Instruments

The instrument primarily used for leveling is the (engineer's) level in association with a graduated rod known as leveling rod or leveling staff.

Level

A schematic diagram of an engineer's level is shown in Figure 11.1. An engineer's level primarily consists of a telescope mounted upon a level bar which is rigidly fastened to the spindle. Inside the tube of the telescope, there are objective and eye piece lens at the either end of the tube. A diaphragm fitted with cross hairs is present near the eye piece end. A focussing screw is attached with the telescope. A level tube housing a sensitive plate bubble is attached to the telescope (or to the level bar) and parallel to it. The spindle fits into a cone-shaped bearing of the leveling head. The leveling head consists of tribrach and trivet with three foot screws known as leveling screws in between. The trivet is attached to a tripod stand.

Functions of Salient Parts

Telescope : used to sight a staff placed at desired station and to read staff reading distinctly.

Diaphragm : holds the cross hairs (fitted with it).

Eye piece : magnifies the image formed in the plane of the diaphragm and thus to read staff during leveling.

Level Tube : used to make the axis of the telescope horizontal and thus the line of sight.

Leveling screws : to adjust instrument (level) so that the line of sight is horizontal for any orientation of the telescope.

Tripod stand : to fix the instrument (level) at a convenient height of an observer.

Dumpy Level

A dumpy level is most suitable when from one setting of the instrument, elevations of several points are to be determined. (Figure 11.2)

(a) (b)

Figure 11.2 Two Types of Dumpy Levels

Distinctive Features of an Dumpy Level

The optical axis of the telescope of a dumpy is placed perpendicular to the axis of the centre spindle. The axis of its level tube is permanently placed so that it lies in the same vertical plane as the optical axis

IOP Level

(Figure 11.3) A IOP level is most suitable when only few readings are to be taken from one setting of the instrument.

Figure 11.3 IOP Level

Distinctive Features of an IOP Level

The telescope is mounted on a transverse fulcrum at the vertical axis fitted with a micrometer screw at the eye-piece end of the telescope.

Instrument is leveled using circular spirit level. The sensitive plate-bubble is to be leveled using micrometer screw, at the time of taking measurement. Thus, the line of sight is made horizontal quickly, even though the instrument as a whole may not be exactly level.

Digital level

There are fundamentally two types of automatic levels.

First, the optical one whose distinguishing feature is self-leveling i.e., the instruments gets approximately leveled by means of a circular spirit level and then it maintains a horizontal line of sight of its own.

Second, the digital levels whose distinguishing features are automatic leveling, reading and recording (Figure 11.4).

The chief features of a digital level are:

A CCD (Charged coupled device) at the plane of diaphragm. It captures an image of the rod and processes it resulting in a rod reading and a distance to the rod.

A data collector which keeps the level notes, performs checks and keeps a record of every rod reading and elevation automatically.

A bar-coded rod having a scale represented through a series of bars of different widths. Bars are spaced constantly or variably. The spacing and width of the bars denote the code.

Advantages of digital levels include the speed of leveling, the virtual elimination of rod reading and calculation errors and the accuracy in reading rod.

Limitation of digital level lies in its range. Beyond a certain limit it is to be used in “manual mode”.

Leveling Staff

It is a self-reading graduated wooden rod having rectangular cross section. The lower end of the rod is shod with metal to protect it from wear and usually point of zero measurement from which the graduations are numbered. Staff are either solid (having single piece of 3 meter height) (Figure 11.5) or folding staff (of 4 meter height into two or three pieces) (Figure 11.6). The least count of a leveling staff is 5 mm.

Temporary Adjustment of Level At each set up of a level instrument, temporary adjustment is required to be carried out prior to any staff observation. It involves some well defined operations which are required to be carried out in proper sequence.

Temporary Adjustment of a Dumpy Level

The temporary adjustment of a dumpy level consists of Setting , Leveling and Focusing .

During Setting, the tripod stand is set up at a convenient height having its head horizontal (through eye estimation). The instrument is then fixed on the head by rotating the lower part of the instrument with right hand and holding firmly the upper part with left hand. Before fixing, the leveling screws are required to be brought in between the tribrach and trivet. The bull's eye bubble (circular bubble), if present, is then brought to the centre by adjusting the tripod legs.

Next, Leveling of the instrument is done to make the vertical axis of the instrument truly vertical.

It is achieved by carrying out the following steps:

Step 1: The level tube is brought parallel to any two of the foot screws, by rotating the upper part of the instrument.

Step 2: The bubble is brought to the centre of the level tube by rotating both the foot screws either inward or outward. (The bubble moves in the same direction as the left thumb.)

Step 3: The level tube is then brought over the third foot screw again by rotating the upper part of the instrument.

Step 4: The bubble is then again brought to the centre of the level tube by rotating the third foot screw either inward or outward.

Step 5: Repeat Step 1 by rotating the upper part of the instrument in the same quadrant of the circle and then Step 2.

Step 6: Repeat Step 3 by rotating the upper part of the instrument in the same quadrant of the circle and then Step 4.

Step 7: Repeat Steps 5 and 6, till the bubble remains central in both the positions.

Step 8: By rotating the upper part of the instrument through 180 ° , the level tube is brought parallel to first two foot screws in reverse order. The bubble will remain in the centre if the instrument is in permanent adjustment.

Focusing is required to be done in order to form image through objective lens at the plane of the diaphragm and to view the clear image of the object through eye-piece. This is being carried out by removing parallax by proper focusing of objective and eye-piece. For focusing the eye-piece, the telescope is first pointed towards the sky. Then the ring of eye-piece is turned either in or out until the cross-hairs are seen sharp and distinct. Focusing of eye-piece depends on the vision of observer and thus required whenever there is a change in observer. For focusing the objective, the telescope is first pointed towards the object. Then, the focusing screw is turned until the image of the object appears clear and sharp and there is no relative movement between the image and the cross-hairs. This is required to be done before taking any observation.

Temporary Adjustment of an IOP Level

Temporary adjustment of a tilting level requires the same operations as in case of a dumpy level except the operations involved in leveling. During leveling, first the IOP instrument is leveled roughly with the leveling screws till the circular bubble is in the centre. Then, the bubble of the level tube is brought to the centre by using the tilting screw. In case of IOP level, the bubble is required to be leveled using tilting screw before each reading is taken.

Permanent Adjustment of Level

Introduction

An instrument from manufacturer is generally available in perfect adjustments. However, the instrument gets out of adjustments due to worn out and loose fittings or due to mishandling. So it is required to check the instruments occasionally especially before any precise survey work to ensure that the instrument is in perfect adjustment.

Fundamental Lines of a Level

There are three fundamental lines in a level instrument (Figure 12.1). These are

Vertical axis Axis of the level tube Line of sight

Relations among Fundamental Lines

(Figure 12.2) In a properly adjusted dumpy level, desired relations among fundamental lines are

1. Axis of the level tube is perpendicular to the Vertical axis 2. Horizontal cross hair should lie in a plane perpendicular to the Vertical axis, so that it will lie

in a Horizontal plane when the instrument is properly leveled. 3. The Line of sight is parallel to the axis of the level tube.

Also, the optical axis, the axis of the objective lens and the line of sight should coincide.

Permanent Adjustment of Level

The permanent adjustment of a level is tested by finding the relative position of fundamental lines.

Permanent Adjustment of Dumpy Level

If any fundamental relation is found to be disturbed in a dumpy level, the cross-hairs and level tube are adjusted so that the fundamental relations get satisfied. The reference line for the adjustments in dumpy level is the vertical line which remain fixed in direction, as it depends upon the direction of gravity.

Axis of the Level Tube is Perpendicular to the Vertical axis

Test

After setting and leveling the level, turn the telescope through 180 ° about its vertical axis. If the bubble remains central, the axis of the level tube is perpendicular to the Vertical axis. Otherwise, a displacement of the bubble from the central position indicates that the tube is not in adjustment. The amount of displacement is double the amount of error, by the principle of reversion (Figure 12.3).

Adjustment

Step 1: With the help of capstan screw, one end of the level tube is raised or lowered, as needed, so

that the bubble is halfway back to the centre position.

Step 2: With the help of leveling screws, the other half of the displacement is moved further to bring the bubble at centre.

The steps are repeated until the adjustment is perfected.

Horizontal Cross Hair Should Lie in a Plane Perpendicular to the Vertical axis

Test

A well-defined point is focused along the horizontal cross hair on one side of the field of view. The instrument (telescope) is then rotated about its vertical axis. If the point appears to travel along the horizontal cross-hair, the instrument is in adjustment i.e., the horizontal cross-hair lies in a plane perpendicular to the Vertical axis. Otherwise, there is a need for adjustment.

Adjustment

Let us rotate the instrument in such a way that the well defined point occupy a position on the opposite side of the field of view, say X' (Figure 12.4). The cross hair ring is then rotated by loosening two adjacent capstan screws. Repeat the process until the point travels along the horizontal cross hair.

The Line of Sight is Parallel to the axis of the Bubble Tube

Test

Two pegs are set at some distance (of about 60 to 90 m) on a fairly level ground. A dumpy level is set up on a point which is equidistant from the pegs and preferably, in a line with the pegs. Staff readings are taken at the pegs, say the readings are a and b respectively. Then, the true difference in elevation between the points is h = (a b). Now, the instrument is set on the line joining the pegs near one of the pegs but opposite to the other peg, as shown in Figure 12.5. Let D1 and D2 are the distances of the near and far peg from the instrument position. Staff readings are again taken at the pegs, say the readings are c and d respectively. Then, the apparent difference in elevation between the points is h' = (c d). Now, if h' is found to be equal to h, the line of sight of the level is parallel to the axis of the bubble tube. Otherwise, an adjustment of the bubble tube is required.

Adjustment

Step 1: The amount of error (e) associated with the observation is determined from

e = h h ' = (a b) – (c d)

Step 2: The error e occurs in a distance of D = D2 - D1. Assuming the error e is positive and the line of sight is inclined upward, the error in distance D2

Step 3: Calculate the correct staff reading at the distant peg as

Step 4: The capstan screws at the top and bottom of the diaphragm ring is then loosened and the ring is moved vertically so that the line of sight intersect the distant staff at d'.

Step 5: To check the adjustment, read the staff reading on the near peg and it should read

If the near staff reading is not c', then repeat Step 4 and till Step 5 is satisfied.

This method is known as two peg method. In this method, due account need to be taken about sign throughout the test.

Example

Ex12-1 A dumpy level was set up midway between two peg points 100m apart. The readings on the staff at the two pegs were 1.650m and 1.210m respectively. The instrument was then moved, by 10 m ahead of the second peg, in line with the two pegs. The respective staff readings were 1.405m and 0.935m. Calculate the staff readings on the two pegs to provide a horizontal line of sight.

Solution:

Let A and B be the two peg points at a distance of 100m and the instrument position be C when midway and D when 10m from B.

While the instrument is at C,

True difference in elevation between the peg points is obtained and is given by, d = 1.650-1.210 = 0.440m (B higher than A)

Assuming there is no error in the line of collimation of the instrument, while the instrument is at D,

If the staff reading at B i.e., 0.935 is correct. Then, the staff reading at A should be = (0.935 +0.440) m = 1.375 m (< observed reading i.e., 1.405m)

This shows that the line of collimation of the instrument is not in adjustment and it is inclined upward.

The amount of error = 1.405 - 1.375 =0.030m in 100m

Thus, error in 10m i.e., the staff reading at B while the instrument is at D = 0.003m

The correct staff reading at B while the instrument is at D should be = 0.935- 0.003 = 0.932m

And that at A, 0.932+0.440=1.372m

(Verification: The correct staff reading at B while the instrument is at D should be = 1.405 - 0.003 x 11 = 1.372 m)

Permanent Adjustment of Tilting Level

In case of tilting level, it is not essential that the vertical axis of the instrument should be truly vertical. Therefore, the first fundamental relation is not required to be satisfied.

The second fundamental relation is being tested and if necessary, adjusted as given in case of dumpy level.

The third fundamental relation is tested and if necessary, adjusted as given in case of dumpy level, with following modifications after Step 3.

Step 4: The tilting screw is used to bring the line of sight to intersect the distant staff at d'.

Step 5: The bubble is then brought to the centre by means of the capstan screws on the bubble tube.

Step 6: The test and adjustment is repeated till the bubble remains central when the staff reading is d'.

Note:

In case of a dumpy level, the line of sight is moved by adjusting the diaphragm but in case of tilting level bubble is centred by adjusting capstan screws on the bubble tube.

Permanent Adjustment of Automatic Level

In case of automatic level, prior to leveling, the circular bubble and the activity of the compensator are required to be checked. In this case, after setting the instrument, the circular bubble is brought to the centre of the engraved circle. Then, the instrument is rotated through 180° or to a direction in which the displacement of the bubble is maximum. If the displacement is less than half the diameter of the bubble, the instrument is in adjustment. Otherwise, an adjustment is necessary.

Adjustment is performed in two steps by reducing the horizontal and vertical components of the displacement and bringing the bubble to the centre of the engraved circle. First remove the half of horizontal component of displacement using the appropriate level screws.and then remove the remaining half by manipulating the adjusting screws. Next, one-half the vertical component of displacement (Figure 12.6) is then removed by the level screws and the remainder is compensated using the adjusting screws to bring the bubble to the center of the engraved circle. Turn 180° and check the bubble. Repeat the entire procedure until the bubble remains centered in all positions.

To check the compensator, sight a target about 30 m away. Center the bull's-eye bubble. Next, tap one tripod leg with a hand. The image of the target will appear to swing in the field of view but the target will return to its original position. Next, turn a level screw, causing the line of sight to slope slightly. Once again the target will appear to swing but will return to the original Position. This indicates that the instrument is in adjustment. Otherwise, an adjustment is necessary.

For automatic level also, the third fundamental relation is tested by two peg test but for permanent adjustment manual of the instrument is required to be referred.

Basic Principle of Leveling

The fundamental principle of leveling lies in finding out the separation of level lines passing through a point of known elevation (B.M.) and that through an unknown point (whose elevation is required to be determined).

With reference to Figure 13.1, let X represents a point of known elevation (Hx) or a B.M. and Y be a point whose elevation is required to be determined. To find out the unknown elevation of Y, a level is set up at L in between X and Y. A leveling staff is first held at X and a reading hx is observed, by sighting the staff (held vertical to the line of sight of the level). The staff reading at Y, say hy is then observed. The elevation of the point Y (say Hy) is thus given by Hx + (hx ~ hy) i.e., known elevation (Hx ) added to the separation of level lines (hx ~ hy) passing through the points.

Methods of Leveling

Direct Leveling : Direct measurement, precise, most commonly used; types:

Simple leveling : One set up of level. To find elevation of points.

Differential leveling : Numbers of set-ups of level. To find elevation of non-intervisible points.

Fly leveling : Low precision, to find/check approximate level, generally used during reconnaissance survey.

Precise leveling : Precise form of differential leveling.

Profile leveling : finding of elevation along a line and its cross section.

Reciprocal leveling : Along a river or pond. Two level simultaneously used, one at either end.

Indirect or Trigonometric Leveling : By measuring vertical angles and horizontal distance; Less precise.

Stadia Leveling : Using tacheometric principles.

Barometric Leveling : Based on atmospheric pressure difference; Using altimeter; Very rough estimation.

Differential Leveling

Applied to determine the elevation of point which is some distant apart from B.M i.e., the unknown elevation of a point cannot be determined in a single set up of an instrument. Thus, in this method, instrument gets setup number of times to observe reading along a route in between observed points. For each set up, staff readings are taken back to a point of known elevation (first sight from the B.M and forward to a point of unknown elevation) final sight to the terminal station.

Procedure

Let us consider a station B whose elevation is to be established with reference to a B.M station A, quite a distant apart. In establishing the station B as B.M., differential leveling is carried out starting from A and terminating at B. In order to carry out the leveling, first the instrument is set up at some location, say I1 (Figure 13.2), in such a way that backsight reading taken on A can be read clearly. The staffman is then directed to move forward towards B and choose a point, say S1 which is firm and stable. It is preferable that the distance of S1 from I1be the same as that of station A from I1. After proper selection of the point S1, staff is held to take the foresight reading for this instrument set up. The instrument is then shifted to some other position in forward direction, say I2 towards B and take the backsight reading on S1. Thus, point S1 is used as a turning point. From I2 foresight reading is taken to another well chosen (as followed in S1) turning point S2. Finally, from I3 backsight is taken on S2 and last sight at the terminal point B.

Field Book

A field book, also called level book is being used for taking down each staff reading during leveling and subsequently, used for finding out the elevation of points/ stations. There are two types of level books (Table 13.1 and Table 13.2). Usually, level book contains columns of both the types together (Table 13.3) and it is for a surveyor to use only the relevant columns only.

Reduction of Level

The observed staff readings as noted in a level book are further required to be manipulated to find out the elevation of points. The operation is known as reduction of level. There are two methods for reduction of levels:

1. Rise and Fall method and 2. Height of instrument method.

Rise and Fall Method

For the same set up of an instrument, Staff reading is more at a lower point and less for a higher point. Thus, staff readings provide information regarding relative rise and fall of terrain points. This provides the basics behind rise and fall method for finding out elevation of unknown points.

With reference to Figure 13.2, when the instrument is at I1, the staff reading at A (2.365m) is more

than that at S1 which indicates that there is a rise from station A to S1 and accordingly the difference

between them (1.130m) is entered under the rise column in Table 13.1. To find the elevation of S1 (

101.130m), the rise (1.130m) has been added to the elevation of A (100.0m). For instrument set up

at I2 , S1 has been treated as a point of known elevation and considered for backsight (having

reading 0.685m) . Foresight is taken at S2 and read as 3.570m i.e, S2 is at lower than S1 . Thus,

there is a fall from S1 a nd S2 and there difference (2.885m) is entered under the fall column in Table

13.1. To find the elevation of S2 ( 98.245m), the fall (2.885m) has been subtracted from the elevation

of S1(101.130m). In this way, elevation of points are calculated by Rise and Fall method.

Height of Instrument Method

In any particular set up of an instrument height of instrument, which is the elevation of the line of sight, is constant. The elevation of unknown points can be obtained by subtracting the staff readings at the desired points from the height of instrument. This is the basic behind the height of instrument method for reduction of level.

With reference to Figure 13.2 and Table 13.2, when the instrument is at I1, the staff reading

observed at A is 2.365m. The elevation of the line of sight i.e., the height of instrument is 102.365m

obtained by adding the elevation of A (100.0m) with the staff reading observed at A (2.365m). The

elevation of S1 (101.130m) is determined by subtracting its foresight reading (1.235m) from the the

height of instrument (102.365m) when the instrument is at I1 . Next, the instrument is set up at I2.

S1 is considered as a point of known elevation and backsight reading ( 0.685m) is taken . The height

of the instrument (101.815 m) is then calculated by adding backsight reading ( 0.685m) with the

elevation (R.L.) of point S1 (101.130m). Foresight is taken at S2 and its elevation (98.245m) is

determined by subtracting the foresight (3.570m) from the height of the instrument (101.815 m). In

this way, elevation of points are calculated by Height of instrument method.

Ex13-1 Data from a differential leveling have been found in the order of B.S., F.S..... etc. starting with the initial reading on B.M. (elevation 150.485 m) are as follows : 1.205, 1.860, 0.125, 1.915, 0.395, 2.615, 0.880, 1.760, 1.960, 0.920, 2.595, 0.915, 2.255, 0.515, 2.305, 1.170. The final reading

closes on B.M.. Put the data in a complete field note form and carry out reduction of level by Rise and Fall method. All units are in meters.

Solution :

B.S. (m) F.S. (m) Rise (m) Fall (m) Elevation (m) Remark 1.205 150.485 B.M.

0.125 1.860 0.655 149.830

0.395 1.915 1.7290 148.040

0.880 2.615 2.220 145.820

1.960 1.760 0.880 144.940

2.595 0.920 1.040 145.980

2.255 0.915 1.680 147.660

2.305 0.515 1.740 149.450

1.170 1.135 150.535 B.M.

Arithmetic Check for Reduction of Level

In case of Rise and Fall method for Reduction of level, following arithmetic checks are applied to verify calculations.

B.S. - F.S. = Rise - Fall = Last R.L. - First R.L.

With reference to Table 13.3:

B.S. - F.S. = 4.795 - 7.145 = - 2.350

Rise - Fall. = 1.130 - 3.480 = - 2.350

Last R.L. - First R.L.= 97.650 - 100.000 = -2.350

Table 13.3 Field book for Reduction of level

Staff Reading (m) Difference in elevation (m) H.I (m) R.L. (m) Remarks

Points B.S. I.S. F.S. Rise Fall

A 2.365 102.365 100.000 B.M.

S 1 0.685 1.235 1.130 101.815 101.130 T.P.1

S2 1.745 3.570 2.885 99.990 98.245 T.P.2

B 2.340 0.595 102.365 97.650

4.795 7.145 3.480 101.815

Ex13-2 Carry out the arithmetic checks for Reduction of level of Ex13-1.

Solution :

B.S. = 11.720 m; F.S. = 11.670 m

Therefore B.S - F.S. = 0.050 m

Rise = 5.595 m; Fall = 5.545 m

Therefore Rise - Fall = 0.050 m

Last R.L. - First R.L. = 150.535 - 150.485 = 0.050 m.

B.S - F.S. = Rise - Fall = Last R.L. - First R.L.

Ex13-3 Complete the differential-level notes and determine the error of closure of the level circuit and adjust the elevations of B.M.2 and B.M.3 assuming that the error is constant per set up.

Level book note for Level Net

Staff Reading Height of Instrument (m)

R.L. (m)

Points B.S (m) F.S.(m)

B.M.1 2.125

T.P.1 1.830 2.945

T.P.2 2.100 3.225

T.P.3 1.650 3.605

B.M.2 2.365 2.805

T.P.4 2.885 2.530

T.P.5 3.065 2.350

B.M.3 3.855 1.100

T.P.6 3.270 1.660

T.P.7 3.865 2.110

B.M.1 3.455

Solution :

Staff Reading Height of Instrument (m)

R.L. (m)

Points B.S (m) F.S.(m)

B.M.1 2.125 102.125 100.000

T.P.1 1.830 2.945 101.010 99.18

T.P.2 2.100 3.225 99.885 97.785

T.P.3 1.650 3.605 97.93 96.280

B.M.2 2.365 2.805 97.49 95.125

T.P.4 2.885 2.530 97.845 94.960

T.P.5 3.065 2.350 98.56 95.495

B.M.3 3.855 1.100 101.315 97.46

T.P.6 3.270 1.660 102.925 99.655

T.P.7 3.865 2.110 104.680 100.815

B.M.1 3.455 101.225

Error of closure = 101.225 - 100 = + 1.225 m

There are ten (10) set up for the instrument. Thus for each set up, there is an error of 0.1225 m.

Therefore correction for each set up = - 0.1225 m

Adjusted elevation of B.M.2 = 95.125 - 4 x .1225 = 94.635 m

Adjusted elevation of B.M. 3 = 97.46 - 7 x .1225 = 96.603 m

Level Net

To establish a set of bench marks, each B.M. is also used as a turning point. Elevation of B.Ms are checked by terminating to a previously established bench mark or by returning to the initial bench mark. A line of levels that ends at the point of beginning is known as level net. The final observation in a level net is thus a foresight on the initial B.M. The elevation of each B.M. is to be kept checked within the prescribed limit of error.

Tale 13.4 Permissible limit of error in level net

Order Class Limit (mm) Remark

First I

K is the distance in km

II

Second I

II

Third

Ex.13-3 Data from a differential leveling have been found in the order of B.S., F.S..... etc. starting with the initial reading on B.M. (elevation 150.485 m) are as follows : 1.205, 1.860, 0.125, 1.915, 0.395, 2.615, 0.880, 1.760, 1.960, 0.920, 2.595, 0.915, 2.255, 0.515, 2.305, 1.170. The final reading closes on B.M.. Put the data in a complete field note form and carry out reduction of level by Height of instrument method. All units are in meters.

For Exercise 13

Ex.13-3

B.S. (m) F.S. (m) Rise (m) Fall (m) Elevation (m) Remarks

1.205 150.485 B.M.

0.125 1.860 0.655 149.830

0.395 1.915 1.790 148.040

0.880 2.615 2.220 145.820

1.960 1.760 0.880 144.940

2.595 0.920 1.040 145.980

2.255 0.915 1.680 147.660

2.305 0.515 1.740 149.400

1.170 1.135 150.535 B.M.

B.S. - F.S. = 11.720 - 11.670 = 0.05 m

Rise - Fall = 5.595 - 5.545 = 0.05 m

Profile Leveling

Profile leveling is a method of surveying that has been carried out along the central line of a track of land on which a linear engineering work is to be constructed/ laid. The operations involved in determining the elevation of ground surface at small spatial interval along a line is called profile leveling. The route along which a profile is run may be single straight line, as in case of a short sidewalk; a broken line, as in the case of a transmission line or sewer; or a series of straight lines connected by curves, as in case of a railroad, highway or canal.

Stations

The line along which the profile is to be run is to be marked on the ground before taking any observation. Stakes are usually set at some regular interval which depends on the topography, accuracy required, nature of work, scale of plotting etc. It is usually taken to be 10 meter. In addition, stakes are placed at locations where marked changes in slope occur; a change in direction occur; at critical points like culverts, bridges and other features crossing the alignment. The beginning station of profile leveling is termed as 0+00. Points at multiples of 100m from this point are termed as full stations. Intermediate points are designated as pluses. For example, a point that is 153.25m from the beginning point of the survey is station 1+53.25 i.e., the point is 53.25m beyond the first full station.

Procedure

In carrying out profile leveling, a level is placed at a convenient location (say I1) not necessarily along the line of observation (Figure 14.1). The instrument is to be positioned in such a way that first backsight can be taken clearly on a B.M. Then, observations are taken at regular intervals (say at 1, 2, 3, 4) along the central line and foresight to a properly selected turning point (say TP1). The instrument is then re-positioned to some other convenient location (say I2). After proper adjustment of the instrument, observations are started from TP1 and then at regular intervals (say at 5, 6 etc) terminating at another turning point, say TP2 . Staff readings are also taken at salient points where marked changes in slope occur, such as that at X.

The distance as well as direction of lines are also measured.

Field Book Note

The notes of profile leveling are recorded in a level note book where backsights, intermediate sights and foresights are placed in independent columns. The distances of points as well as direction of lines are also noted in separate columns (Table 14.1).

In case of profile leveling as shown in Figure 14.1, for instrument position at l1, the first backsight (B.S) is taken at B.M and the reading of 3.005m is placed in its column in the row of station A (Table 14.1). Then, intermediate sights 2.285m, 1.560m, 1.785m, 2.105m respectively at stakes 1,2,3,4 are placed in the corresponding row. The first foresight 3.105m taken at station B is placed in its row. From changed instrument location l2, a backsight 2.875m is taken at B and it is entered in the B.S. column in the row of B. Thus, at station B, both backsight and foresight readings are entered. The intermediate sights 3.465m, 3.955m, 3.120m, 3.015m, 2.580m, 1.955m respectively at stakes 5, X, 6, 7, 8, 9 are placed in their corresponding row. The foresight 1.465m taken at station C is placed in its row.

Table 14.1 Field book for Reduction of Level

Pegs Distance(m) Direction Staff Reading (m)

Difference in Elevation (m) H.I (m) R.L(m) Remarks

B.S I.S F.S Rise Fall

A 3.005 108.620 105.615 B.M.

1 0+00 2.285 0.720 106.335

2 0+10 1.560 0.725 107.060

3 0+20 1.785 0.225 106.835

4 0+30 2.105 0.320 106.515

B 0+40 2.875 3.105 1.000 108.390 105.515 T.P.1

5 0+50 3.465 0.590 104.925

X 0+53.35 3.955 0.490 104.435

6 0+60 3.120 0.835 105.270

7 0+70 3.015 0.105 105.375

8 0+80 2.580 0.435 105.810

9 0+90 1.955 0.625 106.435

C 1+00 1.465 0.490 106.925 T.P.2

5.880 4.570 3.935 2.625

Calculation of Reduced Level

Reduction of levels can be done either by height of instrument method or by rise and fall method. In Table 14.1, computations have been carried out by both the methods and subsequently their checks are done.

Table 14.1 Field book for Reduction of Level

Pegs Distance(m) Direction Staff Reading (m)

Difference in Elevation (m) H.I (m) R.L(m) Remarks

B.S I.S F.S Rise Fall

A 3.005 108.620 105.615 B.M.

1 0+00 2.285 0.720 106.335

2 0+10 1.560 0.725 107.060

3 0+20 1.785 0.225 106.835

4 0+30 2.105 0.320 106.515

B 0+40 2.875 3.105 1.000 108.390 105.515 T.P.1

5 0+50 3.465 0.590 104.925

X 0+53.35 3.955 0.490 104.435

6 0+60 3.120 0.835 105.270

7 0+70 3.015 0.105 105.375

8 0+80 2.580 0.435 105.810

9 0+90 1.955 0.625 106.435

C 1+00 1.465 0.490 106.925

5.880 4.570 3.935 2.625

B.S. - F.S. = 5.880 – 4.570 = 1.310m

Rise- Fall = 3.935 – 2.625 = 1.310m

Last R.L. - First R.L.= 106.925 - 105.615 = 1.310m

Plotting of Profile

Plotting of profile leveling provides a graphical representation of the ground points on a longitudinal section along the alignment. It is being used to determine the depth of cutting or filling on the proposed gradient (for highways, railways, canals, etc.), to study grade crossing problems, to select appropriate grade, to locate depth of sewer, tunnels etc. In this, a datum line is drawn along which distance of the stakes are marked and reduced levels are plotted along vertical lines drawn on the marked points. Segmented straight lines joining the reduced level points represent the longitudinal profile of the ground surface. Profile is generally drawn so that the vertical scale is much larger than the horizontal scale in order to accentuate the differences of elevations.

Figure 14.2 shows the longitudinal section of the profile leveling (Figure 14.1). In this, the datum and ground lines are drawn in black and the ordinates in blue. The value of the datum line is given and the reduced levels are written against ordinates.

Cross Sectioning

In many projects, terrain information transverse to the longitudinal section (through profile leveling) is also required such as for highways, railways, canals etc. In those cases, surveying is carried out at right angle to the central line, generally, at regular interval is being carried out and is termed as cross- sectioning. If, for any reason, a cross-section is run in any other direction, the angle with the centre line is required to be noted. The observations are then recorded as being to the left or right of the centre line. The notes of the readings are maintained as shown in Table 14.2 for taking a cross-section along the stake point 4. Reduction of levels, Plotting etc. can be done as in case of profile leveling. A plotting of the cross section at stake 4 is as shown in Figure 14.3.

Table 14.2 Field book for Reduction of level

Pegs Distance(m) Direction Staff reading (m)

Difference in elevation (m)

H.I (m) R.L (m) Remark B.S. I.S. F.S. Rise

(m) Fall (m)

A 3.005 108.620 105.615 B.M.

:

4 0+30 2.105 0.320 106.515 0m

1.850 106.770 2m left

1.725 106.895 4m left

1.680 106.940 6m left

1.985 106.635 2m right

1.875 106.745 4m right

1.780 106.840 6m right

B 0+40 2.875 3.105 1.000 108.390 105.515 T.P.1

:

Ex14-1 Following staff readings were taken with a level. The instrument having been shifted after the 4th, 7th and 10th reading. R.L. of the starting B.M. is 100.00 m. Enter the reading in the form of a level book page. Find the R.L. of stations and apply usual checks.

2.665, 3.745, 3.830, 2.275, 2.645, 0.385, 0.960, 1.640, 2.845, 3.845, 2.680 and 3.265

Solution :

Observation Station B.S.(m) I.S.(m) F.S.(m) H.I.(m) R.L.(m) Remark 1 2.655 102.655 100.00 B.M.

2 3.745 98.910

3 3.830 98.825

4 2.645 2.275 103.025 100.380 CP1

5 0.385 102.640

6 1.640 0.960 103.705 102.065 CP2

7 2.845 100.860

8 2.680 3.485 102.900 100.220 CP3

9 3.265 99.635

9.620 9.985

B.S. - F.S. = 9.620 - 9.985 = - 0.365 m

Last R.L. - First R.L. = 99.636 - 100.00 = - 0.365 m

Ex.14-1 The following consecutive readings were taken with a level and a 4 m staff on a continuously sloping ground at a common interval of 30 m.

0.780; 1.535; 1.955; 2.430; 2.985; 3.480; 1.155; 1.960; 2.365; 3.640; 0.935; 1.045; 1.630 and 2.545.

The reduced level of the first point A was 218.750 m. Rule out a page of a level book and enter the above readings. Calculate the reduced levels of the points by the collimation method, and rise and fall method. Also, calculate the gradient of the slope.

For Exercise 14

Ex.14-1

Objective B.S. (m) I.S. (m) F.S. (m) Rise (m) Fall (m) R.L. (m) Remarks H.I. (m)

1 0.780 218.750 A. Bench Mark

219.53

2 1.535 0.755 217.995 3 1.955 0.420 217.575 4 2.430 0.475 217.100 5 2.985 0.555 216.545

6 1.155 3.480 0.495 216.050 CP2 217.205

7 1.960 0.805 215.245 8 2.365 0.405 214.840 9 0.935 3.640 1.275 213.565 CP2 214.500

10 1.045 0.110 213.455 11 1.630 0.585 212.870 12 2.545 0.915 211.955

å 2.87 9.665

B.S. - F.S. = 2.870 - 9.665 = -6.795 m

Rise - Fall = - 6.795 m

Last R.L. – First R.L. = -6.795 m

Gradient (fall) = [6.795 / (11 x 30)] = 1 in 48.565 (downward from A)

Reciprocal Leveling

To find accurate relative elevations of two widely separated intervisible points (between which levels cannot be set), reciprocal leveling is being used.

To find the difference in elevation between two points, say X and Y (Figure 15.1), a level is set up at L near X and readings (X1 and Y1) are observed with staff on both X and Y respectively. The level is then set up near Y and staff readings (Y2 and X2 ) are taken respectively to the near and distant points. If the differences in the set of observations are not same, then the observations are fraught with errors. The errors may arise out of the curvature of the earth or intervening atmosphere (associated with variation in temperature and refraction) or instrument (due to error in collimation) or

any combination of these.

The true difference in elevation and errors associated with observation, if any, can be found as follows:

Let the true difference in elevation between the points be h and the total error be e. Assuming, no

error on observation of staff near the level (as the distance is very small)

Then, h = X1 ~ (Y1 - e) [From first set of observation]

and h = (X2 - e) ~ Y2 [From second set of observation]

Thus, the true difference in elevation between any two points can be obtained by taking the mean of the two differences in observation.

Thus, total error in observations can be obtained by taking the difference of the two differences in observation. The total error consist of error due to curvature of the earth, atmospheric errors (due to temperature and refraction) and instrumental errors (due to error in collimation) etc.

Example

Ex15-1 In order to transfer reduced level across a canyon, a reciprocal leveling campaign was conducted. Simultaneous readings were observed using two levels one at each side of the canyon. Each of the levels are having same magnifying power and sensitiveness of level tube. With instruments interchanged during leveling operation yielded the following average readings:

Instrument

station

Average near readings, meter

Average distant, readings, meter

R.L of X = 101.345 m

Distance, XY = 1.025Km

e curvature = 0.0785 XY 2

X 1.780 2.345

Y 2.435 1.870

Find out the R.L. of unknown point. Comment on the errors associated with observations.

Solution :

The difference in elevation between X and Y is

= 0.565 m (Y lower than X)

R.L. of Y (unknown Point) = R.L. of X - h = 101.345 - 0.565 = 100.780 m

Since two leveling rods are used and the elapsed time between reading in a set observation is little, the error due to change in atmospheric condition can be neglected. Moreover, since readings were taken with instruments interchanged, instrumental errors get cancelled between different set of observation. As the observations are repeated and averages of the readings have been considered for further calculation, it is expected that error associated with observation is minimized thus removed. Only error present in the observation is that associated with the curvature of the earth.

Trigonometric Leveling

For rapid leveling or leveling in rolling ground or for inaccessible points, trigonometric method of leveling is being used. In this method, theodolite (an instrument which can measure angle) is being generally used as an instrument for taking different measurements.

Let us consider two stations T and X on rolling ground whose difference in elevation is required to be determined (Figure 15.2) by trigonometric method of leveling. At T, a theodolite instrument is set up. TT ' is the height of the instrument above the point T (to be recorded at the time of observation). A

leveling staff is held at X. At the vertical angle of elevation of the actual line of sight , let x1 is the observed staff reading. The difference in level between T and X is given by

where xt' xh is deviation of the horizontal line of sight due to curvature of the earth and refraction of

light (given by 0.0675 T' x h2 ). xh x1is T' x1 sin or T' x h tan , T' x1 is the inclined distance from the instrument to the staff and T' xh is the horizontal distance between the points, x1 X is the staff reading at X.

Examples

Ex15-2 In order to eliminate the uncertainty due to refraction, observations for vertical angle are made at both ends of the line as close in point of time as possible. The vertical angle at the lower of the two peaks to the upper peak is +3° 02' 05"?. The reciprocal vertical angle at the upper peak is - 3° 12' 55"?. The height of instrument are kept to be same in all observation. The slope distance between two mountain peaks determined by EDM measurement is 21,345m. Compute the difference in elevations between the two peaks.

Solution :

Average vertical angle = (3° 02' 05" + 3° 12' 55") / 2 = 6° 15' 00 "

Difference in elevation = 21.345 sin 3° 07' 30 " + 0.0675 (21.345 cos 3° 07' 30 ")2

= (1.163 + 30.662) m

= 31.825 m

Ex.15-1The following reciprocal levels were taken on two stations P and Q:

Instrumentstation Average near readings, meter

Average distant, readings, meter

R.L of P = 101.345 m

Distance, PQ = 1645 Km

P 2.165 3.810

Q 2.335 0.910

Determine the elevation of Q and the error due to refraction when the collimation error is 0.003m downward per 100m.

Ex.15-2 In order to reduce the error in measurement of vertical angle a set of measurements are taken and find the average angle as 9° 02' 05? form a height of instrument as 1.565m to a target height 2.165m. If the elevation of the instrument station is 189.250m above mean sea level, find the elevation of staff station. Assume any data, if required.

For Exercise 15

Ex.15-1 99.810 m; 0.063 m

Ex. 15-2 204.134 m (Hints : Assume, tacheometric observation fitted with anallactic lens and having fixed target of height 1 m)

Errors, Mistakes and Precautions in Leveling

Instrumental Error

Error in permanent adjustment of level : For any major surveying work, instrument needs to be tested and if required, gets to be adjusted. For small works, bubble of the level tube should be brought to the centre before each reading and balancing of sights are to be maintained.

Staff defective and/or of non-standard quality : The graduation in staff may lack standard distance and thus may cause error in reading. In an ordinary leveling, the error may be negligible but in the case of precise leveling, the graduations are to be standardized with invar tape.

Error due to defective level tube : The bubble of the level tube may remain central even though the bubble axis is not horizontal due to its sluggishness or it may take considerable time to occupy central position, if it is very sensitive. Also, there may be irregularity in the curvature of the tube causing delirious effect.

Error due to defective tripod : The tripod stand should be strong and stable otherwise it causes setting of the instrument unstable and considerable time is required to make it level. The nuts provided at the joints of the legs to the tripod head should be well-tightened before mounting the instrument. The tripod should be set up on a stable, firm ground.

Personal Error

Due to imperfection in temporary adjustment of the instrument

These errors are caused due to careless setting up of the level, improper leveling of the instrument, lack in focus of eyepiece or/and objective and error in sighting of the staff.

Careless set-up of the instrument: If the instrument is not set up firmly, it gets disturbed easily. If the ground is not firm, it may settled down and on hard ground, it may get slipped.

Imperfect leveling of the instrument : Due to improper leveling of the instrument, bubble does not remain at the centre when the sights are taken resulting error in reading. To avoid the error, the bubble should be brought to the centre before each reading.

Imperfect focusing . If either the eye-piece or the objective or both are not properly focused, parallax and thus error in the staff readings occur. Due to movement of eyes if there is any apparent change in the staff reading the eye-piece and objective need proper focusing.

Errors in sighting : This occurs when the horizontal cross-hair does not exactly coincide with the staff graduation or it is difficult to see the exact coincidence of the cross hairs and the staff graduations. The error can be minimised by keeping the sight distance small.

Error due to staff held Non-vertical . If the staff is not held vertical, the staff reading obtained is greater than the correct reading. To reduce the error, the staff should be held exactly vertical or the staff man should be asked to waive the staff towards the instrument and then away from the

instrument and the lowest reading should be taken.

Errors in reading the staff: These errors occur if staff is read upward, instead of downwards, read against the top or bottom hair instead of the central hair, mistakes in reading the decimal part and reading the whole meter wrongly.

Errors in recording: The common errors are entering a wrong reading (with digits interchanged or mistaking the numerical value of a reading called by the level man), recording in wrong column, e.g., B.S. as I.S., omitting an entry, entering the inverted staff reading without a minus sign etc.

Errors in computing: adding the fore sight reading instead of subtracting it and or subtracting a back sight reading instead of adding.

Error due to Natural Cause

Error due to curvature : In case of small sight distance error due to the curvature are negligible, but if the sight distances are large, the error should be estimated and accounted for, as discussed below. However, the error can be minimized through balancing of sight or reciprocal observation.

With reference to Figure 16.1, the horizontal line of sight through an instrument set at L is L' x h. The level line passing through L' is L' x l. The correct staff reading at X is x l. Thus, horizontal staff reading at station X, x h is associated with an error x h x l due to curvature of the earth.

In Figure 16.2, PH is a horizontal line tangent at P to the level line along the mean radius, Rm of the earth. At station L, LH is the amount of departure of the horizontal line from level line and thus the error due to curvature of the earth (ec). This can be calculated from the triangle OPH in which

(Neglecting ec in the denominator as it is very small in comparison to Rm ).

Assuming, mean radius of the earth as 6367 Km, and D is the distance in Km from the instrument position to the staff station, the error due to the curvature of the earth is

ec = 0.0785 D2

It is subtractive in nature as curvature of the earth always provides increase in staff reading.

Error due to refraction: It varies with temperature, terrain and other atmospheric conditions. It is usually considered to be one seventh times but in opposite nature to the error due to curvature. To minimize this error, reciprocal observation at the same instant of time is required to be adopted.

In actual field condition, the line of sight through a level is not straight but it bends downward due to the refraction of rays of light as it passes through the intervening medium. Thus, reduces the error due to curvature of the earth by approximately 14%. With reference to Figure 16.1, the actual line of sight of the instrument set at L is thus L' x a. The observed staff reading at station X is x a. Thus, the compensation due to refraction is thus x h x a which is error due to refraction (er ) through intervening atmosphere. In Figure 16.2, HA is the error due to refraction (er ).

Error due to Earth's Curvature & Refraction

The combined error due to curvature and refraction (ecomb ) is thus given by

ecomb = 0.0675 D2 m where D is the distance in km

It is finally subtractive in nature as the combined effect provides increase in staff reading. In Figure 16.1, x l x a represents the combined error due to curvature and refraction and in Figure 16.2, it is AL .

In most ordinary leveling operation, the line of sight is rarely more than 2 meter above the ground (where the variation in temperature causes substantial uncertainties in the refraction index of air). Fortunately, most lines of sights in leveling are relatively short (< 30 m) and B.S. & F.S. are balanced. Consequently, curvature and refraction corrections are relatively small thus insignificant except for precise leveling.

Errors due to wind: Strong wind disturbs leveling of an instrument and verticality of staff. Thus, it is advisable to suspend the work in this condition.

Errors due to sun : Due to bright sunshine on the objective, staff reading cannot be taken properly. To avoid such error, it is recommended to maintain a shed to the objective.

Errors due to temperature: Temperature of the atmosphere disturbs setting of parts of instrument as well as causes fluctuation in the refraction of the intervening medium. These lead to error in staff reading. Disturbance caused to instrument may be minimized by placing the instrument under shed.

Mistakes in Leveling

The following mistakes (blunders) may occur if the surveyor is not careful and attentive.

Mistakes in Reading Mistakes in Recording Mistakes in Computations Improper Holding of the Staff

Mistakes in Reading

Reading the staff in the wrong direction. It should be read in the direction in which the graduations increase.

Reading the stadia hairs instead of the central horizontal hair.

Reading the wrong figure of meter and other decimal components.

Reading the wrong graduations or omitting a zero from a staff reading. For example, reading 1.250 m instead of 1.025 m.

Mistakes in Recording

Recording the reading in the wrong column of the level book.

Recording the reading with the digits interchanged. For example, 2.425 for 2.245.

Omitting the recording of an entry altogether.

Recording remarks against a wrong line.

Recording a reading different from the one called by the instrument man.

Mistakes in Computations

The mistakes in computation can be detected by applying arithmetic checks. As far as possible, the rise and fall method should be used

Precaution in Leveling

While leveling, the following precautions should be taken:

The staff should be held vertical while taking the reading;

The bubble in the level tube is to be brought to central before taking any reading;

Readings should be taken in the proper direction depending on the type of staff;

Balancing of sight is to be maintained as far as possible;

Reading and recording of observation correctly.

Error Propagation in Leveling

The propagated error in level of a line varies as the square root of the number of instrument set up or as the square root of the distance leveled and the square root of the lengths of the sights.

Ex.16-1 A surveyor standing on seashore can just see the top of a ship through the telescope of a levelling instrument. The height of the line of sight at instrument location is 1.65 meter above msl and the top of ship is 50 meter above sea level. How far is the ship from the surveyor?

The following notes refer to the reciprocal levels taken with one level:

Instrument Station Staff Readings on Remarks

Near Station Further station

P 1.03 1.630 Distance PQ = 800 m

Q 2.74 0.950 R.L. of P = 450 m

Find (i) the true R.L. of Q;

combined correction for curvature and refraction

the error in collimation adjustment of the instrument.