ON THE ISSUE OF ORIENTING THE SURVEY OF SECONDARY WORKINGS

A. I. VOLKOV, P. A. MARCHENKO

(Presented by the scientific seminar of the Department of Mine Surveying and Geodesy)

The distinctive feature of orienting secondary workings is that it can be performed with low accuracy, but necessarily within extremely short time limits.

This circumstance permits the use of rougher instruments and requires the application of such methods of orientation as would make it possible to obtain quickly, under mine conditions, the value of the directional angle of the side being oriented, for the purpose of using it, for example, in setting out directions.

For the reasons indicated, the development of the most rational methods for orienting secondary workings is of great practical interest. At present a whole series of different methods for solving this problem has been proposed; however, in practice the problem of orientation is most often ultimately solved by connecting to the line of plumb bobs by means of a connecting triangle.

Connection by the method of the connecting triangle is very cumbersome, since, in addition to measuring angles, it requires precise linear measurements. Determining the directional angle of the side being oriented in this case is associated with rather complicated computations, which cannot be performed under mine conditions.

In the present article, methods are considered for orienting secondary workings that make it possible, with minimal expenditure of labor and time on field and office work, to solve the stated problem.

1st method. Connection to the line of plumb bobs by an isosceles triangle

The essence of the method, as follows from Fig. 1, is as follows. To determine the directional angle of the side \(CD\), when the directional angle of the line of plumb bobs \(AB\) is known, it is sufficient to measure the angle \(\Theta\) of the isosceles triangle \(1 - C - 2\) and the connection angle \(\beta\). The directional angle of the side \(CD\), from these measurements, is determined from the expression

\[ (CD) = (AB) + \beta - \frac{\Theta}{2} - 90^\circ . \tag{1} \]

An auxiliary isosceles triangle can be created by the method of linear resection of point \(C\) from points \(A\) and \(B\) (plumb lines); however, this requires precise linear measurements and is practically difficult to carry out.

It is very simple to create such a triangle by resecting points 1 and 2 on the alignment of the plumb lines with an inclined sighting ray from point \(C\), located approximately symmetrically with respect to plumb lines \(A\) and \(B\).

Fig. 1. Diagram of connection by an isosceles triangle.

In Fig. 2, the curve \(1abc2\) is the trace of the intersection of the theodolite sighting ray, at a constant inclination angle of the telescope \(-\delta\), with the vertical plane \(V\) passing through the alignment of plumb lines \(AB\). If this curve is intersected by a horizontal straight line, we obtain points 1 and 2, which are the vertices of the isosceles triangle \(1—C—2\), since they are equidistant from point \(C\). The validity of this statement follows from the expression

\[ S_1 = h_1 \cdot \operatorname{ctg}\delta, \tag{2} \]

where \(h_1\) is the height of the horizontal straight line above the instrument horizon (Fig. 2);

\(S_1\) is the horizontal distance from the projections of points 1 and 2 to point \(C\);

\(\delta\) is the inclination angle of the theodolite telescope \((\delta = const)\).

Fig. 2.

The creation of the auxiliary triangle and the solution of the connection problem in this case constitute a single process, since points 1 and 2 on the alignment of the plumb lines are not fixed, but are found in the process of connection.

Performing the Orientation

First of all, plumb lines \(A\) and \(B\) are connected by a horizontal string at such a height that the angle of inclination of the theodolite’s sighting ray, \(\delta\), when sighting from point \(C\), would be no less than \(10\)–\(15^\circ\). This is necessary so that the points of intersection of the sighting ray with the horizontal string are obtained more distinctly. The connecting string must be set strictly horizontally, which can best be done with the aid of a level. However, taking into account the purpose of the orientation, this task can also be performed with a theodolite whose telescope has first been brought into a horizontal position. The connecting string must be light, thin, and well stretched in order to avoid sagging.

Point \(C\) is chosen from the conditions of its symmetry with respect to plumb lines \(A\) and \(B\) and the magnitude of the angle \(\delta\).

The measurement of the angles \(\Theta\) and \(\beta\) at point \(C\) is carried out by the method of repetitions in the following order.

After bringing the theodolite at point \(C\) into working position, the telescope is set at the angle of inclination \(\delta\), and the zero of the horizontal circle limb is brought into coincidence with the zero of the alidade. After this, the connecting string at plumb line \(A\) is sighted, and the reading \((a_1)\) is taken on the horizontal circle.

Fig. 3. View in the field of vision of the theodolite telescope when sighting a horizontal string.

The coincidence of the crosshairs of the reticle with the connecting string, i.e., the determination of the position of point 1 on the alignment of the plumb lines (Fig. 3—a), is accomplished by the micrometer screw of the limb. Having released the alidade, the connecting string at plumb line \(B\) is sighted and the reading \((a_2)\) is taken. The coincidence of the crosshairs of the reticle with the connecting string, i.e., the determination of the position of point 2 on the alignment of the plumb lines (Fig. 3—b), is carried out with the micrometer screw of the alidade. By sighting point \(D\) and taking the reading \((a_3)\), the first half-set of measurements of the angles \(\Theta\) and \(\beta\) is completed. The second half-set, after transiting the telescope through the zenith, is carried out at the same approximate angle of inclination of the telescope \(\delta\) in the manner described above.

The directional angle of the side \(CD\) being oriented, from the angles \(\Theta\) and \(\beta\), should be computed by formula (1) for each half-set separately. The final value of the directional angle of side \(CD\) is taken as the mean value from the half-sets. For control and to increase the accuracy of the orientation, the plumbing should be carried out twice, at different angles \(\delta\) and different positions of the connecting string.

To determine the coordinates of point \(C\), it is necessary to carry out plumbing to one of the plumb lines in its free position by the usual method.

Table 1 gives the values of the directional angles of the oriented side obtained in an experimental orientation as a result of plumbing to the alignment of the plumb lines with a connecting triangle of advantageous form and an isosceles triangle.

The data presented show good agreement of the orientation results when plumbing with connecting and isosceles triangles.

Table 1

Factors Affecting the Accuracy of Adjoining by an Isosceles Triangle

Analysis shows that the accuracy of adjoining by this method depends substantially on two factors: the magnitude of the inclination angle of the theodolite telescope \(\delta\) and the nonhorizontality of the tightening thread. The smaller the angle \(\delta\), the smaller the angle \(\gamma\), visible in the field of view of the telescope, between the tightening thread and the horizontal thread of the reticle (Fig. 3). For a small value of the angle \(\gamma\), the intersection of the above-mentioned threads becomes blurred, and therefore the position of points 1 and 2 is determined with lower accuracy. Experience shows that a value of the angle \(\delta\) of \(10\text{–}15^\circ\) ensures sufficient accuracy of orientation with respect to this factor. The nonhorizontality of the tightening thread has the greatest influence on the accuracy of orientation. When the tightening thread is in a nonhorizontal position, its intersection with the curve \(1abc2\) will occur at different heights; consequently, the distances \(S\), calculated by formula (2), will be different to points 1 and 2, and therefore the triangle will not be isosceles.

The error in determining the direction angle due to this factor, for two independent settings of the tightening thread, may be calculated by the formula

\[ M_{(CD)}'=\pm \frac{L\cdot \operatorname{ctg}\delta \cdot \cos \frac{\Theta}{2}}{V\cdot C}, \tag{3} \]

where \(L\) is the distance from the level (theodolite) to the plumb lines;
\(V\) is the magnification of the telescope;
\(C\) is the distance between the plumb lines.

Calculations show that, under unfavorable conditions of adjoining, when the distance between the plumb lines is no more than one meter and the nonhorizontality of the tightening thread is determined by the difference in height of its ends (on the plumb lines) of 1 mm, the error of the direction angle of the oriented side will be determined with an accuracy of up to \(\pm 10'\).

Method 2. Connecting survey by projecting a direction with angle-measuring instruments

The essence of the method consists in projecting a direction, with the aid of the vertical thread of the reticle of angle-measuring instruments, which makes it possible to sight at large inclination angles.

Projection of a direction by the vertical thread is carried out as follows. The instrument is set up on the upper level near the mouth (or above the mouth) of the raise working in such a way that, when sighting downward, the vertical thread of the telescope is directed along the working of the lower level. On the lower level, a thin wire (cord) is first stretched along the working, one end of which must be firmly fixed at point \(II\) of the theodolite traverse (Fig. 4). The projection of the direction consists

Fig. 4. Scheme for projecting a direction by an inclined ray.

in bringing the vertical thread of the instrument telescope into coincidence with the above-mentioned wire; this is accomplished by moving the unsecured end of the wire and by rotating the instrument about its vertical axis.

In practice, projection and tie-in in this case are performed simultaneously in the following order.

After the instrument has been brought into working position at point \(C\), the zero of the limb of the horizontal circle is brought into coincidence with the zero of the alidade, and sighting is performed

onto point \(B\); on the instrument horizon a reading \((a_1)\) is taken. Having unclamped the alidade, they sight on the wire, bringing the latter into coincidence with the vertical thread, and take a reading \((a_2)\). The moving end of the wire at this time (at the moment of coincidence) is marked by point \(I'\). The tube is transited through the zenith, and the actions indicated above are performed for the other position of the tube. As a result, the reading \((a_3)\) and point \(I''\) are obtained.

The final value of the contact angle is taken to be the angle \(\beta\), computed by the formula

\[ \beta = \frac{a_3 - a_1}{2}, \tag{4} \]

and the oriented direction is taken to be the direction \(II-I\), drawn through point \(II\) and point \(I\), which bisects the distance \(I' - I''\) (Figs. 4–6).

If the lower horizon is being oriented, the work on it is completed at this point. When orienting the upper horizon, it is additionally necessary to measure the angle \(\beta_1\) at point \(II\)—between the fixed direction \(II-III\) and the direction \(II-I\). To transfer coordinates, it is necessary to mark an arbitrary point \(K\) on the wire and to measure the angle of inclination and the inclined length \(C-K\), as well as the distance \(K-II\).

3rd method. Connecting survey by direct contact with the side being oriented

The essence of this method is based on the property of perpendicularity of the collimation plane of an angle-measuring instrument and the plane passing through the line of sight and the horizontal thread of the reticle.

Figure labels: line of sight of the telescope; horizontal thread of the reticle, brought into coincidence with direction \(1-2\); \(90^\circ\); \(\beta\); points \(1\), \(2\), \(C\), \(B\).

Fig. 5. Diagram of contact with the direction being oriented.

As can be seen from Fig. 5, in order to determine the direction angle of the oriented side \(1-2\) (on the lower horizon) or \(CB\) (on the upper horizon), it is necessary to bring the horizontal thread of the instrument into coincidence,

installed at point \(C\), with direction \(1—2\), and measure the angle \(\beta\). Then the directional angle of side \(1—2\) is determined by the formula

\[ \alpha_{(1—2)} = \alpha_{(BC)} + \beta - 90^\circ, \tag{5} \]

and, correspondingly, for side \(CB\) we shall have

\[ \alpha_{(CB)} = \alpha_{(1—2)} - \beta + 270^\circ. \tag{6} \]

In practice, the task of carrying out the connection is performed in the following order.

Near the mouth of the raise working, or above it at point \(C\), the instrument is set up. After bringing the instrument into working position, the zero of the limb of the horizontal circle is aligned with the zero of the alidade and sighted on point \(B\), and a reading \((a_1)\) is taken. Having unclamped the alidade, they sight through the raise with the horizontal thread onto a wire previously stretched between points 1 and 2 in such a way that the horizontal thread of the reticle can be brought into coincidence with it, and take a reading \((a_2)\). Turning the telescope through the zenith, measurements are made at the other position of the telescope, ending the measurements by taking a reading \((a_3)\). The value of the angle \(\beta\) is computed by formula (4). To transfer the coordinates it is necessary to mark the cross of the reticle threads on the wire (point \(K\)) at the moment when the latter is brought into coincidence with the horizontal thread, to measure the inclined distance \(C—K\) and the angle of inclination, and also the distance from point \(K\) to points 1 or 2.

If, when sighting on the wire, the angle of inclination is less than \(90^\circ\), then the wire must be set horizontally, since non-horizontality of the wire, in this case, affects the accuracy of determining the directional angle of the side being oriented.

Before work, the horizontal thread of the reticle of the theodolite telescope must be set horizontally, since it should be remembered that orientation at two positions of the telescope does not eliminate the error due to this factor¹.

Depending on the arrangement of the mine workings on the upper and lower horizons, the wire may occupy different positions relative to the axes of these workings, i.e., it may be situated simultaneously along one of them and perpendicular to the other. In this case, for carrying out the connection survey, a combination of the three methods indicated above may be applied.

Instruments

For connection to the alignment of plumb lines by an isosceles triangle, any available mine theodolite or angle meter may be used.

When carrying out a connection survey by the second and third methods, mine theodolites and angle meters may be used which, as indicated above, permit sighting at a large angle of inclination.

These requirements are met by angle meters (U-1, U-2, U-3, UTG), mine theodolites TGO and TGS, theodolites equipped with an objective attachment, and also theodolites with eccentric telescopes².

The design of type-U inclinometers, as can be seen from Fig. 6, makes it possible to carry out sighting at any angle of inclination. This is achieved thanks to the eccentric arrangement of the telescope relative to its horizontal axis of rotation. Since the line of sight of the telescope, in any of its positions, coincides with the plane passing through the vertical axis of the instrument, horizontal angles are measured with these inclinometers without distortion.

Sighting with the TGO theodolite at an inclination angle of up to 80° is accomplished by means of a window in the limb and two windows in the limb casing (Figs. 7, 8). The TGS theodolite differs from the TGO theodolite in that it has a limb with spokes. Experimental models of these theodolites were manufactured by the Kharkov Plant of Mine-Surveying Instruments and successfully passed production tests at the Severnaya mine of the Kemerovougol trust.

Fig. 6.

Such theodolites can be manufactured by any workshop for the repair of mine-surveying and geodetic instruments, using for this purpose an ordinary mining theodolite (of any make), the telescope of which can be moved through the zenith by means of an objective elbow.

4th method. Connecting survey by means of a traverse through steeply inclined and vertical workings

A connecting survey by laying a traverse through steeply inclined and vertical workings can be carried out with any inclinometer instruments that make it possible to sight at large angles of inclination; however, a special inclinometer may be used more conveniently for this purpose (Fig. 9).

The design of the inclinometer consists of a limb (1), the vertical axis of which (2) rotates in special bearings (3) mounted in a rigid bracket (4). The inclinometer is provided with a vernier (5), which makes it possible to take readings, the accuracy of which depends on the division value of the limb and the number of divisions of the vernier. The sighting device of the inclinometer is a tape or measuring cord (6), which, by means of a light arc (7), is fastened to the limb at two points located on its diameter. For operation, the inclinometer is mounted on brackets. Measurement of inclination angles is carried out with a suspended semicircle.

Surveying with the inclinometer is performed in the following order. The inclinometer is set in working position at the vertex of the angle being measured. The tape (cord) is stretched so that it passes through the rear sighting point. In this position of the tape, a reading is taken on the limb \((a_1)\), and the length and angle of inclination of the sighting line are measured. Sighting to the forward point is carried out in the same way. As a result, a reading \((a_2)\), the distance to the forward point, and

Fig. 8. General view of a theodolite of the TTO and TTS type.

Fig. 7. The limb of the theodolite with a window for sighting.

angle of inclination. The traverse angle is taken as the angle \(\beta = a_2 - a_1\). With this method of carrying out the survey, the lengths of the lines and the angles of inclination are measured in the forward and reverse directions.

Fig. 9. Angle meter for surveying steeply dipping workings.

An angle meter of this design was proposed and manufactured by the Department of Mine Surveying of the Tomsk Polytechnic Institute in 1951 and tested at mine 9—15 of the “Anzherougol” trust.

Later, on the basis of this model, such an angle meter was manufactured by employees of the mine-surveying bureau of the Tashtagol mine of the KMK, which they use at the present time for surveying secondary workings, including the surveying of boreholes.

Tests of this angle meter at the same mine showed the following results. In a closed traverse laid out with this angle meter from the main level to the level of the raises and back, 10 horizontal angles and 10 sides were measured (with a total length of 52 m). Two sides of this traverse had angles of inclination \(+54^\circ\) and \(-59^\circ\). The angular misclosure of the traverse was \(\pm 4'\), and the relative linear misclosure was \(\frac{1}{200}\).

The conditions for orienting secondary workings are very diverse, and therefore it is difficult to propose a single universal method. Depending on the specific conditions, the mine surveyor must himself choose

…to choose one of the most rational methods, or a combination of them, so as to solve the problem posed in the simplest and most reliable way. The methods considered in the present work make it possible to broaden the scope for such a choice.

REFERENCES

1. Volkov, A. I.; Marchenko, P. A. Connection to the plumb-line alignment by means of an isosceles triangle. Proceedings of Higher Educational Institutions, Mining Journal, No. 11, 1960.

2. Volkov, A. I. Mining theodolites TGO and TTS. Proceedings of the Tomsk Polytechnic Institute, No. 118, 1961.

3. Orlovskii, V. S. Surveying steeply dipping workings using optical orientation. Collection of Articles on Problems of Mine Surveying, Collection XXXVII, VNIMI publication, 1959.

1. The influence of non-horizontality of the horizontal thread of the theodolite telescope on the accuracy of orientation can be eliminated only provided that the theodolite is set up, at the first and second positions of the telescope, on opposite sides of the direction being oriented. ↩

2. The use of theodolites with an eccentric telescope for carrying out a connection survey is described in the journal Ugol’, No. 5, 1950. ↩