ON THE INFLUENCE OF BRAKING DISTANCE ON THE SIZE OF THE TRAIN OF A MINE ELECTRIC LOCOMOTIVE

V. A. TIMOFEEV

(Presented by the scientific seminar of the Mining-Mechanical Faculty)

The major tasks facing the coal industry with regard to the further development and increase of mine output can be properly solved only through the full-scale mechanization and automation of all mine production processes.

One of the most important production processes within a mine is the transportation of the mineral from the loading points of the sections to the pit-bottom yard. At present, the principal form of transport along the main horizontal workings is electric-locomotive transport, owing to its considerable advantages over other types of transport. Therefore, improving the efficiency of underground electric-locomotive haulage is currently one of the most important tasks in increasing mine productivity.

In addition to the quantitative growth of the electric-locomotive fleet, one direction in the further development of underground electric-locomotive haulage is the introduction of heavy types of electric locomotives, possessing significant adhesive weight, traction-motor power, and continuous-rating speed. Whereas previously only seven-ton contact and storage-battery electric locomotives were used, now 10-ton contact locomotives and 8—8.5-ton storage-battery locomotives have become the most widespread, and 12-ton storage-battery and 14-ton contact electric locomotives are beginning to be introduced into the mining industry. The power of the traction motors, the continuous tractive effort, and the continuous speed of the electric locomotive have increased accordingly. Thus, if the one-hour power of the two traction motors of a 7- or 10-ton contact electric locomotive is 41.2 kW, the continuous tractive effort 370 kg, and the continuous speed 16 km/hour (4.4 m/sec), then for a 14-ton contact electric locomotive the corresponding figures are 92 kW, 600 kg, and 19 km/hour (5.3 m/sec). These figures are not a limit, and in the future, with the growth of mine productivity, a further increase in the adhesive weight, power, and other characteristics of electric locomotives should be expected, as is confirmed by the practice of American mines.

Another direction in the further development of underground electric-locomotive transport is an increase in the capacity of mine cars, the introduc-

of 3.5- and even 10-ton cars instead of one-ton and, in part, two-ton cars. This circumstance is to a certain extent relevant to the question under consideration, since the specific resistance to the motion of higher-capacity cars is lower than the resistance to the motion of cars of small capacity, and, consequently, all other conditions being equal, when higher-capacity cars are used the weight of the train consist is greater than with cars of small capacity. In addition, in this case the internal braking capabilities, the internal braking means of the train consist itself, are reduced, so that, all other conditions being equal, the braking distance of a train consist made up of higher-capacity cars will be greater than that of a consist made up of cars of small capacity.

The indicated directions in the development of underground electric-locomotive haulage, along with others, make it possible to increase substantially the productivity of underground electric-locomotive transport.

However, the introduction into underground transport of heavy-type electric locomotives, capable of hauling higher-capacity train consists and possessing high continuous-service speeds exceeding 4 m/sec, has considerably complicated the question of braking such consists within the length of track permitted by the Safety Rules for coal mines, which stipulate that the braking distance must not exceed 40 m for freight consists and 20 m for consists carrying people.

When light- and medium-weight contact electric locomotives are used (for example, 7-ton locomotives), the braking of possible consists in a number of cases is quite satisfactory, and there is a sufficiently satisfactory correspondence among the magnitudes of the consist for such electric locomotives obtained by calculation on the basis of the principal conditions, namely: by the adhesive weight of the electric locomotive, tractive force, heating of the traction motors, and the permissible length of the braking distance.

When, however, heavy-type contact electric locomotives are used (10-ton and especially 14-ton locomotives), in the overwhelming majority of cases the consists selected by tractive force, adhesive weight, and the condition of permissible heating of the traction motors for such electric locomotives prove, under the braking conditions for the permissible length of braking distance, to be excessively large; in other words, a consist selected according to the limiting one of the indicated conditions cannot be braked within the length of track permitted by the Safety Rules. Thus, for such electric locomotives under normal mine-haulage conditions (i.e., at gradients of 3–5‰), the limiting condition for the size of the train consist will be the permissible length of braking distance, or, in other words, the braking means of the electric locomotive. At the same time, the difference in the size of the consists found from the braking conditions and from the conditions of adhesion, tractive force, or heating may be substantial. It should be noted that all the foregoing applies only to direct-current contact electric locomotives. For battery and capacitor electric locomotives used in our industry, since their continuous speed does not exceed 3 m/sec, the limiting condition in selecting the size of the consist will not be the magnitude of the braking distance, because both battery and capacitor electric locomotives under normal conditions will always be able to brake the consist permissible for them within the permissible braking distance of 40 m. The limiting condition in selecting the size of the consist for battery electric locomotives in most cases will be the heating of the traction motors; for capacitor electric locomotives, the conditions of adhesion of the electric-locomotive wheels to the rails during starting

of the loaded train on the prevailing ascent with minimum acceleration.

Let us explain the above with examples.

We assume:

track gradient \(i = 3\permil\); cars with roller bearings, with capacity \(q = 3\ \mathrm{t}\); running resistance to the motion of a loaded car \(w_{gr} = 5\ \mathrm{kg/t}\); running resistance to the motion of an empty car \(w_{por} = 7\ \mathrm{kg/t}\). Starting resistance to the motion of a loaded car

\[ w'_{gr} = 7\ \mathrm{kg/t}. \]

Starting resistance to the motion of an empty car

\[ w'_{por} = 9\ \mathrm{kg/t}. \]

The indicated values of resistance to motion are recommended for use in calculations by Order No. 270 of the Ministry of Coal Industry of the USSR dated May 31, 1952.

For the 10KR electric locomotive.

a) The maximum permissible weight of the loaded train, based on adhesion conditions when starting the loaded train on the prevailing (average) ascent,

\[ P + Q_{gr} = \frac{1000\psi P}{w'_{gr} + i + 110J} = \frac{1000 \cdot 0.25 \cdot 10}{7 + 3 + 110 \cdot 0.04} = 173\ \mathrm{t}, \]

where \(P = 10\ \mathrm{t}\) is the weight of the electric locomotive;

\(Q_{gr}\) is the total weight of the loaded train, \(\mathrm{t}\);

\(\psi\) is the coefficient of adhesion when starting with sanding, taken equal to 0.25;

\(J\) is the acceleration at starting, taken equal to \(0.04\ \mathrm{m/sec.^2}\).

b) The maximum permissible weight of the loaded train, based on heating conditions, i.e., on tractive force,

\[ P + Q_{gr} = \frac{F_{dl}}{\alpha \sqrt{\tau}\left(w'_{gr}-i_{r.s}\right)} = \frac{370}{1.15 \sqrt{0.57}\,(5-2)} = 143\ \mathrm{t}, \]

where \(F_{dl} = 370\ \mathrm{kg}\) is the continuous tractive force of the electric locomotive;

\(i_{r.s} = 2\permil\) is the equivalent-resistance gradient;

\(\alpha\) is a coefficient accounting for the operation of the electric locomotive during maneuvers, taken equal to 1.15;

\(\tau\) is the relative duration of motion, determined by the formula

\[ \tau = \frac{T_{dv}}{T_{dv} + \Theta}, \]

where \(T_{dv}\) is the duration of motion in both directions during one trip, min;

\(\Theta\) is the total duration of pauses and maneuvers, min.

The duration of motion \(T_{dv}\) is determined from the expression

\[ T_{dv} = \frac{2L \cdot 1000}{60 \cdot 0.75 \cdot V_{ust}}, \]

where \(L\) is the average haulage distance, taken equal to \(2\ \mathrm{km}\);

\(V_{ust} = 4.4\ \mathrm{m/sec}\) \((16\ \mathrm{km/hour})\) is the steady speed of motion, taken equal to the continuous speed of motion of the electric locomotive.

0.75 is a coefficient allowing for the reduction in the average running speed during periods of starting, stopping, passing switches, curves, etc.

Then

\[ T_{ob}=\frac{2\cdot 2\cdot 1000}{60\cdot 0{,}75\cdot 4{,}4}=20\ \text{min}. \]

Thus, with the adopted duration of pauses and maneuvers \(\Theta = 15\) min,

\[ \tau=\frac{20}{20+15}=0{,}57. \]

c) The maximum permissible weight of a loaded train, based on the braking conditions of a loaded consist moving at steady speed down the governing grade, for the permissible length of braking distance,

\[ P+Q_{gr}=\frac{1000\psi P_t}{110j_t-W_{gr}+i} =\frac{1000\cdot 0{,}20\cdot 10}{110\cdot 0{,}24-5+3}=82\ t, \]

where \(\psi\) is the coefficient of adhesion when braking with sand application. We take \(\psi=0{,}20\);

\(j_t\) is the braking deceleration \((m/sec^2)\), determined from the expression

\[ j_t=\frac{V_{\text{ust}}^2}{2l_{t.\,dop}} =\frac{4{,}4^2}{2\cdot 40}=0{,}24\ m/sec^2, \]

where \(V_{\text{ust}}=4{,}4\ m/sec\) is the steady speed at the beginning of braking, taken equal to the continuous operating speed of the electric locomotive;

\(l_{t.\,dop}=40\ m\) is the permissible length of the braking distance.

If the size of the train consist is taken according to the heating condition, then for such a consist the braking distance for the most severe case—namely, braking of a loaded consist moving down the governing grade at full steady speed to a complete stop—is determined as follows.

We take the coefficient of friction between the brake shoe and the wheel rim as \(\varphi=0{,}20\), and the coefficient of brake-shoe pressure as \(\delta=0{,}85\).

Then the total braking force is

\[ B=1000\varphi\delta P=1000\cdot 0{,}2\cdot 0{,}85\cdot 10=1700\ kg. \]

The specific braking force for the loaded consist is

\[ b=\frac{B}{P+Q_{gr}}=\frac{1700}{143}=12\ kg/t. \]

The braking deceleration is

\[ j_t=\frac{w_{gr}-i+b}{110} =\frac{5-3+12}{110}=0{,}127\ m/sec^2. \]

The tractive force of the electric locomotive for the loaded consist is

\[ F_{gr}=(P+Q_{gr})(w_{gr}-i)=143(5-3)=286\ kg. \]

The steady speed of motion of the loaded train, found from the characteristic of the traction motor DK—801—A—1 of this electric locomotive, is \(V_{\text{st}\cdot gr}=16.5\ \text{km/hour}\), or \(4.6\ \text{m/sec}\). The braking time is

\[ t_t=\frac{V_{\text{st}\cdot gr}}{j_t}=\frac{4.6}{0.127}=36\ \text{sec}. \]

The braking distance is

\[ l_t=\frac{V_{\text{st}\cdot gr}t_t}{2}=\frac{4.6\cdot 36}{2}=83\ \text{m}. \]

Analogous calculations are made for the 14 KR contact electric locomotive, the 12 ARV storage-battery electric locomotive, and the KE-2 condenser locomotive. The results obtained are summarized in Table 1.

Table 1

The train possible by the tractive force of the KE—2 electric locomotive \((P+Q_{gr}=432\ t)\) is excessive for this locomotive under the conditions of adhesion and braking. With its adhesive weight, the electric locomotive can only with great difficulty start a loaded train from rest even on a downgrade, since the maximum possible acceleration when starting such a train downhill is negligibly small. In fact, when starting a loaded train downhill,

\[ P+Q_{gr}=\frac{1000\psi P}{w_{gr}-i+110j}, \quad \text{whence} \]

\[ j=\frac{1000\psi P-(P+Q_{gr})(w_{gr}-i)}{110(P+Q_{gr})}= \]

\[ =\frac{1000\cdot0.25\cdot7-432(7-3)}{110\cdot432}=0.005\ \text{m/sec}^2, \]

i.e., the maximum possible acceleration is approximately 100 times less than the normally recommended acceleration at starting. Starting the loaded train on the preceding upgrade is impossible, since the acceleration becomes negative,

\[ j=\frac{1000\cdot0.25\cdot7-432(7+3)}{110\cdot432}\simeq -0.05\ \text{m/sec}^2. \]

Let us determine the braking distance for such a train in the most severe case. The total braking force, with the brake-shoe pressure coefficient \(\delta = 0.9\), is

\[ B = 1000 \varphi \delta P = 1000 \cdot 0.2 \cdot 0.9 \cdot 7 = 1260 \text{ kg}. \]

The specific braking force is

\[ b = \frac{B}{P + Q_{\text{gr}}} = \frac{1260}{432} = 2.9 \text{ kg/t}. \]

The braking deceleration is

\[ j_t = \frac{w'_{\text{gr}} - i + b}{110} = \frac{5 - 3 + 2.9}{110} = 0.045 \text{ m/sec}^2. \]

The braking time is

\[ t_t = \frac{V_{\text{ust.gr}}}{j_t} = \frac{3}{0.045} = 67 \text{ sec}. \]

The braking distance is

\[ l_t = \frac{V_{\text{ust.gr}} \cdot t_t}{2} = \frac{3 \cdot 67}{2} \approx 100 \text{ m}, \]

which is considerably greater than \(40\) m.

The MAK-61-6/12 electric motors of the KE-2 electric locomotive have a stiff characteristic. Even a considerable change in load causes only an insignificant change in the speed of motion. Thus, at continuous tractive effort \(F_{\text{dl}} = 1210\) kg, the speed of motion is \(v_{\text{dl}} = 10.3\) km/h, whereas at one-hour tractive effort \(F_{\text{chas}} = 1575\) kg, the speed of motion is

\[ v_{\text{chas}} = 10.1 \text{ km/h}. \]

A change in effort by

\[ \frac{(1575 - 1210)100}{1210} = 30\% \]

causes a change in speed of only

\[ \frac{(10.3 - 10.1)100}{10.1} = 2\%. \]

Therefore, with sufficient accuracy, the established speed of motion (the speed at the start of braking) may be taken as constant, independent of the size of the train and not exceeding \(3\) m/sec \((10.8\) km/h).

Thus, because of the insufficient adhesion weight of the KE-2 electric locomotive (\(7\) t), the weight of the loaded train according to the adhesion condition, and also according to the braking condition, is such that the power of the locomotive motors cannot be used to the full extent.

In our case, determination of the train size for the KE-2 electric locomotive according to the adhesion condition was carried out under the condition of starting on the prevailing up-grade with acceleration \(j = 0.04\) m/sec\(^2\).

For some increase in the train weight according to the adhesion condition, it is possible to start the loaded train on the prevailing up-grade with a somewhat lower acceleration. In this case, at acceleration \(j = 0.03\) m/sec\(^2\),

\[ P + Q_{\text{gr}} = \frac{1000 \psi P}{w'_{\text{gr}} + i + 110j} = \frac{1000 \cdot 0.25 \cdot 7}{7 + 3 + 110 \cdot 0.03} = 131 \text{ t}, \]

at acceleration \(j = 0.02\ \text{m/sec}^2\)

\[ P + Q_{gr} = \frac{1000 \cdot 0.25 \cdot 7}{7 + 3 + 110 \cdot 0.02} = 143\ \text{t}. \]

However, the trains obtained may prove excessive under the condition of braking a loaded train on the prevailing grade.

For a train \(P + Q_{gr} = 131\ \text{t}\)

\[ \text{specific braking force } b = \frac{1260}{131} = 9.6\ \text{kg/t}, \]

\[ \text{braking deceleration } j_t = \frac{5 - 3 + 9.6}{110} = 0.105\ \text{m/sec}^2, \]

\[ \text{braking time } t_t = \frac{3}{0.105} = 28.5\ \text{sec}, \]

\[ \text{braking distance } l_t = \frac{3 \cdot 28.5}{2} = 43\ \text{m}. \]

For a train \(P + Q_{gr} = 143\ \text{t}\)

\[ b = \frac{1260}{143} = 8.8\ \text{kg/t}, \]

\[ j_t = \frac{5 - 3 + 8.8}{110} = 0.1\ \text{m/sec}^2, \]

\[ t_t = \frac{3}{0.1} = 30\ \text{sec}, \]

\[ l_t = \frac{3 \cdot 30}{2} = 45\ \text{m}, \]

i.e., the braking distance somewhat exceeds the permissible value.

The results of analogous calculations for cases of two-ton and one-ton mine cars with roller bearings are given, respectively, in Tables 2 and 3. In doing so, the values of the specific resistance to motion were adopted in accordance with Order No. 270 of the Ministry of Coal Industry of the USSR of May 31, 1952, namely:

for two-ton loaded mine cars \(w_{gr} = 6\ \text{kg/t}\), \(w'_{gr} = 8\ \text{kg/t}\);

for two-ton empty mine cars \(w_{por} = 8\ \text{kg/t}\), \(w'_{por} = 10\ \text{kg/t}\);

for one-ton loaded mine cars \(w_{gr} = 7\ \text{kg/t}\), \(w'_{gr} = 9\ \text{kg/t}\);

for one-ton empty mine cars \(w_{por} = 9\ \text{kg/t}\), \(w'_{por} = 12\ \text{kg/t}\).

In the case of one-ton and two-ton mine cars, the possible size of train obtained from the tractive force of the KÉ-2 electric locomotive is excessive for this locomotive under the conditions of adhesion and braking. Therefore, for fuller utilization of the power of the traction motors of the KÉ-2 electric locomotive, determination of the possible size of train by adhesion of the locomotive wheels with the rails in these cases

Table 2

Table 3

was carried out under the condition of starting on the predominant upgrade with a minimum acceleration \(j = 0.02\ \mathrm{m/sec^2}\).

Thus, if for contact electric locomotives one adopts a train size that meets the requirements for the permissible braking-distance length, then the productive capacity of the electric locomotive will be considerably underutilized. If, however, one adopts a train size at which the productive capacity of the electric locomotive is fully utilized, then in this case the electric locomotive, using its own braking means, will not be able to brake such a train within the length of track permitted by the Safety Rules; and in order in this case to satisfy the latter, some special measures will be required.

The calculations presented above were made for certain average conditions, assuming a grade of \(3\%\) and the use of sand during braking in order to increase the coefficient of adhesion of the electric locomotive wheels with the rails.

When the grade is increased to \(4 \div 5\permil\) and higher, which occurs frequently in mines, the braking distance for a train size corresponding to the productive capacity of the electric locomotive increases substantially.

In addition, if braking is carried out without the use of sand, then, owing to the reduction of the coefficient of adhesion, the length of the braking distance, all other conditions being equal, increases considerably. This circumstance imposes definite requirements for improving the quality of the design and the effectiveness of operation of the sand-

locomotive system, since from this point of view the sanding system used on modern mine electric locomotives cannot be considered entirely satisfactory. Moreover, this increases the number of operations that the driver must perform during braking (switching off the controller, opening the sandboxes, turning the brake handwheel), which leads to an increase in the actuation time of the braking system and, as a consequence, to an increase in braking distance. With an increase in gradient above 3‰, it may turn out that battery locomotives and especially capacitor locomotives will not be able to satisfy the braking requirements for the permissible braking distance.

Consequently, the braking systems of modern mine electric locomotives, in which, when braking a train, only the locomotive itself is braked, cannot be considered fully reliable from the standpoint of ensuring traffic safety. This leads to the need to replace these braking systems with more advanced and more reliable ones.

Without this, any further increase in the weight and speed of locomotives, while ensuring proper traffic safety, is impossible. The use of double-heading of a train by two locomotives with one driver, with the existing manual mechanical braking system, when only one locomotive will be braked, does not ensure a permissible braking distance. Likewise, replacement of the existing manual mechanical braking system by a faster-acting system that is lighter and more convenient to control is necessary from the standpoint of performing shunting operations, when especially frequent application of the braking system is required. In this case, ease and convenience of control and the speed of actuation of the braking system acquire primary importance.

Thus, one of the factors in ensuring complete traffic safety and the high-productivity operation of electric-locomotive haulage, as well as convenient and easy control of electric locomotives, is the increase of the braking means of the entire train through the application of new, more advanced braking systems that meet the basic requirements imposed on rational braking systems, allowing smooth regulation of the force pressing the shoes and propagation of the braking wave over the entire length of the train. The creation and introduction into industry of a reliable braking system will make it possible to significantly increase the train weight and running speed, improve traffic safety, and improve the working conditions of electric-locomotive drivers.

There is every reason to believe that such a system will be an electric or pneumatic system, which to the greatest extent satisfies all the requirements indicated. With these braking systems, a certain number of ordinary mine cars are included in the train, but equipped with shoe brakes with electric or pneumatic drives, actuated centrally and remotely from the driver’s cab simultaneously with the braking system of the locomotive.

Let us determine, for the above conditions, the minimum necessary number of mine cars equipped with a braking system that must be included in the train so that, in the most difficult braking case, the length of the braking distance does not exceed the permissible value.

Electric locomotive 10KR. Three-ton cars. The braking deceleration, with the permissible braking distance \(l_{t\,dop}=40\ m\) and the established speed of motion of the loaded train \(V_{ust.gr}\), must be equal to

\[ j_t=\frac{V_{ust.gr}^{2}}{2l_{t.dop}}=\frac{4.6^{2}}{2\cdot 40}=0.265\ m/sec^{2}. \]

Then the specific braking force is

\[ b=110\,j_t-w_{gr}+i=110\cdot 0.265-5+3=27\ kg/t, \]

and the total braking force for the train adopted for this locomotive under the given conditions according to tractive force is

\[ B=b(P+Q_{gr})=27\cdot 143=3860\ kg. \]

With this braking force the braking weight of the train must be equal to

\[ P_t=\frac{B}{1000\varphi}=\frac{3860}{1000\cdot 0.2\cdot 0.85}=23\ t, \]

or the braking weight falling on the cars is

\[ P_{t.vag}=P_t-P=23-10=13\ t. \]

In this case the number of cars equipped with brakes is

\[ n_t=\frac{P_{t.vag}}{G_{gr}}=\frac{13}{4.5}=3, \]

where \(G\) is the weight of a loaded car, \(t\).

The total number of cars in the adopted train is

\[ n=\frac{143-P}{G_{gr}}=\frac{143-10}{4.5}\simeq 30, \]

i.e. the number of cars equipped with brakes must amount to approximately \(10\%\) of the total number of cars in the train. The results of analogous calculations for trains with two-

Table 4

…with two-ton and one-ton mine cars are given in Table 4, and for the case of the 14 KR electric locomotive in Table 5.

Table 5

Consequently, it is sufficient to equip only a part of the total number of mine cars in the train with brakes. The number of braked mine cars introduced into the train will depend on the specific conditions of electric-locomotive haulage at the given mine, namely: the type of electric locomotive used, the type of mine car, the magnitude of the prevailing gradient, etc. Hence it is clear that there is no need to equip the entire mine-car fleet of a mine with a braking system. There are grounds to believe that, for mine electric-locomotive haulage, preference should be given to a braking system with an electric drive, owing to its simplicity in operation as compared with a pneumatic braking system.

With an electric system, the braking system of each braked mine car is actuated by an electromagnet. Switching the electromagnets on and off during braking, regulating the current consumed by the electromagnets, and consequently also the force with which the brake shoes are pressed against the wheel rims of the mine cars, are carried out remotely and centrally from the driver’s cab by means of a controller.

To supply current to the braking electromagnets, a flexible or armored main cable is laid along the train, composed of separate sections connected accordingly to each mine car. The separate sections of cable are connected into a common line during train make-up by means of plug connections. The contact wire is used to supply the braking electromagnets; because of this, it is sufficient to have a single-core cable with single-conductor plug connections.

What, then, should be recommended as a temporary measure in selecting the size of a train that satisfies all present conditions, while mine electric-locomotive transport still lacks an adequate braking system?

Obviously, if the size of the train found from the braking conditions proves to be less than the size of the train determined from the conditions of heating of the traction motors or from the adhesion conditions, then in such cases it should be recommended not to reduce the size of the train, but to reduce the speed of motion of the electric locomotive, with the aim of reducing

initial braking speed. Since the most difficult case from the standpoint of the magnitude of the braking distance will be the braking of a loaded train traveling downhill on a grade, it should be recommended, when moving in the loaded direction, in order to reduce the initial braking speed, either to periodically switch off the traction motors so that the traveling speed does not reach the steady-state value (if the train size found from the braking conditions is not much smaller than the train size found from the heating or adhesion conditions), or to change over to operation with the traction motors connected in series (if the train size according to the braking conditions is significantly smaller than the train size according to the heating or adhesion conditions). The indicated measure, although it leads to a reduction in the possible productivity of the electric locomotive, will make it possible to brake, within the permissible length of track, a train corresponding to the production capacity of a heavy-type contact electric locomotive that has a considerable continuous-service speed.

From the standpoint of reducing the possible productivity of the electric locomotive, this measure has an advantage over reducing the train size to that corresponding to the braking conditions for the permissible braking distance.

First, the electric locomotive travels at half speed for only one half of the trip.

Second, in this case the average running speed when moving in the loaded direction is closer to the steady-state speed than when operating with the motors connected in parallel. If, with the motors connected in parallel, the average running speed is approximately 75% of the steady-state speed, then when operating with the motors connected in series it may be assumed that the average running speed will be approximately 85--90% of the steady-state speed corresponding to series connection of the traction motors.

Thus, the reduction in the possible productivity of the electric locomotive in this case will not be so significant.

If the travel time in the loaded direction with the traction motors connected in parallel, \(T_{gr}\), is taken equal to the travel time with the empty cars, \(T_{por}\), and equal to the pause time \(\Theta\), i.e. \(T_{gr} = T_{por} = \Theta\), and the possible productivity of the electric locomotive in this case is taken as 100%, then, upon changing over to operation with the motors connected in series, the possible productivity of the electric locomotive will decrease by approximately 20%, while remaining sufficiently high. In actuality, in mines, in most cases the pause time \(\Theta\) is greater than the times \(T_{gr}\) and \(T_{por}\). Under these conditions the reduction in the possible productivity of electric-locomotive haulage will be still smaller.

When the train size is reduced, because of the resulting increase in traveling speed, the reduction in braking distance occurs more slowly. In order to reduce the length of the braking distance to the permissible value, it is usually necessary to reduce the train size corresponding to the production capacity of the electric locomotive by several times. Therefore, despite some increase in traveling speed, the reduction in the possible productivity of electric-locomotive haulage with this method will be considerably greater than with the first variant, to which preference should be given. In addition, as shown in the work of Associate Professor A. S. Betekhtin, “Determination of the Train Size of a Mine Electric Locomotive by the Permissible Braking Distance,” the functional dependence of the braking-distance length on the train size \(l_t = f(p + Q)\) has a minimum, i.e., for cer-

for some definite train size the braking distance will be minimal. If, for a given train size, the length of the braking distance exceeds the permissible value, then when the train weight is reduced the braking distance will not decrease, but will increase. Therefore, in a whole number of cases, reducing the size of the train will not lead to the desired result at all.

Literature

1. Volotkovskii, S. A. Mine Electric-Locomotive Traction. Ugletekhizdat, 1955.

2. Collection of Articles for the 70th Anniversary of Professor D. A. Strelnikov. Problems in the Mining of Thick Seams of the Kuzbass. Article by Associate Professor A. S. Berekhtin, “Determination of the Size of the Train of a Mine Electric Locomotive by the Permissible Length of the Braking Distance.” Ugletekhizdat, 1953.