1. Eng. Mysa.A.AL-Khassawneh Jordan university Of science and technology
Surveying CE 341
Eng. Mysa.A.AL-Khassawneh
Jordan university Of science and technology

2. Surveying: The science that deals with earth measurements

3. Values could be : Measured: using instruments contain errors Computed: no instrumented needed no errors

4. Instrument: human operation environmental effect (temp) error Measurement: direct: Angles height , point positing indirect: area , volume, surfaces , contour maps

6. Measurement categorization : Linear: length width height ( elevation or altitude) Non linear: Angles ( horizontal and vertical) Surface in 3D

7. Type of surveying:
Control survey:
Establish a network of horizontal and vertical monuments that serves a reference framework for initiating other surveys
2. Topographic survey:
Determine locations of natural and artificial features and elevations used in map making
3. Boundary (property) surveying
Establish property lines and property corner markers

8. 4. Hydrographic surveys : Define shoreline and depths of lakes, streams , oceans, reservoirs, and other bodies of water 5. Rout surveying : Surveying used to plan, design and construction high ways , railroads, pipelines, and other linear projects ( different alternatives for the hwy) 6. Construction survey: Provide base line, grade, control elevations, horizontal positions, dimensions for construction operations( pay quantities)

9. Construction surveying:

10. 7. Engineering surveying: Laying out and construction of different engineering projects such as highways, dams buildings….. 8. Inventory survey: Population density, forest areas, zonation….

11. Branches of surveying Plane surveying horizontal plane x-y
neglect curvature of the earth
suitable for a small area and short lines(r<10 miles)
2. Geodesy :
-consider the curvature of the earth(sphere)
- applicable for large area ,long lines

12. 3. GIS: geographic information system
link a data base to a map
4. GPS: global positioning system
Obtain (x,y,z) for point
5. Remote sensing:
Qualitative (color intensity)
Recognition of classification
Spacing image

13. Theory of measurement:
Type of measurements in surveying:
There are five measurement in plane surveying:
horizontal distance
Horizontal angles
Vertical distances
Vertical angles
Slops distances

14. Error, types and magnitude of error in measurements:
True error in a measurement: It is the difference between the measured value of a parameter and its true value ei = xi-x Where : ei= true error Xi = measured value X = true value of the measured parameter - The true value of a survey measurement is never known and can never be determined exactly Therefore , true error can never be determined

15. Ѵi= xi-xᴖ Where : Ѵi = estimate of the true error ei xᴖ = estimated true value Xi = measured value - how close the estimates Ѵi to the true ei Depends on the closeness of xᴖ to the true value X

16. error types :
blunders
Systematic errors
Constant errors
Random errors

17. Blunders errors:
Definitions: personal mistakes Cause: human carelessness, fatigue and hast Detection: huge value of error Vi > 3σ Correction: delete the measurement

18. Systematic errors:
Definitions: Errors associated with mathematical formula Cause: some maladjustment of the surveying instruments, personal bias and the natural environment such as temperature (expansion or contraction) Detection: environmental phenomenon Correction: modeling ( mathematical expression)

19. Example : the change in length of steel measuring tape due to change in temp Systematic errors can be any sign (- or +)

20. Random errors:
Definitions: Small value error associated with random less Cause: Human nature and instrument capability Detection: Vi < 3σ ( its follows the normal distribution) Correction: Repeat measurement , use better instrument Example: Reading tape measurements several times (trial)

21. Characteristic of random errors:
positive and negative errors of the same magnitude occur with equal frequency
Small errors occur more frequently than large ones
Very large error seldom occur
If we have a specific distance measured times. The mean is computed, and the estimated error in each measurement is computed by abstracting the mean vale from the measured value( called deviation from the mean)

23. The curve is symmetrical about v=0

24. Normal (Gaussian ) distribution:

25. Normal distribution:

26. Probability of random error

27. Normal distribution: Error Range Probability(%) 50.0 68.3 90.0 95.4
99.7

28. Example 1: a measured distance has a standard error of + 0.05 m
- there is 68.3 % probability that the random error in the measured value falls within the range m (1σ)
there is 95.4 % probability that the random error in the measured value falls within the range m (2σ)
there is 99.7% probability that the random error in the measured value falls within the range m (3σ)

29. The standard error of a measurement can be determined if the exact distribution pattern of the random error is known. This means the measurements should be repeated infinite number of times
In practice , number of measurements is limited (< 10 times), therefore, only an estimated value of the standard error can be computed

30. Mean, Standard Deviation, and Standard error of the Mean

31. Standard error of the mean

32. Example 2:
A distance was measured ten times yielding the following results:
, , , , ,
, , , , ,
Compute:
The mean
Standard deviation
Estimated standard error of the mean

36. Probable error and maximum error
Probable error of a measurement = σ -i.e their is 50% probability that the actual error exceeds the probable error, as well as 50% probability that is less than the probable error Example-3: If the standard error of an angle is sec, the probable error of the angle = *1.5 = +1.0 sec

37. maximum error of a measurement i. e there is 99
maximum error of a measurement i.e there is 99.7% probability that the actual error falls within 3σ , and there is only 0.3% probability the actual error exceeds 3σ Example 4: If the standard error of a distance measured is ft, then the maximum error = + 3*0.05ft = ft

38. Precision and accuracy:
Precision: how far the measurements are from each other (for repeated measurements)
Accuracy:
How far the measurements are from the true value
If σ is low then precision is high
If σ is high then precision is low

39. Example: measurement “A” with standard deviation + 0
Example: measurement “A” with standard deviation m and measurement “B” with standard deviation +0.10
Measurement “A” more precise than measurement “B”
High accuracy close to the true value

42. High accuracy, but low precision high precession, but low accuracy

46. Repeated measurements

48. Law of propagation of random errors

50. Law of Propagation of random errors relates the estimated standard error of computed parameter to the estimated standard error of the measured parameters

53. Error of sum: Example: A line is measured in three sections as follows: L1= L2= L3= Determine the lines total length and its anticipated standard error

54. Solution: Total length= L1+L2+L3 = 753. 81+1238. 4+1062. 95 = 3055
Solution: Total length= L1+L2+L3 = = = ft

55. Principles of least square
The method of least square is based on:
There are more measurements than the min number needed to determine the unknown parameters
The measurements contain only random error
The measurements are made independently from each other

56. Let X1, x2, ……, xn be the measured value of n parameters And v1, v2, ……, vn be the error in theses measured values And σi be the standard error of the measurement Xi then the most probable solution to the unknown survey parameters is that which satisfies the following condition: where σo = constant

58. Weight and weighted mean

61. Example-9
Given the following independent measurement
Compute the weighted mean and an estimate of the standard error of the weighted mean

62. Solution:
assume

63. Cont…..

64. Cont……

65. Significant figures
The significant figures in a number are those digits with known values. They are identified by proceeding from left to right beginning with non zero digits and ending with the last digits of the number
All non zero digits are significant
Zeros at the beginning of the number are not significant
Zeros between digits are significant
Zeros at the end of a decimal number are significant

66. Example 10
7 significant figures
6 significant figures
2 significant figures

67.
4 significant figures
7 significant figures
51.0
3 significant figures

68. Example 11: r 4 or 5 significant figure It can be written as : 72.3*10^3 3 S.F 72.30*10^3 4 S.F *10^3 5 S.F

69. Rounding off
- If the result is to be expressed to n significant figure , the nth figure should be retained as is if the (n+1)nt place < 5 - The nth sholud be increased by one unit if the (n+1)nt Figure is >5 - If the (n+1) digit is 5, round off to the nearest even digit in the nth place

70. Example 12:
round off to 5 significant places
6746.6
round off to 5 significant places
468.77
round off to 5 significant places
568.76
round off to 5 significant places
468.76
round off to 5 significant places
468.74

71. Example 13
S.F 3.S.F
S.F
S.F Odd case
S.F Even case

72. Rounding off
When performing addition of or subtraction the sum cannot be more precise than the least precise number included in the addition
Example -14
24.217
468.46
1,553.1
2, ft
The sum should be expressed as 2,055.8 (one digit after the decimal)

73. Unit of measurement
Unit of measurement used in US are: Length: 1 foot = 12 inches 1 yard = 3 feet 1 meter = inches = feet 1 Rod = 16.5 feet 1 Gunter's chain = 66 feet = 4 rods 1 mile = 5280 feet= 80 Gunter's chains Area: Acre= 10 square chains = 43, 560 ft2 Hectare = 10,000 m2 = acres

74. Unit of measurement used in SI system : Length: 1 meter = 1,000,000 micrometer 1 meter = 1,000 millimeters 1 meter = 100 centimeters 1 kilometer(km) = 1,000 meters Area : Acre = 43,560 ft2 Hectare = 10, 000 m2 = acres

75. Conversion of length unit
1 US yard = meter = inches 1 foot = meter 1 inches = 25.4 millimeters

76. Method of Measuring Distances
Pacing:
for short distances < 100m
Accuracy 1/50 to 1/100
2. Stadia
Horizontal distance is measured through measuring the vertical angle and elevation differences (will be discussed later)

77. 3. odometer: Measured distance = no of rounds 4
3. odometer: Measured distance = no of rounds 4. speedometer: Approximate 5. Knowing the time: By knowing the travel time and velocity then the distance can be found as :

78. 6. Electronic distance measuring (EDM) equipment:
- use electromagnetic waves to measure distances with high accuracy (will be discussed later)
7. chain:
Set of chains connected together with 10, 20 or 25 meter in length
8. tapes:

80. Tapes:
Steel tapes
nickel tape
Woven tapes

81. Tapes:
Type of tape:
Woven tape
Steel tape

82. Tapping accessories Range poles: to clear the line of tapping
2. Chaining pins(arrow):
to mark tape ends ends on the ground
3. Tension handle:
used to apply appropriate pull to the tape
4. Thermometer
5. Plumb bob: the position of the end of the tape is transferred to the ground

83. Range poles: chaining pins

84. Tension clamp:
No never tension neither sag
2. Thermometer to find out the expansion

85. Measuring Distances Horizontal distances Vertical distances
Slope distances
Horizontal distances most common used

86. Measuring horizontal distances
Direct measurement
Indirect measurement
a) horizontal distance calculated from the slope distance “s” and the vertical angle “α” then the horizontal “L” distance will be:

87. b) Horizontal distance calculated from the slope distance “S” and the difference in elevation between the beginning and the end of the sloped distance

88. c) Horizontal distance calculated from the difference in elevation between the beginning and the end of the sloped distance “h” and the vertical angle “α”

89. Measuring distances Short distance at flat terrain (d<L)
Long distance at the flat terrain (d>L)
Short distance at slope terrain
Long distance at slope terrain
Tape length = L
Measured distance = d

90. Measuring distance Short distance at flat terrain d<L
Ranging to keep the same line

91. b) Long distance at flat terrain D>L Use 3 poles at straight line ranging. Put chaining pins

92. Long distance at flat terrain

93. c) Short distance at slope terrain d<L Ranging + plumb bob

94. Long distance at slope terrain d>L ranging + plumb bob

95. Long Distance at Slope Terrain

96. Chain surveying
It is based on measuring the longitudinal distances in addition to some other tools to establish offset direction (perpendicular lines)
It is used in surveying small area (few acres)
It is used in open areas no obstacles
Tools used in chain (tape) surveying:
Tapes and its accessories
Double right angle prism
Cross staff

97. Double right angle prism:
To establish the offset direction
Consist of two right angle prisms, a piece of viewing glass, and alight weight plummet
The upper prism provides a view to the right
The lower prism provides a view to the left
The view in the front of the prism is seen through the flat viewing glass mounted between the two right angle prism

98. double right angle prism

99. Ranging out survey lines:
Direct ranging by eye
a) forward ranging

100. Ranging out survey lines: b) Backward ranging

101. Ranging out survey lines
2. Indirect or Reciprocal Ranging
used when the two fixed points A and B can not be seen from each other

103. 3. Ranging out in valleys and steep slops
Fix two ranging poles out side the steep area then use another pole with plumb bob fixed to it with a line ( about 1.5 m long)

104. 3. Ranging out in valleys and steep slops

105. Setting out right angle
1. Double right angle prisim

106. 2. Cross staff

107. 4. Pythagorean theory

108. 3. Pythagorean theory

109. Drawing arcs:

110. 5. Drawing half circle

111. Taking offset
1. Double right angle prisim

112. 2. Cross staff

113. 3. Draw arc: to take offset from point D (out side line AB) to the line AB:

114. 4. The shortest line from a point to the line AB is the

115. Establish a line parallel to the base line and pass in a point
Base line AB, to draw a line parallel to AB and passes through a point such as M

116. 2. Base line is AB, to draw a line parallel to AB and passes through a point such as M:

117. Establish a line parallel to the base line pass in a point
3. Base line AB, to draw a line parallel to AB and passes through a point such as M : N M D A C E B

118. 4. Base line AB, to draw a line parallel to AB and passes through a point such as M:

119. Overcome obstacles
1. obstcals obstructing chaining but not (vision ) ranging:
Measure the distance between points A and B, given that both points can be seen from each other of them can not be reached
Case 1:
Make perpendicular line from point B to point C
From another point B to point D make another perpendicular to point E on the line of AC

120. Cont…
1. obstacles obstructing chaining but not (vision ) ranging case 1:

121. Cont….
1. obstacles obstructing chaining but not (vision ) ranging case 2:
Choose a point on AB say D then make perpendicular from point D to point D
Divide DE at middle say at point N
From point E make perpendicular line on point C given that C on line AN (same extension)
From another point on AB say point D make another perpendicular to point E on the line of AC

122. Case 2 cont….
Note : the symmetery between the two triangles AND & NCE, then AD = EC
AB = AD + DB
AB = EC + DB

124. 1. obstacles obstructing chaining but not (vision ) ranging , two points separated by an obstacles
Case 1:
From point B mke perpendicular line to point D
From point A make perpendicular line to point C that BD=AC

125. 1. obstacles obstructing chaining but not (vision ) ranging , two points separated by an obstacles Case 1:

126. corrections Length correction
Length correction : the difference between the nominal length of a tape and the actual length under the conditions of calibration
E.g if nominal length of a tape is 100 ft but actual length after calibration was found to be = ft this tape is too long (add the differences to be measured between two fixed points)
E.g if nominal length of a tape is 100ft but actual length after calibration was found to be ft this tape is too short ( substract the difference on distances to be measured between two fixed points)

128. Example 15: The nominal tape length is 100 ft and actual length is 100
Example 15: The nominal tape length is 100 ft and actual length is fr, a distance is measured using this tape found to be ft, what is the corrected length for this measurement? Sol:

129. Temperature correction
Temperature correction: to correct the observed length of a survey line because of the effect of temperature on the steel Where: is the coefficient of thermal expansion of steel per 1 F is the coefficient of thermal expansion of steel per 1 C T1: field temp To: temp under which the tape is calibrated L: the length of the line

130. Example 16:
A distance was measured to be 500 ft at 83⁰ F, the tape was calibrated at tempreture of 86⁰ F , find the corrected length of the distance:
Corrected length =
= ft

131. Sag correction
Sag correction: the difference between the axial length of the tape hanging in the space and the chord distance between the ends
where:
W:the total weight of the section of the tape between supports
w: weight per foot of the tape
P: the tension on the tape
L:the interval between supports
Units should be compatible for weight and tension (i.e lb or kg)

132. Example 17:
A 100 ft steel tape weight 2 lb and is supported at the ends only with a pull of 12 lb, find the sag correction

133. Example 18:
A 30 m steel tape weight kg and is supported at 0, 15 , and 30 m points with a pull of 5 kg, find the sag correction

134. Tension correction:
Tension correction: the elongation of the tape of length L in feet
Where :
Cp: the elongation of the tape of length L in feet
P1: applied tension in lb
P0: the calibration tension in lb
A: cross sectional area of the tape in in2
E: the modulus of elasticity of the tape material(for steel 29,000,000 psi)

135. Example19
A 100 ft steel tape having a cross sectional area of in2 , is correct length under a pull of 12 lb, calculate the elongation (nearest ft)due to a tension of 20 lb)

136. Slope correction: Where: s: slope correction h: vertical distance
d: horizontal distance

137. Where :
Cg: slope correction
S: slope distance
h : vertical distance
d: horizontal distance

138. Slope and alignment errors
Example 20:
What error results from having one end of the 30 m tape:
Off line by 0.1 m
b) Too low by 0.8 m

139. Accuracy
- Under normal field conditions good field procedure, using , and using a good quality tape (calibrated to ft) a standard error 1/3000 can be achieved without applying any corrections
By applying corrections for all known sources of a systematic errors , a standard errors of 15,000 may be achieved:
Tape length calibrated with standard error=+0.006ft
Field tension measured with standard error of + 2 lb
Field temperature measured with standard error of +5 F
Slope determined with standard error of +0.5%
Standard error of pin marking <+0.01ft

140. Basic principle of geomatric tape surveying
Basic triangle: measure the three sides of the triangle to locate the three points
If two points on the triangle are defined the thired point can be defined using the intersection method
If the two points A and B are defined then any other points can be defined by measuring offset distance from the line AB
A right triangle can be established by using the proportion for the three sides

141. Leveling

142. DEFINITIONS
Elevation of a point : is vertical distance above ore below a surface of reference called datum
Leveling: the operation of determining the difference in elevation between points
Elevation datum: Datum surface is any level surface to which the elevations of all points may be referred. The mean sea level is usually adopted as datum.
Mean sea level(MSL): the average height of the surface of the sea for all stages of the tide at that particular location

143. Bench marks
Bench marks are stable reference points the reduced levels of which are accurately determined by leveling.
Temporary bench mark:
A point with known elevation within the project itself used as a reference to determine the elevation for other points in the project site

144. Back sight (BS)
This is the first reading taken with a leveling instrument in a leveling operation.
Foresight (FS)
This is the last reading taken in a leveling operation.
Intermediate Sight (IS)
This is the reading taken between the back sight and foresight in a leveling operation.

145. Turning Point (TP)
A change point or turning point is a staff station on which two staff readings are taken without changing the position of the instrument.
Instrument hight (IH)
The elevation of the sight line

150. Staff reading:
M= (U+L)\2
Leveling
Rough sighting
Focusing
Take reading

154. Reciprocal leveling
Example 23 Find RLB if you know RLA = A1=3.5 , b1 = 2.8 A2 = 3.95 , b2= 3.2 Solution:

155. How right location for the leveling instrument
The right location for the leveling instrument is between the two target points at the middle (not necessary on the same line)
When the level at the middle between the two points (not necessary on the same line ) the error will have no effect

156. The right reading on staff A is a1, and on staff B is b1
There is an error because of the sight line not horizontal (there is angle α)

157. The difference in elevation between A and B is
a1 – b1=
But a1= a2- L tan α
And b1= b2-L tan α
Then
a2-L tan α –(b2- L tan α)= a2-b2
a1-b1=a2-b2
If the level located between two points at the middle then the difference in elevation between these two points is the same even if there is an error in the reading due to instrument , weather or earth curvature

168. Profile Leveling The process of determining the elevations of a series of points at measured intervals along a line such as the centerline of a proposed ditch or road or the centerline of a natural feature such as a stream bed.

169. Profile leveling yields elevations at definite points along a reference line.
• Used in designing linear facilities:
Highways
Railways
Canals
Sewers

170. Staking and Stationing the Reference Line
To Stake the proposed RL
Staring, ending and angle points will be set first
♦ Intermediate stakes will be placed on line (50 to 100 ft
English units or 10 to 50 m SI units)
♦ Distances for staking will be taped, measured (using
EDM …)

171. Example of Profile leveling

174. determine the area of a tract of land bordered by the high water line of a stream, offsets from a transit line were measured at regular intervals of 30 ft as follows: 20.8, 16.7, 21.5, 29.3, 31.0, 25.1, 15.7, 18.0, and 23.2ft. fined the area by using trapezoidal rule in (ft2)