CHAPTER 3
LINEAR
MEASUREMENTS
By,
VANSHIKA MUCHHARA
ASSISTANT PROFESSOR
CIVIL DEPT-PIET DEG 1ST SHIFT
PARUL UNIVERSITY
RANGING OUT SURVEY LINES
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1.
2.
In measuring the length of a survey line called chain line, it is
necessary that the chain should be laid out on the ground in a
straight line between the end stations.
“The process of establishing intermediate point on a straight line
between two end points is known as ranging”.
Ranging must be done before a survey line is chained. It may be
necessary to establish a number of intermediate points prior to
chaining when chain line is much longer. Ranging may be done by
direct observation by the naked eye or by line ranger or by
theodolite. Generally, ranging is done by naked eye with the help of
three ranging rods.
Ranging is of two kinds:
Direct Ranging
Indirect or reciprocal ranging
DIRECT RANGING
 When
intermediate ranging rods are fixed on a straight line by
direct observation from end stations, the process is known as
direct ranging. Direct ranging is possible when the end stations
are intervisible.
 Two methods are used for Direct Ranging
a)
b)
Ranging by eye
Ranging by line ranger
RANGING BY EYE

Two points A and B are at the ends of survey line. Distance AB is
greater than one chain length.

Ranging rods are fixed at stations A and B

It is require to fix a intermediate point C between A and B.

The surveyor stands about half meter behind the ranging rod at A by
looking towards line AB. The assistant holds ranging rod at C
vertically at arms length the rod should be held tightly by the thumb
and forefinger.

Now the surveyor direct the assistant to move the ranging rod to the
left or right until the three ranging rods come exactly the same
straight line.
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The ranging will be perfect, when the three ranging rods coincide
and appear as a single rod.
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When the surveyor is satisfied that the ranging is prefect, he
signals the assistant to fix the ranging rod on the ground.

By following the same procedure, the other ranging rods may be
fixed on the line.
.
Line ranger is a light and easy to use instrument which can be
used for ranging. It consists of 2 plane mirrors or 2 right-angled
isosceles prism places one above the another.
 Diagonals of two prism are silvered so as to reflect light. Lower
prism is fixed while the upper prism is moveable. Instrument is
provided with handle at bottom which gives ease to the user for
using the instrument.

Suppose Point L is to
be located between
points A and B.
Observer stands in
line and place the
instrument on a rod or
holds it at eye level
until the image of rod
at A is seen in field
view.
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Then surveyor moves with the line ranger.
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The point where two images A and B coincide in line ranger is the point in
line with two fixed ranging rods. At this point a pebble is dropped from
the handle of line ranger and point L is traced on ground.
INDIRECT RANGING OR
RECIPROCAL RANGING
 End
stations are not intervisible due to rising ground between
them.
 End stations not visible due to long distances.
 For
such above cases, intermediate points can be fixed on line
by process known as reciprocal ranging.
 Consider two points A & B as in figure
 Chainmans
should stand at P1 and R1 such that P1 is able to
see R1 and B & chainman at R1 can see P1 and A
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R1 will direct P1 to move to P2 such that R1P2, A are in line.
P2 will direct R1 to move to R2 such that P2, R2, B are in line.
By successive directing each other, the two chainmen proceed such that A,
P, R & B lies in a line.
P and R are the intermediate points between A and B.
TYPES OF OFFSETS

Offsets
are
the
lateral
measurements from the base
line to fix the positions of the
different objects of the work
with respect to base line.

These are generally set at right
angle offsets. It can also be
drawn with the help of a tape.
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There are two kinds of offsets:
1.
Perpendicular offsets
2.
Oblique offsets.
INSTRUMENTS USED FOR LAYING
OFFSETS
Figure shows three different
types of cross staffs used for
setting perpendicular offsets.
All cross staffs are having two
perpendicular lines of sights.
The cross staffs are mounted
on stand.
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One pair of vertical slit is to bisect ranging rod at the end of the given
chain line by standing on chain line & other pair of vertical slit is
required to be in line with ranging rod at object for perpendicular offset.

First line of sight is set along the chain line and without disturbing
setting right angle line of sight is checked to locate the object.
 With
open cross staff (Fig a) it is possible to set
perpendicular only, while with french cross staff (Fig. b),
even 45º angle can be set. Adjustable cross staff (Fig c)
can be used to set any angle also, since there are
graduations and upper drum can be rotated over lower
drum.
Optical square
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Instrument used for perpendicular
offsets only.
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Consists of circular box 50 mm in
diameter & 12.5 mm in depth.
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Three silts at E, G, F.
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In line EG a glass B is provided
silvered at top, plain at bottom.
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Opposite of C, silver painted glass A
called index glass is fixed so that the
inclined edge of glass A & inclined
face of glass B makes angle 45 deg.
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Opening F, when faced towards
object P, image will strike at A and
reflected to horizon B which will
be seen at E. Thus he can set the
ranging rod at Q by object image
seen at B.
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If observer finds that the ranging
rod Q and image of object P do
not concide ,then he should move
forward or backward along chain
line until ranging rod Q and image
of P exactly coincide.
Indian Optical Square
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Brass wedge shaped hollow box of
5 cm sides & 3 cm deep with handle
about 8 cm long fixed undeneath.
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m1, m2 are two mirrors fixed to
inclined sides of box at 45 deg.
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ab, cd are two rectangular openings
above mirrors.
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PQRS is open face turned towards
object to which the offset is taken.
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Principle is same as that of Optical
square.
Prism Square
 Same principle of optical
square.
 Instead of two mirrors,
prism is used which has
two reflecting surfaces I
and H fixed at 45 deg.
 Procedure is same as that
of Optical square.
ERRORS IN CHAINING

Instrumental: Surveying error may arise due to imperfection or
faulty adjustment of the instrument with which measurement is
being taken. For example, a tape may be too long or an angle
measuring instrument may be out of adjustment. Such errors are
known as instrumental errors.

Personal: Error may also arise due to want of perfection of human
sight in observing and of touch in manipulating instruments. Such
errors are known as personal errors.
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Natural: Error in surveying may also be due to variations in natural
phenomena such as temperature, humidity, gravity, wind, refraction
and magnetic declination. If they are not properly observed while
taking measurements, the results will be incorrect. For example, a
tape may be 20 meters at 200 deg celcius but its length may change
if the field temperature is different.

Systematic or Cumulative Errors: A systematic or cumulative
error is an error that, under the same conditions, will always
be of the same size and sign.

A systematic error always follows some definite
mathematical or physical law and correction can be
determined and applied.
 Such errors are of constant character and are regarded as
positive or negative according as they make the result great
or small. Their effect is, therefore, cumulative.

For example, if a tape is P cm short and if it is stretched N
times, the total error in the measurement of the length will
be P´N cm.
 The
systematic errors may arise due to (i) variations of
temperature, humidity, pressure, current velocity,
curvature, refraction, etc. and (ii) faulty setting or improper
levelling of any instrument and personal vision of an
individual. The following are the examples:
 If undetected, systematic errors are very serious.
 Therefore,
(1) all surveying equipment must be designed
and used so that, whenever possible, systematic errors will
be automatically eliminated, (2) all systematic errors that
cannot be surely eliminated by this means must be
evaluated and their relationship to the conditions that
cause them must be determined.
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Compensating Errors: This type or surveying error tends to
occur in both directions, i.e. the error may sometimes
tend to be positive and sometimes negative thereby
compensating each other. They tend sometimes in on
direction and sometimes in the other, i.e. they are equally
likely to make the apparent result large or small. The
following are a few examples:
 Incorrect holding of chain
 Displacement of arrows
 Adding or omitting a full length of chain
 Reading wrongly
 Booking wrongly
 So we can say that errors in chaining may arise from
1.
2.
3.
4.
5.
6.
7.
8.
Incorrect length of chain or tape.
Bad Ranging
Careless holding and marking.
Bad straightening
Non –horizontality.
Sag in chain
Variation in temperature.
Variation in pull, etc.