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An art of measuring the relative heights or elevations of the points or objects on the surface of the earth is called as levelling. Levelling deals with the measurements in a vertical plane. It can also be defined as an operation for the measurements in a vertical plane. Levelling is defined as an operation for the measurement of the difference in the elevations between points above some given plane or surface known as datum surface which may be purely an arbitrary one for small surveys but generally taken as the mean sea level (m.s.l.) for major surveys. Here datum means any surface of which exact elevations are known. The mean sea level is often considered or referred to as the datum all over the world. Thus levelling is a branch of surveying which deals with the following objectives: To find the elevations of points with respect to a given datum and To establish points at a given elevation with respect to a certain datum. In engineering projects, levelling is necessary for various purposes such as: calculation of the depth of cutting and filling, setting out grades for sewers, roads, railway track and pipe lines and the estimation of reservoir capacities. With the help of levelling work, ground levels are found out so that undulation of ground can be understood and further it enables an easy path or way of plotting the contour map, ground profile from which various construction works like dam, bridges, water mains and industrial sheds etc. can be progressed. Determination of elevations or heights of points or objects helps in selecting the alignments of highways, water supply line, railway track, electric transmission towers, drainage pipe line etc.
The dumpy level is commonly used for levelling work being compact and stable type instrument The purpose of dumpy level is to provide a horizontal line of sight after the adjustments are done. The levelling staff is a device which makes the surveyor or observer to measure the vertical distance by which the station is above or below the line of sight. The most commonly used staff is the self-reading staff.
Setting up of the dumpy level Levelling Focusing the eyepiece Focusing the object glass This is the first operation which includes the following steps: Step 1: By turning round the lower part of level, the instrument is fixed on the tripod stand. The dumpy level has threads on the inner side whereas the tripod top has threads on the outer side. These threadings of level and tripod stand enable the surveyor to fa the instrument and to make the instrument stable on the tripod. Step 2: By the legs adjustment of the tripod stand, the instrument is approximately levelled Following steps are involved in the approximate levelling by legs adjustments: All the three-foot screws of the dumpy level are first of all brought at the center of its run. Any of the two legs of the tripod stand are firmly fixed in the ground. The level is adjusted to a convenient height as per the height of surveyor of operator. The third leg is moved either circumferentially or radially till the bubble approximately at the center. After the approximate levelling by leg adjustments, the accurate levelling is properly done with the help of foot screws. The accurate levelling is essential so as to make the vertical axis truly vertical. Accurate levelling with the help of three-foot screws includes the following steps: Step 1: Keep the telescope parallel to any one pair of foot screws. Let the telescope be parallel to one pair of foot screws say P-Q. Move these foot screws either both outwards or both inwards simultaneously till the bubble comes in the center of its run. See Fig. Step 2: Rotate the telescope in 90° and bring it over the third foot screw 'R' and bubble is brought in the center of its run by operating the third foot screw either clockwise or anticlockwise. See Fig. Step 3: Again bring the telescope back to its original position as it was in step 1 i.e. along foot screws P-Q and check the centering of the bubble. Again move the pair of foot screws either both outwards or both inwards simultaneously till the bubble comes in the center of its run. Step 4: Again turn the telescope through 90° over the third foot screw 'R' and check whether the bubble remains in center or not. If not, repeat these operations till the bubble remains in center for both positions of the telescope. Step 5: Now turn the telescope in any position through 360° and observe the bubble. If the bubble remains in center for all positions of the telescope, then telescope is now in accurate levelling and ready for further work of levelling. Focusing of the eyepiece enables to make the cross hair clear and distinct. This is achieved by holding a sheet of white paper in front of the object glass and the eyepiece is rotated in clockwise or anticlockwise direction till the cross hairs are clear, sharp and distinct. Now the telescope is directed towards the staff and focusing screw is rotated in forward or backward direction till the image of the staff is clear, distinct and sharp. Setting up of the dumpy level Levelling Focusing the eyepiece Focusing the object glass
Relation between the principal axis (line) of a level Refer Fig. The axis of the bubble tube should be perpendicular to vertical axis. The line of sight (line of collimation) should be parallel to the axis of bubble tube. In the examination of the level with reference to the quality of the non-adjustable parts, the important requirements are stability and a proper relationship between line sensitiveness of the bubble and the resolving power of the telescope. There is only one fundamental requirement for the permanent adjustment of a level and it is that the line of sight shall be horizontal. To test a level, it is first necessary to establish a line which is known to be horizontal. This is done by a method known as 'Two Peg' Method. As shown in Fig. Staff are held at two points P and Q some 50 m apart, and the instrument is set up equidistant from them. If the temporary adjustments are made and readings are taken of the staffs, the difference of the readings is the true difference of height between P and Q because even if the line of sight is not horizontal it will be equally inclined at both points and the equidistance of the sights causes any error to cancel out. Now, the instrument is removed and set up at a place much nearer to staff Qas shown in Fig. The instrument is levelled and reading are taken. If the same difference of reading is not obtained, the line of sight cannot be horizontal. The line of sight may be directed upward or downward (i.e. rise or fall) Add true difference to the reading on the peg Q near the instrument, if it is fall from P to Q or vice versa. Adjust the horizontal hair of diaphragm to the correct reading by means of diaphragm adjustment screws, loosening one and tightening the other. To increase the staff reading, loosen the upper screw of diaphragm and tighten the lower and vice versa. The diaphragm moves towards the screws tightened. Adjustment of the instrument can be made by trial and re-testing, until the true difference of level is given by the readings.
For entering the readings of reduced level of different sights, the following format of level page is commonly used into practice.
Keep the levelling staff on bench mark (B.M.) and take reading and find the reduced level of collimation plane or height of instrument by adding back sight reading to the RL of bench mark. Note that, Height of instrument is equal to R.L. of collimation plane, Reduced level of intermediate points can be found out as follows: The instrument is shifted and set up and levelled at new position so that reading os levelling staff would be clear and distinct. Then take back sight reading on change point (CP) and find the R.L. of new collimation plane or new height of instrument. Refer to Fig. Find the reduced levels of the remaining points from new set up of instrument with respect to new height of instrument or new R.L. of collimation plane. Repeat the above procedure till all the levelling work is over. After completion of levelling work, arithmetical check is found out. From this check, accuracy of the field work of levelling can be cross-checked. This check can be taken at each level page. Sum of backsights - sum of foresights = Last R.L. - First R.L.. In short, 
-F.S. =Last R.L. - First R.L.
In this method, instead of H.I. column in the format of level page, two columns of rise and fall are introduced for calculation of R.L's. Difference of levels between consecutive points is found by comparing the staff readings on the two points for the same setting of the instrument. Rise and fall method are stepwise explained as follows: Step 1: Prepare the format of level page before levelling work start, as shown below:
Step 2: The difference in staff readings between the consecutive points is found out. Step 3: Step 4: Repeat the same procedure till the levelling work is over. Step 5: After completion of levelling work, the arithmetical is found out, which shows accuracy and cross check of the field work in levelling. Arithmetical check: In this method calculation work is more, therefore it is tedious but there is check on every point; hence it is accurate method rather than H.I. method.
In precise levelling work or when the sights are long, the effects of curvature and refraction have to be taken into account. It is evident that a horizontal line departs from a level surface because of the curvature of earth. And in the long sights, the horizontal line of sight does not remain straight but it slightly bends downwards having concavity towards earth surface due to refraction. The effect of curvature is to cause the objects sighted to appear lower than they really are. While that of refraction is to make them appear higher than they really are. The combined effect of curvature and refraction is such that objects appear lower than they really are. The vertical distance between the horizontal line and the level line represents the effect of the curvature of the earth. The correction for curvature in meter = 0.0785 d True staff reading may, therefore, be obtained by subtracting the correction for curvature from the observed staff reading The effect of refraction is the same as if the line sight was curved downwards or concave towards the earth's surface and hence the rod reading is decreased. The correction of refraction, C, is 0.01122d2 meters
Sensitiveness or the sensitivity of a stage tube is its functionality of displaying small deviations of the tube from the horizontal. This fine relies upon specifically upon the radius of curvature of the extent tube which may also range from 10 to three hundred metres —the bigger the radius, the more the sensitiveness. Sensitiveness is likewise improved through boom withinside the period of bubble and through lower of viscosity and floor anxiety of the liquid withinside the stage tube. Sensitiveness is from time to time special in phrases of the radius of curvature of the extent tube, however the higher manner is to kingdom the attitude thru which the axis has to be tilted to purpose the bubble to tour thru one department of the scale (i.e., the angular fee of 1 department of the extent tube.) The angular fee of 1 ‘2 mm’ department may also range from eight to forty-five seconds relying upon the kind of the device. When the bubble isn't a lot sensitive, the mistake in analyzing over lengthy attractions may be very marked and the splendid accuracy isn't possibly. And if the sensitiveness is more than is certainly necessary, time is wasted in levelling the device and the accuracy in readings isn't anyt any manner improved. Therefore, for higher efficiency, handiest such units as have the needful sensitiveness must be used for special purposes.
When it is necessary to carry levelling across a river or any obstacle a long sight between two points so situated that no place for the level can be found from which the lengths of foresight and backsight will be even approximately equal. Special method i.e. reciprocal levelling must be used to obtain accuracy and to eliminate the following errors due to Curvature and refraction Error in instrument adjustment. Reciprocal levelling involves: Two sets of observations yielding two erroneous differences of level, the mean of which is the true result. Thus, to ascertain the difference of level between P and Q, on the opposite banks of a wide river and remote from a bridge reading on a staff held on each point are taken from instrument station I. The instrument is then transferred to position 2, so that 2P is equal to 20. The staff is again observed on P and Q. If due to the combined effect of instrumental error, curvature and refraction on the long and short sights, the difference of level between P and Q, as determined from one of the instrument stations is made too great, the other determination evidently makes it too small by the same amount. The mean of the two differences of level so obtained is therefore the required difference.
The line of sight will be inclined upwards or downwards when the level is not in adjustment because of which, The axis of the bubble not being at right angles to the vertical axis. The line of collimation not being parallel to the bubble axis and this will cause serious errors. The error due to the inclination of the line of collimation may be eliminated by equalizing the backsight and foresight distance while taking change point. If the bubble is sluggish, it may apparently be in the correct position (in the centre) even though the bubble line is not horizontal. However, the error may be partially avoided by observing the bubble after the target has been sighted. The error is compensating. Sometimes the objective slide does not move in horizontal plane but moves in inclined direction during focusing, because of faulty focusing tube. Error can be eliminated by balancing back sight and foresight, since in that case, focus is not changed and hence, the slide is not moved. The error is compensating. Erroneous division of the levelling staff will cause some errors. Earth's curvature: The effect of curvature is to increase the staff readings. When the distance is small the error is negligible, but for greater distances error is considerably more. Refraction: Due to refraction, the ray of light bends downwards in the form of curve with its concavity towards the earth surface, thus affects the staff reading. Error due to refraction may compensate over a long period but may be cumulative on a full day's work. Variation in temperature: The effect of variation in temperature on the adjustment of the instrument is not of much consequence in levelling of ordinary work, but it may produce an appreciable error in precise work. Errors due to settlement of staff and level: The level, staff settles if proper precautions are not taken and cause cumulative errors. Wind vibrations: High wind shakes the instrument and thus disturbs the bubble and the staff. Precise levelling work should never be done in high wind. setting up the level imperfect focusing of eye-piece and objective errors in centering the bubble. Failure to watch it after each sight. errors due to resting the hands-on tripods or telescope. staff not being held exactly vertical. Reading upwards, instead of downwards. Taking reading on top or bottom hair instead of central hair on stadia diaphragm. To omit a zero or even two zeros from a reading. Mistakes in recording such as entering B.S in F.S and vice versa. Mistaking the numerical values of reading called out by the level man. Omitting the entry. Mistakes in calculation of H.I or Rise and Fall. Instrumental errors Natural errors Personal error
It is an automatic level consisting of pendulum compensator. It is capable for normal optical levelling with a rod graduated in meter or feet. Digital level have a provision to take readings automatically by using a bar code. Digital level and bar code is as shown in Fig. It is an automatic level consisting of pendulum compensator. It is capable for normal optical levelling with a rod graduated in meter or feet. Digital level has a provision to take readings automatically by using a bar code. Digital level and bar code is as shown in Fig. It has digital and electronic image processing features which can be used to determine the heights and distances with the automatic recording of data which can further be transferred to computer database. Length of the rod is 4,05 m and this rod is graduated in bar code on one side or on the both sides as shown in fig. After capturing and processing the image of the bar code rod, this processed image of the rod reading is then compared with the image of the complete rod which is permanently Mored in memory module of level so as to determine elevation i.e. height and distances. First of all the instrument is properly leveled. The surveyor or observer focus the image of the bar code properly. The observer or surveyor press the measure button to begin the image processing. This is normally done in 4 second. The heights and distances are automatically measured along with horizontal angles. In digital level, coding can be similar as used in total station which helps to collect processed levelling data which is further transferred directly to computer. Note that of the rod is not held perfectly vertical or in plumb and then an error message will automatically flash on the screen. Accuracy for distance can be obtained within the range of 1/2500 to 1/3000. Levelling accuracy is having standard deviation for a 1000 m double run of 2mm for optical measurement and that of for electronic measurement, it is 1.5 m. Surveying Vol.1 by B.C. Punmia, Laxmi Publication Surveying and leveling by R. Subramanian, Oxford University Press Surveying Vol-1 by R. Agor, Khanna Publishers
Unit - 2
Levelling
Key Takeaways:
It is the art of measuring the relative heights or elevations of the points or objects on the surface of the earth is called as levelling.
When the dumpy level is to be set on a new point on ground, then the temporary adjustments are to be made.
Temporary adjustments are carried out in the following steps:
a) Setting up of the dumpy level
b) Levelling:
Fig.2.1: Levelling up with three-foot screws ‘PQR’
c) Focusing the eyepiece:
d) Focusing the object glass
Key Takeaways:
Temporary adjustments are carried out in the following steps:
In this method, the reduced level of collimation plane or height of instrument is determined for each set up of dumpy level and then reduced levels (R.L.) of the other points are found out with respect to the plane of collimation or height of instrument.
Procedure:
Step 1: To prepare the format of level page before levelling work start:
Staff Station | B.S | I.S | F.S | H.I | R.L | Remark |
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Step 2: To find the height of instrument (H.I.) or R.L. of plane of collimation:
Height of instrument (H.I.) = R.L. of bench mark + B.S. reading.
Step 3: To find R.L. of intermediate points or change points:
R.L. of intermediate points= Height of instrument – Intermediate sight reading
=H.I.-I.S. reading
R.L.. of change point =Height of instrument - Fore sight reading =H.I.-F.S. reading
Step 4: To find new height of instrument or new plane of collimation:
R.L. of new height of instrument = R.L. of change point + B.S.
Step 5: To find reduced levels of the remaining points:
Step 6: To finish the levelling work:
Step 7: To find arithmetical check:
Fig.2.2: H.I Reading Method
Arithmetical check:
Key Takeaways:
In this method, the reduced level of collimation plane or height of instrument is determined for each set up of dumpy level and then reduced levels (R.L.) of the other points are found out with respect to the plane of collimation or height of instrument
Staff Station | B.S | I.S | F.S | Rise | Fall | R.I | Remark |
B.M |
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If the staff reading of second point in level page is higher than the first, then it indicates fall which is then to be subtracted from R.L. of previous point.
If the staff reading of second point in level page is lower than the first one, then it indicates rise which is further to be added to the R.L. of previous point. Refer to Fig.
Fig.2.3: Rise and Fall method
Note that, the check can be taken at each level page and on R.L. of every intermediate points.
Sum of backsights- sum of foresights=Sum of all rise-sum of all fall
In short, EB.S.-EF.S. = Rise-Fall= Last R.L. -First R.L.
Key Takeaways:
In this method, instead of H.I. column in the format of level page, two columns of rise and fall are introduced for calculation of R.L's. Difference of levels between consecutive points is found by comparing the staff readings on the two points for the same setting of the instrument.
Curvature:
where,
d is the distance in km from the level to the staff station.
True staff reading = observed staff reading -0.0785 d²
Refraction:
where d is taken in km.
Key Takeaways:
In precise levelling work or when the sights are long, the effects of curvature and refraction have to be taken into account. It is evident that a horizontal line departs from a level surface because of the curvature of earth.
Key Takeaways:
Sensitiveness or the sensitivity of a stage tube is its functionality of displaying small deviations of the tube from the horizontal.
Fig.2.4: Reciprocal Levelling
Instrumental errors:
1. Error due to imperfect adjustment:
2. Error due to sluggish Bubble:
3. Faulty Focusing tube:
4. The levelling staff:
Natural errors:
Personal errors:
Mistakes in manipulation:
Mistakes in manipulation includes mistakes in
Mistake in reading the staff:
The common mistakes in reading the staff are
Mistakes in recording and computing:
Key Takeaways:
There are three types of errors:
Procedure:
The range of bar code is 1.8 m to 100 m and the bar code can read within this range of 1.8 m to 100 m away from the instrument.
The messages line 'instrument not level", low battery and memory full are displayed on the screen.
Fig.2.5: Digital level
Key Takeaways:
It is an automatic level consisting of pendulum compensator. It is capable for normal optical levelling with a rod graduated in meter or feet. Digital level have a provision to take readings automatically by using a bar code.
References:
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