Theory of Errors and AdjustmentsLecture 3

Caraga State UniversityCollege of Engineering and Information Technology

Broddett B. Abatayo, GE Lecturer

In a two peg test using model wild NA2 dumpy level, the following observations were taken:

Rod reading Instrument M set

up near at AInstrument P set

up near at B

on point A 1.623 0.362

on point B 2.875 1.622

1. What is the true difference in elevation between A and B?2. Determine the error in the line of sight for the net distance AB ?3. Determine the correct reading at A that will give level line of sight with the instrument still

at point P.

A

B

M

PEG METHOD OF ADJUSTMENTSITUATION 1: SITUATION 1:

P

In a two peg test using model wild NA2 dumpy level, the following observations were taken:

1. What is the true difference in elevation between A and B?2. Determine the error in the line of sight for the net distance AB ?3. Determine the correct reading at A that will give level line of sight with the instrument still

at point P. Ans. 1.) 1.256m 2.) 0.004m 3.) 0.366m

PEG METHOD OF ADJUSTMENT

A

B

SITUATION 1: SITUATION 1:

Rod reading Instrument M set

up near at AInstrument P set

up near at B

on point A 1.623 0.362

on point B 2.875 1.622

The line of sight of a wye level was tested by setting up exactly midway between two points A and B.

Instrument at M Instrument at P

Rod reading on A 1.520m 1.683m

Rod reading on B 1.395m 1.490m

1. What is the true difference in elevation between A and B?2. What is the error in the line of sight?3. Determine the reading at A that will make the line of sight horizontal?

A

B

M

PEG METHOD OF ADJUSTMENTSITUATION 2: SITUATION 2:

The line of sight of a wye level was tested by setting up exactly midway between two points A and B.

Instrument at M Instrument at P

Rod reading on A 1.520m 1.683m

Rod reading on B 1.395m 1.490m

1. What is the true difference in elevation between A and B?2. What is the error in the line of sight?3. Determine the reading at A that will make the line of sight horizontal?

Ans. 1.) 0.125m 2.) 0.068m 3.) 1.615m

A

B

P

PEG METHOD OF ADJUSTMENTSITUATION 2: SITUATION 2:

A

1

To make peg adjustment, the following notes were taken.

Wye level @ 1 Wye level @ 2

Rod reading @ P 0.75m 1.906m

Rod reading @ Q 2.766m 3.789m

Point 1 is on the line PQ and midway between P and Q. Point 2 is on the same line as P and Q but not between them. Point 2 is 25m from P and 230m from Q. With the wye level at point 2, what is the rod reading at P for a level sight?

PEG METHOD OF ADJUSTMENTSITUATION 3: SITUATION 3:

B

To make peg adjustment, the following notes were taken.

Point 1 is on the line PQ and midway between P and Q. Point 2 is on the same line as P and Q but not between them. Point 2 is 25m from P and 230m from Q. With the wye level at point 2, what is the rod reading at P for a level sight?

Ans. 1.921

2

PEG METHOD OF ADJUSTMENTSITUATION 3: SITUATION 3:

A

B

Wye level @ 1 Wye level @ 2

Rod reading @ P 0.75m 1.906m

Rod reading @ Q 2.766m 3.789m

SITUATION 4: SITUATION 4:

A line of levels 6km long is run from BM1 to BM2 with a computed elevation of 165.80m. The average BS and FS distances are 100m and 150m respectively. 1.) It was found out however that the line of sight of the instrument is inclined upward by 0.003m in a distance of 10m. Determine the correct elevation of BM2.

2.) If the level settles by 5mm between the instant of every BS and FS readings. Find the correct elevation of BM2.

3.) If the leveling rod is inclined 4⁰ from the vertical every time the backsight is taken and the average BS reading is 2.4m. Determine the correct elevation of BM2.

SITUATION 4: SITUATION 4:

A line of levels 6km long is run from BM1 to BM2 with a computed elevation of 165.80m. The average BS and FS distances are 100m and 150m respectively. 1.) It was found out however that the line of sight of the instrument is inclined upward by 0.003m in a distance of 10m. Determine the correct elevation of BM2.

2.) If the level settles by 5mm between the instant of every BS and FS readings. Find the correct elevation of BM2.

3.) If the leveling rod is inclined 4⁰ from the vertical every time the backsight is taken and the average BS reading is 2.4m. Determine the correct elevation of BM2.

SITUATION 4: SITUATION 4:

A line of levels 6km long is run from BM1 to BM2 with a computed elevation of 165.80m. The average BS and FS distances are 100m and 150m respectively. 1.) It was found out however that the line of sight of the instrument is inclined upward by 0.003m in a distance of 10m. Determine the correct elevation of BM2.

2.) If the level settles by 5mm between the instant of every BS and FS readings. Find the correct elevation of BM2.

3.) If the leveling rod is inclined 4⁰ from the vertical every time the backsight is taken and the average BS reading is 2.4m. Determine the correct elevation of BM2.

Adjustment of LEVEL CIRCUITSThe known elevation of BM1 is 738.730m. A 30,500km long level circuit is run, closing back on BM1 with an elevation, as determined from the notes, of 728.486m. The observed elevations of other bench marks which were established during the run, and their distances from the initial bench mark are given as follows:

SITUATION 5: SITUATION 5:

Sta Distance from BM1 km

Observed elevation m

BM6

BM1

BM2

BM3

BM5

BM4

BM1 0.000 728.730

BM2 5.245 783.213

BM3 11.271 891.764

BM4 17.718 843.195

BM6 25.247 702.956

BM1 30.500 728.486

BM5 21.964 739.708

3.283km

4.246km

6.447km

6.026km5.245km

728.486m

702.956m

739.708m

843.195m

891.764m

783.213m

728.730m

5.253km

Determine the ff:

1.) The error of closure.2.) Correction to be applied to each observed elevation.3.) Adjusted elevations of the bench marks along the level route.

SITUATION 5: SITUATION 5: Adjustment of LEVEL CIRCUITS

BM6

BM1

BM2

BM3

BM5

BM4

3.283km

4.246km

6.447km

6.026km5.245km

728.486m

702.956m

739.708m

843.195m

891.764m

783.213m

728.730m

5.253km

Determine the ff:

1.) The error of closure.2.) Correction to be applied to each observed elevation.3.) Adjusted elevations of the bench marks along the level route.

Adjustment of LEVEL NETSITUATION 6: SITUATION 6:

- 10.64

- 15.96

+20.64

- 4.95

+4.76

From the level net shown , it is required to compute the adjusted elevations of BM2, BM3 and BM4 if BM1 = 100m.

BM2 – 100 = 20.64BM3 – BM2 = 4.76BM4 – BM3 = -10.64 100 – BM4 = -15.96BM4 – BM2 = -4.95

VARIABLES = CONSTANT

BM2 = 120.64 -BM2 + BM3 = 4.76 -BM3 + BM4 = -10.64 -BM4 = -115.96-BM2 + BM4 = -4.95

ABCDE

BM1

BM2

BM3

BM4

SITUATION 6: SITUATION 6: