METHOD OF LEVELLING - COMPUTING REDUCED LEVELS USING HEIGHT OF COLLIMATION METHOD (HI METHOD)

COMPUTING REDUCED LEVELS USING HEIGHT OF COLLIMATION METHOD (HI METHOD)

In this method, the reduced levels of points are computed by calculating the reduced levels of the plane of collimation for each set up of the instrument.

The height of collimation is obtained by adding the staff reading, which must be back sight to the known reduced level of the point on which the staff stands. Reduced levels of all the other points are obtained by subtracting the staff reading from the height of collimation. When the instrument is changed to a new station, a new height of collimation is obtained by adding the new backsight with the reduced level of the last point obtained from the previous set up of the instrument. The steps involved in booking and reading the level in the height of the collimation method are illustrated with the help of an extract from a field book given below.

Station	BS	IS	FS	HI	RL	Remarks
A	0.665			100.665	100.00	BM
B		0.825			99.840
C		2.540			98.125
D	3.200		0.385	103.480	100.280	CP
E	1.565		1.400	103.645	102.080	CP
F		2.000			101.645
G			2.450		101.195

 

In this table, the back sight, intermediate sight and foresight are the readings taken in the field and in the remarks column benchmarks and change points are specified. Then, with the help of this available data the height of the instrument and reduced levels are calculated and the usual checks are carried out.

 

1. To begin with, the elevation of the plane of collimation of the first instrument station (I1) is to be calculated. This is done by adding the back sight to the reduced level of the benchmark. The reduced level of the benchmark, i.e., point A, is taken as 100.00 and backsight is taken by holding a staff at point A (i.e., 0.665).

 

Elevation of the plane of collimation = 100 + 0.665 = 100.665

This is entered as the height of the instrument (HI) as seen in the table.

 

2. Then, from the same instrument station, readings are taken of the staff held at B and C and entered as the intermediate sight. Then the reduced level of B and C are calculated.

For example, RL of B = HI - IS = 100.665 - 0.825 = 99.840

 

3. Now the instrument is shifted to the next point I2 and the backsight and foresight are taken. Then, the HI and reduced level at this point is calculated.

RL = HI at first point - FS

= 100.665 - 0.385

= 100.280

HI = RL + BS

= 100.280 + 3.200

= 103.480

 

4. This procedure is followed till the last point is reached.

 

5. Now the checks are carried out to ascertain the correctness of the readings. i.e., ΣBS – ΣFS = Last RL – First RL

ΣBS = 5.430; ΣFS = 4.235; First RL = 100.00; Last RL = 101.195

5.430 – 4.235 = 101.195 – 100 = 1.195

Hence checked.

 

Problem-1

Complete the levelling table given below

Station	BS	IS	FS	HI	RL	Remarks
BM	3.10				193.62	BM
1		2.56
2		1.07
3	1.92		3.96			CP
4	1.20		0.67			CP
5		4.24
6	0.22		1.87			CP
7		3.03
8			1.41

 

Solution: The levels are computed as below

 

Station	BS	IS	FS	HI	RL	Remarks
BM	3.10			196.72	193.62	BM
1		2.56			194.16
2		1.07			195.65
3	1.92		3.96	194.68	192.76	CP
4	1.20		0.67	195.21	194.01	CP
5		4.24			190.97
6	0.22		1.87	193.56	193.34	CP
7		3.03			190.53
8			1.41		192.15
	Σ 6.44		Σ 7.91

 

Check: ΣBS – ΣFS = Last RL – First RL

ΣBS = 6.44; ΣFS = 7.91; Last RL = 192.15; First RL = 193.62

i.e., 6.44 – 7.91 = –1.47 m

192.15 – 193.62 = –1.47 m

Hence checked.

Problem-2

Compute the levels from the levelling field book using HI method.

BS	IS	FS	HI	RL	Remarks
3.39				23.10	BM
	2.81
	2.51
1.92	2.22	3.96	194.68		CP
1.20		0.67	195.21		CP
	4.24
0.22		1.87	193.56		CP
	3.03

 

Solution. The levels are computed as below.

 

BS	IS	FS	HI	RL	Remarks
3.39			26.49	23.10	BM
	2.81			23.68
	2.51			23.98
	2.22			24.27
2.61		1.88	27.22	24.61	CP
	2.32			24.90
	1.92			25.30
		1.54		25.68

 

Check: ΣBS – ΣFS = Last RL – First RL

ΣBS = 6.00; ΣFS = 3.42; Last RL = 25.68; First RL = 23.10

i.e., 6.00 – 3.42 = 2.58 m

25.68 – 23.10 = 2.58 m

Hence checked.

Problem-3

The following are the staff readings taken while making levels of a field. The back sights are underlined. Tabulate the levels in a field book and compute the level difference using HI method. 0.813, 2.170, 2.908, 2.630, 3.133, 3.752, 3.277, 1.899 and 2.390,

Here, in this problem, the readings have to be entered in a book form, entries are checked and the reduced levels found.

BS	IS	FS	HI	RL	Remarks
0.813			40.376	39.563	BM
	2.170			38.206
	2.908			37.468
	2.630			37.746
3.752		3.133	40.995	37.243	CP
	3.277			37.718
	1.899			39.096
		2.390		38.605
Σ4.565		Σ5.523

 

Check: ΣBS – ΣFS = Last RL – First RL

ΣBS = 4.565; ΣFS = 5.523; Last RL = 38.605; First RL = 39.563 4.565 – 5.523 = –0.958

38.605 – 39.563 = –0.958

Hence checked.

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