1. Surveying
Tony Price
&
Nikki Meads

2. Surveying
The main object of surveying is the preparation of maps or plans which are the basis in the planning and design of engineering projects such as route location, e.g. roads, railway lines, pipelines, tunnels, etc.

3. Classification of Surveys
Surveying is divided into two main categories- i) Plane survey ii) Geodetic Survey

4. Geodetic Survey
Where a survey extends over a large area greater than 200 sq. km. and the required degree of accuracy is also great.
The curvature of earth is taken into account.
Used to provide control points to which small surveys can be connected.
Not common in Civil works.

5. Plane Survey For small projects covering an area less than 200 sq.km.
Earth’s curvature is not accounted for in distances. Earth surface is considered as a plane. (Angular error of 1” in 200 sq. km. area by assuming plane).

6. Basic Principles in Surveying
Ruling principles of surveying are : i) “ to work from whole to part”. For surveying you should establish control points of high precision by use of triangulation and precise levelling. This area is further divided into smaller triangles which are surveyed with less accuracy. ii) to fix the position of new stations by at least two independent processes – e.g. linear and angular

7. Setting-out
Whereas surveying maps the existing world, setting-out establishes points for the control of construction processes, e.g.
Positioning foundations
Placing the line of a road or service
Controlling levels and gradients on earthworks

8. Health & Safety

9. Health & Safety
Police said the surveyor was pinned beneath a 12-wheel truck Friday morning for more than an hour. The truck was backing up when it struck the worker. A 60-year-old man was taken to hospital with critical injuries. He was pronounced dead Friday afternoon.

10. Health & Safety Surveyor electrocuted - Employer fined
20 year old Surveyor Russell Donald died after he was electrocuted passing under a high-voltage power line with a metal pole in Echt, Aberdeenshire. His employer, W A Fairhurst and Partner, has been fined £25,200.
The Glasgow based engineering firm were charged with failing to instruct Mr Donald that it was inappropriate to use a long surveying pole in the vicinity of electric lines.

11. Principles of Measurements

12. Principles of Measurements

13. Principles of Measurements

14. Source of Errors
Personal Errors - no surveyor has perfect senses of sight and touch
Instrument Errors - devices cannot be manufactured perfectly, wear and tear and compatibility with other components
Natural Errors - temperature, wind, moisture, magnetic variation, etc.

15. Systematic and Accidental Errors
Systematic or Cumulative Errors -typically stays constant in sign and magnitude
Accidental, Compensating, or Random Errors - the magnitude and direction of the error is beyond the control of the surveyor
Gross Errors – operator stupidity?

16. Normal Distribution Curve
This is the target value

17. Precision

18. Accuracy & Precision

19. Accuracy and Precision
Better precision does not necessarily mean better accuracy
In measuring distance, precision is defined as:

20. Standard Deviation is an individual measurement
is the arithmetic mean (most probable value)
is a residual such that

21. Standard Error is an individual measurement
is the arithmetic mean (most probable value)
is a residual such that
(n-1) is known as the number of degrees of freedom or redundancy

22. Standard Error of Arithmetic Mean
Example: 30 m tape with a standard error of 6 mm. If we require a standard error of 3 mm on the distance measured, how many measurements are required?
Giving n = 4

23. Probabilities Associated with the Normal Distribution
Probability %
Confidence interval
68.3
 1
90.0
1.65
95.0
 1.96
95.4
 2
99.0
 2.58
99.7
 3
99.9
 3.29
-1 s x _
+1 s x _
Assumes normal distribution without gross or systematic errors
-2 s x _
+2 s x _
+3 s x _
-3 s x _

24. Example: Most Probable Value and Standard Error
Calculate the most probable value and its standard error.

25. Solution
The most probable value is given by the arithmetic mean as:

26. Solution cont.
Based upon the most probable value, the residuals and squares of these are calculated:

27. Solution cont.
Therefore the most probable value of the angle is:

28. Example : Distance
Calculate the most probable value for this distance, its standard error and confidence interval for a 95% probability.

29. Solution

30. For 95% probability level the confidence interval for the true value is:
REJECT

31. Recalculate with remaining measurements:

32. Propagation of Standard Error
Special law of propagation of standard error for a quantity U
D=a+b or a-b
A=xy

33. Example

35. Converts “ to radians

36. Propagation of Errors Activity Standard Error Levelling
Angular measurement
Trigonometrical heighting
Traversing
Ss = standard error of reading staff; D = distance; l = sight length (foresight, backsight)
Sm = std. error in angle reading; Sb = std. error bisecting target; n = number of measurements; SHA = std. error height of station A; Shi = std.error of height of total station above A; Shr = std.error of height of reflector above B; SL = std.error of slope length; Sa = std.error of angle;

37. Example
If total station has a precision of 6” and targets and observers are such that Sb = 7.5” how many readings must be taken to achieve a precision of 5” in ?
Sm =  6, hence
4 readings are required.

38. Levelling

39. Profile Boards Define level Define slope, e.g. on bank

42. (after CIRIA Manual of Setting-out Procedures)

43. Closed Traverse N

44. What is a traverse? A polygon of 2D (or 3D) vectors
Sides are expressed as either polar coordinates (,d) or as rectangular coordinate differences (E,N)
A traverse must either close on itself
Or be measured between points with known rectangular coordinates
A closed
traverse
A traverse between
known points

45. Rectangular coordinates
Point A
Point B
North
East EB NB
(EB,NB)
N=NB-NA EA NA
(EA,NA)
E=EB-EA

46. Polar coordinates North Point B d  Point A  ~ whole-circle bearing
East
Point A
Point B d 
 ~ whole-circle bearing
d ~ distance

47. Whole circle bearings North 0o Bearing are measured
clockwise from NORTH
and must lie in the range
0o   < 360o
4th quadrant
1st quadrant
West
270o
East
90o
3rd quadrant
2nd quadrant
South
180o

48. Coordinate conversions
Rectangular to polar
Polar to rectangular E N d  d  E N

49. Applications of traversing
Establishing coordinates for new points
(E,N)known
(,d)
(,d)
(,d)
(E,N)new
(E,N)new

50. These new points can then be used as a framework for mapping existing features
(E,N)new
(E,N)known
(E,N)new
(E,N)new
(E,N)new
(,d)
(,d)

51. They can also be used as a basis for setting out new work
(E,N)new
(E,N)known

52. Equipment Traversing requires :
An instrument to measure angles (theodolite) or bearings (magnetic compass)
An instrument to measure distances (EDM or tape)

53. Measurement sequence You start with a known point and bearing AB
At each station measure the internal horizontal angle
Measure the vertical angle between each station
Measure the distance between each station

54. Whole circle bearing A to B: WCBAB= 038° 17’ 34”
Point A has coordinates: E, N
Sum of internal angles = (2n – 4)x90° = 720° because n = 6
090° 33’ 04”
083° 58’ 44”
114° 04’ 38”
237° 11’ 31”
105° 59’ 45”
088° 13’ 30”

55. Computation sequence Calculate angular misclosure
Adjust angular misclosure
Calculate adjusted bearings
Reduce distances for slope etc…
Compute (E, N) for each traverse line
Calculate linear misclosure
Adjust linear misclosure

56. Correction to angles Station Accepted Angle Correction Corrected Angle´´ A
114 04 38
-12 26 B
090 33 32 52 C
083 58 44 D
237 11 31 19 E
088 13 30 18 F
105 59 45 
720 01 12 00
Correction = -72”/6 = -12” to each angle

57. Proportional Error between
Tape Lengths
Stations
Proportional Error between
Horizontal distance
From To
Out & back lengths
(m) A B
1:6100
90.202 C
1:7020
86.756 D
1:5010
48.928 E
1:8230
69.187 F
1:5930
57.345
1:4930

58. Bowditch adjustment
The adjustment to the easting component of any traverse side is given by :
Eadj = Emisc * side length/total perimeter
The adjustment to the northing component of any traverse side is given by :
Nadj = Nmisc * side length/total perimeter

59. Bowditch Adjustment Knowns Checks Line Stn Back B’g Corr’d Angle
Forward B’g
Horiz dist
Unadjusted
Correction
Adjusted
Coords ‘ “ E N E N E N AB
038 17 34 A
114 04 26 AF
152 22 00
50.455
0.021
-0.033
50.476 FA
332 F
105 59 33 FE
078 21
57.345
56.166
11.571
0.011
-0.017
56.176
11.554 EF
258
088 13 18 ED
346 51
69.187
67.298
0.013
-0.021
67.277 DE
166 D
237 11 19 DC
043 46 10
48.928
33.846
35.332
0.009
-0.015
33.856
35.318 CD
223 C
083 58 32 CB
307 44 42
86.756
53.108
0.016
-0.026
53.082 BC
127 B
090 52 BA
90.202
0.017
-0.027 
-0.087
0.138
0.000
Knowns
Checks

60. Linear misclosure & accuracy
Convert the rectangular misclosure components to polar coordinates
Accuracy is given by
Beware of quadrant when
calculating  using tan-1

61. Quadrants and tan functionE + 
negative
add 360o +
positive
okay 
positive
add 180o  +
negative
add 180o

62. For the example… Misclosure (E, N) Convert to polar (,d) Accuracy
(-0.087, 0.138)
Convert to polar (,d)
 = o (4th quadrant) = o
d = m
Accuracy
1:( / 0.163) = 1:2827

63. Curve Ranging

64. Location Methods (a) right angle offset tie.B B B P P P C A A A
(a) right angle offset tie.
(b) the angle distance tie (polar tie).
(c) angle at A and B of distance BP of AP (intersection technique).

65. Means of fixing a curve r a

66. Means of fixing a curve
Establish line through ROr on line of radius. – How?
ROr
Locate position of pegs measuring angles at T from line to Q in combination with cord lengths T-1, 1-2, 2-3 and 3-4.
You cannot tape between 4 and 5 so how will you establish 5, 6 and 7?

67. Means of fixing a curve How far should R1 be from T?
Locate lines through the position of pegs 5, 6 and 7 by measuring angles at R1. Which direction should angles be read from and why?
ROr
Method 1: R1
How far should R1 be from T?

68. Means of fixing a curve
ROr
Method 2: R1 R2

69. First line of sight marked by pegs and string
Second line of sight marked by pegs and string
Point marked by peg and nail at intersection of strings
Pegs must be firmly anchored in the ground