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7 proposed in Equation 2.4, takes the AOA, the maximum 2 1.8 0.1 0.2 0.3 0.4 flange angle, and flange length as parameters. Nadal L/V Value 1.6 1.4 0.5 A * B * Len 1.2 D< (2.4) 1 AOA + B * Len 0.8 0.6 1.0 where D is limiting climb distance in feet and AOA is in 0.4 mrad. Coefficients A, B are functions of the maximum flange 0.2 0 angle Ang (degrees) and flange length Len (in.) as defined in 45 55 65 75 85 Section 2.4: Flange Angle (Degree) 100 A = + 3.1 * -1.9128 Ang + 146.56 Figure 2.1. Nadal criterion as a function of flange angle and friction coefficients in a range of 0.1 to 1.0. 1 Len - + 1.23 -0.0092( Ang) + 1.2152 Ang - 39.031 2 10 B = + 0.05 * 1.2 -21.157 Len + 2.1052 Wheel L/V Ratio 1.1 1 10 0.9 Modified Limit Ang + -5 Nadal Limit 0.2688 Len - 0.0266 0.8 0.7 0.6 The limiting climb distance for a specific transit wheel 0 5 10 15 20 profile can be derived from the above general criterion by AOA (mrad) substituting the maximum flange angle and flange length into Equation 2.4. It is especially useful for the transit wheel pro- Figure 2.2. Comparison of Nadal L/V ratio limit and files that were not simulated in this report. modified L/V ratio limit. Table 2.1 lists a range of limiting flange-climb-distance values computed using Equation 2.4 for a specified range of with the wheel L/V ratio limit. Flange climb derailment flange angles, flange length, and AOA. Table 2.1 indicates would occur only if both wheel L/V ratio limit and distance that at an AOA of 5 mrad, the limiting flange-climb distance limit are exceeded. increases as increased wheel flange angle and flange length. A general form of flange-climb-distance criterion is pro- At an AOA of 10 mrad, flange length has more effect on the posed in this section that applies to an L/V ratio equal to or distance limit than flange angle. less than 1.99. In summary, considering that flange climb generally occurs at a higher AOA, increasing wheel flange angle can increase the wheel L/V ratio limit required for flange climb and increasing 2.2.1 A General Flange-Climb-Distance flange length can increase the limiting flange climb distance. Criterion A general flange-climb-distance criterion was developed 2.3 DETERMINATION OF EFFECTIVE AOA by using the technique described in Appendix C of this report. Sixteen combinations of wheel flange angle and The flange climb criteria, including both wheel L/V ratio flange length, covering a wide range of these values on actual limit and climbing distance limit, are closely related to wheels, were used for the derivation. This general criterion, the wheelset AOA. Because the wheelset AOA may not be TABLE 2.1 Limiting flange-climb-distance computed using Equation 2.4 AOA = 5 mrad AOA = 10 mrad Flange Angle (deg) 63 deg 68 deg 72 deg 75 deg 63 deg 68 deg 72 deg 75 deg Flange Length (inch) 0.4 inch 2.0 2.2 2.4 3.3 1.5 1.5 1.5 1.9 0.52 inch 2.4 2.6 2.9 3.8 1.8 1.8 1.8 2.1 0.75 inch 3.2 3.5 3.7 4.3 2.3 2.3 2.2 2.4