On the Issue of Determining the Required Capacity of Railway Loading Bunkers

Associate Professor A. T. Martynenko.

Railway loading bunkers, up to the present time, have been the predominant means of mechanizing the shipment of minerals at mines¹, and the possibility of their use in new mine construction in the future is also not excluded.

An essential question in designing the loading-and-storage facilities of mines is the correct choice of the required capacity of loading bunkers, made on the basis of a critical analysis of all the factors affecting it. Unfortunately, up to now sufficient attention has not been paid to this question in our literature.

The methods available in the literature for determining the useful capacity of bunkers, proposed by Kharkov Shakhtstroy as normative material², by engineer D. L. Tartakovsky, A. A. Lukashev, and A. G. Frolov, cannot be used in practice, because the formulas they have compiled give such a contradictory result, and one so far from actual conditions, that workers in the field are simply forced to decide this question in their own way, proceeding from the specific conditions of operation of railway transport in hauling the mineral.

Therefore, in this article we set ourselves the task of establishing the invalidity of the formulas for determining the useful capacity of bunkers published in our literature, and of giving a new method for establishing the required capacity of bunkers, proceeding from the specific conditions of organizing the work of railway transport in the carriage of bulk cargoes.

In the book Railway Loading Bunkers: Standards of Shakhtstroy, published in 1934, it is proposed to determine the capacity of bunkers for ordinary coal by the following expression:

$$ W = \frac{A}{m} \cdot \frac{n_1}{n_2} K_1 K_2, \tag{1} $$

where \(A\) is the mine’s annual output, in tons, passing through the bunker;

\(m\) is the number of working days in the year;

\(n_1\) is the number of hours per day during which work is performed to load the bunker, including intervals between shifts;

\(n_2\) is the number of hours per day during which coal is unloaded from the bunkers into wagons;

\(k_1\) is the coefficient of nonuniformity of the mine’s daily output;

\(k_2\) is the coefficient of nonuniformity of wagon supply.

Thus, as we see, the formula does not take into account an essential factor—the weight of the dispatch route; and the organization of wagon supply for loading is represented by the very vague coefficient \(k_2\), whose value Shakhtstroi recommends taking within the range of 10–25%. The standards also indicate that unloading the bunker lasts for 20 hours (\(n_2\)).

As is known from practice, the coefficient of nonuniformity of wagon supply for loading varies within very wide limits; that is, in essence it is a variable quantity. Therefore, in the present case it is best to base all conclusions not on the conditions of some unknown coefficient, but to proceed from a normal, i.e., completely definite, organization of wagon supply to the mines. At the same time, every slightest deviation from the adopted organization must be accounted for by the capacity of the emergency storage facility, but under no circumstances should it be reflected in the capacity of the bunker, even if only for economic considerations.

As already mentioned above, Shakhtstroi’s formula provides for unloading coal from the bunker over 20 hours, i.e., in fact, almost three full shifts of the mine’s work in extracting the useful mineral.

By the same Shakhtstroi standards, the intensity of bunker loading for various types of rolling stock is, it must be said, assumed to be fairly high for that time. Thus, for example, for open rolling stock of the wagon fleet, the standards recommend taking 0.2 minutes per 1 ton.

Thus, by assuming 20 hours of time for unloading the bunker, we in fact turn it into a loading funnel for dispatching the mine’s current output; and in this case the capacity of the bunker, as such, loses all physical meaning.

Under present-day conditions (at the large mines of Kuzbass), no more than 2 hours are allotted for loading a heavy-weight route from bunkers. Therefore, under any conditions, much less time will be required for unloading the bunker than is provided for by Shakhtstroi’s formula. In establishing this value, one must proceed, first, from the weight of the dispatch route adopted for the given mine and, second, from the conditions of loading intensity under modern methods of organizing loading operations.

Eng. D. L. Tartakovsky, in his book Loading Ore from Bunkers and Warehouses into Railway Cars, publ. 1936 (p. 35), determines the capacity of bunkers very simply—“taking into account improvements in railway transport operations, the capacity of loading bunkers should be designed as not exceeding the one-shift output of a mine or ore mine,” and further recommends checking the resulting capacity of the loading bunker, in case of a “possible” discrepancy between the productivity of the mine and the intensity of loading ore into cars, by the following expression:

\[ W=\frac{A}{m}K_1K_2\left(1-\frac{n_1}{n_2}\right)^{1} \tag{2} \]

where: \(n_1\) is the number of hours of operation of the mine hoist per day.

According to the Shakhtstroy formula, this time corresponds to the number of hours of work for filling the bunker over the course of a day, including intervals between shifts, i.e., in fact this is one and the same quantity.

Thus, as we see, this formula essentially takes into account the very same factors as the Shakhtstroy formula. Therefore there is no need to dwell on it. It need only be noted that the ratio \(\frac{n_1}{n_2}\) will always be greater than unity, and consequently the bunker capacity will be a negative quantity.

A. A. Lukashev, in his book Transport on the Surface of Ore Mines, Part 2, publ. 1935, on p. 88 gives this formula in the following form:^2)

\[ W=\frac{A}{m}\frac{K_2}{Z}\left(K_1-\frac{n_1}{n_2}\right), \tag{3} \]

where \(z\) is the number of working shifts per day.

In this formula, as compared with the one cited above, the coefficient of nonuniformity of daily output has been placed inside the parentheses, as a result of which a negative value of the capacity is obtained when the bunker operates 18 hours for unloading. And since the unloading of the bunker over the course of a day will require far less time, the value of the capacity will always be a negative quantity.

Without dwelling on an analysis of this formula, since in essence it does not include any new factors, let us proceed directly to a numerical example for all the formulas considered above.

Let us find the useful capacity of a bunker for identical conditions, with the following adopted data:

\(A_1=500\) thousand tons; \(m=300\); \(Z=3\); \(K_1=1.1\); \(K_2=1.25\);
\(n_1=21\); \(n_2=20\).

^1) In order to avoid repetition, in the capacity formula of Eng. Tartakovsky and Lukashev the letter designations have been replaced.

^2) This formula is given in the book Basic Provisions of the General Plan for the Mechanization of Mines of the Donets Basin, publ. 1933.

According to the Shakhtstroy formula,

\[ W=\frac{500000}{300}\cdot\frac{21}{20}\cdot 1.1\cdot 1.25=\sim 2400\ \text{tons}. \]

According to the formula of Eng. Tartakovsky,

\[ W=\frac{500000}{300}\cdot 1.1\cdot 1.25\left(1-\frac{21}{20}\right)=\sim -114\ \text{tons}. \]

According to the formula of Eng. Lukashev,

\[ W=\frac{500000}{300}\cdot \frac{1.25}{3}\left(1.1-\frac{21}{20}\right)=34.7\ \text{tons}. \]

Thus, as can be seen from the example given, the proposed formulas for determining the useful capacity of bunkers give highly contradictory results, and their absolute value is far from corresponding to the actual conditions of practice. Therefore we believe that the fact that these formulas have been published in our educational literature is an unfortunate error, which must be corrected by the joint efforts of the engineering-technical and scientific workers in this field.

A. G. Frolov, in his book The Arrangement of the Surface of Mines, publ. 1938, gives an approximate method for determining the capacity of railway loading bunkers, according to the following formula:

\[ W=Q_1+Q_2, \]

where \(Q_1\) is the partial capacity of the bunker, expressed by a one-and-a-half-hour or 2-hour reserve of the normal output of the mine, depending on the hoisting system, with the addition of a certain capacity for protecting the bottom of the bunker, the amount of which is unknown even to the author of the book.

By the quantity \(Q_2\) is meant the bunker capacity required to accelerate the process of loading railway cars.

The analytical expression for \(Q_2\) is presented by the author in the following form:

\[ Q_2=\frac{Q_{\text{train}}\,[nr(1+R)-tp]}{nr}\ \text{tons}, \]

where \(Q_{\text{train}}\) is the weight of the dispatched train in tons;

\(n\) is the number of cars simultaneously loaded under the bunkers;

\(r\) is the capacity of one car in tons;

\((1+R)\) is, in fact, the coefficient \((K_2)\), already known to us, of the irregularity of the delivery of cars for loading, taken by the author on average as 1.25;

\(t\) is the loading time of one car in hours (it is recommended that it be taken according to actual data);

\(p\) is the average hourly inflow of mineral into the railway bunker, in t/h.

Thus, as we see, in addition to what was stated above, this formula takes into account the weight of the dispatch train; but it does not take into account the organization of car supply—or, rather, the author leaves this factor to be taken into account by the coefficient \(K_2\), already known to us. Moreover, for some unknown reason this formula is supposed to take into account the intensity and the front of loading operations. It seems to us that these last two factors are functions of the organization of railway transport work in hauling out the mineral; and since the author has assumed an obviously incorrect organization (which is accounted for by the coefficient \((1+R)=K_2\)), the calculation formula as a whole is doubtful.

To confirm the above, let us carry out a numerical example for the S. M. Kirov mine of the Leningugol trust, Kuzbass Combine.

The mine has an annual output of 1,500 thousand tons. Let us take 345 working days per year. The weight of the dispatch train for this mine is 1,450 tons net. The mineral is shipped in 60-ton hoppers. Let us take the loading time of one car as 10 min. The mine has 3 loading tracks, and one car is loaded simultaneously on each track. Then the required bunker capacity according to the second part of the equation should be:

\[ Q_2 = 1450 \frac{3 \cdot 60 \cdot 1.25 - \frac{1}{6}\cdot 200}{60 \cdot 3} = 1540 \text{ tons.} \]

With 2 loading tracks, the bunker capacity comes out to be \(\sim 1400\) tons; with 5 loading tracks, \(\sim 1650\).

Proceeding from the specific operating conditions of the Kirov mine, according to Frolov’s formula, for this mine the weight of the dispatch train should be 700 tons net, with an existing bunker capacity of 750 tons; although we know that this mine dispatches heavy-weight trains without any excessive idle time of cars under loading.

Thus the second part of Engineer Frolov’s formula gives a bunker capacity approximately corresponding to the capacity of the adopted train, which of course is far from reality; and the author has vainly clothed simple things to the highest degree in a confused algebraic expression.

As for the first part of the formula for bunker capacity, \(Q_1\), it gives an entirely unjustified increase in the already unnecessarily inflated results obtained from the second part of the equation.

In conclusion to the brief critical review we have carried out, it is necessary to note the complete untenability of the proposed methods for determining bunker capacity. According to all the formulas considered, the results obtained are so contradictory that it is difficult even to recommend any one of them as the \(n\)-th degree of approximation in solving this question. There-

therefore below we propose our own method for determining the required capacity of bunkers.

Associate Professor S. I. Kozlovsky, as early as 1932, when investigating bunker and storage loading at the mines of the Donbass¹, in his work gave, in the main, a completely correct method for determining the capacity of mine loading bunkers, where he based his conclusions on the existing organization of the work of railway transport in removing the mineral. It is regrettable that S. I. Kozlovsky limited himself to constructing a graph, without giving a mathematical dependence. True, under the present conditions of organizing the work of railway transport, it is impossible to make use of the proposed graph, since over this period of time there has been a very sharp change in the relation of all the factors affecting the capacity of loading bunkers. Therefore we base our conclusions on entirely new premises.

Method for determining the required capacity of railway loading bunkers

In establishing the required capacity of bunkers, we proceed from the following basic conditions:

1. The existing organization of the placement of cars for loading.
2. The accepted weight of the dispatch train.
3. The capacity of the mine.
4. The presence of an emergency storage yard and its equipment.
5. The type of rolling stock.
6. The organization of loading operations.

All the above-listed factors, directly or indirectly, will correspondingly affect the capacity of bunker installations.

At present, the organization of railway transport for removing the mineral provides for placing cars at mines according to a timetable or by notification. In either case, the adopted system of organization will be known to be stable. Only the time interval for notification may undergo change. Therefore we base all our conclusions on a completely precise, known in advance, organization of railway-transport work.

The weight of the dispatch train in each individual case is, generally speaking, determined by the conditions of the mine capacity and other preceding circumstances (track profile, type of locomotive, organization of railway haulage, etc.). That is, briefly speaking, the weight of the dispatch train is a given quantity; but if these conditions do not restrict it, then it is best and most correct, in each individual case, under the specific conditions of the mine, to determine the weight of the dispatch train in conjunction with the equipment of the mine’s loading-and-storage facilities.

A significant influence on bunker capacity will be exerted by the presence of an emergency stockpile and its transport equipment. On the basis of the operating experience of existing mines, we come to the conclusion that the storage facilities are, in essence, an active link. Therefore, the capacity of the bunkers must be determined in combination with the mine’s emergency facilities. In the final analysis, even under the condition of precise operation of railway transport in removing the mineral, the mine must have reserve and emergency stockpiles, both as being of defense significance and also in case of natural disasters (snowdrifts, river floods).

The emergency stockpile of a modern mine must certainly be mechanized. The productivity of the transport equipment for returning coal from the stockpile, given the possible minimum capacity of the bunker facilities, must be determined from the conditions of the weight of the dispatch train and the accepted organization of railway transport operations for supplying cars.

The type of cars supplied will not directly affect the bunker capacity; this factor must be taken into account by the design of the loading bunker and by the organization of loading operations. In other words, the type of railway rolling stock must be taken into account by the loading intensity, which, within the limits of the specified time allowance for loading, will establish the necessary front for loading operations.

Therefore the latter 2 factors, under our conditions, must provide a check on the accepted organization of supplying cars for loading.

Let us first consider the organization of supplying cars to the mine according to schedule.

We shall adopt the following notation:

\(W\) — bunker capacity, in tons.
\(Q\) — daily output of the mine, in tons.
\(G\) — weight of the dispatch train, in tons.
\(n\) — number of hours per day during which the mine operates in issuing coal.
\(q\) — hourly output of the mine, in tons.
\(p\) — hourly productivity of the transport equipment for returning coal from the stockpile.
\(t\) — standard time of the train’s idle time under loading.

Practically, we always have the following condition:

\[ Q > W \quad \text{and} \quad G > W. \]

If the mine must receive trains according to a schedule, then, first of all, proceeding from the conditions of the productivity of the mine and of the transport equipment of the storage facilities, it is necessary to draw up a schedule for receiving trains.

In this case it is necessary to supply the first train at the moment when the mine has prepared a sufficient quantity of coal from current output, accumulated in the bunkers and in the stockpile, for dispatch in the train. Here we must distinguish two possible cases:

1. When there is coal in storage, the first trainload can be accepted at the mine after \(T\) hours from the beginning of the mine’s coal-output operation, which will be equal to:

\[ T=\frac{W}{q}\ \text{hours.} \]

1. When there is no coal in storage, then the first trainload must

\[ \text{be accepted after } T=\frac{W}{q}+\frac{pt}{q}\ \text{hours.} \]

Thus, in both the former and the latter case, the mine will be ready to receive empties after a time \(T\) hours.

During the time that the trainload stands under loading, it is possible additionally, by using the mine’s current output, to load into the cars through the bunkers, as funnels, \(H_T\) tons.

\[ H_T=qt\ \text{tons.} \]

At the same time, during this same period, \(C\) tons must be shipped from the mine storage into the trainload. \(C=pt\) tons.

The next consist of empties can be accepted again after the time interval of a new accumulation of coal necessary for shipping a trainload.

Consequently, in order to obtain the minimum possible capacity of the bunker installations, the delivery of empties, counting from the beginning of the mine’s operation for coal output, must be carried out in the following order:

first delivery—after \(T\) hours,
second delivery—after \(2T+t\) hours,
third delivery—after \(3T+2t\) hours,
third delivery—after \(mT+(m-1)t\) hours.

Under these conditions, the necessary minimum capacity of the bunkers must be determined by the following expression:

\[ W=G-t(q+p)\ \text{tons.}\ .\ .\ .\ .\ .\ .\ .\ .\ .\ \text{I.} \]

Let us now consider the case of organizing the delivery of cars to the mine by notification.

Let \(t_0\) be the interval of time from notification to the moment the empties are delivered to the mine.

Here we must consider two cases:

1) The mine has storage facilities connected with the bunkers by a single transport branch; i.e., the reverse issue of coal from the storage passes through the bunker (a bunker with a scraper storage).

In this case, the required capacity of the bunker must be determined from the following expression:

\[ W=t_0(q+p),\ .\ .\ .\ .\ .\ .\ \text{II.} \]

In this case the most advantageous weight of the dispatch route, under the adopted organization of car delivery to the mine, must satisfy the following condition:

\[ G < (t + t_0)(q + p)\ \text{tons}. \]

2) The mine’s storage facilities constitute an independently operating unit, i.e., the return issue of coal from the storage yard is carried out directly into railway cars.

In this case the bunker capacity is determined by the following expression:

\[ W = t_0 q\ \text{tons}, \ldots \ldots \ldots \mathrm{III}, \]

and the most advantageous weight of the dispatch route in this case must have the following value:

\[ G < t_0 q + t(q + p)\ \text{tons}. \]

Thus, when cars are delivered to the mine by notification, the bunker capacity does not directly depend on the weight of the dispatch route. In this case, both the bunker capacity and the most advantageous route weight are determined as a whole, depending on the operating regime of the railway transport for removing the mineral and on the equipment of the mine’s storage facilities.

Next it is necessary to check the loading-work front—depending on the type of rolling stock of the cars delivered to the mine and on the organization of the loading operations.

In this case the most intensive work will occur when the mine has storage facilities connected with the bunkers in its work of issuing coal from storage, especially if the loading tracks are common both for loading from the bunkers and from storage.

Let us take: \(m\) — the number of cars in the dispatch route.
\(Z\) — the number of cars simultaneously being loaded under the bunkers.
\(\psi\) — the time required for the complete handling of one car under the bunkers (loading, movement).

The time for the complete handling of one car will depend on the type of cars delivered in the route, the shunting means used to move the cars under the loading points, the design of the discharge hatches and bunker gates, and the organization of the loading operations carried out within the loading crews.

Therefore this time value must be adopted on the basis of practical data, i.e., in each individual case it is necessary to study it carefully by making time-study observations at mines having conditions analogous to those of the projected mine.

Taking this opportunity, we express the wish that extensive time-study observations be conducted on

for the principal coal regions of the Union, so that this material may serve as the basis for drawing up new standards. The old standards of Shakhtstroy, as is known, are far from corresponding to actual operating conditions because of their obsolescence, and therefore we do not recommend using them.

Thus, in view of the foregoing, the required work front must be checked by the following expression:

\[ \frac{m}{z}\,\psi \leq t \ldots\ldots\ldots IV. \]

Example.
Let us take the Kirov mine with the following data:
\(G = 1450\) tons; \(t = 2\) h; \(t_0 = 2\) h; \(q = 200\) tons; \(p = 120\) tons.
\(m = 24\) cars of 60 tons of hopper capacity; \(Z = 3\); \(\psi = 15\) min. (assumed).

The mine has facilities connected with bunkers, i.e., coal delivered from the storage yard is transferred by skip lifts into the bunkers.

According to formula I.

\[ W = 1450 - 2(200 + 120) = 810\ \text{tons}. \]

According to formula II.

\[ W = 2(200 + 120) = 640\ \text{tons}. \]

In this case the weight of the route, under the given conditions, should be:

\[ G = (2 + 2)(200 + 120) = 1280\ \text{tons}, \]

In order to maintain the route weight (1450 tons), under the condition that cars are supplied upon notification, it is necessary to design the time of car standing under loading as 2.5 hours, with bunker capacity of 640 tons. Or else increase the notification time interval according to the expression:

\[ t_0 = \frac{G - t(q + p)}{q + p},\quad \text{then} \]

the bunker capacity must increase. Specifically, in our example it comes out to 810 tons, i.e., corresponds to the case of organizing the supply of cars according to schedule.

Let us check the loading-work front.

\[ \frac{24}{3}\cdot 15 = 120\ \text{min.}, \]

i.e., exactly corresponds to the time of car standing under loading. If, however, we go beyond the limits of the time allotted for standing, then the number of loading tracks must be increased.

In conclusion it is necessary to note the following:

1) Equipping the loading complex of a mine with bunker facilities, for economic reasons, we recommend adopting only on condition that the organization of railway transport operations for hauling out the mineral is known.

2) If there is proprietary rolling stock or a railway assigned to the mine, and provided that the distances to the consumer of the mine’s coal are comparatively short, we recommend bunker facilities in all cases.

3) If the railway cannot guarantee any definite arrangement for supplying cars to the mine, we recommend using a bunkerless loading-and-storage system.

1. Bulletin of Scientific-Research Works of the Dnipropetrovsk Branch of the Coal Institute, Nos. 1–2, 1932. ↩↩

2. Railway Loading Bunkers: Standards of Shakhtstroy, 1934 ed.; Basic Provisions of the General Plan for the Mechanization of Mines of the Donets Basin, 1933 ed. ↩