Another look at the single wheel derailment criteria

The friction force in the plane of contact, between the wheel flange of a rail vehicle and the rail, reaches its Coulomb's limit only when the direction of sliding coincides with the net resultant tangential force in this plane. Therefore, for derivation of any derailment criterion, it becomes necessary to embed the inequality that relates the friction force to the normal contact force and coefficient of friction into the equations of action and reaction equilibrium between the two contacting surfaces at the point of contact. Assuming a quasi static state, it is natural to ignore all the detailed and microscopic considerations such as whether the lateral creep is due to spin or lateral velocity or both etc.. However, by ignoring the spin moment, the method remains general and it recognizes that there are lateral and longitudinal creep forces which are due to longitudinal, lateral, and spin creepages. The main consideration is based upon balancing the action and reaction between the two contacting surfaces at the point of flange contact. It is further assumed that the effect of wheel yaw in the contact angle is negligible. This can be proved by geometrical considerations. The mathematical solutions show why Nadal's limit (Nadal, 1896) is the most conservative derailment criterion. They also provide the ranges of L/V for which the wheel has potential to climb or slide up the rail. The solutions also reveal why, at times, the wheel withstands a much higher L/V ratio than Nadal's limit without derailing.