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Faculty of Applied Engineering and Urban Planning. Surveying. Second Semester 2009/2010. Leveling Part II: Differential Leveling. Content. Computation of elevations using Method of Instrument Height Calculations Check Computation of elevations using Method of Rise and Fall

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slide1

Faculty of Applied Engineering and Urban Planning

Surveying

Second Semester 2009/2010

Leveling

Part II: Differential Leveling

slide2

Content

  • Computation of elevations using Method of Instrument Height
  • Calculations Check
  • Computation of elevations using Method of Rise and Fall
  • Calculations Check
slide3

Measuring Elevation Difference Using a level

  • The basic operation in differential leveling is the determination of elevation differences between two points
  • Consider two points A and B as shown
  • Set up the level so that readings may be made on a staff held vertically at A and then at B

B

A

slide4

Rise

2.56

0.93

C

B

A

AC = 2.56 – 0.93 = 1.63 m

slide5

Fall

0.64

2.97

K

M

NK = 0.64 – 2.97 = -2.33 m

N

slide6

Calculation of Elevation

The height of instrument method

Elevation of Point A = 520.43 m AMSL

Height of Instrument HI = Elevation Of A + Staff Reading

= 520.43 + 2.56 = 522.99 m AMSL

Elevation of B = HI – Staff Reading at B

= 522.99 – 0.93 = 522.06 m AMSL

0.93

2.56

C

B

A

slide7

Calculation of Elevation

The height of instrument method

Elevation of Point M = 520.43 m AMSL

Height of Instrument HI = Elevation Of M + Staff Reading

= 520.43 + 0.64 = 521.07 m AMSL

Elevation of N = HI – Staff Reading at N

= 521.07 – 2.97 = 518.10 m AMSL

2.97

0.64

K

M

N

slide8

Calculation of Elevation

The rise and fall method

Elevation of Point A = 520.43 m AMSL

Elevation Difference = Elevation Of A - Elevation Of B

= 2.56 – 0.93 = 1.63 m (rise)

Elevation of B = Elevation at A + rise

= 520.43 + 1.63 = 522.06 m AMSL

0.93

2.56

C

B

A

slide9

Calculation of Elevation

The rise and fall method

Elevation of Point M = 520.43 m AMSL

Elevation Difference = Elevation Of M - Elevation Of N

= 0.64 – 2.97 = - 2.33 m (fall)

Elevation of N = Elevation at M + rise

= 520.43 - 2.33 = 518.10 m AMSL

2.97

0.64

K

M

N

slide10

Definitions

Backsight (BS)

This is the first reading taken by the observer at every instrument station after setting up the level

Foresight (FS)

This is the last reading taken at every instrument station before moving the level

Intermediate Sight (IS)

This is any reading taken at an instrument station between the backsight and the foresight

Turning point (TP)

This point at which both a foresight and a backsight are taken before moving the staff

slide11

Calculation of Elevation

B

A

1

C

G

D

F

E

BM

RL = 98.76 m AMSL

Plan

G

F

1 BM

B

E

C

D

A

0

20

40

60

80

100

120

Distance (m)

Longitudinal Section

slide12

Calculation of Elevation

Instrument Station

1

P

BM

RL = 98.76 m AMSL

Plan

Backsight (BS)

0.663

1 BM

0

Distance (m)

Longitudinal Section

slide13

Calculation of Elevation

B

A

1

C

P

G

D

F

E

BM

Q

RL = 98.76 m AMSL

Plan

2.270

2.787

1.218

0.646

1.153

1.946

1.008

1.585

0.663

G

F

Q

1 BM

B

P

E

C

D

A

0

20

40

60

80

100

120

Distance (m)

Longitudinal Section

slide15

Calculation of Elevation

B

A

1

C

P

BM

RL = 98.76 m AMSL

Plan

Intermediate Sights (IS)

1.153

1.946

1.008

0.663

1 BM

B

P

C

A

0

20

40

Distance (m)

Longitudinal Section

slide17

Calculation of Elevation

B

A

1

C

P

D

BM

RL = 98.76 m AMSL

Plan

Foresight (FS)

1.153

1.946

1.008

1.585

0.663

1 BM

B

P

C

D

A

0

20

40

60

Distance (m)

Longitudinal Section

slide19

Calculation of Elevation

B

A

1

C

P

D

BM

Q

RL = 98.76 m AMSL

Plan

Turning Point (TP)

Backsight (BS)

2.787

1.153

1.946

1.008

1.585

0.663

Q

1 BM

B

P

C

D

A

0

20

40

60

Distance (m)

Longitudinal Section

slide21

Calculation of Elevation

B

A

1

C

P

G

D

D

F

E

BM

Q

RL = 98.76 m AMSL

Plan

2.270

2.787

1.218

0.646

1.153

1.946

1.008

1.585

0.663

G

F

Q

1 BM

B

E

P

C

D

A

80

100

120

0

20

40

60

Distance (m)

Distance (m)

Longitudinal Section

slide23

Check 1

No. of BS = No. of FS

No. of BS = 2

No. of FS = 2

slide24

Check 2

ΣBS - ΣFS = RL of last point - RL of first point

ΣBS - ΣFS = 3.450 – 2.231 = 1.219

RLlast - RLfirst = 99.979 – 98.760 = 1.219

slide25

Check 3

ΣRL – RLfirst point = [Σ (No. of IS and FS × HI)] - Σ IS- Σ FS

ΣRL – RLfirst point = 689.741

[Σ (No. of (IS and FS) × HI)] - Σ IS- Σ FS

= [ 99.423×4 + 100.625×3] – 7.595 – 2.231 = 689.741

slide26

Calculation of Elevation

B

A

1

C

P

G

D

F

E

BM

Q

RL = 98.76 m AMSL

Plan

2.270

2.787

1.218

0.646

1.153

1.946

1.008

1.585

0.663

G

F

Q

1 BM

B

P

E

C

D

A

0

20

40

60

80

100

120

Distance (m)

Longitudinal Section

slide27

Calculation of Elevation

The rise and fall method

Elevation of Point A = 520.43 m AMSL

Elevation Difference = Elevation Of A - Elevation Of B

= 2.56 – 0.93 = 1.63 m (rise)

Elevation of B = Elevation at A + rise

= 520.43 + 1.63 = 522.06 m AMSL

0.93

2.56

C

B

A

slide28

Calculation of Elevation

The rise and fall method

Elevation of Point A = 520.43 m AMSL

Elevation Difference = Elevation Of A - Elevation Of B

= 0.64 – 2.97 = - 2.33 m (fall)

Elevation of B = Elevation at A + rise

= 520.43 - 2.33 = 518.10 m AMSL

2.97

0.64

C

A

B

slide29

Calculation of Elevation

B

A

1

C

G

D

F

E

BM

RL = 98.76 m AMSL

Plan

G

F

1 BM

B

E

C

D

A

0

20

40

60

80

100

120

Distance (m)

Longitudinal Section

slide30

Calculation of Elevation

Instrument Station

1

P

BM

RL = 98.76 m AMSL

Plan

Backsight (BS)

0.663

1 BM

0

Distance (m)

Longitudinal Section

slide31

ΔH1A = BS – IS

= 0.633 – 1.946 = -1.283 (fall)

slide32

Calculation of Elevation

B

A

1

C

P

D

BM

RL = 98.76 m AMSL

Plan

Intermediate Sights (IS)

Foresight (FS)

1.153

1.946

1.008

1.585

0.663

1 BM

B

P

C

D

A

0

20

40

Distance (m)

Longitudinal Section

slide34

Calculation of Elevation

B

A

1

C

P

D

BM

Q

RL = 98.76 m AMSL

Plan

Turning Point (TP)

Backsight (BS)

2.787

1.153

1.946

1.008

1.585

0.663

Q

1 BM

B

P

C

D

A

0

20

40

60

Distance (m)

Longitudinal Section

slide36

Calculation of Elevation

B

A

1

C

P

G

D

D

F

E

BM

Q

RL = 98.76 m AMSL

Plan

2.270

2.787

1.218

0.646

1.153

1.946

1.008

1.585

0.663

G

F

Q

1 BM

B

E

P

C

D

A

80

100

120

0

20

40

60

Distance (m)

Distance (m)

Longitudinal Section

slide38

Check 1

No. of BS = No. of FS

No. of BS = 2

No. of FS = 2

slide39

Check 2

ΣBS - ΣFS = ΣRise – ΣFall = RLlast – RLfirst

3.450 – 2.231 = 3.079 – 1.860 = 99.979 - 98.760

1.219 = 1.219 = 1.219