The friction force in the plane of contact, between the wheelflange of a rail vehicle and the rail, reaches its Coulomb's limit onlywhen the direction of sliding coincides with the net resultanttangential force in this plane. Therefore, for derivation of anyderailment criterion, it becomes necessary to embed the inequality thatrelates the friction force to the normal contact force and coefficientof friction into the equations of action and reaction equilibriumbetween the two contacting surfaces at the point of contact. Assuming aquasi static state, it is natural to ignore all the detailed andmicroscopic considerations such as whether the lateral creep is due tospin or lateral velocity or both etc.. However, by ignoring the spinmoment, the method remains general and it recognizes that there arelateral and longitudinal creep forces which are due to longitudinal,lateral, and spin creepages. The main consideration is based uponbalancing the action and reaction between the two contacting surfaces atthe point of flange contact. It is further assumed that the effect ofwheel yaw in the contact angle is negligible. This can be proved bygeometrical considerations. The mathematical solutions show why Nadal'slimit (Nadal, 1896) is the most conservative derailment criterion. Theyalso provide the ranges of L/V for which the wheel has potential toclimb or slide up the rail. The solutions also reveal why, at times, thewheel withstands a much higher L/V ratio than Nadal's limit withoutderailing
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