Classification of levelling

CLASSIFICATION OF LEVELLING

1. SIMPLE LEVELLING (Fig. 43)

In Simple Levelling, we find the difference of level between two stations which are not far away.

Fig. 43 shows a levelling instrument setup at station O, placed approximately midway between the two stations A and B. Station O need not lie on the line joining A and B.

To determine the Elevation of Station B

Bench Mark (B.M.) of staff A is 10 m, which is the known elevation of A. The reading of the staff at A is first noted as 0.88 m. Then, reading of the staff at B is noted as 0.46 m, after adjusting the bubble to be at the center and the telescope becomes horizontal.

The difference in elevation between A and B = 0:88 m - 0.46 m = 0.42. m. Further, the station A on which a greater staff reading is obtained, is at a lower level. That is, A is at a lower level than B by 0.42 m.

Note:

If the Reduced Level (R.L.) of A is 10, then R.L. of B is found as follows:

Height of the instrument at O H.I. = (10 + 0.88) m   = 10.88 m  

R.L. of B (i.e., elevation of B) = [(10 + 0.88) -0.46] m

= (10 + 0.42) m

= 10.42 m

PROBLEM 1: The staff readings taken at stations A and B are 2.750 and 0.725 m respectively. Find the R.L. of B if the R.L. of A is 50.000 and the difference in level between A and B. (UD)

Solution:

Given: R.L. of A = 50.000;      B.S. = 2.750;    F.S. = 0.725

Height of Instrument (H.I.)    = R.L. + B.S. = 50.000 + 2.750 = 52.750

R.L. of B = H.I. - F.S.

= 52.750 – 0.725 = 52.025 m

Difference in level between A & B = R.L. of B - R.L. of A = 52.025 – 50.000 = 2.025 m

Or Difference in level between A & B = B.S. on A - F.S. on B = 2.750 - 0.725 = 2.025 m

2. DIFFERENTIAL LEVELLING or SERIES LEVELLING or COMPOUND LEVELLING

Differential Levelling requires more than one setting of the levelling instrument to determine the difference in level (elevation) between two points,

- when they are too far apart, - when the difference in elevation between them is too great, or

- when they are intervened by obstacles and the levels could not be found from a single setup of the instrument.

In differential levelling, the principle of simple levelling is employed in series, in successive stages, to find the level difference between the points which are quite far apart. Hence, it is known as Series Levelling or Compound Levelling.

See Fig. 44. A and D are the two points whose difference in elevation is to be determined. The levelling staff reading at A is noted as a from the station point Sı. After adjusting the bubble, the staff reading at a point B is noted from Si as bı. B is selected such that AS, is approximately equal to S₁B.

Note that the staff reading a is the Back Sight (B.S.) and bi is the Fore Sight (F.S.).

Then, the levelling instrument is shifted to the station point S2. The staff reading at B from S2 is noted as b2. Another point C is selected for the levelling staff. The above procedure is repeated till the end point D is reached.

The difference in level between the levelling staffs A and B is (a - bi). Similarly, the difference in level between levelling staffs B and C is (b2 - ci) and so on. Thus, the difference in level between the end points A and D

= algebraic sum of the differences calculated above

= (a - b₁) + (b₂ – C₁) + (C₂ – d)