Rail vehicle resistance

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Definition

The total force necessary to maintain a rail vehicle in motion at a certain speed is the rail vehicle resistance (or simply resistance). This force depends on a number of variables and is of crucial importance for the energy efficiency of the vehicle as it is proportional to the tractive effort ^[1]. For the speed of the vehicle to remian the same, the locomotive must express the proper tractive force, otherwise the speed of the vehicle will change until this condition is met ^[2].

Davis equation

A number of experimental measurements ^[3] ^[4] ^[5] of the train resistance have shown that this force can be expressed as a quadratic equation with respect to speed as shown below:

$R=A+BV+CV^{2}$

Where $R$ is the resistance, $V$ is the speed of the rail vehicle and $A$ , $B$ , and $C$ are experimentally determined coefficients. The most well-known of these relations was proposed by Davis^[3] and is named after him.

Speed-independent term

The first term of the equation accounts for the contributions to the resistance that are independent from speed. Track slope and acceleration contribute to this term, since the work produced by the locoomtive is respectively converted into potential and kinetic energy of the vehicle. Others are rolling bearing friction and rolling friction to the the local deformation of the rail at the point of contact with the wheels, these contributions would be independent from vehicle speed but would be affected by number of axles and axle loads ^[6].

Speed-linear term

rolling friction (negligable?)

Speed-quadratic term

Aerodynamic forces.

Measurement of tractive force

External links

References

^ "Power - physics". Encyclopedia Britannica. Retrieved July 8, 2024.
^ "Newton's laws of motion". Encyclopedia Britannica. Retrieved July 8, 2024.
^ ^a ^b Davis, W. J. (1926). "The Tractive Resistance of Electric Locomotives and Cars,". General Electric Review. p. 3.
^ Schmidt, E. C. (1910). ""Freight Train Resistance; Its Relation to Average Car Weight". University of Illinois Engineering Experiment Station.
^ Tuthil, J. K. (1938). "High-Speed Freight Train Resistance: Its Relation to Average Car Weight". University of Illinois Engineering Bulletin: 376.
^ Lukaszewicz, P (2007-03-01). "Running resistance - results and analysis of full-scale tests with passenger and freight trains in Sweden". Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 221 (2): 183–193. doi:10.1243/0954409JRRT89. ISSN 0954-4097.