METHODS OF CALCULATION OF REDUCE LEVEL

 

METHODS OF CALCULATION OF REDUCE LEVEL

The following are two systems of calculating reduce level:

   [1]. The collimation systems or height of instrument system (HI)

   [2]. The rise and fall system.

[1]. The collimation systems or height of instrument system (HI). 

   The reduce level of the line of collimations is said to be the height of instrument. In this system, the height of line of collimation is found out by adding the backsight reading to the RL of the BM on which of the BS is taken. Then the RL of the intermediate points and the change points are obtained by subtracting the respective staff readings from the height of the instrument (HI).

   The level is then shifted for the next set up and again height of the line of collimation is obtained by adding the backsight reading to the RL of the change point (which was calculated in the first set up).

   So, the height the height of instrument is different in different set up of the level. Two adjacent planes of collimation correlated at the change point by an FS reading from one setting and a BS reading from the next setting.

   It should be remembered that, in this system, the RLs of unknown points are to be found out by deducting the staff readings from the RL of the height of the instrument. 

Consider Fig.-L.24

[a]. RL of HI in first setting = 100.00 + 1.150 = 101.150

       RL of A = 101.150 – 1.355 = 99.795

       RL of B = 101.150 – 2.45 = 98.700

[b]. RL of HI in second setting = 98.700 + 1.875 = 100.575

       RL of C = 100.575 – 0.890 = 99.685

       RL of D = 100.575 – 1.655 = 98.920     and so on,

Arithmetical check:    ΣBS – ΣFS = Last RL – 1^st RL

   The difference between the sum of backsight and that of foresight must be equal to the difference between the last RL and the first RL. This check verifies the calculation of the RL of the HI and that of the change point. There is no check on RLs of the intermediate points.

[2]. The rise-and-fall system. 

   In this system, the difference of level between two consecutive points is determined by comparing each forward staff reading with the staff reading at the immediately preceding point.

   If the forward staff reading is smaller than the immediately preceding staff reading, a rise is said to have occurred. The rise is added to the RL of the preceding point to get the RL of forward point.

   If the forward staff reading is greater than the immediately preceding staff reading, its means there has been a fall. The fall is subtracted from the RL of the preceding point to get the RL of forward point.

Consider Fig.-L.25

Point A (with respect to BM) = 0.90 – 1.32 = -0.42           (fall)

Point B (with respect to A) = 1.32 – 2.23 = -0.91              (fall)

Point C (with respect to B) = 2.23 – 1.58 = +0.65             (rise)

Point D (with respect to C) = 1.58 – 2.27 = -0.69              (fall)

 

RL of BM = 100.00

RL of A = 100.00 – 0.42 = 99.58

RL of B = 99.58 – 0.91 = 98.67

RL of C = 98.67 + 0.65 = 99.32

RL of D = 99.32 - 0.69 = 98.63 

Arithmetical check:    ΣBS – ΣFS = Σrise - Σfall = Last RL – 1^st RL

   In this method, the difference between the sum of BSs and that of FSs the difference between the sum of rises and that of falls and the difference between the last RL and first RL must be equal.

Example  The following consecutive readings were taken with an automatic level along a chain line with a common interval of 15 metre. The first reading was at a chainage of 180 metre where the RL is 103.345. The instrument was shifted after the fifth and eleventh readings.

 2.450, 3.775, 1.605, 0.875, 0.790, 1.670, 1.485, 2.065, 1.385, 1.570, 1.295, 1.440, 2.495, 1.370, 0.945 and 1.070

1. By collimation System:
Station Point	Chainage (in Metre)	BS	IS	FS	RL of collimation line (HI)	Reduce Level (RL)	Remarks
1	180.00	2.450			105.795	103.345
2	195.00		3.775		105.795	102.020
3	210.00		1.605		105.795	104.190
4	225.00		0.875		105.795	104.920
5	240.00	1.670		0.790	106.675	105.005	Change Point  (CP)
6	255.00		1.485		106.675	105.190
7	270.00		2.065		106.675	104.610
8	285.00		1.385		106.675	105.290
9	300.00		1.570		106.675	105.105
10	315.00	1.440		1.295	106.820	105.380	Change Point (CP)
11	330.00		2.495		106.820	104.325
12	345.00		1.370		106.820	105.450
13	360.00		0.945		106.820	105.875
14	375.00			1.070	106.820	105.750
Total =		5.560		3.155

Arithmetical Check:
	ΣBS - ΣFS = 5.560 - 3.155 = + 2.405 Last RL - 1st RL = 105.750 - 103.345 = + 2.405

2. By rise-and fall System: Station Point Chainage  (in Metre) BS IS FS Rise (+) Fall (-) Reduce Level (RL) Remarks 1 180.00 2.450       103.345   2 195.00   3.775   105.795 1.325 102.020   3 210.00   1.605   2.170   104.190   4 225.00   0.875   0.730   104.920   5 240.00 1.670   0.790 0.085   105.005 Change Point (CP) 6 255.00   1.485   0.185   105.190   7 270.00   2.065   106.675 0.580 104.610   8 285.00   1.385   0.680   105.290   9 300.00   1.570   0.185 105.105   10 315.00 1.440   1.295 0.275   105.380 Change Point (CP) 11 330.00   2.495   106.820 1.055 104.325   12 345.00   1.370   1.125   105.450   13 360.00   0.945   0.425   105.875   14 375.00     1.070 106.820 0.125 105.750   Total = 5.560 3.155  5.675       3.270

Arithmetical Check: ΣBS - ΣFS = 5.560 - 3.155 = + 2.405 ΣRise - ΣFall = 5.675 - 3.270 = + 2.406 Last RL - 1st RL = 105.750 - 103.345 = + 2.405

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