Leveling, Methods of leveling

Leveling is nothing but the process in which height of different objects available on earth surface are determined with reference to some known datum.

Some Basic definitions:-

(i) Reduced level: The elevation of a point with respect to either Mean Sea Level (MSL) or with respect to a fixed point of known height is called reduced level.

(ii) Bench mark: Bench mark is relatively permanent point of reference whose elevation with respect to some assumed datum is known. It is used either as a starting point for leveling or as a point upon which to close as a check.

Instrument Setup

(iii) Back sight: After setting up the instrument I^st reading taken is called back sight. It is also known as plus sight.

(iv) Fore sight: Last reading taken from an instrument station is called fore sight. It is also known as minus sight.

(v) Intermediate sight: All readings other than back sight and fore sight are intermediate sight.

(vi) Height of instrument: It is the Reduced Level (RL) of line of sight of the instrument set up at different stations.

H.I = R.L + B.S

R.L = H.I – F.S

Arithmetic Check

(i) For rise and fall method

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

(ii) Height of instrument method

∑ B.S - ∑ F.S = Last R.L – First R.L

Reciprocal Levelling

Reciprocal leveling

Here, X = error due to inclined line of sight, and

e = error due to curvature and refraction

Reciprocal Leveling

When instrument is set up at A

Reading on staff at A = h_A

Reading on staff at B = h_B

When an instrument is set up at B

Reading on staff at A = h’_A

Reading on staff at B = h’_B

h_A – h_B = h’_A – h’_B If instrument is correct.

Here ‘H’ is the true difference of R.L between A and B.

True Readings

Tabular Column

Curvature Correction (C_C)

Here, d = horizontal distance between A and B

R = radius of earth

If R = 6370 km

Than C_C = -0.07849d²

here ‘C_C’ is in meter and ‘d’ is in kilometer

Curvature Correction

Refraction Correction (C_R)

Here d is in kilometer.

Combined Correction Due to Curvature and Refraction (C)

C = -0.06728d² meter Here d is in kilometer.

Distance of Visible Horizon

d = 3.8553√ckm

Here ‘C’ being in meters. (taking both curvature and refraction into accounts)

Sensitiveness of Bubble Tube

Sensitiveness of the bubble tube is defined as the angular value of one division of the bubble tube.

α' = sensitivity of the bubble tube

= angular value of one division

Here, S = difference between two staff readings.

n = no. of divisions of bubble

where, l = length of one division

R = radius of curvature of bubble tube.

Contouring

Contours: Contour is an imaginary line joining points of equal elevation on earth surface.

Contour interval: Vertical distance between two contour is called contour internal.

Some suitable value of contour intervals

value of Contours Interval

Contour internal for various purposes are suggested as:

Contours Interval for Various Purpose

Methods of Levelling:

1.                         Height of Collimation Method

2.        Rise and Fall Method

                 

1.      Collimation Method:

 It consist of finding the elevation of the plane of collimation ( H.I.) for every set up of the instrument, and then obtaining the reduced level of point with reference to the respective plane of collimation.

  1.        Elevation of plane of collimation for the first set of the level determined by adding back side to R.L. of B.M.

 2.      The R.L. of intermediate point and first change point are then obtained by starching the staff reading taken on respective point (IS& FS) from the elation of the plane collimation. [H.I.] 

 3.        When the instrument is shifted to the second position a new plane  collimation is set up. The elevation of this plane is obtained by adding B.S. taken on the C.P. From the second position of the level to the R.L. C.P. The R.L. of successive point and second C.P. are found by subtract these staff reading from the elevation of second                               

               plane of collimation Arithmetical check

                Sum of B.S. – sum of F.S. = last R.L. – First R.L. 

                This method is simple and easy.

Reduction of levels is easy.

Visualization is not necessary regarding the nature of the ground. There is no check for intermediate sight readings

This method is generally used where more number of readings can be taken with less number of change points for constructional work and profile leveling.

2.  Rise and Fall Method:

It consists of determining the difference of elevation between consecutive points by comparing each point after the first that immediately preceding it. The difference between there staff reading indicates a rise fall according to the staff reading at the point. The R.L is then found adding the rise to, or subtracting the fall from the reduced level of preceding point.

Arithmetic check

Sum of B.S. – sum of F. S. = sum of rise – sum of fall = last R. L. – first R.L.

This method is complicated and is not easy to carry out. Reduction of levels takes more time.

Visualization is necessary regarding the nature of the ground. Complete check is there for all readings.

This method is preferable for check levelling where number of change points are more.

     Common sources of errors in levelling

1.  Instrument not correctly levelled.

2.  Telescope not correctly focused.

3.  The wrong cross-hair reading recorded (e.g. top instead of middle).

4.  Staff incorrectly read or not held vertical.

5.  Staff incorrectly booked.

                                 

All the above are mistakes (blunders) and cannot be corrected unless the work is repeated.

  Tabular example of leveling

(BOOKING)                             (REDUCTION)
Station	remark	BS	IS	FS	Rise	Fall	RL
1	BM
1	A
1	B
2	B
2	C
2	D
2	E
3	E
3	F
3	BM
Sum

Arithmetic checks (necessary for checking the reduction)

Σ (BS) - Σ (FS) =

Σ (RISES) – Σ (FALLS) = LAST (RL) – FIRST (RL) =

Allowable misclosure = ±5 √n mm         ; where n = no. of instrument positions

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