Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes

Jack Youqin Huang

doi:doi:10.11648/j.ep.20210501.12

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Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes

Jack Youqin Huang

Published in Engineering Physics (Volume 5, Issue 1)

Received: 9 May 2021 Accepted: 25 May 2021 Published: 30 June 2021

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Abstract

This paper did a theoretical study on the Nadal’s L/V ratio. The analysis is based on a mechanical model of an object sliding on an incline (or slope), which is widely used in college physics. The key is that the direction of frictional forces is always opposite to the direction of the motion of the sliding object. Therefore, there are two directions (upward or downward) for the frictional forces between the object and incline depending on the states of motion of the object. Thus, there must be two L/V ratios for the object sliding on the incline for the same reason. The theoretical demonstration shows that Nadal’s L/V is the same with the L/V which governs the downward motion of the object on the incline, because the direction of frictional force between the object and the incline is set to be upwards in the derivation of the Nadal’s L/V. Thus, Nadal’s L/V is for the object going down the incline. A detail examination was performed on the Nadal’s L/V for some typical configurations, such as the critical angle; the zero and 90 degrees angles, further proving that the Nadal’s L/V is not for an object going up on the incline, thus cannot be used as the criterion for wheel climb. A new L/V ratio was created by setting the direction of frictional force downwards to simulate the object going up on the incline, and was named as Huang’s L/V. Wheel flange/rail contact produces frictional forces between them to consume the pulling power, like a braking to slowdown wheel rotation. Thus, wheel climb is only 1/3 of the whole story of wheel flange/rail contact. The other two are 1). A retarder derailment mode is created by the braking and 2). A braking, large enough, will cause a wheel locked. Therefore, there are two derailment modes with wheel/flange rail contact, wheel climb modes and retarder mode. A method to determine which mode was initiated was demonstrated in the paper. Angle of Attack (AoA) introduces a complicated scenario for wheel climb calculations. It is almost impossible to determine a correct L/V ratio under AoA.

Published in	Engineering Physics (Volume 5, Issue 1)
DOI	10.11648/j.ep.20210501.12
Page(s)	8-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Nadal’s L/V, Huang’s L/V, Friction, Directions of Frictional Forces, Wheel Climb Derailment, Retarder Derailment Mode, Braking and Wheel Locked, Angle of Attack

References

[1]	AAR Chapter XI, Association of American Railroads, Technical Services Division-Mechanical Section Manual of Standards and Recommended Practices, November 1993.
[2]	Marks’ Standard Handbook for Mechanical Engineers, Ninth Edition, Eugene A. Avallone and Theodore Baumeister III, McGraw Hill, Inc., 1987.
[3]	Wegner, S., “Derailment Risk Assessment”, degree of Master of Engineering thesis, Center for Railway Engineering, Central Queensland University, Australia, June 2004.
[4]	Nadal, M. J., 1896, "Theore de la Stabilite des Locomotives, part 2," Movement de Lacet, Annales des Mines, 10, 232.
[5]	Harry, T., Wu, H., and Guins, T., The Influence of Hollow-Worn Wheels on the Incidence and Costs of Derailments, Association of American Railroads/Transportation Technology Center, Inc. report R-965, February 2004.
[6]	Wu, H., Shu, X., and Wilson, N., Flange Climb Derailment Criteria and Wheel/Rail Profile Management and Maintenance Guidelines for Transit Operations — Appendix B, Transit Cooperate Research Program Report 71, Vol. 5, 2005.
[7]	Wilson, N., Shu, X., Wu, H., and Tunna, J., Distance-Based Flange Climb L/V Criteria, Association of American Railroads/Transportation Technology Center, Institute of Technology Digest, TD-04-012, July 2004.
[8]	Liu, Y. and Magel, E., Understanding Wheel-climb Derailments, Railway Track & Structures, pp. 37-41. Chicago, Ill., December 2007.
[9]	Burgelman, N.; Li, Z. and Dollevoet, R., Fast estimation of the Derailment Risk of a Braking Train in Curves and Turnouts, International Journal of Heavy Vehicle Systems, 2016.
[10]	Wilson, N., Shu, X., and Kramp, K., Effect of Independently Rolling Wheels on Flange Climb Derailment, Proceedings of ASME International Mechanical Engineering Congress.
[11]	Yao, S, Zhu, H, Yan, K, et al., The Derailment Behavior and Mechanism of a Subway Train under Frontal Oblique Collisions, Int J Crashworthiness 2019; 1–14. DOI: 10.1080/13588265.2019.1692506.
[12]	Zhu, T, Yang, B, Yang, C, et al., The Mechanism for the Coupler and Draft Gear and its Influence on Safety During a Train Collision, Veh Syst Dyn 2018; 56: 1375–1393.
[13]	Lin H.; Yong P. and Dong S., Dynamic Analysis of Railway Vehicle Derailment Mechanism in Train-to-Train Collision Accidents, Proc IMechE Part F: J Rail and Rapid Transit 0 (0) 1–13, IMechE 2020.
[14]	Marquis, B. and Greif, R., Application of Nadal limit in the Prediction of Wheel Climb Derailment, Proceedings of the ASME/ASCE/IEEE 2011 Joint Rail Conference.
[15]	Katz, L., Preventing Wheel-Climb Derailments, Railway Track & Structures, 2016.

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APA Style

Jack Youqin Huang. (2021). Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes. Engineering Physics, 5(1), 8-14. https://doi.org/10.11648/j.ep.20210501.12

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Jack Youqin Huang. Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes. Eng. Phys. 2021, 5(1), 8-14. doi: 10.11648/j.ep.20210501.12

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Jack Youqin Huang. Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes. Eng Phys. 2021;5(1):8-14. doi: 10.11648/j.ep.20210501.12

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@article{10.11648/j.ep.20210501.12,
  author = {Jack Youqin Huang},
  title = {Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes},
  journal = {Engineering Physics},
  volume = {5},
  number = {1},
  pages = {8-14},
  doi = {10.11648/j.ep.20210501.12},
  url = {https://doi.org/10.11648/j.ep.20210501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ep.20210501.12},
  abstract = {This paper did a theoretical study on the Nadal’s L/V ratio. The analysis is based on a mechanical model of an object sliding on an incline (or slope), which is widely used in college physics. The key is that the direction of frictional forces is always opposite to the direction of the motion of the sliding object. Therefore, there are two directions (upward or downward) for the frictional forces between the object and incline depending on the states of motion of the object. Thus, there must be two L/V ratios for the object sliding on the incline for the same reason. The theoretical demonstration shows that Nadal’s L/V is the same with the L/V which governs the downward motion of the object on the incline, because the direction of frictional force between the object and the incline is set to be upwards in the derivation of the Nadal’s L/V. Thus, Nadal’s L/V is for the object going down the incline. A detail examination was performed on the Nadal’s L/V for some typical configurations, such as the critical angle; the zero and 90 degrees angles, further proving that the Nadal’s L/V is not for an object going up on the incline, thus cannot be used as the criterion for wheel climb. A new L/V ratio was created by setting the direction of frictional force downwards to simulate the object going up on the incline, and was named as Huang’s L/V. Wheel flange/rail contact produces frictional forces between them to consume the pulling power, like a braking to slowdown wheel rotation. Thus, wheel climb is only 1/3 of the whole story of wheel flange/rail contact. The other two are 1). A retarder derailment mode is created by the braking and 2). A braking, large enough, will cause a wheel locked. Therefore, there are two derailment modes with wheel/flange rail contact, wheel climb modes and retarder mode. A method to determine which mode was initiated was demonstrated in the paper. Angle of Attack (AoA) introduces a complicated scenario for wheel climb calculations. It is almost impossible to determine a correct L/V ratio under AoA.},
 year = {2021}
}

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TY - JOUR
T1 - Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes
AU - Jack Youqin Huang
Y1 - 2021/06/30
PY - 2021
N1 - https://doi.org/10.11648/j.ep.20210501.12
DO - 10.11648/j.ep.20210501.12
T2 - Engineering Physics
JF - Engineering Physics
JO - Engineering Physics
SP - 8
EP - 14
PB - Science Publishing Group
SN - 2640-1029
UR - https://doi.org/10.11648/j.ep.20210501.12
AB - This paper did a theoretical study on the Nadal’s L/V ratio. The analysis is based on a mechanical model of an object sliding on an incline (or slope), which is widely used in college physics. The key is that the direction of frictional forces is always opposite to the direction of the motion of the sliding object. Therefore, there are two directions (upward or downward) for the frictional forces between the object and incline depending on the states of motion of the object. Thus, there must be two L/V ratios for the object sliding on the incline for the same reason. The theoretical demonstration shows that Nadal’s L/V is the same with the L/V which governs the downward motion of the object on the incline, because the direction of frictional force between the object and the incline is set to be upwards in the derivation of the Nadal’s L/V. Thus, Nadal’s L/V is for the object going down the incline. A detail examination was performed on the Nadal’s L/V for some typical configurations, such as the critical angle; the zero and 90 degrees angles, further proving that the Nadal’s L/V is not for an object going up on the incline, thus cannot be used as the criterion for wheel climb. A new L/V ratio was created by setting the direction of frictional force downwards to simulate the object going up on the incline, and was named as Huang’s L/V. Wheel flange/rail contact produces frictional forces between them to consume the pulling power, like a braking to slowdown wheel rotation. Thus, wheel climb is only 1/3 of the whole story of wheel flange/rail contact. The other two are 1). A retarder derailment mode is created by the braking and 2). A braking, large enough, will cause a wheel locked. Therefore, there are two derailment modes with wheel/flange rail contact, wheel climb modes and retarder mode. A method to determine which mode was initiated was demonstrated in the paper. Angle of Attack (AoA) introduces a complicated scenario for wheel climb calculations. It is almost impossible to determine a correct L/V ratio under AoA.
VL - 5
IS - 1
ER -

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Jack Youqin Huang

High Tech Pressure Safety, Glen Carbon, the United States

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APA Style

Jack Youqin Huang. (2021). Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes. Engineering Physics, 5(1), 8-14. https://doi.org/10.11648/j.ep.20210501.12

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ACS Style

Jack Youqin Huang. Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes. Eng. Phys. 2021, 5(1), 8-14. doi: 10.11648/j.ep.20210501.12

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AMA Style

Jack Youqin Huang. Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes. Eng Phys. 2021;5(1):8-14. doi: 10.11648/j.ep.20210501.12

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@article{10.11648/j.ep.20210501.12,
  author = {Jack Youqin Huang},
  title = {Nadal’s Limit (L/V) to Wheel Climb and Two Derailment Modes},
  journal = {Engineering Physics},
  volume = {5},
  number = {1},
  pages = {8-14},
  doi = {10.11648/j.ep.20210501.12},
  url = {https://doi.org/10.11648/j.ep.20210501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ep.20210501.12},
  abstract = {This paper did a theoretical study on the Nadal’s L/V ratio. The analysis is based on a mechanical model of an object sliding on an incline (or slope), which is widely used in college physics. The key is that the direction of frictional forces is always opposite to the direction of the motion of the sliding object. Therefore, there are two directions (upward or downward) for the frictional forces between the object and incline depending on the states of motion of the object. Thus, there must be two L/V ratios for the object sliding on the incline for the same reason. The theoretical demonstration shows that Nadal’s L/V is the same with the L/V which governs the downward motion of the object on the incline, because the direction of frictional force between the object and the incline is set to be upwards in the derivation of the Nadal’s L/V. Thus, Nadal’s L/V is for the object going down the incline. A detail examination was performed on the Nadal’s L/V for some typical configurations, such as the critical angle; the zero and 90 degrees angles, further proving that the Nadal’s L/V is not for an object going up on the incline, thus cannot be used as the criterion for wheel climb. A new L/V ratio was created by setting the direction of frictional force downwards to simulate the object going up on the incline, and was named as Huang’s L/V. Wheel flange/rail contact produces frictional forces between them to consume the pulling power, like a braking to slowdown wheel rotation. Thus, wheel climb is only 1/3 of the whole story of wheel flange/rail contact. The other two are 1). A retarder derailment mode is created by the braking and 2). A braking, large enough, will cause a wheel locked. Therefore, there are two derailment modes with wheel/flange rail contact, wheel climb modes and retarder mode. A method to determine which mode was initiated was demonstrated in the paper. Angle of Attack (AoA) introduces a complicated scenario for wheel climb calculations. It is almost impossible to determine a correct L/V ratio under AoA.},
 year = {2021}
}

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