rather it would create a million problems.
Proving such as true, would mean that the standards and definitions currently accepted by Physics and the other sciences, (those that rely on the accuracy of Newton’s equation F = m a ) would need to be replaced and reworked. Newton’s laws of motion relate to linear motion, to all motion in a straight line, when such motion is not found, not possible on the Earth. The cosmological planet Earth is turning on its axis in 23 hours 56 minutes 4. 1 seconds, a rotational speed of 0. 0000116057615 rps. This may be slow, but it is rotating, for even Galileo’s last words “And the Earth still moves” made this message clear.
The rotation on the Sun is much slower for one revolution takes about 28 days, giving a rotational speed of 0. 0000004145 rps. Jupiter’s rotation is the most rapid of all the planets completing a single rotation in 9 hours 50 minutes, a rotational speed of 0. 0000282485875 rps. The equatorial tip-speed of astronomical objects, even at low rotational speeds can be an awesome number, due to the radius of the object. A galaxy just a thousand light years across, having a circumference of 3,141. 59 light years does not need to rotate very quickly for the tip-speed to present a red-shift approaching light speed.
An annual difference in position of a light year would need to equal the distance light travels in that year, so, the galaxy would need to turn just once in 3,141. 59 years, at which point the outer stars and nebulosity would reach light speed. Generally, galaxies rotate very slowly, but this does not make them any different to normal matter, for the Laws of Nature apply across and throughout the Universe. The major forces involved in a galaxy are rotational. Although magnetism and gravity are far less powerful forces, they shape the galaxy, promoting other fantastic effects.
The source of cosmological rotational energy can originate from near-miss gravitational interactions, such as when a galactic body of stars is pulled towards a passing galaxy, the gravitational disturbance produces a sling-shot-effect and the distribution of energy causes both galactic bodies to respond to such motion. But to understand a galaxy means understanding rotation. Foucault’s gyroscope is the most amazing scientific toy to observe rotational energy. The toy can be purchased from most toy stores, newsagents and educational supply companies for less than $20.
The basic gyroscope can be made for less than a dollar from odds and ends, constructed by attaching a small shaft through the centre of a balanced disk. All spinning objects are gyroscopes; a truck’s spinning tyre; a spinning thumb tack; a child’s top; a motor; the flywheel and the turbine. As a disk is spun at a high rotational speed, several strange events will be noticed, but be careful, basic safety procedures should be observed, for spinning objects have a habit of breaking apart, grabbing hair, causing deep wounds, and racing across the floor, possessing a definite tendency to break the most expensive piece of pottery in the house.
Murphey’s laws apply. There are many observational illusions that lurk in rotating devices. With the axis vertical, merely placing the stationary gyroscope on the floor, shows the force of gravity, for it falls over. However, when the disk is spun as rapidly as possible, the device defies gravity’s pull, standing upright without falling over, yet the spinning disk and its frame have the same weight. The spinning disk may develop a strange wobble, where the top-most point of the axis seems to follow a circular path, but no matter what is done, this precession follows the direction of rotation.
This is the precession of the axis. There seems to be no way of making the precession travel in the reverse direction to the rotation. One can shake, vibrate, thump it, flick or attack the frame, without any change to the direction of precession. It could be easy to argue using simple observations to conclude that precession has something to do with the direction of rotation, gravity, or the bearing drag, but this is not so. Turning the spinning gyroscope upside-down or making it spin in the opposite direction, does not alter the direction of precession for it still follows the direction of spin.
Most Physics educators fall head-first into the because-it-is-done-this-way trap, because an observational illusion dictates the mathematics and international scientific agreement alters the truth, hiding the mechanism. The method locks the bottom axle bearing to a hypothetical x-y-z coordinate point in relating precession to the force of gravity on the entire structure acting at that point. This is not the true reference point for the gyroscope is not a terrestrially referenced device, yet the terrestrial frame of reference is repeatedly used. The gyroscope’s frame of reference is Universal.
To prove this, it is necessary to do something so trivial, the feat escapes the attention of the most observant. Simply pick the spinning gyroscope up by the top-most bearing and it is seen to precess in the opposite direction to the spin! Immediately, all gravitational and bearing drag effects have been eliminated. An obvious observational error has introduced a nasty knowledge virus into Science where all observations of the gyroscope use the terrestrial frame of reference. The mathematical explanations of the gyroscope and its precession are illusions with physical manifestations producing complex physical properties!
The gyroscope precesses around the gyroscope’s axial centre, not the bottom-most bearing or the centre of mass. Mass irregularities between the axial centre and the centre of mass result in several commonly observed gyroscopic effects. If precession were a terrestrial event, then it would present opposite motion in each hemisphere, but then the Earth also precesses so where is the gravity pulling the Earth? Figure 14-1 changes the mathematical explanations in a single blow. Having realised the error, the mechanism must be found. But what happens when two disks are fixed to the same shaft?
A train has such wheels, where a steel axle shaft supports a gyroscopic tyre on each end. Effectively, two independent gyroscopes are connected to a common shaft. The direction and speed of both gyroscopes can only be identical, where any differences will result from the mass distribution and balance of the tyres. The axle is connected to the bogie frame supporting each end of the shaft with a bearing. As the two disks rotate together, the left hand gyroscope has a precession clockwise on the left side and anti-clockwise to the right side.
The right hand gyroscope is identical, meaning that along the centre shaft, there is a conflict in precession. The left wheel is twisting the shaft anti-clockwise, while the right wheel is twisting the shaft clockwise. At certain speeds, dangerous resonances occur in the shaft as the dual precession twists and strains the shaft. Figure 14-1 Reversing precession The complete bogie mounts two or more independent axle-wheel pairs. As the axles roll on the track, the left side wheels are twisting with a clockwise precession, while the right hand wheels are twisting with an anti-clockwise precession to the outside.
Each wheel may be precessing at different rates. Bogie-slap is the term sometimes used to describe this effect, for no matter how well balanced the wheels may be, the bogie will wobble between the rails so erratically, it is to the discomfort of passengers, knocking the tracks apart, which, if not corrected can lead to a derailment. The solution to bogie-slap is to independently support inclined wheels on their own axles (figure 14-2). Figure 14-2 The Method of Correcting the dangerous gyroscopic instabilities in train wheels What happens when one continually flexes a thin wire?
Even though the shaft may be 20 cm diameter machined steel, with time it must suffer metal fatigue, a molecular failure. The broken axle is generally attributed to mechanical failure not gyroscopically produced metal fatigue. Figure 14-2 illustrates this effect where the dual gyroscope action causes flexing, bending and distortion of the axle. When a motor is connected to a pulley, it forms the same dual structure with the same inherent twisting and resonance problems. As the motor spins up in speed, the connecting shaft enters regular periods of stability and instability as the twisting forces resonate through the shaft.
This effect has nothing to do with gravity! With high speed drink mixers, the motor’s rotation passes through a speed-up gear system. The drive shaft of the high speed blender, has at one end, a very small gear coupled to a large motor gear. The beauty of this design is that it reduces the dual gyroscope effect, allowing the blender to reach speeds in excess of 10,000 rpm (166. 6 rps). Geologists have a great deal of trouble explaining why the Earth’s interior is hot. They believe that the internal temperature is related absolutely to the breakdown of atoms through nuclear events, where radioactive decay is the only accepted explanation.
If this were the case, evidence should be found to substantiate the claim, like, everyone living near an active volcano should suffer radiation sickness and have mutant children. Radioactive decay need not be the full picture, for the rotating Earth must be considered as a rotating object, not as a static object. Any sphere can be considered as made up of many parallel balanced disk pairs, layer by layer, mounted on the axis. Each pair of disks forms the dual gyroscopic structure where the twisting forces are at loggerheads with each other, causing flexure, heating and stirring in the Earth’s interior.
As long as the Earth turns on its axis, it will remain hot. Once a planet loses it rotation it will rapidly cool and solidify. Such dead non-rotating planets include Venus, Mercury and The Moon. Seismically, these dead planetary objects, when struck would all ring-like-a-bell. Massive dark objects, perhaps greater in size and mass than the Sun, will be found to exist in the Galaxy, as collapsed, non-rotating dead-stars. Such objects would contain normal matter, with normal densities, perhaps with a crust much like the Earth, of silicates and frozen gasses, water, Helium, Hydrogen, and Carbon structures.
Gravitational differentiation (settling and separation of different mass molecules) in the cooling stellar mass may lead to critical mass conditions developing unstable shells at particular radial distances within the mass, causing an explosion that may regularly blow the dead-star apart, in many supernova events forming dangerous dark rubble-stars. Effectively, as the Earth is slowing down, it is losing heat ever so slightly. The current rate of slow down may be a second every century, but it is still a slow down. Back when the dinosaurs existed, the Earth would have experienced a much faster rotation.
Perhaps, when the primordial Coriolis blob formed the Sun and Earth, the rotation may have been once every eight hours. This leads to a problem, because mankind is attempting to extract electrical power from geothermal sources. The greater the rate that power is removed, the cooler the Earth will become and the greater the rate of slow-down. Rotational energy does not work like gravity. It is not related to the actual or inferred centre of mass. The centre of mass is only a hypothetical point of maximum signal strength used in gravitational-feedback calculations.
Nature does not work through calculations, rather she works with cause and effect, selectively evolving through survivors. Over-and-over-again, Nature will try the same experiment, even though failures occur, but one experiment will create a survivor. Many survivors create a colony. The key needed to solve Nature’s rotational trick is the direction of the axis itself. With any rotating object, a sphere, shell, cube, box, cylinder or, tube, prism or block, the axis must be considered as having no mass. The axle may have a mass, but the axis itself has zero mass.
The axis is a hypothetical line joining all positions of zero motion, about which centrifugal forces radiate. Relativity shows there are actually two primary forces involved here, the centripetal force and the centrifugal force. The centripetal force holds matter together and allows energy to be transferred from the axis to the circumference of the object or vice versa. The centrifugal force is the radial spin-out force remaining perpendicular to the axis, from the particular axial height to the circumference at that height in the perpendicular direction.
The gyroscope is not defying gravity, rather it is locking onto a fixed universal stationary direction, having a slipping plane direction. Figure 14-3 addresses the attributes of the gyroscope. Figure 14-3 The Gyroscope’s forces. One demonstration of this is the nylon fibre lawn edge trimmer, where a single strand of 8 or 10 gauge nylon thread is twirled around a central hub so rapidly that it takes on the resilience of blade steel. Slow motion images of this cord show it to be absolutely taut, at an angle perpendicular to the axis of rotation.
Equally, when a thin plastic disk is rotated, even at relatively low speeds, the disk takes on a rigidity perpendicular to the axis. Typical applications of this include the floppy disk drive and CD player. A soft plastic disk when rotated can be used to cut through much harder materials, due to the change in molecular strength. Describe the motion of a spinning woollen pom-pom with respect to the rotation. Across the surface of a rotating disk, the atmosphere is pulled around with the disk to be spun off creating a super high speed wind immediately above the disk’s surface.
So powerful is this molecular wind, it is capable of holding tightly sprung disk-drive heads well apart and away from the surface of the floppy disk. A method of killing a disk drive is to evacuate the disk-head chamber. The same occurs in the hard disk drive (HDA), but rather than having one disk, the computer’s HDA may have as many as twenty four pancaked disks. The disk drive heads are virtually clamped together, but as the head assembly approaches the disk, the wind opens the heads and blows them apart, holding then at a constant height at that radius.
The slower the disk speed (towards the centre), the closer the heads are to the surface. A particle of smoke hitting the head can cause gyroscopic instabilities between the head and the platter resulting in a head crash. This does not normally eventuate, though, when it does, the event is to be remembered, for nothing much remains. Typically, the head crash causes the disk to be cut away near the axis whereupon the disk sheers away. Needless to say, all the data stored on that disk drive is lost.
Due to the seek times and storage needed in major mainframe computer installations, removable disk platters were used. Some of these drives spun the 8 plate 30cm diameter platters at speeds above 5,000 rpm ( 83. 3 rps producing a tip speed of some 178. 53 m/s or 282 Km/h). The head crash could cut the disk from the platter in a second. Once airborne, the disk would smash through the protective housing, the casing, flying-off across the computer room to bury itself edge-wise into any distant object, with such an impact force, chemical reactions take place between the disk and the object it entered.
These disks do not strike objects, they enter them and form chemical bonds. As the gyroscope spins, it passes through periods of absolute stability, followed by periods of instability. As the disk slows, the precession becomes more and more pronounced. Eventually as the rotation fails, the force of gravity grounds the gyroscope. This effect indicates an atomic and molecular resonance in the gyroscope, where the centrifugal and centripetal forces are continually compensating. A magnetic shock travels along the axis and rebounds, but in the mean time, the disk has rotated.
If the reflection point is immediately below or 180 degrees out of phase, stability exists in the gyroscope, however, as the reflection point drifts out of phase, the system’s instability increases as the axis is knocked from the vertical position and then precession follows the rotation. The precession may cause the object to violently wobble when the phase shift is 90 degrees. This is a molecular resonance effect and is different between different materials. This is the G-wave, an effect caused by matter’s elasticity.
The effect can be seen and heard during instability where the forces are so great, bearing grab presents a drag force causing maximum axial deviation and the observed precession. As the disk precesses, the bearings are pushed and pulled sideways with greater friction, transferring considerable rotation to the mounting frame. At high speeds the bearing drag pulls the gyroscope’s mounting frame around rapidly but as soon as stability returns the frame ceases to be dragged around. With the on-set of stability, the pressure on the bearings is constant and minimal while the energy losses to the mounting frame are minimised.
A worst case scenario is called bike-slap. It is a problem that has killed many expert motor bike riders. This is not a rider error, it is a serious motor bike problem. The effect results from numerous design errors in both the design and manufacture of the bike frame. It is a manufacturing fault and as such the manufacturers should be made to pay compensation to the families of those they have murdered and maimed through negligence. There is no justification for an inferior design in the market place, however one often observes the effect during motor bike races (to the amusement of the crowd).
Basically, the frame holds the motor and its flywheel (the first gyroscope). As the steering geometry changes at speed, a small displacement in the angle of the front forks caused by a twist in the front wheel (the second gyroscope) to a slightly different angle to the real wheel (the third gyroscope) and the engine. The frame is allowed to flex within reason and within certain tolerances. The frame absorbs and stores the twisting forces as the rider enters a corner with the power on.
As the corner is negotiated, the power applied to the back wheel is changed, but then without any warning, the twist forces stored in the frame suddenly release causing the bike to slap to one side, immediately throwing the front and rear wheels sideways, initiating precession at different rates in different respective directions, violently establishing an uncontrollable buckling oscillation in the bike, causing each gyroscope to slip, creating an effect much like sitting on a bucking bull. The rider can be lucky riding this bull and be thrown clear.
Then again, one can be thrown under the oncoming traffic, into a curb, or have the bike come crashing down on top of oneself. This is not a pleasant experience and may occur by simply turning a corner at slow speed. Some very interesting effects are noted when the gyroscope’s curved steel frame is supported by a moderately strong bar magnet (figure 14-4). An electrical eddy current flows in the spinning disk, effectively holding the gyroscope against the precession forces. To walk the square pole piece of the magnet into a different supporting position, (without touching the frame with the hands) is quite difficult.
The bearings apply changing forces on the spinning mass, causing the axis to precess differently. One can hear the bearings grab as the axis attempts to remain pointing in the same direction. The energy transfer from the frame to the disk and back to the frame causes sudden and rapid axial direction changes. Moving the support position towards the axis reverses the precession while moving the support from the axis to the circumference produces a normal but temporary precession. In each case, the precession is sudden, and locks to a new direction. But there is more. Figure 14-4 Hanging the Gyroscope
When the bar magnet is hung from 35 cm of string or wire, so that the magnet is vertical and away from any nearby obstruction, just hanging in space, the gyroscope’s precession oscillates, due to the interaction between the magnet, the Earth’s rotation and magnetic field as well as the support position changes taking place. A small 1. 5 cm steel ball bearing placed in the magnetic circuit between the pole piece and the support housing removes the support position component caused by the square face of the magnet. With this change, normal precession is still resisted, giving a wobble until the disk starts to slow down.
A great deal of bearing grab is heard as the gyroscope twists the string. With the axis slipping to the vertical, a great deal of vibration will be seen in the string. When prevented from slipping, the vibration in the string becomes pronounced. This stored twist force does not release until the rotation virtually ceases. The Gaxis seems to favour coming to rest pointing more vertically in the East-West direction. A well known child’s toy, called the topsy-turvey-top, establishes a scientific problem of the first order. This has been addressed in several outstanding scientific papers.
Basically, the top is weighted differently so that when spun between the fingers, it lands on the surface on its point, as do most other tops, but then completely does a back-flip to spin in the opposite direction, without any loss of rotational speed, balancing on the top’s top point with stability. This is not really “balancing” as such. This is a demonstration of the conflict between rotational energy and gravity. How is the direction reversed? To change the direction of a gyroscope involves overcoming the centrifugal forces holding the axis in place.
Once sufficient force is obtained, the axis can be made to move, to slip or yaw, rolling over so that the rotation of the axis is in the opposite direction, so any precession reverses, being relative to the direction of motion around the axis. For a locomotive pulling a train, travelling on a single track to change direction, requires slowing down, stopping completely and then pushing the train in the opposite direction. The same happens when a ball strikes a wall. Particle reflection takes a great deal of time and uses considerable energy to reverse the direction. However, the train may travel.