In railroad wheel climb \({L \mathord{\left/ {\vphantom {L V}} \right. \kern-0pt} V}\) derailment criteria, it is assumed that the direction of the relative velocity of the flange-contact point in its totality is downward, leading to an upward friction force along the wheel flange profile. That is, the longitudinal component of the relative velocity of the flange-contact point is assumed negligible. It is further assumed that the climb progresses along a flange profile, and consequently, the flange-contact point trajectory is defined by the flange profile curve or a straight line. This paper examines these two basic assumptions by developing a three-dimensional wheel climb model that relaxes the assumptions used in deriving the planar \({L \mathord{\left/ {\vphantom {L V}} \right. \kern-0pt} V}\) ratio. The results obtained show that, in case of flange contact at a large angle of attack, there is a nonzero longitudinal velocity component of the wheel flange-contact point, and the trajectory of this point is not, in general, defined by the flange profile or a straight line. Consequently, the phenomenon of wheel climb at a large angle of attack is three-dimensional, demonstrating the need for further investigations of the derailment criteria based on planar analysis.
