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Chapter-02
Measurements & Errors
2.1 Units, System of Units, Significant figures and rounding
off numbers
2.2 Errors, Sources & Types
2.3 Precision, Accuracy & permissible error

off numbers
Linear Measurement
Metric System/SI system
FPS System
(British Engineering System)
Length in meter (m) Length in Foot (ft.)
Mass in Kilogram (Kg) Mass in Pound (lb)
Time in Second (s) Time in second (s)

Angular Measurement:
1. Sexagesimal System (English system)
 degrees, minutes, seconds
2. Centesimal System (French System)
 grade, minutes, seconds
 1 right angle = 100 grades
 1 grades = 100 minutes
 1 minutes = 100 seconds
3. Circular System (radians)
Aradian is an angle subtended at the center of a circle by an arc whose length is equal to the radius.
radians=degree∗(PI/180)
90° = π/2 rad, 180° = π rad, 360° = 2π rad
off numbers

off numbers
Ropani
Aana
16
Bigha
Paisa
4 64
Kattha
20
Daam
4 16 256
Dhur
20 400
1.99 m2
7.95 m2
31.80 m2
508.74 m2
16.93 m2
338.63 m2
6772.63 m2
21.39 ft2
85.56 ft2
342.25 ft2
5476 ft2
182.25 ft2
3645 ft2
72900 ft2

Error in an observation is the difference between a measured
value of a quantity and the true value of that quantity.
Error = Measured Value – True Value
Types of Errors
A. Mistakes/Blunders
B. Systematic errors
C. Random errors/Accidental error

A. Mistakes/Blunders
 Mistakes or blunders are unpredictable human mistakes caused
due to carelessness, misunderstanding, confusion or poor
judgment.
 Mistakes can be avoided by alertness, common sense and good
judgment.
Common types of Mistakes/Blunders are:
oTransposition of numbers
oNeglecting to level an instrument
oMisplacing decimal point
oSighting on incorrect control point

B. Systematic Errors
 Systematic error is such type of error which have same magnitude and the same
algebraic sign under the same conditions.
 In most cases, systematic errors are caused by physical and natural conditions that
vary in accordance with fixed mathematical and physical laws.
 Systematic errors are cumulative in nature.
 can be minimized by procedural changes such as standardizing the tapes, balancing of
sights etc.
 corrections must be applied to measurements.
Common examples of systematic errors are:
o Thermal contractions or expansion of steel tape.
o Incorrect length of a level rods and staff.
o Curvature and refractions.
o Incorrect prism constant on a total station etc.

C. Random Errors
 Random errors are also called Accidental errors, which do not follow any
fixed relation to the conditions of observations.
 Random errors obey the laws of chance and are analyzed by the laws of
probability.
 Theoretically, random errors have an equal chance of being negative or
positive.
 Thus, errors of this type tend to be compensating.
 Can be minimized by repeating the measurements.

Sources of Errors
a) Personal Errors
 Personal errors are caused by physical limitations and observing habits of an observer. They
can be either systematic or random.
b) Instrumental Errors
 Instrumental errors are caused by the imperfections in the design, construction, and
adjustment of instruments and other accessories.
 Most instrumental errors are eliminated by using proper procedures such as observing
angles direct and reverse, balancing foresights and back sights and repeating measurements.
 Minimized by periodically checking and adjusting (or calibrating) instruments and other
equipment.
Example:
 Wrong calibration in the tape or staff.
 Wrong calibration of EDM
 Bubble out problem in level, theodolite

Sources of Errors…..
from natural
temperature,
physical
humidity,
conditions
gravity, wind
such as
and
c) Natural Errors
 Natural errors result
atmospheric pressure,
atmospheric refraction.
 Natural errors are removed from a measurement by determining
corresponding corrections from known relationships between an error
and the related natural phenomena.

COMMON MISTAKES IN CHAINING/TAPPING:
 Displacement of the arrows.
 Failure to observe the zero point of the tape.
 Reading from the wrong end of the chain/tape.
 Reading numbers wrongly/ Reading wrong meter marks.
 Wrong recording in the field book.
 Calling numbers wrongly.

Accuracy:
 Accuracy is defined as ‘The degree of closeness with the ‘standard value’ and
essentially refers to how close a measurement is to its agreed value.
 Degree of perfection obtained in the measurement.
Precision:
 Precision refers to closeness of two or more measurements to each other.
 Precision indicates the level of detail, refinement, or granularity in the
measurement.

2.3 Precision, Accuracy & Permissible error

Discrepancy: is the difference between two measured values of the same
quantity.
 Discrepancy may be small, yet the errors can be large if both the
observed values contain almost equal error.
Error: in an observation is the difference between a measured value of a
quantity and the true value of that quantity.
Error = Measured Value – True Value

Q. In angular measurement of a triangle ABC, the internal angles are found A= 60
30, B= 45 20, C= 75 30. Calculate the error in measurement and
accuracy of the work.

Permissible error:
• Refers to the acceptable level of error or tolerance allowed in the
measurement of survey data.
• The specific permissible error varies depending on the type of survey, the
purpose of the survey, and the accuracy requirements of the project.
• Different surveying applications may have different permissible error
standards.

Assignments
Make a proper note of this Chapter in your note copy

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