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Transcript
What is the Centrifugal Force? Elchanan Shochat – Mechanization Director, Extension Services, Ministry of Agricultural and Rural Development (For more information, please visit http://www.agrosif.com.) In the field of agriculture, centrifugal force is put to use in a number of different machines: machines that separate between honey and honeycomb, fertilization spreading vehicles, mechanical harvesting tree shakers, etc. On which principles are these based on and how does it work? What is the difference between King David and a modern day fertilizer spreader? The story of how the young David defeated the mighty Goliath is aptly described in the Bible. What King David didn't know, however, is that the stone which he released from his sling and dealt a fatal blow to the head of Goliath was powered using centrifugal force – the same force used in modern day fertilizer spreaders. Already in ancient times, man knew how to apply the laws of physics for his own good (and bad), despite not knowing th actual laws of physics themselves, and certainly not the equations that govern them. It was known, however, that using a sling provided more power, and hence speed, to the stone being slung than merely throwing it with one's bare hand. Thousands of years later, the French Scientist Gustave Coriolis (1792-1843) formulated and explained the eponymous phenomenon. Coriolis worked in the French Army and studied the motion of cannonballs fired from cannons. The centrifugal occurs when a body rotates around a point not coincident with its center of mass. In of agriculture, centrifugal force is put to use in various types of machines. Bee keepers use centrifugal force to separate the honey from the honeycombs. The faster the honey removal basket rotates, the better the extraction is of the honey from the wax. The rotational speed, or angular velocity, is noted by the Greek letter omega – ω. Since it is essentially a vector, comprised of angular velocities in three dimensions, we denote it with an over-bar - , an accepted notation of a vector quantity. In fertilizer spreaders, centrifugal force is used by a rotating disk with arms to spread the fertilizer particles in the field, and are thus called centrifugal fertilizers. Their accuracy depends first and foremost on the spacing between the traversals of the spreader. The larger the spacing, the less overlap there is. The amount of overlap largely determines the quality of the fertilizer dispersion throughout the area. A computer program that could calculate the estimated dispersion of fertilizer for each traversal would enable the determination of optimal spreader traversal for pattern. Centrifugal forces are also used to form droplets in pesticide sprayers. In a hydraulic nozzle, forces are built up by swirling within the nozzle, resulting in mechanical fragmentation, with the rotating disk releasing liquid droplets. The mechanism by which mechanical nozzles spray liquid is more straightforward than that of hydraulic nozzles. In lawnmowers and trimmers, centrifugal forces help to properly straighten out and position the fragments as specified by the user. For example, one may select a vertical mower with single or multiple mowing chains. In this type of mower, a disk spins around a vertical axis with a pair of chains attached to the disk. The rotation of the chains creates a centrifugal force around the axis which stretches the chains outward from center of rotation. This is the direction of the centrifugal force, always toward the center of rotation. The opposing tendency – from the outside toward the center, is called a centripetal force. In a horizontal lawnmower, where the axis and blade-drum are horizontal, the centrifugal forces position and stabilize the blades in the desired position relative to the stalks being cut. Seed extraction systems are also based on centrifugal force to extract the water from the final product. Seed production lines include a number of machines which for the most part are custom made for a specific type of product. Producing quality seeds demands much professionalism on the part of the farmer. The knowledge and experience that farmers here have with state-of-the-art machinery enables Israel to produce vegetables seeds of the highest quality in the world. The standards of survival and germination rates of seeds are raised each year, presenting a challenge to farmers to meet a higher standard. From time to time, the farmer must upgrade his machinery, and it is generally costly. The scientist Gustav Coriolis, mentioned earlier, understood that the rate of change in time of a vector depends not only on the change of its magnitude, but also of its direction. Just as the change in either magnitude or direction of a position vector is its velocity, similarly, the change in magnitude or direction of a velocity vector is its acceleration. The velocity vector thereby provides the acceleration vector, which in turn is provided by the position vector. In a system where the accelerations are known, ostensibly the forces are also known by Newton's Second Law. Take, for example, an ant crawling on a rotating disc. Newton's Third Law dictates that the forces which act upon the ant are equal to the forces that the ant reacts with onto the disc. The ant's location is described by the vector R: R= x i y j where: x – position of the ant on the x axis y – position on the y axis i – direction of the local x axis j – direction of the local y axis A dot above a letter with an arrow above it means a change of the vector in time, so the velocity, V can also be written as ̇ R , or: ̇ R= ẋ i ẏ j x i̇ y j̇ The first two terms are the time change of the position vector relative to the frame, expressed as V rel , while the second two terms are the time change of the vector's direction and is equal to × R . The ̈ acceleration of R, or the change in time of the change of time of R, is written as R , and thus ̈ R=V˙rel × ̇ Ṙ× R Any change in the direction of a position vector counts as its velocity. Therefore, in a similar vein, the change in direction of the velocity vector constitutes part of its acceleration. Expanding the above term by inserting the expressions for vectorial change in time, we obtain: V̇ = a =arel ×Vrel× Vrel× R ̇×R , or a=a rel R2 V rel2 R The explanation of each term is as follows: The component arel is the acceleration of the ant relative to the disc. The component αR is the acceleration of the ant due to rotational acceleration of the disc The component 2ωVrel is the Coriolis effect. The component ω2R is the centrifugal acceleration. Hence, the expression for acceleration includes its four components: relative acceleration between the object and the rotating frame, acceleration due to angular acceleration of the frame, Coriolis acceleration, and centrifugal acceleration, the latter resulting in a fictitious centrifugal force acting in the opposite direction. Mechanical harvester that shake the tree (“shakers”) detach the fruit using centrifugal forces. Commercial shakers are based on a mechanism consisting of two discs rotating with unbalanced masses. Were the masses to be balanced, no force would be generated between the disc and the masses, as there is no relative velocity between them and thus no centripetal or Coriolis forces. Perhaps we may now ask: What is the centrifugal force? The centrifugal force acting acting on the weights of the shaker depends on their mass m, the square of the disc's rotational velocity ω2, and it's mass center's distance from the center of mass R, given by the well known formula: F = mω2R. As is often the case, where the explanations to a perplexing phenomenon are found to be lacking, several answers are offered up. One explanation for how centripetal acceleration exerts centrifugal force uses a reformulation of Newton's Second Law, De Alembert 's principle. This principle states that when an object accelerates, it feels a force in the opposite direction. A good example of this is when a passenger is in an accelerating car. He feels a push backwards, even though he is accelerating forward. So too, when an object undergoes centripetal acceleration inward toward the center of rotation, it experiences a centrifugal force outward from the center. Tree shakers are built with a pair of rotating discs and weights. Each disc and weight exert a centrifugal force. The pair of discs thus exerts a pair of centrifugal forces. One may thereby adjust the force by choosing different weights, rotational speeds, and radial distances. The resultant force is found by vector addition of the two centrifugal forces. The force, being a vector, may be represented graphically by a rotating arrow. As the force vector rotates, the arrow may be thought of as plotting a point at each position its head is. The plot of all points plotted in one rotation cycle is a complete curve, and is called the shaking pattern. Since the disc rotation pattern is cyclical, a shaking pattern completely describes the map of force loci throughout the entire range of operation. Different centrifugal forces will result in different shaking patterns. Different types of crops require different shaking patterns. For almonds, a triangular pattern is preferred, while a looped pattern is preferred for citrus fruits. A six-petaled pattern is recommended for pecans. I personally recommend that a new pattern, a seven pointed star as shown in the figure, should be looked into. Summary: In this article, we used the simple example of an ant crawling on a disc to illustrate the principle of centrifugal forces, which is what tree shakers are based upon. In depth research of shaking systems, study of various shaking patterns, and matching them to the right kind of crop using a new type of tree shaker will result in an increased detachment rate of fruit, reduce the costs of harvesting, and increase the profits of the crop growers. Acknowledgements: The author would like to thank the farmers of Jezreel Valley for their help and generosity. Special thanks to Nissim Machlouf for his perseverance in disseminating this knowledge.