Practical Guide To Railway Engineering
AMERICAN RAILWAY ENGINEERING AND MAINTENANCE OF WAY ASSOCIATION Practical Guide to Railway Engineering Railway Structures.
1 Chapter AMERICAN RAILWAY ENGINEERING AND MAINTENANCE OF WAY ASSOCIATION Practical Guide to Railway Engineering Railway Track Design 6-1 2 AREMA COMMITTEE 24 - EDUCATION & TRAINING Railway Track Design Brian Lindamood, P.E. Hanson-Wilson, Inc. Fort Worth, TX James C. Parsons Transportation Group Martinex, CA James McLeod, P.
Edmonton, AB. T5S 1G3 6-2 3 Chapter Railway Track Design Basic considerations and guidelines to be used in the establishment of railway horizontal and vertical alignments. The route upon which a train travels and the track is constructed is defined as an alignment.
An alignment is defined in two fashions. First, the horizontal alignment defines physically where the route or track goes (mathematically the XY plane). The second component is a vertical alignment, which defines the elevation, rise and fall (the Z component). Alignment considerations weigh more heavily on railway design versus highway design for several reasons.
First, unlike most other transportation modes, the operator of a train has no control over horizontal movements (i.e. The guidance mechanism for railway vehicles is defined almost exclusively by track location and thus the track alignment.
The operator only has direct control over longitudinal aspects of train movement over an alignment defined by the track, such as speed and forward/reverse direction. Secondly, the relative power available for locomotion relative to the mass to be moved is significantly less than for other forms of transportation, such as air or highway vehicles. (See Table 6-1) Finally, the physical dimension of the vehicular unit (the train) is extremely long and thin, sometimes approaching two miles in length. This compares, for example, with a barge tow, which may encompass 2-3 full trains, but may only be 1200 feet in length. These factors result in much more limited constraints to the designer when considering alignments of small terminal and yard facilities as well as new routes between distant locations.
The designer MUST take into account the type of train traffic (freight, passenger, light rail, length, etc.), volume of traffic (number of vehicles per day, week, year, life cycle) and speed when establishing alignments. The design criteria for a new coal route across the prairie handling 15,000 ton coal trains a mile and a half long ten times per day will be significantly different than the extension of a light rail (trolley) line in downtown San Francisco.
6-3 4 Carrier Horsepower per Net Ton Horsepower per Passenger 'Typical' Average Horsepower/Net Ton Railways-freight Railways-passenger Highway trucks and semi-trailers Passenger automobiles River tows Bulk-cargo ships Airplanes-freight Airplanes-passenger Pipelines Conveyors Aerial tramways (cableways) Table 6-1 Typical Horsepower-per-net-ton Ratios 6.1 Stationing Points along an alignment are usually defined by miles, stationing or both. The latter is customary with railway routes throughout North America. Within yards, terminals, and sidings, the miles (termed mileposts or mile boards ) are dropped due to the relative close proximity of the tracks to a common point. Stationing (also termed chaining ) is merely the sequential numbering of feet from a beginning point to an ending point.
A single station is 100 feet long in US units or 1000 meters in metric units. A point one mile from a beginning station of 0+00 would then be denoted station (or 52.8). In metric, that same point would be At the time of construction, all alignments had stationing. Most items along an alignment can be located by stations. This is the primary system used for locations within many engineering records. However, if an alignment has been in place for any long period of time, such as most North American railways, it likely has been changed or relocated since its original construction.
These changes usually introduce what is termed a station equation, which is required because the relative length of the alignment has been changed with the alteration. Other causes for a station equation (but certainly not all grounds) include the combination of two separate routes, lost records, or an extended period of time between the stages of construction for the overall alignment. Mileposts are more commonly used by operating departments for location identification. Though less precise, they are more easily identified and they are referenced along the right-of-way with signs. Bridges are normally identified by 6-4 5 mileposts, though they also have stationing associated with them. Likewise, it is not uncommon for mileposts to have stationing shown in railway records. Both the use of mileposts and stationing for the reference of existing railway features are not without pitfalls.
This is of concern to the designer when contemplating work along an existing track. The direction of increasing stationing and increasing mileposts may not be the same. There is no guarantee that the records maintained by a railway are correct, or have the most current information (this is more often the case).
It is not unheard of for a railway to have re-stationed a line, or even given new mileposts. There are lines on which this has occurred at least two or three times since construction. Though the stationing and mileposts may have changed on the alignment records, many old right-of-way instruments, bridge plans and other information may still reference what was there and not what is there today. The use of milepost information is particularly hazardous for several reasons. First, the initial stationing over 100 years ago to establish mileposts was not always significantly accurate.
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The actual length between mileposts may vary by thousands of feet, though most are reasonably close (less than feet). Adding further variance to the length was the common railway practice to place the milepost marker on the nearest telegraph pole rather than on a dedicated signpost. As the poles were moved, replaced and changed, the sign moved with them. Signs were lost and replaced, but probably not relocated with any great precision. Stationing to the mileposts, along with other items which have a tendency to be somewhat transient over the long term, including grade crossings, turnouts, rail rests, etc., should always be subject to much scrutiny before being used as a basis for design. The designer should always establish existing stationing from some item, which has not moved in some time, preferable the abutment of an older structure or culvert, or best of all, a defined right-of-way corner or marker. Though the milepost location and terminology will not generally change as a result of re-establishing its true location, it will provide a frame of reference for the location of new facilities.
6.2 Horizontal Alignments Nearly any alignment can be physically defined with variances of two components: tangents and curves. Horizontal alignments of existing and proposed railway tracks generally are given the highest interest as their location seem to be the easiest to grasp when reviewing the location of facilities relative to one another. A tangent is simply a straight line between two points. Tangents are usually denoted with bearings (N E for instance). However, it must be noted that without an accompanying starting point and length associated with that bearing (and thus establishing the location of the second point), there is no way to definitively establish 6-5 6 the tangent s location in space. Other points along a given tangent can be defined in this manner.
Tangents, because they are the most defining parts of alignments and are usually the components used in the establishment of such, should be considered the highest order component. Curves as discussed below, which effectively connect these tangents, are second order as they are fundamentally defined by the location of tangents and can be easily changed without relative wholesale shifts in physical alignment location. Where an existing tangent must be established and where two points are not easily defined or known, obtain at least three points, which are believed to be along this line. Because a tangent can be defined by only two points, two points located along a curve can define a tangent. It is only through working from at least three points and comparing the bearings established relative to each other, that a true tangent can be established. Though the difference in bearing between three points on a tangent should be zero, the precision afforded by surveying equipment and construction methods is generally less than that calculated from data obtained, particularly when the person performing the calculation has no appreciation for significant digits.
Most means for performing linear regression on a set of data points for the purpose of establishing tangents have no allowance for this situation. Therefore, it must be understood when reviewing the data collected between points, there is a margin within which any three points can be assumed to be tangent. This margin is based upon the judgment of the designer and takes into consideration the relative condition of the existing item upon which the tangent is to be defined, the level of accuracy required, and the overall margin of error, which limits the functionality of the facility. An alignment comprised of more than one tangent will generally include a set of points known as Points of Intersection, or PI s. The defining points of each tangent are shared with those two tangents to which are immediately adjacent to it. As these points define the tangents, as well as any points, which may have defined the location of the connecting tangents, they should be considered the cardinal points of the alignment.
Though second order points, such as Points of Curve (PC s) and points along curves, can be defining, it is the existence of the PI, which must exist for a curve to exist. It is the PI that will remain constant between two tangents despite what changes are made to the curvature itself. Curves are alignment elements allowing for easy transition between two tangents. Horizontal curves are considered circular though they are actually arcs, which represent only a portion of a complete circle. All curves can be defined by two aspects. The angle of deflection (I) is defined at the Point of Intersection (PI) by the difference in bearing between the two tangents.
This aspect is fixed by the tangents. With I, the curve may be defined by any of the other following aspects (See Figure 6-2). 6-6 7 Curves are general specified in one of two ways, by Degree of Curve or by Radius R. Degree of curve can be defined in two ways.
The chord definition (D c ) is defined as the angle subtended per 100-foot chord. The arc definition (D) is defined as the angle subtended per 100-foot arc.
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(See Figure 6-3) In either case, the severity or sharpness of the curve is specified as the degree of curve, with larger Figure 6-2 Point of Intersection (PI) numbers representing tighter (smaller radius) curves. Though the differences between the chord definition and arc definition are slight at smaller degrees of curvature, the difference gets progressively larger as the curves get tighter (See Figure 6-4). Furthermore, chord defined curves are stationed about the chords subtended, while arc defined curves are stationed about the actual path of the curve (or arc).
Again, the differences are slight at small degrees of curvature, but increase, as the curves get sharper. The stationing difference is further magnified by the length of curve. Figure 6-3 Degree of Curve by Chord & Arc Definition 6-7 8 Figure 6-4 Chord Length vs. Arc Length for Degree of Curve North American freight railways use the chord-defined curve exclusively. This is in contrast to highway design, some light rail systems and nearly all other alignments historically and currently being designed with arc defined curves. Though the individual differences between chord and arc defined curves may be considered slight for specific curves, this difference can be magnified considerably on longer alignments with moderate amounts of curvature.
Though a curve denoted by a degree of curve is easily recognized and accepted by most engineers as establishing a certain severity of curvature, the relationship between two curves with different degrees of curvature is not as widely comprehended. It must be understood, that the radius of a six-degree curve is not exactly half of that of a threedegree curve. Due to the sinusoidal nature of the formulae, which produce the degrees of curve nomenclature, the relative differences in radii are more logarithmic. For example, the radius for a two-degree curve is feet and feet for a two-and-a-half-degree curve. This compares with feet and feet for twelve and twelve-and-a-halfdegree curves respectively. Degree of Curve Radius R c Figure 6-5 Degree of Curve to Radius Relationship There have been some alignments established about the turn of the 20 th century in mountainous areas along the west coast, which used curves defined by the angle subtended by a 50-foot chord. It is not known if or how many of these alignments and records may still exist today.
There has been some reference made to defining metric 6-8 9 curves as D (degrees per 20 meter arc). However, there does not seem to be any widespread incorporation of this practice. When working with light rail or in metric units, current practice employs curves defined by radius. As a vehicle traverses a curve, the vehicle transmits a centrifugal force to the rail at the point of wheel contact. This force is a function of the severity of the curve, speed of the vehicle and the mass (weight) of the vehicle. This force acts at the center of gravity of the rail vehicle.
This force is resisted by the track. If the vehicle is traveling fast enough, it may derail due to rail rollover, the car rolling over or simply derailing from the combined transverse force exceeding the limit allowed by rail-flange contact. This centrifugal force can be counteracted by the application of superelevation (or banking), which effectively raises the outside rail in the curve by rotating the track structure about the inside rail.
(See Figure 6-6) The point, at which this elevation of the outer rail relative to the inner rail is such that the weight is again equally distributed on both rails, is considered the equilibrium elevation. Track is rarely superelevated to the equilibrium elevation. The difference between the equilibrium elevation and the actual superelevation is termed underbalance. Though trains rarely overturn strictly from centrifugal force from speed Figure 6-6 Effects of Centrifugal Force (they usually derail first).
This same logic can be used to derive the overturning speed. Conventional wisdom dictates that the rail vehicle is generally considered stable if the resultant of forces falls within the middle third of the track. This equates to the middle 20 inches for standard gauge track assuming that the wheel load upon the rail head is approximately 60-inches apart.
As this resultant force begins to fall outside the two rails, the vehicle will begin to tip and eventually overturn. It should be noted that this overturning speed would vary depending upon where the center of gravity of the vehicle is assumed to be. There are several factors, which are considered in establishing the elevation for a curve. The limit established by many railways is between five and six-inches for freight operation and most passenger tracks. There is also a limit imposed by the Federal Railroad Administration (FRA) in the amount of underbalance employed, which is generally three inches for freight equipment and most passenger equipment. 6-9 10 Underbalance limits above three to four inches (to as much as five or six inches upon FRA approval of a waiver request) for specific passenger equipment may be granted after testing is conducted. Track is rarely elevated to equilibrium elevation because not all trains will be moving at equilibrium speed through the curve.
Furthermore, to reduce both the maximum Center of Gravity OVERBALANCE V E D Gravity max a Centrifugal Force Resultant Superelevation V max EQUILIBRIUM Superelevation Figure 6-7 Overbalance, Equilibrium and Underbalanced UNDERBALANCE Superelevation allowable superelevation along with a reduction of underbalance provides a margin for maintenance. Superelevation should be applied in 1/4-inch increments in most situations. In some situations, increments may be reduced to 1/8 inch if it can be determined that construction and maintenance equipment can establish and maintain such a tolerance. Even if it is determined that no superelevation is required for a curve, it is generally accepted practice to superelevate all curves a minimum amount (1/2 to 3/4 of an inch). Each railway will have its own standards for superelevation and underbalance, which should be used unless directed otherwise.
The transition from level track on tangents to curves can be accomplished in two ways. For low speed tracks with minimum superelevation, which is commonly found in yards and industry tracks, the superelevation is run-out before and after the curve, or through the beginning of the curve if space prevents the latter. A commonly used value for this run-out is 31-feet per half inch of superelevation. On main tracks, it is preferred to establish the transition from tangent level track and curved superelevated track by the use of a spiral or easement curve. A spiral is a curve whose degree of curve varies exponentially from infinity (tangent) to the degree of the body curve. The spiral completes two functions, including the gradual introduction of superelevation as well as guiding the railway vehicle from tangent track to curved track.
Without it, there would be very high lateral dynamic load acting on the first portion of the curve and the first portion of tangent past the curve due to the sudden introduction and removal of centrifugal forces associated with the body curve. There are several different types of mathematical spirals available for use, including the clothoid, the cubic parabola and the lemniscate. Of more common use on railways are the Searles, the Talbot and the AREMA 10-Chord spirals, which are empirical approximations of true spirals. Though all have been applied to railway applications to = Center of Gravity Gravity Centrifugal Force Resultant Ea D Center of Gravity = Maximum allowable operating speed (mph). = Average elevation of the outside rail (inches). = Degree of curvature (degrees). Gravity Resultant Amount of Underbalance Centrifugal Force 6-10 11 some degree over the past 200 years, it is the AREMA 10-Chord spiral, which gained acceptance in the early part of the 20 th century.
The difference in results between the AREMA 10-chord spiral and a cubic parabola upon which it was based are negligible for s less than 15, which is sufficient for all situations except some tight light rail curves. Spirals are defined by length in increments of ten-feet. There are two criteria generally used for the establishment of spiral length. The first is the rotational acceleration of the railway vehicle about its longitudinal axis. The second is the limiting value of twist along the car body. The rotational acceleration criteria will generally only apply at higher speeds. In the event that the rotational acceleration dictates a spiral, which is too long for the location desired, the shorter car body twist value can be used.
Though AREMA has long established values for spiral lengths based upon these criteria, many railways use other criteria.
Written by a group of over 50 railroad professionals, representing over 1200 years of experience, the NEW Practical Guide to Railway Engineering may be the most useful tool since the spike maul. Whether you’re new to the industry or a long-time contributor who simply wishes to learn more, this book offers in-depth coverage of railway fundamentals and serves as an excellent reference. This text combines and consolidates the most useful information from a multitude of sources including:. BCOLOR=redSIZE=4AREMA /SIZE/COLOR/BManuals. Railway Engineering by W.W. Hay. Railway Curves and Earthwork by C.
Frank Allen. FRA, USDOT and other agency sources.