Train Derailment

Aim - This page is dedicated to describing the factors that can result in a train derailing.

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Flange Climbing Derailment

Useful References


The derailment of a train occurs when the train comes off the tracks. A train derailment can be a minor affair with a small impact, for example if a single wheel comes of the track in an isolated section of the rail network. Alternatively it can be a major cost and reputational impact to the railway comapany, for example if a complete train leaves the tracks and passengers are ikilled or injured.

There are two typical types of derailments:

  • Sudden Derailment - where the forces involved cause the wheel to leave the track almost instantaneoulsy.
  • Flange climbing Derailment - occurs where the forces involved are lower, and the wheel gradually climbs onto the rail head before leaving the rail head altogether.


Flange Climbing Derailment

The ratio of the "Lateral Force / Vertical Force" (L/V) is used to determine when a car is likely to climb the rail and come off the railhead. Once the L/V value is "exceeded" then the wheel potentially starts climbing up the rail. If this is allowd to continue then the wheel will eventually leave the rails. The travel distance for this to take place is called the flange climb distance.

Nadal Criteria for L/V

In 1908 Nadal developed a formula for determing the L/V ratio of a wheel, and was expressed by the following formula:

L/V = ( tan(a) - u ) / (1 + u * tan(a) )

a = flange angle of the wheel
u = coefficient of friction between the wheel and the rail.

Once the actual L/V ratio starts to exceed this value then the wheel commences climbing up the rail.

It should be noted that wheels with higher flange angles will be better at staying on the rails, and also as the speed of the train increases, so the friction starts to decrease, and thus the L/V ratio increases.

Factors Influencing Wheel Climb

A number of fcators influence wheel climb, and whilst these include track related factors, such as track wear, wheel wear and damage, track movement, etc. Only those directly associated with calculating the wheel climbing characteristics will be considered below.

Angle of Attack (AoA)

Angle of Attack is the angle between the face of wheel and the tangent of the rail. A wheel that is aligned with the rail will present an AoA of zero. The AoA is influenced by the distance between the axles in a bogie, and the curve radius. Sharpe curves will have increased angles of AoA, whilst long sweeping curves will have smaller AoA.

Flange Climbing Distance

Flange climbing distance is influenced by the flange angle and flange depth on the wheel, as well as the AoA.

Real Time L/V

As indicated above once the real time L/V exceeds the Nadal Criteria then wheel climb and ultimately derailment may occur.

The L component is influenced by the in train forces.

In train forces are created by four factors as follows:

  • Train resistance - are forces acting on the train due to the resistance of the train as it climbs a grade, goes around a curve, faces wind resistance, or just the rolling resistance of a car.
  • Tractive Forces - is the force required to move the train. Obviously the higher the train resistance, the more tractive force generated within the train.
  • Braking - is the force required to stop the train.
  • Coupler Slack - is designed into a train to assist its movement. Coupler slack movement can generate forces within the train as the couplers reach their limits of movement.

These in train forces by nature are typically either steady state (are applied over a longer period of time), or dynamic (are only applied over a short duration).

High steady state forces can cause the following:

  • Train separation - where the forces between the cars are sufficient to cause the couplers or some other component to break, thus causing the train to separate.
  • Stringlining - is where the train is going around a curve, and the forces try to pull the train into a straight line ("stringline") thus potentially causing the inner wheel on the curve to climb the rail, or alternatively push the rail over, and thus derail the train.
  • Jackknifing - is where the train is compressed as it is going around a curve, and the forces try to push the train into a more pronounced curved shape (like a "jackknife") thus potentially causing the outer wheel on the curve to climb the rail, or alternatively push the rail over, and thus derail the train.

High dynamic forces tend to occur when the train is travelling over the crest of a hill, or through the valley between two hills. Thus undulating track can cause issues for train staff.

The V component is influenced by the weight of the car, and the superelevation of the track, as these two factors determine the downward acting force which will balance the lateral force (L).

From the L/V ratio, it can be seen that low values of V, such as when cars are empty are at even more risk of derailment then fully loaded cars, hence special attention needs to be paid to how trains operate with empty cars in them. Railway companies often have rules in regard to the tonnage ratings and composition of trains with empty cars.

To further highlight the importance of considering empty cars in the train composition, the following information has been sourced from the "Canadian Pacific Railway, Train Accident Cause Finding Manual (Train Accident Prevention and Testing), Safety & Regulatory Affairs, Chapter 11, Section 11.2". String-lining derailments are caused by heavy draft loading, including steady-state draft loading or (more often) dynamic run-outs of slack. String-lining derailments exhibit the following characteristics:

The increasing use of "Distributed Power" scenarios has further highlighted the importance of correct train marshalling/composition. The Canadian Pacific describes the importance of considering the derailment risk, and how to ensure that the in train forces for each section of the train in their document, "Train Marshalling Process at Canadian Pacific".

Accident Investigation Reports

Accident investigation reports often give a valuable insight to the derailing issues faced by railway companies, and the measure that they have adopted to mitigate the risks of derailing.

Here is a selection of reports as an example.

R13D0077 - Derailment of Freight Train as it travelled through Yard

R05V0141 - Derailment of Freight Train travelled up a gradient and around a sharpe curve.

R02C0050 - Derailment of Freight Train due to buff forces in a sharpe curve.


Useful References

The Investigation of Derailments - Indian Railways Institute of Civil Engineering.