Abstract Nadal and Weinstock derailment criteria are applied in maintenance standards to assess the risk of flange climbing derailment. However, they are overly conservative, while modified versions have limited field usage due to the large number of required variables and the need for nonlinear iterative calculations. This study aims to derive accurate and simplified single wheel and wheelset derailment criteria to assess the risk of flange climbing derailment on curved tracks. First, complete single wheel and wheelset derailment criteria were derived to analyse the risk of flange climbing in a wheelset negotiating a curved track. Second, the critical derailment limits were calculated based on creep force theories and validated using published TLV, NUCARS and JNR data. Finally, as a case study, simplified single wheel and wheelset derailment criteria were developed through curve fitting for a nominal UIC60 rail and S1002 wheel profile. The simplified single wheel and wheelset derailment criteria agree well with the complete criteria with the maximum relative error of 1.9% and 11.7%, respectively, when the distribution of vertical force is similar. Furthermore, the simplified single wheel derailment criterion has the lowest maximum relative error compared with published derailment criteria. However, the simplified wheelset derailment criterion is only valid when the wheelset limit is higher than 0.1. Additionally, the study found that, to prevent flange climbing, the maximum allowable negative vertical force difference between the non-flanging and flanging wheels to be −9%, −18%, and -25.8% when the maximum contact angles are 60°, 65°, and 70°, respectively.
Sugathapala et al. (2026) studied this question.