Levelling
LEVELLING Introduction Levelling is a branch of surveying the object of which is: 1. To find the elevations of given points with respect to a given or assumed datum 2. To establish points at a given elevation or at different elevations with respect to a given or assumed datum. The first operation is required to enable the works to be designed while the second operation is required in the setting out of all kinds of engineering works. Levelling deals with measurements in a vertical plane. The information obtained by the process of levelling proves very much useful in the initial stages of design of the project as well as during the execution of various units of the project. The process of levelling involves the operation of making linear measurements in the vertical plane and it is because of the measurements in the vertical plane that the levelling differs both in the methods and instruments of the measurements. For engineering projects, the levelling is required for various purposes such as for estimating the reservoir capacities, for setting out grades for sewers, for calculating depth of cuttings, etc.
Definitions of some common terms in levelling: Bench Mark: It is a relatively permanent point of reference whose elevation with respect to some assumed datum is known. Datum: Datum is any surface to which elevations are referred. The mean sea level affords a convenient datum world over, and elevations are commonly given as so much above or below sea level. It is often more convenient, however, to assume some other datum, especially if only the relative elevations of points are required. Horizontal Plane: The horizontal plane is defined as the plane which is normal to the direction of gravity at every point. The operations of chain survey, theodolite traverse survey and plane table survey involve measurements in the horizontal plane. Horizontal Line: It is the straight line tangential to the level line at a point. It is the line in a horizontal plane. Vertical Line or Plumb Line: The line normal to the level line at a point is known as a vertical line or a plumb line. It is the line normal to a level surface. Vertical Angle: The angle formed by the intersection of two lines in a vertical plane is known as the vertical angle. Level Line: It is the line drawn on a level surface. It is, therefore, normal to the plumb line at all points. Level Surface: A level surface is defined as a curved surface which at each point is perpendicular to the direction of gravity at the point. This is a surface on which all the points are equidistant from the centre of earth. As earth is a sphere, a level surface will be a curved surface. The surface of a still water is a truly level surface. Mean Sea Level: The average height of the sea for all stages of the tides is known as mean sea level or M.S.L. Prepared by: Ms. Nitika Kabra
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Reduced Level: The elevation of a point or its vertical distance above or below the datum is known as its reduced level or R.L. Elevation: The vertical distance of a point with respect to a given datum, either positive or negative, is known as the elevation of that point. The difference in elevation between two points is the vertical distance between the two level surfaces in which the two points lie. Line of Collimation: The line joining the intersection of cross-hairs and optical centre of the object glass and its continuation is known as the line of collimation. It is also sometimes referred to as the line of sight. Station: The point whose elevation is to be ascertained or the point that is to be established at a given elevation is known as the station and it thus indicates the point at which the staff is held and not the point at which the level is set up. Height of Instrument: The elevation or R.L. of the line of collimation, when the instrument is correctly levelled, is known as the height of instrument or the height of plane of collimation. Or the height of instrument is the elevation of the plane of sight (line of sight) with respect to an assumed datum. It may be noted that the term height of instrument does not mean the height of the centre of the telescope above the ground where the level is set up. Back Sight: It is the sight taken on a rod held at a point of known elevation, to ascertain the amount by which the line of sight is above that point and thus ascertain the height of instrument. Back Sighting is equivalent to measuring up from the point of known elevation to the line of sight. It is also known as plus sight as the back sight reading is always added to the datum to get the height of the instrument. The object of back sighting is therefore to ascertain the height of the plane of sight. Fore Sight: It is the sight taken on a rod held at a point of unknown elevation, too ascertain the amount by which the point is below the line of sight and thus obtain the elevation of the station. Fore sighting is measuring down from the line of sight. It is also known as minus sight at the reading is always subtracted from the height of instrument to get the elevation of the point. The object of fore – sighting is to ascertain the elevation of the point. Intermediate Sight: All sights taken between B.S. and F.S. are known as intermediate sights or I.S. It may be noted that the word sight does not imply any direction, but it denotes the reading. Turning Point: It is also known as change point. It is the point on which both the minus sight and the plus sight are taken on a direct line of direct levels. The minus sight is taken on the point in one set of the instrument to get the level while the plus sign is taken on the same point in other set of instrument to establish the new line of sight. Intermediate Station: It is a point intermediate between two turning points, on which only one sight (minus sight) is taken to determine the elevation of the station. Parallax: The term parallax is used to indicate the apparent movement of the image with respect to the cross – hairs and it occurs when the plane of image does not coincide with the plane of cross – hairs. It can be eliminated with the process of focussing. Focussing: It is used to indicate the operation or process by which the clear image of the object is brought in fixed plane of cross – hairs. The process of focussing can be carried out either by adjusting the eye-piece or the objective. It involves two processes: i. Focussing the eye-piece: The eye-piece unit is moved in or out with respect to the cross-hairs so that the latter are clearly visible. ii. Focussing the objective: The purpose of focusing the objective is to bring the image of object in the plane of cross-hairs which are clearly visible. The focusing can be done externally or internally. Prepared by: Ms. Nitika Kabra
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Methods of levelling: Three principal methods are used for determining difference in elevation. They are: 1. Barometric levelling: Barometric levelling makes use of the phenomenon that difference in elevation between two points is proportional to the difference in atmospheric pressures at these points. A barometer, therefore, may be used and the readings observed at different points would yield a measure of the relative elevations of those points. At a given point, the atmospheric pressure does not remain constant in the course of the day, even in the course of an hour. The method is, therefore, relatively inaccurate and is little used in surveying work except on reconnaissance or exploratory surveys. 2. Trigonometric Levelling (Indirect levelling): Trigonometric or Indirect levelling is the process of levelling in which the elevations of points are computed from the vertical angles and horizontal distances measured in the field, just as the length of, any side in any triangle can be computed from proper trigonometric relations. In a modified form called stadia levelling, commonly used in mapping, both the difference in elevation and the horizontal distance between the points are directly computed from the measured vertical angles and staff readings. 3. Spirit Levelling (Direct Levelling): It is that branch of levelling in which the vertical distances with respect to a horizontal line (perpendicular to the direction of gravity) may be used to determine the relative difference in elevation between two adjacent points. The method is also known as direct levelling. It is the most precise method of determining elevations and the one most commonly used by engineers.
Levelling Instruments The instruments commonly used for direct levelling are: 1. A level 2. A levelling staff 1. Level: The purpose of a level is to provide a horizontal line of sight. Essentially, a level consists of the following four parts: a. A telescope to provide line of sight b. A level tube to make the line of sight horizontal c. A levelling head (tribrach and trivet stage) to bring the bubble in its centre of run d. A tripod to support the instrument. 2. Levelling Staff: A levelling staff is a straight rectangular rod having graduations, the foot of the staff representing zero reading. The purpose of a level is to establish a horizontal line of sight. The purpose of the levelling staff is to determine the amount by which the station (i.e., foot of the staff) is above or below the line of sight. Levelling staves may be divided into two classes: a. Self-reading staff: It is the one which can be read directly by the instrument man through the telescope. The graduations are inverted so that they are seen in erect position when looked through the telescope. It is of three types: Prepared by: Ms. Nitika Kabra
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Solid staff Folding staff Telescopic staff Target staff: It contains a moving target against which the reading is taken by staff man. A target is provided on the staff and under the instructions received from the surveyor, the target is moved by the person holding the staff. The target is clamped and the reading is then recorded by the staff-man. The target is provided with a vernier and it helps in taking very accurate readings. This type of staff is useful when the distances for taking readings exceed 100 m. i. ii. iii.
b.
S. No. 1. 2. 3. 4.
Self – Reading Staff The fineness of reading taken is less.
Target Staff The fineness of reading taken is more than that of self reading staff. The level-man records the readingsThe in staff-holder takes the readings in case case of self reading staff. of target staff. The staff man need not be a trained The staff-man should be a trained person. person. The readings from self-reading staff The taking of readings from target staff can be taken easily and speedily takes time and is not easy.
Precautions to be taken while using a levelling staff: a. Holding the staff: The level staff should be held truly vertical. b. Reading the staff: The reading to be taken on the staff depends on the manner in which the figures arc written on the staff. Essential parts of a level: Any type of level contains the following three essential parts: 1. Bubble tube: This is also known as a level tube, and it helps in establishing a horizontal plane. It is designed on the principle that any liquid surface at rest will always be perpendicular to the direction of gravity. 2. Levelling head: It assists in bringing the bubble in the central position. It consists of two plates which are held at a constant distance apart with the help of foot screws. The bottom plate is known as foot plate and the hole in it is treaded so that the instrument can be fixed on treaded tripod head to ensure stability. The top plate is known as bush plate. 3. Telescope: It is the most important part of the level and it helps in taking the readings from the levelling staff. The telescope has four essential parts: a. Objective: The objective is invariably a compound lens consisting of i. The front double convex lens made of crown glass ii. The back concavo-convex lens made of flint glass The two being cemented together with balsm at their common surface. Such compound lens is known as achromatic lens, and two serious optical defects viz., spherical aberration and chromatic aberration are nearly eliminated. b. Eye Piece: It is also called as eye lens. It is required to see the object and its size corresponds to the size of human eye so that other rays are avoided to see the Prepared by: Ms. Nitika Kabra
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c.
d.
object clearly. The eye piece may be of erecting type or non-erecting type. Diaphragm: The cross – hairs, designed to give a definite line of sight, consist of a vertical and horizontal hair held in a flat metal ring called reticule. In modern instruments interchangeable cross – hairs are used and they are carried in a cell or a capsule. The cross – hairs must be clean, fine, opaque and without fringes. The cross – hairs are usually made up of spider's web, silk web, lines on glass, fine platinum wire, etc. Cross – hairs (a), (b) and (c) in the diagram are used in levels. Body and Focusing Device: The focusing device depends upon whether it is an external focussing telescope or an internal focussing telescope. i. External Focussing: The movement of the objective or eye-piece is carried out externally and the body of telescope consists of two tubes, one capable of sliding axially within the other, by means of rack gearing. The focussing screw controls the gearing arrangement and it is moved in clockwise or anticlockwise direction till the image falls at the plane of diaphragm. This type of focussing is not favoured. ii. Internal focussing: The objective and eye – piece are kept fixed in position and the focussing is achieved by moving an extra double concave lens provided in the telescope between the objective and diaphragm hairs. Thus, a short tube carrying the lens is moved along and inside the tube carrying the objective by means of gearing arrangement. The modern instruments contain internal focussing arrangement
Types of Levels 1. Dumpy Level: It is a very simple, compact and stable level. It can be used for rough work. The telescope is rigidly fixed with the support and hence, it is not possible to rotate it about its own axis. The instrument gives fairly accurate work and possesses greater stability of adjustments. The modern form of dumpy level has the telescope tube and the vertical spindle cast in one piece and a long bubble tube is attached to the top of the telescope. This form is known as solid dumpy. In some of the instruments, a Prepared by: Ms. Nitika Kabra
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2.
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clamp screw is provided to control the movement of the spindle about the vertical axis. For small or precise movement, a slow motion screw (or tangent screw) is also provided. The levelling head generally consists of two parallel plates with either three-foot screws or four-foot screws. The upper plate is known as tribrach and the lower plate is known as trivet which can be screwed on to a tripod. The advantages of the dumpy level over the Wye level are: a. Simpler construction with fewer movable parts b. Fewer adjustments to be made c. Longer life of the adjustments Cooke's Reversible Level: This level combines the advantages of dumpy level and Vlevel. It contains the arrangements such that it can be rotated about its own axis in its sockets and it can be removed and ends can be exchanged. The telescope is supported by two rigid sockets into which the telescope can be introduced from either end and then fixed in position by a screw. The sockets are rigidly connected to the spindle through a stage. Once the telescope is pushed into the sockets and the screw is tightened, the level acts as a dumpy level. This type of instrument is heavy because there is an addition of an extra tube. There is also possibility of the instrument being disturbed while changing the telescope end to end. Wye or Y-level: The essential difference between the dumpy level and the Wye level is that in the former case the telescope is fixed to the spindle while in the Wye level, the telescope is carried in two vertical 'Wye' supports. It is a very delicate instrument consisting of various loose parts. Hence, it requires careful handling. The telescope is put up on the supports having the shape of letter Y and it can be removed and its ends can be exchanged. It thus grants the facility of carrying out the permanent adjustments indoors. However, the adjustments soon get disturbed due to loose supports and hence, it becomes necessary to check them quite often. Cushing's level: In this type of level, the telescope is firmly secured in collars as in case of a dumpy level. The ends of the telescope tube are enlarged to form two exactly equal sockets, ground carefully to receive either the objective lens cell or the eyepiece and diaphragm cell. It is thus possible to interchange objective for eye – piece and vice versa. This type of level is heavy due to the addition of the collar fittings. Tilting Level: It is used for very precise work. A tilting screw is provided at the base of telescope and at every observation; the line of collimation is made truly horizontal. The line of sight can be tilted slightly without tilting the vertical axis. Thus, the line of sight and the vertical axis need not be exactly perpendicular to each other. This feature of this type of level helps in quick levelling. The instrument is levelled roughly by the three-foot screws with respect either to the
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bubble tube or to a small circular bubble, thus making the vertical axis approximately vertical. While taking the sight to a staff, the line of sight is made exactly horizontal by centring the bubble by means of a fine pitched tilting screw which tilts the telescope with respect to the vertical axis.
S. No. 1.
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3. 6.
Dumpy Level The vertical axis and the axis of bubble are fixed rigidly at right angles to each other and hence, when the bubble is in the centre i.e. axis of the bubble is horizontal; the vertical axis is truly vertical. The line of collimation may get tilted upwards or downwards and in that case, the line of collimation and the axis of the telescope will not coincide. Thus, the adjustment will have to be carried out with the diaphragm screw. Two permanent adjustments are required.
Tilting Level The telescope and the bubble are independent of the vertical axis and as such, the line of sight and the axis of the bubble can be made horizontal without the vertical axis being truly vertical. In tilting level, the line of collimation and the axis of the telescope are made one and the same.
Only one permanent adjustment is required.
Gradientor or Gradiometer: In this level, the arrangement is made in such a way that any desired gradient can be set up with the minimum interval of time. It thus facilitates the measurement or setting out of long uniform gradients. It consists of a level in which the telescope is so mounted that it may be set at various inclinations to the horizontal and the gradient is registered on a drum.
Bench Marks Following are the four types of bench marks: 1. Arbitrary bench marks: Some permanent objects are selected to serve the purpose of bench marks and they are given some arbitrary value. Such objects are known as arbitrary or assumed bench marks and they are used for small levelling operations. 2. G.T.S. bench marks: The survey department of Govt. of India has established all over the country certain bench marks known as Great Trigonometrical Survey or G.T.S. bench marks at intervals of about 100 km. These bench marks are established with high precision and their positions and elevations are -published in catalogues or shown on G.T.S. maps. The standard datum adopted for G.T.S. bench marks is the mean sea-level at Karachi or Bombay. 3. Permanent bench marks: The bench marks established as reference points on some permanent objects between the G.T.S. bench marks by the state P.W.D. are known as Prepared by: Ms. Nitika Kabra
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4.
permanent bench marks. The permanent objects chosen for this type of bench marks include tops of culverts or bridge kilometre stones, pillars, railway platform, isolated rock, etc. Temporary bench marks: The bench marks established for short duration at the end of day's work or for some break in the work are of temporary nature and hence, they are referred to as temporary bench marks. The unfinished work is started again with reference to these temporary bench marks. The permanent objects chosen for this type of bench marks include floor or verandahs, roots of the trees, tops of parapet; gate posts, etc.
Temporary Adjustments of Levels Each surveying instrument needs two types of adjustments: 1. Temporary adjustments: These are also known as station adjustments and are those which are made at every instrument setting and are preparatory to taking observations with the instrument. 2. Permanent adjustments: These need to be made when the fundamental relations between some parts or lines are disturbed. Temporary adjustments of a level consist of the following: 1. Setting up the level: It includes: a. Fixing the instrument on the stand b. Levelling the instrument approximately by leg adjustment. The instrument is removed from the box. To fix the level on the tripod, the clamp is released; the instrument is held in the hand and is fixed on the tripod by turning around the lower part with the other hand. The tripod legs are so adjusted that the instrument is at a convenient height. Any two legs of the tripod are fixed on the ground by pressing with the hand. The movement of the third leg is made in such a way that the bubble remains in the centre. Thus the tribach is made approximately horizontal. 2. Levelling up: After having levelled the instrument approximately, accurate levelling is done with the help of foot screws and with reference to plate levels. The purpose of levelling is to make the vertical axis truly vertical. The manner of levelling the instrument by the plate levels depends upon whether there are three or four levelling screws. For three-screw levelling head; the telescope is placed parallel to a pair of screws and by turning these screws, inwards or outwards, the bubble is brought at the centre. The telescope is then turned through 90° so that it now lies over the third screw and centre of the line joining the other two screws. By turning the third screw, the bubble is centred and then, the telescope is brought in its original position. The procedure is carried out till the bubble Prepared by: Ms. Nitika Kabra
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remains in centre for both the positions which are at right angles to each other. It should be noted that the bubble will move in the direction of movement of the left thumb. For four-screw levelling head, the telescope is placed parallel to two diagonally opposite foot screws in both positions and the above procedure is repeated till the bubble remains in centre for both the positions. In modern instruments, three – foot screw levelling head is used in preference to a four foot screw levelling head. Elimination of parallax: Parallax is a condition arising when the image formed by the objective is not in the plane of the cross – hairs. Unless parallax is eliminated, accurate sighting is impossible. Parallax can be eliminated in two steps: a. Focusing the eyepiece: point the eye – piece unit towards the sky (or hold a sheet of paper in front of the objective) and move eye-piece unit in or out with respect to the cross-hairs so that the latter are seen sharp and distinct. b. Focusing the objective: The purpose of focusing the objective is to bring the image of object in the plane of cross-hairs which are clearly visible. The telescope is directed towards the staff and the focusing screw is turned till the image appears clear and sharp.
Permanent Adjustment of Levels Principles of Levelling Some of the important principles which are to be observed in simple direct levelling are as follows: 1. Change point: The intermediate staff should be carefully selected and it should be in the form of firm point which can be easily located. The elevation of change point should be carefully determined as a slight error in it will be reflected in the subsequent readings. If convenient, a bench mark can be used as a change point. 2. Lengths of B.S. and F.S.: For accurate work, the lengths of B.S. and F.S. should be maintained nearly equal. If this condition is satisfied, the error due to non parallelism of the line of collimation and the bubble line will be reduced to a great extent. When the bubble is in the centre of its 'run; the line of collimation is horizontal. . This is only possible when the line of collimation and the bubble line are exactly parallel. Even if careful adjustments are performed, there are chances of not achieving the absolute parallelism between the line of sight and the axis of the level tube. It will naturally lead to an-error in the staff reading which is proportional to the distance from the instrument to the staff. If the lengths of backsight and foresight are kept nearly equal, the error due to non-parallelism of the line of collimation and the axis of the bubble can be eliminated. This is known as balancing backsight and foresight distances If the back sight and the foresight distances are balanced, the difference in elevation between two points can be directly calculated by taking the difference of the two rod readings and no correction either for the inclination of the line of sight or for curvature and refraction is necessary. 3. Position of level: As such, the level can be set up at any point. It is however desirable to put the level on a firm spot from where maximum number of sights can be taken. The selected spot for level should neither be too high nor too low and it should preferably be located midway between the change points. 4. Starting and ending: The process of levelling at any point should start with backsight or B.S. and it should end with foresight or F.S. Also, the process of levelling should Prepared by: Ms. Nitika Kabra
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always commence from a permanent Bench Mark or B.M. and end on a permanent B.M.
Methods of Levelling The levelling can broadly be divided into the following two categories: 1. Direct levelling or spirit levelling 2. Indirect levelling 1.
Direct Levelling: It is the most commonly used method of levelling. The method employs spirit level and telescope to measure vertical distances on the levelling staff placed on various points. Various forms of direct levelling are as follows: a. Simple levelling: This is used to find out the difference in elevations of two points which are visible from a single position of the level. Following points should be noted: i. If the point is situated at a lower level, the staff reading will be more and if it is situated at a higher level, the staff reading will be less. ii. It should be seen that the bubble remains in its central position, when the readings are taken. b. Differential levelling: The object of this method is solely to determine the difference in elevation of two points regardless of the horizontal positions of the points with respect to each other. It is also known as compound levelling or continuous levelling, is resorted to under the following circumstances: i. The points P and Q. are situated far away from each other. ii. The difference in elevations of points P and Q is too great. iii. There is presence of obstacles between points P and Q. In this process, the change points or C.P. are selected as required. The level is set up at O1 and with the bubble in central position, the staff readings are taken for points P and first C.P. The process is repeated at points O2 and O3 till the point Q is reached. The difference in level of P and Q. can then be worked out by simple calculations. Difference = (b1 – a) + (c1 – b2) + (b – c2)
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c.
d.
If the difference works out to be positive, point Q is higher than point P and if it works out to be negative point Q is lower than point P. It may be noted that the readings at a change point are taken twice i.e. once before and the next after the instrument is shifted. The location and situation of change point should be carried out carefully. The positions O1, O2 and O3 of the instrument should be selected in such a way that the level lies roughly midway between the points to be read. Reciprocal levelling: The process of reciprocal levelling is adopted to calculate accurately the true difference in levels of two points which are situated in such a way that it is not possible to set up the instrument at any intermediate position and from which the lengths of the fore sight and the back sight will be even approximately equal. When this method is adopted, the total error due to curvature, refraction and imperfect collimation adjustment disappears. It is carried out across a river, or a ravine or any obstale requiring a long sight between two points. Profile levelling: The process of levelling carried out along a given line to determine the elevations of points at known distances is known as the profile levelling or the longitudinal sectioning. It is done for short distances. It is done in order to obtain a profile of the surface along a fixed line. The fixed line may be a single straight line, or it may be composed of a succession of straight lines or a series of straight lines connected by curves. It is also known as longitudinal section. By means of such sections the engineer is able to study the relationship between the existing ground and the levels of the proposed construction in the direction of its length. This process is useful for getting the data for the design of engineering structures such as road, railway, canal, sewer, water
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e.
f.
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main, etc. Cross – sectioning: When the width of the proposed project is not in the form of a trip of small width, but exceeds say 30m to 60m, it becomes –necessary to take levels in transverse direction also. Such operation of levelling carried out in the crosswise direction is known as cross-sectioning and in most of the cases, the cross-sections are taken at right angles to the longitudinal line as it is very easy to set up perpendicular lines with the help of simple instruments like cross –staff. The cross-sections are usually run at constant distance along the centre –line. Precise levelling: For very accurate work, such as establishing bench marks, extra-ordinary precautions are taken in the process of levelling to eliminate all the possible errors. The instruments used for such type of levelling are of the highest order and perfectly in working condition. While working in the field, a high degree ofto have any chance of error. For instance, the work of levelling is postponed on rainy and windy days. No unnecessary haste is made to complete the work. The check levels are taken in the opposite direction and preferably by another surveyor. Check levelling: The process of levelling carried out in the reverse direction i.e. from end point to first point, just to check the difference in level between two points, worked out previously, is known as check levelling. Many shortcuts may be taken in check levelling as it is intended for checking the results of accurate levelling done before hand. Fly levelling: It becomes sometimes necessary to carry out levelling work along two or three alternative routes of a proposed project. Hence, if accurate levelling is adopted in such cases, it will take more time without any fruitful purpose. Hence, to get in short time the rough idea about the nature of ground, the levelling work is carried out speedily along each route. Such levelling is known as fly levelling and the accuracy desired in the fly levelling is far less than that in the check levelling.
Indirect Levelling: The relative levels of the points are found out by the indirect observations and the following are the three forms of the indirect levelling. a. Barometric levelling: The principle that atmospheric pressure varies inversely with the altitude of a point is applied in case of barometric levelling. A barometer is therefore used in this method and the readings observed at different points give a measure of the relative elevation of those points. The process of barometric levelling gives approximate results and it is therefore adopted in the reconnaissance or preliminary survey. b. Hypsometry: Init, the temperature at which water boils is taken as the basis for determining the height of a point. As the altitude increases, the atmospheric pressure decreases and due to this, the boiling point of water is lowered down. c. Trigonometrical levelling: In case of trigonometrical levelling, the relative elevations of different stations are worked out by taking the vertical angles and
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measuring or computing the horizontal distances. The vertical angles are measured by means of a theodolite. The main advantage of this method is tha t it brings down the number of change points to a minimum even though the difference in level of two points is very great.
Entering the Staff Readings Reduction of Levels Levelling Problems The following are some of the difficulties commonly encountered in levelling: 1. Levelling on steep slopes: When levelling is to be carried out, either uphill or downhill, care should be taken to avoid the errors due to the non verticality of the staff and imperfect adjustment of the level. The former error is minimised by holding the staff vertical and using a pendulum plumb bob. The latter error is minimised by equating; as far as possible, the backsight and foresight distances. It is quite evident that while levelling down hill, the foresights will be near the top of the staff and the backsights will be near the foot of the staff. The reverse will be the case for levelling, uphill. 2. Levelling on summits and hollows: In levelling over summit, the level should be set up sufficiently high so that the summit can be sighted without extra setting. Similarly, in levelling across a hollow, the level should be set only sufficiently low to enable the levels of all the required points to be observed. 3. Taking level of an overhead point: When the point under observation is higher than the line of sight, staff should be kept inverted on the overhead point keeping the foot of the staff touching the point and reading should be taken. Such readings show the height of that point above the line of sight and should be added to the H.I. to get the R.L. of the point. 4. Levelling ponds and lakes: When the ponds and lakes are too wide to be sighted across, advantage may be taken of the fact that the surface of still water is a level surface. 5. Levelling across river: If the width of the river is less, the method of reciprocal levelling is Prepared by: Ms. Nitika Kabra
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6.
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to be used. If the river is too wide to be sighted across, levelling may be continued from one side to the other with little error, provided care is taken to choose the comparatively still stretch and to see that the water levels are taken at points directly opposite each other. Levelling past high wall: The problem of crossing a high wall during the process of levelling can be solved in one of the following ways: i. Two pegs P and Q may be driven on either side of wall. The R.L. of point P is obtained by taking a F.S. on it. The height of wall is measured and R.L. of top wall is determined. The distance between top of wall and peg Q is measured and subtracting this distance from the R.L. of top of wall, the R.L. of peg Q is obtained. Then, a B.S. is taken on peg Q and a new line of sight is worked out. The levelling work is then continued. ii. The line of sight is made to cut at point A on wall and from this point A, the distance of top of wall is measured. The R.L. of top of wall is then worked out. Now, the instrument is transferred on the other side of wall and line of sight is made to cut the wall at point B. The distance between point B and top of wall is measured and then, new H.I. is obtained by deducting this measurement from the R.L. of the top of wall. The levelling is then continued. Taking reading when B.M. or staff station is above the line of sight: It becomes sometimes necessary to adopt the underside of a girder, a string course beam, lintel or some such feature to adopt as a B.M. and the situation arises in which the point is above the line of sight. A very simple operation is performed to overcome this difficulty. The staff is held inverted on the point and the reading is taken and ids designated as negative. It is treated either as negative F.S. or negative B.S., as the case may be. A note stating, that the reading is taken by keeping the staff in inverted position is entered in the remarks column. As far as possible, the situation leading to the inverted staff reading should be avoided. Following are the disadvantages of holding the staff inverted: i. In some cases, it may prove very difficult to keep the zero of the staff in line with the point whose level is required. ii. It is difficult to keep the staff truly vertical. iii. The proper sign may not be given while booking the reading. iv. The staff may be read wrong. Taking reading when the staff is too near the level: It is desirable to a void the situation of holding the staff very near to the level. However, when it is not possible to a void such situation, the staff reading can be taken directly by looking through the object glass or by measuring the staff up to the centre of the object glass. Alternatively, a piece of paper may be used to serve the purpose of a target and it should be moved up and down the staff till its edge is bisected by the line of collimation. The reading where the edge of paper cuts the staff is then noted.
Prepared by: Ms. Nitika Kabra
14
Levelling
Errors in Levelling The process of levelling is subject to various errors and suitable precautions should be taken to see that these errors do not cause appreciable effect on the results of the levelling work. The errors can broadly be divided into the following three categories: 1. Instrumental errors: The instruments used for the levelling work may not be of adequate standard. The usual instrumental errors can be enlisted as follows: a. Defective levelling staff with incorrect lengths of graduations b. Faulty focussing arrangement; c. Line of collimation not parallel to the bubble tube axis d. Over – sensitive or under-sensitive bubble tube e. Rigid joints of the tripod 2. Natural errors: The usual natural errors caused by the natural external forces can be enlisted as follows: a. Error due to atmospheric refractions and their changes; b. Error due to curvature of earth; c. Error due to settlement of tripod or change points; d. Error due to vibrations caused by wind and not permitting the staff to be held vertical; e. Error due to variation in temperature; etc. 3. Personal errors: The errors caused by persons carrying the levelling process are serious in the sense that they can be easily avoided, if the work is done with due care. They can be enlisted as follows: a. Bubble not at the centre while taking reading b. Careless levelling of the instrument c. Entering wrong remark against a reading d. Exerting pressure on the telescope while focussing e. The eye-piece and objective f. Improper sighting due to imperfect focussing of the eye-piece and objective g. Incorrect holding of the staff h. Mistake in taking the reading i. Omitting the entry j. Ordinary arithmetical mistakes k. Reading wrong metre mark on the staff l. Wrong booking of the reading
Prepared by: Ms. Nitika Kabra
15
