Editing Derailment (section)

== Causes ==
[[File:British Rail Class 165 165124 derailed at Paddington, 2016.jpg|thumb|A derailed [[British Rail Class 165]] at [[London Paddington station]]. The train moved over a set of [[catch points]] which caused the derailment. After derailing, the rear of the train hit an [[overhead line]] [[stanchion]], severely damaging the driver's side of the front coach.]]
{{unreferenced section|date=January 2015}}
Derailments result from one or more of a number of distinct causes; these may be classified as:

* the primary mechanical failure of a track component (for example broken rails, gauge spread due to sleeper (tie) failure)
* the primary mechanical failure of a component of the running gear of a vehicle (for example axlebox failure, wheel breakage)
* a fault in the geometry of the track components or the running gear that results in a quasi-static failure in running (for example rail climbing due to excessive wear of wheels or rails, earthworks slip)
* a dynamic effect of the track-vehicle interaction (for example extreme [[Hunting oscillation]], vertical bounce, track shift under a train, excessive speed)
* improper operation of points, or improper observance of signals protecting them (signal errors)
* as a secondary event following collision with other trains, road vehicles, or other obstructions ([[level crossing]] collisions, obstructions on the line)
* train handling (snatches due to sudden traction or braking forces, referred to as slack action in North America).

[[File:Off the Rails (1).jpg|thumb|A derailed locomotive unit in Australia at a [[catch point]] hidden from view (January 2007)]]
<ref group=note>The U.S. Federal Railroad Administration categorises derailments differently, for the use of professionals in the industry; these are not completely helpful for external readers, but for completeness, the main groupings are given here:

* Rail, joint bar and anchoring
* Track geometry defect
* General switching rules
* Wheels
* Axles and journal bearings
* Switches
* Frogs, switches and track appliances
* Bogie (truck) components
* Train handling / train make-up
* Highway rail grading

Source: Safety Database Analysis, Transportation Technology Center Inc, Pueblo Col, 2002, quoted in ''Wu and Wilson'', page 210-211</ref>

=== Broken rails ===
Broken rails are a leading cause of derailments. According to data from the Federal Railroad Administration, broken rails and welds are the most common reason for train derailments, making up more than 15 percent of derailment cases.<ref>{{Cite web |last=Tracy |first=Abigail |last2=Reznik |first2=Tal |last3=Volcativ |title=Broken Rails Are Leading Cause of Train Derailments |url=https://www.scientificamerican.com/article/broken-rails-are-leading-cause-of-train-derailments/ |access-date=2022-12-01 |website=Scientific American |language=en}}</ref>[[File:Schienenbruch.jpg|thumb|A broken rail, probably starting from [[hydrogen embrittlement|hydrogen inclusion]] in the rail head]]
A traditional track structure consists of two rails, fixed at a designated distance apart (known as the [[track gauge]]), and supported on transverse sleepers (ties). Some advanced track structures support the rails on a concrete or asphalt slab. The running surface of the rails is required to be practically continuous and of the proper geometrical layout.

In the event of a '''broken or cracked rail''', the rail running surface may be disrupted if a piece has fallen out, or become lodged in an incorrect location, or if a large gap between the remaining rail sections arises. 170 broken (not cracked) rails were reported on Network Rail in the UK in 2008, down from a peak of 988 in 1998/1999.

* In [[jointed track]], rails are usually connected with bolted [[fishplate]]s (joint bars). The web of the rail experiences large [[shear force]]s and these are enhanced around the bolt hole. Where track maintenance is poor, [[Fatigue (material)|metallurgical fatigue]] can result in the propagation of star cracking from the bolthole. In extreme situations this can lead to a triangular piece of rail at the joint becoming detached.
* Metallurgical changes take place due to the phenomenon of gauge corner cracking (in which fatigue microcracking propagates faster than ordinary wear), and also due to the effects of [[hydrogen embrittlement|hydrogen inclusion]] during the manufacturing process, leading to [[crack propagation]] under fatigue loading.
* Local embrittlement of the parent metal may take place due to wheel spin (traction units rotating driving wheels without movement along the track).
* Rail welds (where rail sections are joined by welding) may fail due to poor workmanship; this may be triggered by extremely cold weather or improper stressing of continuously welded rails, such that high tensile forces are generated in the rails.
* The fishplates (joint bars) in jointed track may fail, allowing the rails to pull apart in extremely cold weather; this is usually associated with uncorrected rail creep.

Derailment may take place due to excessive '''gauge widening''' (sometimes known as '''road spread'''), in which the sleepers or other fastenings fail to maintain the proper gauge. In lightly engineered track where rails are spiked (dogged) to timber sleepers, spike hold failure may result in rotation outwards of a rail, usually under the aggravating action of crabbing of bogies (trucks) on curves.<ref name="wu"/>

The mechanism of gauge widening is usually gradual and relatively slow, but if it is undetected, the final failure often takes place under the effect of some additional factor, such as excess speed, poorly maintained running gear on a vehicle, misalignment of rails, and extreme traction effects (such as high propelling forces). The crabbing effect referred to above is more marked in dry conditions, when the coefficient of friction at the wheel to rail interface is high.

=== Defective wheels ===
The running gear – [[Wheelset (rail transport)|wheelsets]], [[bogie]]s (trucks), and suspension—may fail. The most common historical failure mode is collapse of plain bearings due to deficient lubrication, and failure of leaf springs; wheel tyres are also prone to failure due to metallurgical crack propagation.

Modern technologies have reduced the incidence of these failures considerably, both by design (specially the elimination of plain bearings) and intervention (non-destructive testing in service).

=== Unusual track interaction ===
If a vertical, lateral, or crosslevel irregularity is cyclic and takes place at a wavelength corresponding to the natural frequency of certain vehicles traversing the route section, there is a risk of [[resonance|resonant]] [[harmonic oscillation]] in the vehicles, leading to extreme improper movement and possibly derailment. This is most hazardous when a cyclic roll is set up by crosslevel variations, but vertical cyclical errors also can result in vehicles lifting off the track; this is especially the case when the vehicles are in the tare (empty) condition, and if the suspension is not designed to have appropriate characteristics. The last condition applies if the suspension springing has a stiffness optimised for the loaded condition, or for a compromise loading condition, so that it is too stiff in the tare situation.

The vehicle wheelsets become momentarily unloaded vertically so that the guidance required from the flanges or wheel tread contact is inadequate.

A special case is heat related '''buckling''': in hot weather the rail steel expands. This is managed by stressing continuously welded rails (they are tensioned mechanically to be stress neutral at a moderate temperature) and by providing proper expansion gaps at joints and ensuring that fishplates are properly lubricated. In addition, lateral restraint is provided by an adequate ballast shoulder. If any of these measures are inadequate, the track may buckle; a large lateral distortion takes place, which trains are unable to negotiate. (In nine years 2000/1 to 2008/9 there were 429 track buckle incidents in Great Britain).<ref group=note>On Network Rail, so excluding certain "Metro" networks.</ref><ref name="cummersdale">Rail Accident Investigation Board (UK), ''Derailment of a Train at Cummersdale, Cumbria, 1 June 2009'', Derby, England, 2010</ref>

=== Improper operation of control systems ===
Junctions and other changes of routing on railways are generally made by means of points (switches – movable sections capable of changing the onward route of vehicles). In the early days of railways these were moved independently by local staff. Accidents – usually collisions – took place when staff forgot which route the points were set for, or overlooked the approach of a train on a conflicting route. If the points were not correctly set for either route – set in mid-stroke – it is possible for a train passing to derail.

The first concentration of levers for signals and points brought together for operation was at Bricklayer's Arms Junction in south-east London in the period 1843–1844. The signal control location (forerunner of the signalbox) was enhanced by the provision of interlocking (preventing a clear signal being set for a route that was not available) in 1856.<ref name="solomon">Brian Solomon, ''Railroad Signaling'', Voyageur Press, Minneapolis, MN, 2003, {{ISBN|978-0-7603-1360-2}}</ref>

To prevent the unintended movement of freight vehicles from sidings to running lines, and other analogous improper movements, trap points and derails are provided at the exit from the sidings. In some cases these are provided at the convergence of running lines. It occasionally happens that a driver incorrectly believes they have authority to proceed over the trap points, or that the signaller improperly gives such permission; this results in derailment. The resulting derailment does not always fully protect the other line: a trap point derailment at speed may well result in considerable damage and obstruction, and even a single vehicle may obstruct the clear line.

=== Derailment following collision ===
If a train collides with a massive object, it is clear that derailment of the proper running of vehicle wheels on the track may take place. Although very large obstructions are imagined, it has been known for a cow [[estray|straying]] on to the line to derail a passenger train at speed such as occurred in the [[Polmont rail accident]].

The most common obstructions encountered are '''road vehicles at level crossings''' (grade crossings); malicious persons sometimes place materials on the rails, and in some cases relatively small objects cause a derailment by guiding one wheel over the rail (rather than by gross collision).

Derailment has also been brought about in situations of war or other conflict, such as during hostility by Native Americans, and more especially during periods when military personnel and materiel<!-- this is the correct spelling --> was being moved by rail.<ref name="denevi">Don DeNevi and Bob Hall, ''United States Military Railway Service America's Soldier Railroaders in WWII'', 1992, Boston Mills Press, Erin, Ontario, {{ISBN|1-55046-021-8}}.</ref><ref name="wolmar">Christian Wolmar, ''Engines of War: How Wars Were Won & Lost on the Railways'', Atlantic Books, 2010, {{ISBN|978-1-84887-172-4}}</ref><ref>{{Cite web |url=https://www.pbs.org/wgbh/americanexperience/features/general-article/tcrr-tribes/ |work=American Experience |title=Native Americans and the Transcontinental Railroad |publisher=[[PBS]] |access-date=26 August 2017 |archive-date=10 March 2017 |archive-url=https://web.archive.org/web/20170310195100/http://www.pbs.org/wgbh/americanexperience/features/general-article/tcrr-tribes/ |url-status=dead }}</ref>

=== Harsh train handling ===
The handling of a train can also cause derailments. The vehicles of a train are connected by couplings; in the early days of railways these were short lengths of chain ("loose couplings") that connected adjacent vehicles with considerable slack. Even with later improvements there may be a considerable slack between the traction situation (power unit pulling the couplings tight), and power unit braking (locomotive applying brakes and compressing buffers throughout the train). This results in '''coupling surge'''.

More sophisticated technologies in use nowadays generally employ couplings that have no loose slack, although there is elastic movement at the couplings; continuous braking is provided, so that every vehicle on the train has brakes controlled by the driver. Generally this uses compressed air as a control medium, and there is a measurable time lag as the signal (to apply or release brakes) propagates along the train.

If a train driver applies the train brakes suddenly and severely, the front part of the train is subject to braking forces first. (Where only the locomotive has braking, this effect is obviously more extreme). The rear part of the train may overrun the front part, and in cases where coupling condition is imperfect, the resultant sudden closing up (an effect referred to as a "run-in") may result in a vehicle in tare condition (an empty freight vehicle) being lifted momentarily, and leaving the track. This effect was relatively common in the nineteenth century.<ref name="cole">Colin Cole, ''Longitudinal Train Dynamics'', in ''Handbook of Railway Vehicle Dynamics''</ref>

On curved sections, the longitudinal (traction or braking) forces between vehicles have a component inward or outward respectively on the curve. In extreme situations these lateral forces may be enough to produce derailment.

A special case of train handling problems is '''overspeed on sharp curves'''. This generally arises when a driver fails to slow the train for a sharp curved section in a route that otherwise has higher speed conditions. In the extreme this results in the train entering a curve at a speed at which it cannot negotiate the curve, and gross derailment takes place. The specific mechanism of this may involve bodily tipping (rotation) but is likely to involve disruption of the track structure and derailment as the primary failure event, followed by overturning.

Fatal instances include the [[Santiago de Compostela derailment]] in 2013 and the [[2015 Philadelphia train derailment|Philadelphia train derailment two years later]] of trains traveling about {{convert|100|mph}}. Both went at about twice the maximum allowable speed for the curved section of track.

=== Flange climbing ===
The guidance system of practical railway vehicles relies on the steering effect of the conicity of the wheel treads on moderate curves (down to a radius of about 500&nbsp;m, or about 1,500&nbsp;feet). On sharper curves flange contact takes place, and the guiding effect of the flange relies on a vertical force (the vehicle weight).

A '''flange climbing''' derailment can result if the relationship between these forces, L/V, is excessive. The lateral force L results not only from centrifugal effects, but a large component is from the crabbing of a wheelset which has a non-zero angle of attack during running with flange contact. The L/V excess can result from wheel unloading, or from improper rail or wheel tread profiles. The physics of this is more fully described below, in the section ''wheel-rail interaction''.

Wheel unloading can be caused by '''twist''' in the track. This can arise if the cant (crosslevel, or superelevation) of the track varies considerably over the wheelbase of a vehicle, and the vehicle suspension is very stiff in torsion. In the quasi-static situation it may arise in extreme cases of poor load distribution, or on extreme cant at low speed.

If a rail has been subject to extreme sidewear, or a wheel flange has been worn to an improper angle, it is possible for the L/V ratio to exceed the value that the flange angle can resist.

If weld repair of side-worn switches is undertaken, it is possible for poor workmanship to produce a ramp in the profile in the facing direction, that deflects an approaching wheel flange on to the rail head.

In extreme situations, the infrastructure may be grossly distorted or even absent; this may arise from a variety of causes, including earthwork movement (embankment slips and washouts), earthquakes and other major terrestrial disruptions, or deficient protection during work processes, among others.

==== Wheel-rail interaction ====

Nearly all practical railway systems use wheels fixed to a common axle: the wheels on both sides rotate in unison. Tramcars requiring low floor levels are the exception, but much benefit in vehicle guidance is lost by having unlinked wheels.<ref name="ayasse">Jean-Bernard Ayasse and Hugues Chollet, ''Wheel—Rail Contact'', in ''Handbook of Railway Dynamics''</ref>

The benefit of linked wheels derives from the '''conicity of the wheel treads'''—the wheel treads are not [[cylinder (geometry)|cylindrical]], but [[cone|conical]].<ref name="bibel" /><ref name="ayasse"/> On idealised straight track, a wheelset would run centrally, midway between the rails.

The example shown here uses a right-curving section of track. The focus is on the left-side wheel, which is more involved with the forces critical to guiding the railcar through the curve.

Diagram 1 below shows the wheel and rail with the wheelset running straight and central on the track. The wheelset is running away from the observer. (Note that the rail is shown inclined inwards; this is done on modern track to match the rail head profile to the wheel tread profile.)

Diagram 2 shows the wheelset displaced to the left, due to curvature of the track or a geometrical irregularity. The left wheel (shown here) is now running on a slightly larger diameter; the right wheel opposite has moved to the left as well, towards the centre of the track, and is running on a slightly smaller diameter. As the two wheels rotate at the same rate, the forward speed of the left wheel is a little faster than the forward speed of the right wheel. This causes the wheelset to curve to the right, correcting the displacement. This takes place without flange contact; the wheelsets steer themselves on moderate curves without any flange contact.

{{gallery |align=center |title=Wheel-rail interactions
|File:Wheel and rail central running.gif|''Diagram 1.''{{brk}}Wheel tread and rail during central running (perspective is eye level with and looking along left rail){{brk|2}}
|File:Wheel and rail displaced running.gif|''Diagram 2''{{brk}}Wheel and rail with wheel displaced to the left (perspective is eye level with and looking along left rail){{brk|2}}
|File:Bogie in yaw.gif|''Diagram 3''{{brk}}Bogie and wheelset in a right-turning curve (overhead perspective){{brk|2}}
|File:L over V.gif|''Diagram 4''{{brk}}L and V forces in curving (perspective is eye level with and in between the two rails, looking down the track){{brk|2}}
|File:Wheel and rail flange climbing.gif|''Diagram 5''{{brk}}Wheel and rail during flange climbing (perspective is eye level with and looking along left rail){{brk|2}}
|File:Worn wheel and rail flange climbing.gif|''Diagram 6''{{brk}}Worn wheel and rail during flange climbing (perspective is eye level with and looking along left rail){{brk|2}}
}}

The sharper the curve, the greater the lateral displacement necessary to achieve the curving. On a very sharp curve (typically less than about 500&nbsp;m or 1,500&nbsp;feet radius) the width of the wheel tread is not enough to achieve the necessary steering effect, and the wheel flange contacts the face of the high rail.<ref group=note>The high rail is considered to be the outer rail in a curve; the low rail is the inner rail.</ref>

Diagram 3 shows the running of wheelsets in a bogie or a four-wheeled vehicle. The wheelset is not running parallel to the track: it is constrained by the bogie frame and suspension, and it is yawing to the outside of the curve; that is, its natural rolling direction would lead along a less sharply curved path than the actual curve of the track.<ref group=note>Yaw describes the situation when the longitudinal axis of the wheelset is not the same as the longitudinal axis of motion.</ref>

The angle between the natural path and the actual path is called the '''angle of attack''' (or the yaw angle). As the wheelset rolls forward, it is forced to slide across the railhead by the flange contact. The whole wheelset is forced to do this, so the wheel on the low rail is also forced to slide across its rail.<ref group=note>This was understood as early as 1844, when Robert Stephenson gave evidence that "in bringing round the curve, the wheels will all be fixed on the axles, and being of the same size, of course the outside has to go over more ground than the inside and therefore the outside ones slide upon the turn, and consequently, as you see in the Bristol stations [where broad gauge trains were negotiating sharp curves], you will see such wheels grind in their operation." Stephenson was giving evidence in the House of Commons regarding the South Devon Railway bill, on 26 April 1844, quoted in Hugh Howes, ''The Struggle for the South Devon Railway'', Twelveheads Press, Chacewater, 2012, {{ISBN|978 0 906294 74 1}}</ref>

This sliding requires a considerable force to make it happen, and the friction force resisting the sliding is designated "L", the lateral force. The wheelset applies a force L outwards to the rails, and the rails apply a force L inwards to the wheels. Note that this is quite independent of "centrifugal force".<ref group=note>Centrifugal force is a convenient imaginary concept; strictly speaking it is the inertia of a body being accelerated, equal to the product of the mass of the body and the acceleration.</ref> However at higher speeds the centrifugal force is added to the friction force to make L.

The load (vertical force) on the outer wheel is designated V, so that in Diagram 4 the two forces L and V are shown.

The steel-to-steel contact has a [[coefficient of friction]] that may be as high as 0.5 in dry conditions, so that the lateral force may be up to 0.5 of the vertical wheel load.<ref group=note>The value of L is determined by the load on both wheels of the wheelset multiplied by the coefficient of friction, plus the centrifugal force. But the sliding on the wheel on the low rail is not lateral—the wheel tread is actually sliding backwards (i.e rotating less rapidly than the forward speed requires) and the lateral friction force generated is limited by the vector of the sliding action.</ref>

During this flange contact, the wheel on the high rail is experiencing the lateral force L, towards the outside of the curve. As the wheel rotates, the flange tends to climb up the flange angle. It is held down by the vertical load on the wheel V, so that if L/V exceeds the trigonometrical tangent of the flange contact angle, climbing will take place. The wheel flange will climb to the rail head where there is no lateral resistance in rolling movement, and a '''flange climbing derailment''' usually takes place. In Diagram 5 the flange contact angle is quite steep, and flange climbing is unlikely. However, if the rail head is side-worn (side-cut) or the flange is worn, as shown in Diagram 6 the contact angle is much flatter and flange climbing is more likely.<ref name="wu" /><ref name="ayasse"/>

Once the wheel flange has completely climbed onto the rail head, there is no lateral restraint, and the wheelset is likely to follow the yaw angle, resulting in the wheel dropping outside the rail. An L/V ratio greater than 0.6 is considered to be hazardous.<ref name="bibel" />

It is emphasised that this is a much simplified description of the physics; complicating factors are creep, actual wheel and rail profiles, dynamic effects, stiffness of longitudinal restraint at axleboxes, and the lateral component of longitudinal (traction and braking) forces.<ref name="cole" />