Some Basic Principles for Leveling in surveying

Basic principles of Levelling in surveying and concepts of surveying in Civil Engineering

1. Some Basic
Principles for
Leveling

2. Lecture Overview
•Equipment
•Introduction to Leveling
•Observation, Field Notes, and
Computation
•Errors and their effects

3. Equipment

4. Equipment
•Level Instrument
•Tripod
•Staff/Pole
•Change plate (German: Frog/Frosch)
•Pole staff bubble (bull eye)
•Marker

5. Equipment: Level
Instrument
•Automated Levels

Easy to use (not power!)

Needs experience

Robust even in hostile environment
•Digital Levels

Push-button technique

No reading errors, special staff

Readings are stored and analyzed digitally

6. Automated Levels
(Compensator)
Pendulum
Tribrach
Courtesy: Deumlich, Vermessungskunde
Bull Eye

7. Digital Levels
•Uses Barcode staffs
•Internal storage of data

Download to the computer

Automated height computation + adjustment

No feeling for quality anymore

You frequently need power plugs

8. Equipment
•Level Instrument
•Tripod
•Staff/Pole
•Change plate (German: Frog/Frosch)
•Pole staff bubble (bull eye)
•Marker

9. Equipment: Tripod
•Wooden design or aluminum

From “easy to sit” to “ops, this is high”

10. Equipment
•Level Instrument
•Tripod
•Staff/Pole
•Change plate (German: Frog/Frosch)
•Pole staff bubble (bull eye)
•Marker

11. Equipment: Staff/Pole
•Wood, aluminum
•INVAR type for high precision leveling
Conventional (“E”-type)
Barcode
for Digital Levels

12. Equipment
•Level Instrument
•Tripod
•Staff/Pole
•Change plate (German: Frog/Frosch)
•Pole staff bubble (bull eye)
•Marker

13. Equipment: Change Plate
•For long survey lines
•Allows change of instruments

Best is a metal change plate

Screws e.g. at fences

Sharp stones or nails
•Beware of dark colors
It’s not the
Indonesian-
German Dictionary,
It’s the nail!

14. Equipment
•Level Instrument
•Tripod
•Staff/Pole
•Change plate (German: Frog/Frosch)
•Pole staff bubble (bull eye)
•Marker

15. Equipment: Bubble
•Keep the pole upright

Any tilt will disturb your readings

16. Equipment
•Level Instrument
•Tripod
•Staff/Pole
•Change plate (German: Frog/Frosch)
•Pole staff bubble (bull eye)
•Marker

17. Survey Markers
•Gives you a fixed point

Should be of good quality

Should be long-term

Preferable in bedrock, settled buildings, or
bridges

Do not use fences or walls

18. Introduction to
Leveling

19. Some Basic Definitions
•Level surface (e.g. the geoid)

A water surface with no motion

Gravity gradient is the normal to the level surface

The Instrument’s Bubble is in the normal (!)
•Horizontal surface

At the instruments axis, the horizontal surface is
tangent to the level surface

Over short distances (<100 m) the horizontal surface
and the level surface will coincide

For long leveling lines the effects of the gravity field
must be considered

20. Leveling rods
Line of sight
Back sight
Fore sight
Gravity Gradient
Basic Principle of Leveling
•Measures height differences between
points

Along a line

Several points from one occupation
bs
fs
h = bs - fs

21. Definitions
•Back sight (BS)

The first reading from a new instrument stand
point (i.e. take the height to the instrument)
•Fore sight (FS)

The last reading from the current instrument
station (i.e. give the height to a benchmark)
•Intermediate sight (IS)

Any sighting that is not a back sight or fore
sight

22. Reading a Staff
1422
• Read the [m], [dm] & [cm]
• Estimate the [mm]
• Check yourself for
frequent used numbers
(2/3) or (7/8)

23. Basic Rules for Leveling
•Always start and finish a leveling run on a
Benchmark (BM or TGBM) and close the loops
•Keep fore sight and back sight 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
•Beware of shadowing effects and crossing
waters

24. Observation, Field Notes,
and Computation

25. How to: A sample loop
S2
S1
New Benchmark
NB1
Tidal Hut
TH
New Benchmark
NB2

26. How To: Field Notes
Back InterForePoint
TH
NB1
NB2
NB1
TH
1327
3982
S2
S1
New Benchmark
NB1
Tidal Hut
TH
New Benchmark
NB2
2365
09862347
37243753
1101

27. Date, Observer,
Instrument
Instrument Check
F
o
r
e
B
a
c
k



28. Compute levels
BackInterFore dh H Comment
TH
BM1
BM2
BM1
TH
IST
SOLL
1327
3982
0986
3724
2365
2347
3753
1101
1379
2652
9792 9793
-0001
+1
100 000
100 000
0000
0001 (SOLL – IST)
´7345
´8624
0
97 345
98 724
97 348
?
0

29. Loop misclosure
•Misclosure Error

The difference of the measured height
difference (H
meas) to the known height (closed
loops = 0, known benchmarks = height
difference)
Misclosure = H
SOLL – H
IST
•Point errors at double observed points

30. Achievable Accuracy
•Instrument dependent

Roughly from the instrument
NI002 = 0,2mm/km (doubled line)
NI025 = 2.5mm/km (doubled line)
•Survey line length dependent
m
s
= m
1km
s, s in km
m
H = (m
1km/2) s, s in km #(middle of the line)

31. An acceptable misclose?
•Small misclosures in closed level loops are
expected because of the accumulation of
random errors and 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

32. Testing the misclose
•The amount of misclosure acceptable using
a specific instrument and survey line length
•For our example, a second order leveling
standard is adopted
*
…
misclosure  2,5s mm
•where s is the length of the line in km
*
Dependent on your contry’s rules and the instrument used

33. Our example
•The misclosure is +1 mm
•The length of the loop is 0.4 km
•Acceptable error is
2.5(0.4) = ±1.6 mm
•The misclosure of +1 mm is within the limit
•Mean error for NB1 = 2.5/2* (0.4)

34. Errors and their effects
(many, but only a few addressed)

35. Errors in leveling, e.g.
•Collimation, Parallax
•Change point / staff instability
•Instrument or Benchmark instability
•Refraction
•Uncalibrated staff or levels
•Reading, booking, or computation errors
•Fore- and backsight distances different

36. Systematic and Random Errors
•Earth curvature
•Refraction
•Collimation errors

37. Effect of Earth Curvature
C
u
r v
a
t u
r e
e
ff
e
c t
Distance (s) in m 10 20 50 100 1000
Effect (h) in mm 0,008 0,03 0,20,8 80
www.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htm
Horizontal Level
(r +h)
2
= r
2
+ s
2
=>
h  s
2
/(2r)

38. Refraction
www.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htm
Mean Gradient: 0,2 °C / m

39. Collimation error
•Occurs when the line of sight (as defined
by the lens axis and cross-hairs) is not
horizontal
•Leads to an incorrect staff reading
horizontal line
line of sight
error

40. Stand point 1
Stand point 2
´
´
´ ´
Instrument test: Nähbauer
a′
1
= a
1
+e
b′
1
= b
1
+2e
Δh = a
1−b
1
Δh′
1
= a′
1
−b′
1
= a
1
−b
1
−e = Δh−e
With Δh′
1+e = Δh′
2−e
Δh′
2
−Δh′
1
2
a′
2
= a
2
+2e
b′
2 = b
2+e
Δh = a
2
−b
2

Δh′
2
= a′
2
−b′
2
= a
2
+e−b
2
= Δh+e
Δh =Δh′
2
−e
e =

41. Summary

42. Procedure of leveling
1.The instrument must be check before use! (see lecture)
2.The instrument and level must be stable settled-up
3.The bubble tube must be leveled before the reading
•Beware of sun exposure (will wander)
•Ensure the instruments pendulum is in-limit
4.The instrument must be set up in the middle between
two staffs
•Prevents curvature effects
•If impossible, use the same distances, but opposite for the
next readings
5.You must not use the parallax screw between the
backsight and foresight readings

43. 6.Readings must be taken 30-50 cm above the ground
•Surface refractions
•Beware also of temperature gradients (inside/outside
buildings) !!!!
7.Staff should be set up vertically
8.A change plate should be used
9.Leveling must be done in two opposite directions but
the same line (beware of gravity gradients)
10.Staff should be calibrated, especially if INVAR
11.Be careful when crossing rivers (large water surfaces)
•Use “same-time” (mutual) observations
•Repeat it during different times of the day
Procedure of Leveling

44. An Unhappy Surveyor
… having a 2 centimeter difference