Question

The extract below is taken from a Level Book for levels taken between 2 TBMs. Complete the Level Book entries as well as calculate the adjusted RL (reduced levels) for all entries. The misclose error can be assumed acceptable. Note: all staff readings are in meters.

BS	IS	FS	Rise	Fall	RL	Correction	Corrected RL	Notes
1.379								TBM RL 175.5
	2.795							PEG 1
	3.215							PEG 2
	0.595							PEG 3
	1.270							PEG 4
1.280		3.215						CP B
	1.030							PEG 5
	3.045							PEG 6
2.312		3.815						CP C
1.743		3.227						CP D
	2.735							PEG 7
		3.623						TBM RL 168.50

Answer 1

BS	IS	FS	RISE	FALL	RL
1.379					175.5
	2.795			1.416	174.084
	3.215			0.42	173.664
	0.595		2.62		176.284
	1.27			0.675	175.609
1.28		3.215		1.945	173.664
	1.03		0.25		173.914
	3.045			2.015	171.899
2.312		3.815		0.77	171.129
1.743		3.227		0.915	170.214
	2.735			0.992	169.222
		3.623		0.888	168.334
6.714		13.88	2.87	10.036

[Note:

Rise or Fall in any row = BS or IS of previous row - IS or FS of the considered row.

If the obtained value is positive, then write it in rise column.

If the obtained value is negative, then write it in fall column.

For example:

In second row: BS of first row - IS of second row = 1.379 - 2.795 = - 1.416

Obtained value is negative, hence written in fall column.

Similarly in 4th row: IS of 3rd row - IS of 4th row = 3.215 - 0.595 = + 2.62

Obtained value is positive, hence written in rise column.

RL in any row = RL in previous row + Rise in the row ( if rise is present in the row considered)

= RL of previous row - Fall in the row (If fall is present in the row considered) ]

Check:

i)

From the above table we have,

Sum of back sights = 6.714

Sum of fore sights = 13.88

Therefore,

Sum of back sights - Sum of fore sights = 6.714 - 13.88 = -7.166

ii)

Sum of rises = 2.87

Sum of falls = 10.036

Therefore,

Sum of rise - Sum of falls = 2.87 - 10.036 = -7.166

iii)

Last RL = 168.334

First RL = 175.50

Therefore,

Last RL - First RL = 168.334 - 175.50 = -7.166

Therefore we can say that,

Sum of back sights - Sum of fore sights = Sum of rise - Sum of falls = Last RL - First RL

Hence calculations performed are correct.

Error of misclosure (e):

Obtained value of last RL = 168.334

But given that, correct value of last RL = 168.50

Therefore error of misclosure (e) = Obtained RL - Correct RL

= 168.334 - 168.50

Therefore, error of misclosure (e) = -0.166

Correction:

As the error is negative, correction must be positive.

Therefore, total correction = + 0.166

Total number of set up of instruments = 4 (Number of instrument set up = Number of back sights available)

Therefore correction per set up = Total correction / Number of setup

= + 0.166 / 4

= + 0.0415

BS	IS	FS	RISE	FALL	RL	CORRECTION	CORRECTED RL	Notes
1.379					175.5	-	175.5	TBM 1
	2.795			1.416	174.084	0.0415	174.1255	PEG1
	3.215			0.42	173.664	0.0415	173.7055	PEG2
	0.595		2.62		176.284	0.0415	176.3255	PEG3
	1.27			0.675	175.609	0.0415	175.6505	PEG4
1.28		3.215		1.945	173.664	0.0415*2 = 0.083	173.747	CP 1
	1.03		0.25		173.914	0.083	173.997	PEG6
	3.045			2.015	171.899	0.083	171.982	PEG7
2.312		3.815		0.77	171.129	0.0415*3= 0.1245	171.2535	CP2
1.743		3.227		0.915	170.214	0.0415*4=0.166	170.38	CP3
	2.735			0.992	169.222	0.166	169.388	PEG10
		3.623		0.888	168.334	0.166	168.5	TBM 2
6.714		13.88	2.87	10.036