A centripetal force is a force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In the theory of Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits.
In physics, jerk or jolt is the rate at which an object's acceleration changes with respect to time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second (g0/s).
A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
A railway track or railroad track, also known as a train track, permanent way or simply track, is the structure on a railway or railroad consisting of the rails, fasteners, railroad ties and ballast, plus the underlying subgrade. It enables trains to move by providing a dependable surface for their wheels to roll upon. Early tracks were constructed with wooden or cast iron rails, and wooden or stone sleepers; since the 1870s, rails have almost universally been made from steel.
As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total traction that is parallel to the direction of motion.
In rail transport, a derailment occurs when a rail vehicle such as a train comes off its rails. Although many derailments are minor, all result in temporary disruption of the proper operation of the railway system and they are a potentially serious hazard.
Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying.
A banked turn is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.
Hunting oscillation is a self-oscillation, usually unwanted, about an equilibrium. The expression came into use in the 19th century and describes how a system "hunts" for equilibrium. The expression is used to describe phenomena in such diverse fields as electronics, aviation, biology, and railway engineering.
Railway engineering is a multi-faceted engineering discipline dealing with the design, construction and operation of all types of rail transport systems. It encompasses a wide range of engineering disciplines, including civil engineering, computer engineering, electrical engineering, mechanical engineering, industrial engineering and production engineering. A great many other engineering sub-disciplines are also called upon.
A track geometry car is an automated track inspection vehicle on a rail transport system used to test several parameters of the track geometry without obstructing normal railroad operations. Some of the parameters generally measured include position, curvature, alignment of the track, smoothness, and the crosslevel of the two rails. The cars use a variety of sensors, measuring systems, and data management systems to create a profile of the track being inspected.
In railway engineering, cant deficiency is defined in the context of travel of a rail vehicle at constant speed on a constant-radius curve. Cant itself refers to the superelevation of the curve, that is, the difference between the elevations of the outside and inside rails. Cant deficiency is present when a rail vehicle's speed on the curve is greater than the speed at which the components of wheel to rail force are normal to the plane of the track. In that case, the resultant force exerts on the outside rail more than the inside rail, in which it creates lateral acceleration toward the outside of the curve. In order to reduce cant deficiency, the speed can be reduced or the superelevation can be increased. The amount of cant deficiency is expressed in terms of required superelevation to be added in order to bring the resultant force into balance between the two rails.
In railway engineering, curve resistance is a part of train resistance, namely the additional rolling resistance a train must overcome when travelling on a curved section of track. Curve resistance is typically measured in per mille, with the correct physical unit being Newton per kilo-Newton (N/kN). Older texts still use the wrong unit of kilogram-force per tonne (kgf/t).
An Euler spiral is a curve whose curvature changes linearly with its curve length. Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals.
The minimum railway curve radius is the shortest allowable design radius for the centerline of railway tracks under a particular set of conditions. It has an important bearing on construction costs and operating costs and, in combination with superelevation in the case of train tracks, determines the maximum safe speed of a curve. The minimum radius of a curve is one parameter in the design of railway vehicles as well as trams; monorails and automated guideways are also subject to a minimum radius.
The geometric design of roads is the branch of highway engineering concerned with the positioning of the physical elements of the roadway according to standards and constraints. The basic objectives in geometric design are to optimize efficiency and safety while minimizing cost and environmental damage. Geometric design also affects an emerging fifth objective called "livability," which is defined as designing roads to foster broader community goals, including providing access to employment, schools, businesses and residences, accommodate a range of travel modes such as walking, bicycling, transit, and automobiles, and minimizing fuel use, emissions and environmental damage.
A railway or railroad is a track where the vehicle travels over two parallel steel bars, called rails. The rails support and guide the wheels of the vehicles, which are traditionally either trains or trams. Modern light rail is a relatively new innovation which combines aspects of those two modes of transport. However fundamental differences in the track and wheel design are important, especially where trams or light railways and trains have to share a section of track, as sometimes happens in congested areas.
Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track. The term is also applied to measurements used in design, construction and maintenance of track. Track geometry involves standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Standards are usually separately expressed for horizontal and vertical layouts although track geometry is three-dimensional.
The cant of a railway track or camber of a road is the rate of change in elevation (height) between the two rails or edges of the road. This is normally greater where the railway or road is curved; raising the outer rail or the outer edge of the road creates a banked turn, thus allowing vehicles to travel round the curve at faster speeds which would otherwise not be possible if the surface is flat or level.
