Analysis of the movement of an empty car on the longitudinal profile of the hill

. At present, in the existing methods for determining the height of a hump, the height is calculated based on the most difficult conditions - winter temperature and head wind, and a four-axle empty covered wagon is selected for a poor runner. Based on the basic law of dynamics (D'Alembert's principle) as applied to weak links and the use of analytical formulas in the article, the calculation of the kinematic parameters of the movement of cars in the braking zone of the section of the first braking position of the hump is carried out. A sorting hump 3.08 m high is considered, for a four-axle empty covered wagon the winter temperature is -100, the headwind speed is 5 m/s m. When calculating the height of the marshalling yard, it is necessary to take the technical characteristics of a four-axle empty gondola car as a poor runner, since the headwind also acts inside the gondola car and prevents the car from rolling down the hill. It is recommended to study the effect of a headwind on a four-axle empty gondola car.


Introduction
Analyzing the content of the published discussions devoted to the problem of designing sorting slides [1][2][3][4][5][6][7][8][9][10], it can be concluded that until now the dynamics of the car moving along the profile of the sorting slide has not been studied enough.For this reason, it is worth noting the ideas about the importance of controlling, coordinating the speed of a moving car along the profile of a sorting slide.This requires the study of two states: the movement of a 4-axle empty covered car and a gondola car along the profile of a sorting slide [5,7,9,[11][12][13][14][15][16][17].

The main part
Currently, in the existing methods of V.N.Obrazov, I.P. Starshov, V.M. Rudanovsky, H.T. Turanov and other recognized scientists to determine the height of the sorting slide, it is calculated based on the most difficult conditions -winter temperature and headwind, and for a bad runner, a four-axle empty covered wagon is selected.The reason for choosing this car was that the cross-sectional area of the closed car is larger than that of other cars (Table 1) [4,6,8,10,12,14,16,18].The following forces act on a car moving along an inclined plane (Fig. 1): Qgravity; Wresistance forces; Fmain driving force; Pforce exerting normal pressure on the inclined plane.As can be seen from Figure 1, ; ( on the slides, the slope а in practice does not exceed 5 °and can be considered equal , Here islope value, ‰.
The resistance force W is proportional to the weight of the car.
Resistance forces: -continuous (basic ωо, resistance from the environment and wind ωоsh, resistance arising from snow and dew ωqsh); -periodic (resistances arising along the switches ωsw, curves ωcur, for example, at the braking positions ωbp in working condition).
Hence the total resistance force can be calculated using the following formula Resistivity from the environment (air temperature and wind) ωоsh or, kgfpts, is determined by the following formulas: for one car (single uncoupling) for multigroup uncoupling , here Sx -relative coefficient of resistance from the environment for a single car or the first car of uncoupling; Sxxjcoefficient of relative resistance from the environment for uncoupling wagons, except for the first wagon; S, Sj -the cross-sectional area (midsection) of a separate car or the first car of the uncoupling and the other cars of the uncoupling, respectively, m 2 ; -the mass of a car or a decoupling consisting of n cars, t; t 0 -air temperature, °C ; Vnt -relative (final) speed of the car (uncoupling) taking into account the wind direction, mps.
Sх and Sххj are accepted according to Table 1 based on the parameters of the car.The relative speed of the Vnt and the angle a is determined by the following formulas: where, V -average speed of the car on the considered section, mps; Vsh -wind speed (in case of a headwind, the sign "+" is taken, and in case of a headwind, the sign "-"), mps; β -angle between the direction of the wind and the direction of movement of the car (fracture), deg.
If the angle β does not exceed 30 0 , , can be taken equal to (11) If the oncoming wind speed is greater than the descent speed V, then the sign Vnt is negative, and in this case the value of wsh is taken with the sign "-" [1 -5, 7 -13] .
The height of the sorting slide is 3.08 m, for a four-axle empty covered wagon, the winter temperature is -10 0 , the headwind speed is 5 mps m.It is from this calculated height of the slide that the descent of a four-axle empty gondola car on a difficult path is determined.
A headwind on a four-axle empty gondola moving along the profile of the sorting slide has the following effect (Fig. 2).Moving on the profile of the sorting slide (see Fig. 2) for a four-axle empty gondola car, the headwind affects not only the end transverse surface of the car, but also the inner rear partition of the empty gondola car.
∆S -cross-sectional area of the rear bulkhead of the gondola affected by the wind, m 2 From Fig. 3, we conclude that the headwind on the surface of an empty gondola car acts as follows: The transverse area of the end of the gondola car is taken from Table 1: Further, through a 3.08 m high slide defined for a four-axle empty covered wagon, we determine and analyze the kinetic energy heights of a four-axle empty gondola car.The results are shown in Figure 4.As can be seen from Fig. 4, the height of the sorting slide, determined based on the parameters of an empty covered wagon, is low and the empty gondola car does not reach the calculated point of the difficult path, since the kinetic energy height of the empty gondola car graphically crosses the longitudinal profile of the slide.From Fig. 5 it can be seen that a single four-axle empty gondola moving along the sorting hill is affected by a south-easterly (SE), easterly (E), north-easterly (NE) headwind.

Conclusion
When calculating the height of the sorting slide, it is necessary to take as a bad runner the technical characteristics of a four-axle empty gondola car, because the headwind also acts inside the empty gondola car and prevents the normal descent of the car down the hill.It is recommended to study the impact of headwind on a four-axle empty gondola car.

Fig. 1 .
Fig. 1.Forces acting on a car descending from a hill

Fig. 2 .
Fig. 2. The effect of headwind on a four-axle empty gondola car

Fig. 3 .
Fig. 3. Transverse areas of an empty gondola car, which is affected by a headwind.

E3SFig. 4 .
Fig. 4. Construction of kinetic energy heights for four-axle empty covered and gondola cars

Fig. 5 .
Fig. 5.The effect of the headwind on the moving gondola cars on the hill

Table 1 .
The values of the resistivity coefficients S x and S xxj from the environment