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MEASUREMENTS IN SURVEYING
Lecture 21
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MEASUREMENTS IN SURVEYING
There are five major types of measurements in
surveying:
Horizontal distances
Horizontal angles
Vertical distances
Vertical angles
Slope distances
The magnitudes measured must always be
reported in terms of specific units2
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MEASUREMENTS IN SURVEYING
When reporting the measurements, it is very
important to maintain the following:
Integrity
Legibility
Arrangement
Clarity
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SIGNIFICANT FIGURES
The accuracy of the measurement could be
indicated by the number of significant figures
(SF) recorded.
SF of any observed value is the number of
certain digits plus one digit that is estimated or
rounded off.
If a measuring tape smallest division is 0.001 m
and the reported measurement is 3.523 then it
has 4 SF (3 certain and 1 estimated). 4
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SIGNIFICANT FIGURES
Decimal Places may be used to maintain the
correct number of SF.
Two SF: 32, 3.2, 0.32, 0.032, 0.00030
Three SF: 324. 32.4, 0.000324, 0.0320
Four SF: 3245, 32.45, 0.003245, 0.03240, 32.00
32000-------------- ??????
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SIGNIFICANT FIGURES
Zeroes at the end of an integer may be expressed in terms of power of 10 to eliminate any uncertainty about SF
3.2000 x 104 --------------- 5 SF
3.200 x 104 --------------- 4 SF
3.20 x 104 --------------- 3 SF
Or
32000 --------------- 5 SF
32000 --------------- 4 SF
32000 --------------- 3 SF6
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SIGNIFICANT FIGURES
In mathematical operations it is important that
the number of SF reported is consistent with the
data used
(+, -) ------------- rightmost significant digit
(x, /) ------------- least number of SF
45.356 + 2.06 – 5.0 = ??
45.356 / 5.0 = ??
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ROUNDING OFF NUMBERS
Rounding off numbers is usually performed to
have only the SF in a number
Less than 5
Greater than 5
Equals five (nearest even number)
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PRECISION AND ACCURACY
Precision is an indication of the consistency of a
group of readings
Accuracy indicates the absolute nearness of the
readings to their true value
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PRECISION AND ACCURACY
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PRECISION AND ACCURACY
If two teams measured a horizontal 90o angle five
times in the field and the following results were
obtained:
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PRECISION AND ACCURACY
Max difference in readings:
Team 1: 00 00 50
Team 2: 00 00 05 (more precise)
Deviation from the true value:
Team 1: (more accurate)
Team 2:
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ERRORS IN SURVEYING
All types of measurements entail some degree of
error (± ε)
When dealing with errors, surveyors must
understand:
The different kinds of errors
The sources of errors
Estimate the magnitudes of the error
Error propagation
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ERRORS IN SURVEYING
There are three general sources of error:
Natural errors caused by variation in or adverse
weather conditions, refraction….
Instrumental errors caused by imperfect construction
and adjustment of the surveying instruments used
Personal errors caused by the inability of the
individual to make exact observations
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ERRORS IN SURVEYING
Classes of errors:
Blunders
Systematic errors (constant or variable)
Random errors
Constant errors
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ERRORS IN SURVEYING
Weights:
The are expressed numerically and an indication of
the relative precision of quantities within a set
The greater the weight, the greater the precision of
the observation to which it relates
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MEASURING DISTANCES
Frequently measured as a spatial distance in
three-dimensional space, however, it is usually
the horizontal component which is required
There are three basic methods of measuring
distances:
Direct (tape)
Indirect (stadia or tacheometry)
Electronic
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MEASURING DISTANCES
Methods of measurement:
Pacing:
a rapid means of estimating a distance
distance = individual pace distance x number of paces
Odometer:
Distance = number of revolutions of the wheel x
circumference of the wheel
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MEASURING DISTANCES
Stadia (or Tacheometry)
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MEASURING DISTANCES
Stadia (or Tacheometry)
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MEASURING DISTANCES
Chains
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MEASURING DISTANCES
EDM
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MEASURING DISTANCES
Tapes:
Four kinds of tapes are used:
Synthetic/Fibre-Glass Reinforced tape
Synthetic/ Steel - Plastic tapes
Steel tapes
Invar tapes
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MEASURING DISTANCES
Synthetic/Fibre-Glass Reinforced tape
hard-wearing, durable and water proof
materials can easily be stretched
used for measurements that
do not need to be highly precise
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MEASURING DISTANCES
Steel/Plastic Composite Tape
more precise than the fiber-glass tape
temperature and tension variations
can be corrected
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MEASURING DISTANCES
Steel Tapes
more precise and more stable
nominal length:
temperature = 20°C and
applied tension between 50 N to 80 N
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MEASURING DISTANCES
Invar tapes
most precise tape
made from an alloy of 36% nickel and 64% iron
low coefficient of expansion (only 1/13 that of steel
tape)
Disadvantages:
soft and weak
price is more expensive than steel tape
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MEASURING DISTANCES
Tape ancillary tools:
Chaining pins
Ranging poles
Thermometer
Plump bob
Tripod
Tension gauge
Bubble
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MEASURING DISTANCES
Sloping distances
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MEASURING DISTANCES
Errors in taping
Instrumental error
Human error
Natural error
To express the precision, the numerator should
be set to 1 while the denominator should be as
large as possible.
Precision =
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MEASURING DISTANCES
Tape calibration
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MEASURING DISTANCES
Correction for measurement:
Correction = L * α * (tm - ts)
where
L = measured length
α = coefficient of expansion, (0.000 012 per C for
steel)
tm = temperature at measurement
ts = temperature at standardization
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MEASURING DISTANCES
Correction for slope
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MEASURING DISTANCES
Correction for sag:
correction =
Where,
w = unit weight of tape
p = tension applied to the tape
L = length measured
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MEASURING DISTANCES
Examples
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MEASURING DISTANCES
Ranging
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