BS FS

What is levelling?

• A measurement process whereby the difference in height between two or more points can be determined

Difference in height H=BS-FS

When do we level?

• Typical examples include : To establish new vertical control (BM or TBM)

To determine the heights of discrete points

To provide spot heights or contours on a plan

To provide data for road cross-sections or volumes of earthworks

To provide a level or inclined plane in the setting out of construction works

Definitions

• Level surface A surface over which water will not flow The direction of gravity is always normal to a

level surface

• Horizontal surface A horizontal surface will be tangent to a level

surface Over short distances (<100 m) the horizontal

surface and the level surface will coincide

Definitions (cont.)

limit of practical coincidence (~100 m)

direction of gravity

level surface

horizontalsurface

Reading an “E-face” staff

0.3

0.33

0.339

Collimation error

• Occurs when the line of sight (as defined by the cross-hairs) is not horizontal

• Leads to an incorrect staff reading

horizontal line

line of sighterror

Two-peg test

• Identifies whether the level has a collimation error

• Allows the collimation error to be determined

• See the plane surveying web site for the two-peg test procedure

More definitions

• Datum A reference surface to which the heights of

all points in a survey or on a site are referred

May be arbitrary or a national height datum

In Australia we have the Australian Height Datum (AHD)

The surface which defines the AHD is (approximately) Mean Sea Level (MSL)

More definitions

• Reduced Level (RL) The height of a point above the datum

• Benchmark (BM) A stable reference point of known RL Usually used as the starting and finishing

point when levelling

• Temporary Bench Mark (TBM) A point placed (e.g. peg, nail, spike) to

provide a temporary reference point

More definitions

• Backsight (BS) Always the first reading from a new

instrument station

• Foresight (FS) Always the last reading from the current

instrument station

• Intermediate sight (IS) Any sighting that is not a backsight or

foresight

More definitions

• Change point (CP) Location of the staff when the level is

moved Change points should be...

Stable Well defined Recoverable e.g. sharp rock, nail, change plate, etc...

Rules for levelling

• Always commence and finish a level run on a Benchmark (BM or TBM)

• Keep foresight and backsight distances as equal as possible

• Keep lines of sight short (normally < 50m)

• Never read below 0.5m on a staff (refraction)

• Use stable, well defined change points

Levelling procedures

• The example on the plane surveying web site shows… Observation procedures Booking procedures Reduction procedures

A sample loop

BM A

CP 1

CP 2

CP 3

Kerb

Post

Kerb

Setup 1

Setup 2

Setup 3

Setup 4

Booking the observations

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Back Inter Fore Point

BM A

CP 1

1.32

3.98

Booking the observations

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Setup 2

Back Inter Fore Point

1.32 BM A

3.98 CP 1

Kerb

Post

CP 2

2.56

1.25

3.65

0.67

Booking the observations

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Setup 2

Setup 3

Back Inter Fore Point

1.32 BM A

2.56 3.98 CP 1

1.25 Kerb

3.65 Post

0.67 CP 2

Kerb

CP 3

3.49

2.58

1.54

Booking the observations

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Setup 4

Setup 2

Setup 3

Back Inter Fore Point

1.32 BM A

2.56 3.98 CP 1

1.25 Kerb

3.65 Post

3.49 0.67 CP 2

2.58 Kerb

1.54 CP 3

BM A

2.64

3.79

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 CP 1

1.25 Kerb

3.65 Post

3.49 0.67 CP 2

2.58 Kerb

2.64 1.54 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 Kerb

3.65 Post

3.49 0.67 CP 2

2.58 Kerb

2.64 1.54 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 Post

3.49 0.67 CP 2

2.58 Kerb

2.64 1.54 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 CP 2

2.58 Kerb

2.64 1.54 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 Kerb

2.64 1.54 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

10.01

9.98

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

10.01

9.98

(0.03)

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

10.01

9.98 6.24 6.21

(0.03)

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

10.01

9.98 6.24 6.21

(0.03)

(0.03)

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

10.01

9.98 6.24 6.21

(0.03)

(0.03)

(0.03)

Reducing levels (Rise and Fall)Back Inter Fore Rise Fall RL Comment

1.32 50.00 BM A

2.56 3.98 2.66 47.34 CP 1

1.25 1.31 48.65 Kerb

3.65 2.40 46.25 Post

3.49 0.67 2.98 49.23 CP 2

2.58 0.91 50.14 Kerb

2.64 1.54 1.04 51.18 CP 3

3.79 1.15 50.03 BM A

10.01

9.98 6.24 6.21

(0.03)

(0.03)

(0.03)

Loop misclosure

• Misclosure The amount by which the measured height

difference (Hmeas) differs from the known height difference derived from the RLs of the starting and finishing benchmarks (Hknown)

Misclosure = Hknown - Hmeas

An acceptable misclose?

• Small misclosures in closed level loops are expected because of the accumulation of errors

• If the misclosure is small, it can be adjusted

• If the misclosure is large, the loop (or part of it) must be repeated

• Misclosures can also result from errors in published BM levels and from BM instability

Testing the misclose

• The amount of misclosure we are prepared to accept depends on the accuracy we are hoping to achieve

• For routine levelling, the third order levelling standard is adopted…

misclosure 12k mm

• where k is the length of the loop in km

Continuing the example

• The misclosure is +30 mm

• The length of the loop is 0.7 km

• The misclosure limit is…

12(0.7) = ±10 mm

• The misclosure of +30 mm is too big

• The loop must be repeated (or find the error)

Adjusting the misclose

• Adjustment is carried out to ensure that the measured and known RLs of the closing benchmark agree

• The misclosure is linearly distributed according to the number of set-ups

• The adjustment per set-up for the previous example is (0.03/4)...

Adjusting the miscloseMeasured RL

Point Adjustment Adjusted RL

50.00 BM A

47.34 CP 1

48.65 Kerb

46.25 Post

49.23 CP 2

50.14 Kerb

51.18 CP 3

50.03 BM A

Adjusting the miscloseMeasured RL

Point Adjustment Adjusted RL

50.00 BM A 0.000 50.000

47.34 CP 1 0.008 47.332

48.65 Kerb

46.25 Post

49.23 CP 2

50.14 Kerb

51.18 CP 3

50.03 BM A

=1*(0.03/4)

Adjusting the miscloseMeasured RL

Point Adjustment Adjusted RL

50.00 BM A 0.000 50.000

47.34 CP 1 0.008 47.332

48.65 Kerb 0.015 48.635

46.25 Post 0.015 46.235

49.23 CP 2 0.015 49.215

50.14 Kerb

51.18 CP 3

50.03 BM A

=2*(0.03/4)

Adjusting the miscloseMeasured RL

Point Adjustment Adjusted RL

50.00 BM A 0.000 50.000

47.34 CP 1 0.008 47.332

48.65 Kerb 0.015 48.635

46.25 Post 0.015 46.235

49.23 CP 2 0.015 49.215

50.14 Kerb 0.023 50.117

51.18 CP 3 0.023 51.157

50.03 BM A =3*(0.03/4)

Adjusting the miscloseMeasured RL

Point Adjustment Adjusted RL

50.00 BM A 0.000 50.000

47.34 CP 1 0.008 47.332

48.65 Kerb 0.015 48.635

46.25 Post 0.015 46.235

49.23 CP 2 0.015 49.215

50.14 Kerb 0.023

51.18 CP 3 0.023

50.03 BM A 0.030 50.000

=4*(0.03/4)

Adjusting the miscloseMeasured RL

Point Adjustment Adjusted RL

50.00 BM A 0.000 50.000

47.34 CP 1 0.008 47.332

48.65 Kerb 0.015 48.635

46.25 Post 0.015 46.235

49.23 CP 2 0.015 49.215

50.14 Kerb 0.023 50.117

51.18 CP 3 0.023 51.157

50.03 BM A 0.030 50.000

Errors in levelling

• Collimation

• Parallax

• Change point instability

• Instrument instability

• Staff instability

• Benchmark instability

• Refraction

Errors in levelling

• Staff reading and interpolation errors

• Staff verticality

• Instrument shading

• Temperature on staff

• Booking errors (e.g. using just 1 benchmark)

• Earth curvature

• Magnetic field effects on auto level

Applications of levelling

• Point heights (relative to a datum)• Height differences (independent of

datum)• Longitudinal sections and cross sections• Data for volume calculations• Contouring• Setting out

Establishing a new point

Benchmark

New point

RLBM

Datum

RLNEW

Measuring height differences

Benchmark

RLBM

Datum

H1

H2

H3

Profiles and cross-sections

RLBM

Benchmark

Datum

1.100

2.9052.510

A

B C

Plotting contours

The RL’s for points A, B and C have beendetermined by levelling. We are now required to determine the location of thecontours using a 0.5 m contour interval.

Plotting contoursLINE ABHAB = 2.51 - 1.10 = 1.410DAB = 10 m

1.100

2.510

A

B

A

B

1.41

10 m

1.4

9.93

For the 2.5 m contour :D = 10*(2.5 - 1.1)/1.41 = 9.93

0.9

6.38

For the 2.0 m contour :D = 10*(2.0 - 1.1)/1.41 = 6.38

0.42.84

For the 1.5 m contour:D = 10*(1.5 – 1.1)/1.41 = 2.84

Plotting contours

LINE ACHAC = 2.905 - 1.100 = 1.805DAC = 14.14 m

For the 1.5 m contour :D = 14.14*(1.5 - 1.1)/1.805 = 3.13

For the 2.0 m contour :D = 14.14*(2.0 - 1.1)/1.805 = 7.05

For the 2.5 m contour :D = 14.14*(2.5 - 1.1)/1.805 = 10.971.100

2.9052.510

A

B C

Plotting contours

LINE BCDHBC = 2.905 - 2.510 = 0.395DBC = 10 m

no contours cross this line

1.100

2.9052.510

A

B C

1.100

2.9052.510

A

B C

Plotting contours

1.5

2.0

2.5