2-Linear-Measurements.pptx

Engineering Survey I
Lecture - III
BY : Dinesh Prasad Bhatt
dineshbhatt1995428@gmail.com
Department of Geomatics Engineering
Kathmandu University

Unit 2 Linear Measurements
Contents:
• Units of distance and area measurements
• Distance measurements technique
• Distance measurement equipment (Abney Level,
Clinometers, EDM)
• Various corrections for linear measurements

What is linear measurement?
• Linear measurements are methods used for determining horizontal
distances with a tape (or chain) and/or with an electronic distance
measuring instrument such as Total Station.
New building site -
how big is it?
50.5 metres
27.9
metres
50.5 metres
27.9
metres

Distance measurement
• Distance measuring is generally regarded as the most fundamental of
all surveying observations.
• Angles may be read but at least one line must be measured to
supplement the angles in locating points.
• In plane surveying; the distance between two points means horizontal
length between two points projected onto a horizontal plane.
• If the points are at different elevations, the distance is the horizontal
length between vertical lines at the points.

Some things to note…
• Equipment is fairly cheap (except EDM).
• Equipment is easy to maintain and adjust.
• Distances are easy to measure.
• Very accurate results can be achieved.
• Measurement line needs to be unobstructed.
• Errors occur and need to be managed or minimized.

Methods of linear measurements
• Direct methods
• In the direct methods, the distance is actually measured during field work using a chain or a
tape. This is the most commonly used method for linear measurements.
• Optical methods
• In the optical methods, principles of optics are used. The distance is not actually measured in
field but it is computed indirectly. The instrument used for making observation is called
tacheometer.
• E.D.M. methods
• Electronic distance measuring instrument is a surveying instrument for measuring distance
electronically between two points through electromagnetic waves.

Approximate Methods
1. Pacing or Stepping
• For rough and speedy work, distances are measured by pacing, i.e. by counting the
number of walking steps of a man. The walking step of a man is considered as 2.5 ft. or
80 cm. This method is generally employed in the reconnaissance survey of any project.

2. Passometer
• A small instrument just like a stop watch,
used for counting the number of steps
automatically by some mechanical device.
It offers an improvement over the normal
pacing method when a very long distance
is to be measured and when it becomes
very tedious to count and extremely
difficult to remember the number of steps.
Approximate Methods Cont.….

3. Pedometer
This instrument directly gives the distance by multiplying the number of paces with the
average pace length of the person carrying the instrument.

4. Odometer
• A simple device which can be attached to the
wheel of a bicycle or any such vehicle. The
odometer registers the number of revolution
made by the wheel. The distance covered is
equal to the product of the number of
revolutions and perimeter of the wheel.

5. Speedometer
• This is used in automobiles for
recording distances.

1. Ranging Rods
• Rods which are used for ranging (i.e. the
process of making a line straight) a line are
known as ranging rods. Such rods are made
of seasoned timber or seasoned bamboo.
They are generally circular in section, of
diameter 25 mm and length 2 m. Sometimes
wooden ranging rods are square in section.
The rod is divided into equal parts of 20 cm
each and the divisions are painted black and
white or red and white alternately so that
the rod is visible from a long distance. The
lower end of the rod is pointed or provided
with an iron shoe.
Accessories for linear measurements

2. Chains
• A chain is prepared with 100 or 150 pieces of galvanized mild steel wire of diameter
4 mm. The ends of the pieces are connected together with the help of three oval
rings, which make the chain flexible. Two brass handles are provided at the two ends
o the chain. Tallies are provided at every 10 or 25 links for facility of counting. ‘One
link’ means the distance between the centers of adjacent middle rings.
Accessories for linear measurements Cont.….

Types of Chain
• Metric Chain
• Gunter’s Chain or Surveyor’s Chain
• Engineer’s Chain
• Revenue Chain
• Steel band

►Metric Chain
• Metric Chains are available in lengths of 20 m and 30 m. The 20 m chain is
divided into 100 links, each of 0.2 m. Tallies are provided at every 10 links (2
m). This chain is suitable for measuring distances along fairly level ground.

►Gunter’s Chain or Surveyor’s Chain
• It is 66 ft. long and divided into 100 links. So, each link is of 0.66 ft. It was
previously used for measuring distances in miles and furlongs.

►Engineer’s Chain
• The engineer’s chain is 100 ft. long and is divided into 100 links. So, each link
is of 1 ft. Tallies are provided at every 10 links (10 ft.), the central tally being
round. Such chains were previously used for all engineering works.

►Revenue Chain
• The revenue chain is 33 ft. long and divided into 16 links. It is mainly used in
cadastral survey.

►Steel Band
• It consists of a ribbon of steel of width 16 mm and of length 20 or 30 m. It has
a brass handle at each end. It is graduated in meters, decimeters and
centimeters on one side and has 0.2 m links on the other. The steel band is
used in projects where more accuracy is required.

3. Tapes
• Tapes are used for more accurate measurement. The tapes are classified
based on the materials of which they are made of such as:
• Cloth or Linen Tape
• Metallic Tape
• Steel Tape
• Invar Tape

►Cloth or Linen Tape
• Such a tape is made of closely woven linen and is varnished to resist moisture.
It is 15 mm wide and available in lengths of 10 and 15 m. This tape is generally
used for measuring offsets and for ordinary works.

►Metallic Tape
• When linen tape is reinforced with brass or copper wires to make it durable,
then it is called a metallic tape. This tape is available in lengths of 15, 20 and
30 m. It is wound on a leather case with a brass handle at the end. It is
commonly used for all survey works.

►Steel Tape
• The steel tape is made of steel ribbon of width varying from 6 to 16 mm and
available in lengths 10, 15, 20, 30 and 50 m. It is graduated in meters,
decimeters and centimeters. It is not used in the field, but chiefly for
standardizing chains and for measurements in constructional works.

►Invar Tape
• Invar tape is made of an alloy of steel (64%) and nickel (36%). It is not affected
by temperature since its thermal coefficient is very low. It is made in the form
of ribbon of width 6 mm and is available in lengths of 30, 50 and 100 m. It is
used at places where maximum precision is required.

4. Arrows
• Arrows are made of tempered steel wire of diameter 4 mm. One end of the
arrow is bent into a ring of diameter 50 mm and the other end is pointed. Its
overall length is 400 mm. Arrows are used for counting the number of chains
while measuring a chain line.

Tacheometry
• Tacheometry is a branch of surveying in which
horizontal and vertical distances are determined by
taking angular observations with an instrument known
as a tacheometer.
• The chaining operation is completely eliminated in
such survey and is adopted in rough and difficult
terrain where direct levelling and chaining are either
not possible or very tedious. Also used in location
survey for railways, roads, reservoirs, etc. It is
considered as the system of rapid surveying.
Optical Distance Measurement (ODM)

• The principle of tacheometry is based on the property of isosceles triangles, where the
ratio of the distance of the base from the apex and the length of the base is always
constant.
• So, according to the stated principle,
D1/S1 = D2/S2 = D3/S3 = f/i (constant)
The constant f/i is known as the
multiplying constant.
where, f = focal length of objective
i = stadia intercept
Principles of Tacheometry

• The formula most widely used for finding the distances is:
 D = (f/i)*s + (f+d)
Or, D = Ks + c
Where, the value of constant f/i is known as a multiplying constant. It is usually kept
100 by the manufacturers. The value of other constant (f+d), known as an additive
constant is generally kept between 0.3 to 0.5 m.
Principles of Tacheometry Cont.….

29
Electronic Distance Measurement (EDM)
• First developed by Dr. E. Bergstrand in 1950 and called Geodimeter.
• EDM capable of transmitting an electromagnetic signal is set up over
survey station at one end of survey line.
• The signal is directed to a reflector or second transmitter at the other
end of the line, where it is reflected or instantly re-transmitted back to
the transmitter.
• Can be mounted on the telescope of theodolite or directly in a tribrach.
• The distance is calculated either from the time difference between a
transmitted pulse and a return pulse or the phase difference between a
transmitted and a reflected beam of radiation.
• The slope distance measured can be converted to horizontal and vertical
equivalent using measured angle.

30
Principles of EDM
• When electromagnetic wave leaves the EDM and reflects (light wave) or retransmits
(microwaves) back to EDM, double distance = whole no of wave length (nλ), plus partial
wave length (Ø) occurring at the EDM.
L = (nλ+ Ø)/2 m
• The partial wavelength (Ø) is determined in the instrument by noting the phase delay required
to precisely match up the transmitted and reflected or retransmitted waves.
• The instrument either can count the number of full wavelength (nλ) or instead, the instrument
can send out a series ( 3 or 4) of modulated waves at different frequencies.

Units of distance measurements
Meters Yards Feet Inches
1 1.0936 3.2808 39.3701
0.9144 1 3 36
0.3048 0.3333 1 12
0.0254 0.0278 0.0833 1
Km Nautical mile Statute mile
1 0.53996 0.6214
1.852 1 1.1508
1.6093 0.869 1

Various corrections for linear measurements
• Correction for Standard Length (Standardization)
• Correction for Alignment
• Correction for Slope
• Correction for Tension
• Correction for Temperature
• Correction for Sag
• Reduction to Mean Sea Level

1. Correction for Standard Length (Standardization)
Before using a tape, its actual length is ascertained by comparing it with a standard
tape of known length. The designated nominal length of a tape is its designated length e.g.
30 m, or 100 m. The absolute length of a tape is its actual length under specified
conditions.
Cα = (L*C)/l
Where, Cα = correction for absolute length
L = measured length of a line
C = correction to be applied on the tape
l = nominal or designated length of the tape
The sign of the correction will be the same as that of C. Before applying eqn, L & l
must be expressed in the same units and also the units of Cα & C should be the same.

2. Correction for Alignment
Generally a survey line is set out in a continuous straight line. Sometimes, it
becomes necessary, due to obstruction, to follow a bent line which may be composed of
two or more straight portions subtending an angle other than 180°.
Let, AC = l1 , CB = l2
Angle BAC = θ1, Angle ABC = θ2
Length AB = l1cos θ1 + l2cosθ2
Thus, the required correction = (l1+l2) – (l1cos θ1 + l2cos θ2)
= l1(1 – cosθ1) + l2(1 – cosθ2)

In case, stations A and B are not intervisible, the angle ACB(say) may be measured
accurately with a theodolite and the distance AB may be computed with the cosine
formula:
AB = √(AC2 + BC2 - 2AC.BC.cosα)
Note: This correction for alignment is always subtracted from the measured length of the
line.

3. Correction for Slope
The distance measured along the slope between two stations is always greater
than the horizontal distance between them. The difference in slope distance and horizontal
distance is known as slope correction which is always subtractive. Angle of slope is
measured with a theodolite.
The required correction: h2/2L
where, h = difference in reduced levels of A & B
D = horizontal distance AC
L = slope distance AB

4. Correction for Tension
If the pull applied to the tape during measurements is more than the pull at which
it was standardized, its length increases and hence the measured distances become less
than actual. Correction for tension is therefore positive. On the other hand, if the applied
pull is less, its length decreases and consequently the measured distances becomes more.
The correction for tension is negative.
Derivation of the formula: When a tape is subjected to a tension of P Newton weight, it
gets elongated by a small amount within the elastic limits. The ratio of stress and strain
which is known as Young’s Modulus of the Elasticity of the material, is a constant.
Let P = Pull or tension in Newton(N)
A = Cross-sectional area of the tape in square cm.
L = length of the measured line
l = Elongation of the tape
Stress = P/A ; Strain = l/L
Or, E = stress/strain = (P/A)/(l/L) = PL/Al
Or, l = PL/AE

If P0 = Standard pull
P = pull applied during measurements
Then, correction for tension = (PL/AE) – (P0L/AE)
= L(P – P0)/(A*E)
Where,
E = Young’s Modulus of the Elasticity (ratio of stress to strain)
for steel: 2.1*10^5 N/mm2 & for invar: 1.5*10^5 N/mm2
Note: If applied pull(tension) is more, tension correction is positive, and if it is less, the correction is
negative.

5. Correction for Temperature
The length of a tape increases if its temperature is raised and decreases if its
temperature is lowered. If the temperature of a tape is above normal, the correction is
positive and if it is below normal, the correction is negative.
Temperature Correction α = (Tm – T0)*L
where, L = measured length of the line
Tm = mean temperature during measurements
T0 = normal temperature at standardization
α = coefficient of thermal expansion of the tape material
for invar: 0.000000122 per 1°C or less.
Note: For precise measurements, accurate value of the coefficient of expansion of the tape
material must be carefully determined.

6. Correction for Sag
When a tape is suspended from two supports in air, it assumes the shape of a
catenary. The difference between the curved length of the tape and horizontal distance
between the supports is known as sag correction. The apparent length of the tape is too
long and as such sag correction is always negative.
Sag Correction = (L/24)*(W/P)2
where, L = horizontal distance
between supports
W = total weight of the
tape
P = Pull applied

7. Reduction to Mean Sea Level
The measured length of a line at an altitude of h meters above mean sea-level will
be more as compared with the corresponding line on the mean sea-level surface. The
difference in the length of the measured line and its equivalent length at sea-level is known
as an error due to reduction to M.S.L.
Correction due to reduction to M.S.L. = L*(h/R)
where, L = distance AB measured at an altitude h
meters above M.S.L.
L’ = distance A’B’ reduced as M.S.L.
R = radius of the earth

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