Cornering Force
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Cornering Force
Cornering force or side force is the lateral (i.e., parallel to wheel axis) force produced by a vehicle tire during cornering. Cornering force is generated by tire slip and is proportional to slip angle at low slip angles. The rate at which cornering force builds up is described by relaxation length. Slip angle describes the deformation of the tire contact patch, and this deflection of the contact patch deforms the tire in a fashion akin to a spring. As with deformation of a spring, deformation of the tire contact patch generates a reaction force in the tire; the cornering force. Integrating the force generated by every tread element along the contact patch length gives the total cornering force. Although the term, "tread element" is used, the compliance in the tire that leads to this effect is actually a combination of sidewall deflection and deflection of the rubber within the contact patch. The exact ratio of sidewall compliance to tread compliance is a factor in tire c ...
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Rubber
Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds. Thailand, Malaysia, and Indonesia are three of the leading rubber producers. Types of polyisoprene that are used as natural rubbers are classified as elastomers. Currently, rubber is harvested mainly in the form of the latex from the rubber tree (''Hevea brasiliensis'') or others. The latex is a sticky, milky and white colloid drawn off by making incisions in the bark and collecting the fluid in vessels in a process called "tapping". The latex then is refined into the rubber that is ready for commercial processing. In major areas, latex is allowed to coagulate in the collection cup. The coagulated lumps are collected and processed into dry forms for sale. Natural rubber is used extensively in many applications and products, either alone or in combination wit ...
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Tires
A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), traction on the surface over which the wheel travels. Most tires, such as those for automobiles and bicycles, are pneumatically inflated structures, which also provide a flexible cushion that absorbs shock as the tire rolls over rough features on the surface. Tires provide a footprint, called a contact patch, that is designed to match the weight of the vehicle with the bearing strength of the surface that it rolls over by providing a bearing pressure that will not deform the surface excessively. The materials of modern pneumatic tires are synthetic rubber, natural rubber, fabric, and wire, along with carbon black and other chemical compounds. They consist of a tire tread, tread and a body. The tread provides Traction (engineering), traction ...
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Skidpad
A skidpad is a circular area of flat pavement used for various tests of a car's handling. The most common skidpad use is testing lateral acceleration, measured in meters per second squared (m/s2) or the scaled unit ''g''-force. This usage has similarities to that of using a kick plate. Measurement of grip A car’s maximum number of ''g''-forces on a skid pad says something about the grip of the car on winding roads, or how fast it can drive in corners without losing grip. Some factors which can aid in achieving higher ''g''-forces are high power, wide tires, low mass, appropriate suspension setup and large downforce. Test setup The test is carried out on a circular track with a defined radius. A car driving on said track is slowly accelerated, until the outermost tires on the car begin to slip. Going any faster would cause the car to drive outside the defined radius. At this point, the speed of the car is recorded, and given the centripetal acceleration formula (by the fo ...
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Lateral Force Variation
Tires provide for steering, traction, braking, and load support by transmitting forces between the vehicle and the road. Lateral force variation (LFV) is a property of a tire that characterizes its dynamic behavior of these forces. High values of LFV for a given tire reflect a high level of manufacturing variations in the tire structure that will impart ride disturbances into the vehicle in the lateral, or steering, direction. LFV is measured according to processes specified by the ASTM International in ASTM F1806 – Standard Practice for Tire Testing. LFV can best be explained by example. Assume a perfectly uniform tire mounted on a perfectly round wheel loaded with a constant force against a perfectly round test wheel. As the wheel turns, it turns the tire, and the tire carcass undergoes repeated deformation and recovery as it enters and exits the contact area. If we measure the lateral force between the tire and the wheel we will see zero change as the tire turns. If we no ...
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Camber Thrust
Camber thrust and camber force are terms used to describe the force generated perpendicular to the direction of travel of a rolling tire due to its camber angle and finite contact patch. Camber thrust is generated when a point on the outer surface of a leaned and rotating tire, that would normally follow a path that is elliptical when projected onto the ground, is forced to follow a straight path while coming in contact with the ground, due to friction. This deviation towards the direction of the lean causes a deformation in the tire tread and carcass that is transmitted to the vehicle as a force in the direction of the lean. Camber thrust is approximately linearly proportional to camber angle for small angles, reaches its steady-state value nearly instantaneously after a change in camber angle, and so does not have an associated relaxation length. Bias-ply tires have been found to generate more camber thrust than radial tires. Camber stiffness is a parameter used to describe the c ...
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Circle Of Forces
The circle of forces, traction circle, friction circle, or friction ellipse is a useful way to think about the dynamic interaction between a vehicle's tire and the road surface. The diagram below shows the tire from above, so that the road surface lies in the ''xy''-plane. The vehicle to which the tire is attached is moving in the positive ''y'' direction. In this example, the vehicle would be cornering to the right (i.e. the positive ''x'' direction points to the center of the corner). Note that the plane of rotation of the tire is at an angle to the actual direction that the tire is moving (the positive ''y'' direction). Put differently, rather than being allowed to simply "roll" in the direction that it is "pointing" (in this case, rightwards from the positive ''y'' direction), the tire instead must "slip" in a different direction from that which it is pointing in order to maintain its "forward" motion in the positive ''y'' direction. This difference between the direction the ti ...
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Convention (norm)
A convention is a set of agreed, stipulated, or generally accepted standards, norms, social norms, or criteria, often taking the form of a custom. In a social context, a convention may retain the character of an "unwritten law" of custom (for example, the manner in which people greet each other, such as by shaking each other's hands). Certain types of rules or customs may become law and sometimes they may be further codified to formalize or enforce the convention (for example, laws that define on which side of the road vehicles must be driven). In outline of physical science, physical sciences, numerical values (such as constants, quantities, or scales of measurement) are called conventional if they do not represent a measured property of nature, but originate in a convention, for example an average of many measurements, agreed between the scientists working with these values. General A convention is a selection from among two or more alternatives, where the rule or alternativ ...
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Self Aligning Torque
Self aligning torque, also known as aligning torque, aligning moment, SAT, or Mz, is the torque that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis. In the presence of a non-zero slip angle, this torque tends to steer the tire toward the direction in which it is traveling, hence its name. The magnitude of this torque can be calculated as the product of the lateral force generated at the contact patch and the distance behind the wheel centre at which that force acts. This distance is known as the pneumatic trail. The steering torque around a non-vertical steer axis with non-zero mechanical trail is given by : (trail + pneumatic trail) · cos( caster angle) · ''F''''y''. Even if the slip angle and camber angle are zero, and the road is flat, this torque will still be generated due to asymmetries in the tire's construction and the asymmetrical shape and pressure distribution o ...
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Pneumatic Trail
Pneumatic trail or trail of the tire is a trail-like effect generated by compliant tires rolling on a hard surface and subject to side loads, as in a turn. More technically, it is the distance that the resultant force of side-slip occurs behind the geometric center of the contact patch. Causes Pneumatic trail is caused by the progressive build-up of lateral force along the length of the contact patch, such that lateral forces are greater towards the rear of the contact patch (though less so when the rear of the contact patch begins sliding) and this creates a torque on the tire called the self aligning torque. Because the direction of the side-slip is towards the outside of a turn, the force on the tire is towards the center of the turn. Therefore, this torque tends to turn the front wheel in the direction of the side-slip, away from the direction of the turn. Variation Pneumatic trail is at its maximum when the slip angle is zero and decreases as slip angle increases. Pneumatic tr ...
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Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be int ...
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