CHAPTER-FIVE

HORIZONTAL DISTANCE MEASUREMENT

5.1 INRODUTION
Basic operations in surveying
Distance between two points on the earth’s surface is
determined, and it has to be the horizontal distance.
The distance between two points should be reduced in to
its equivalent horizontal distance,
By field procedures or by applying slope corrections.

A H
 5.2. Tape Measurements and methods
Tape Measurements/Chain Surveying
Chain surveying is a method of land surveying where only lin
ear measurement are made.
Instruments used
Chain: - widely used method for measuring distance.
It was 100 ft steel ribbon type.
Tapes: - made in a variety of materials, lengths and weigh
ts.
Steel tapes, some times called the engineers or surveyor’s tape
more commonly used by surveyors and for engineering meas
urements.
The woven metallic and non-metallic tapes.
Woven metallic tape: - is a ribbon of water proofed fabric in
to which are woven small brass or bronze wires to prevent it
s stretching. It is 10,20,30 or 50m long,
Cont….
.

Non-metallic glass fiber tapes: - which are non cond

uctors of electricity have been developed for use near p
ower lines.
Invar tapes: - are used for very precise measurements,
such as for base lines and in city works. Invar is a com
position of nickel and steel with a very low coefficient
of thermal expansion for temperature changes. Invar is
soft metal, and the tape must be handled very carefully
to avoid bends and kinks.
Steel tapes: - are 15, 25, 30 or 50m long. It may be lig
ht box tape or heavier tapes.
 Additional instruments used in taping:
 Range poles: - these are poles of circular section 2m, 2. 5m or 3m long, pai

nted with characteristic red and white bands, which are usually 0.5m long, a

nd tipped with a pointed steel shoe to enable them to be driven into the gro

und. They are used in the measurement of lines with the tapes, and for marki

ng any points that need to be seen. In hard or paved ground a tripod is used t

o support the rods.

 Taping Pins: - are also called chaining pins are commonly employed to mark

the ends of the tape during the process of taping between two points more th

an a tape length apart. They are usually 25 to .35cm long.

 Plumb bob: - It is a pointed metal weight used to project the horizontal loc
ation of a point from one elevation to another or it is used to project a point
on the ground up to the tape.

 Hand level: - can be used to keep the two ends of the tape at the same elev

ation when measuring over irregular terrain.

 5.2.2. Methods of Measurement
1.Pacing:- used for approximate measurements quickly or to check measurements
made by more precise means.
2.Odometer: - for rough measurements by rolling a wheel along the line to be
measured, and counting the number of revolutions. Useful for preliminary surveys.
3.Tacheometry:- a rapid indirect means of determining distance. Useful in
topographic surveying.
4.Electronic Distance Measurement (EDM):- works based on speed of light
/electromagnetic waves. Used for measuring long distance and for construction lay
out.
5.Taping:- steel tapes varying in length from 1m to 300m are used. Formerly, the
engineer’s chain or Gunter’s chain were used for measurements of the highest
precision, special bars were used.
 Choice of Methods
Most boundary, control and construction surveys involving l
ong lines and large areas can be performed most accurately
and economically using modern EDM equipments.
When short distances or specific construction layout require
ments are present, taping the distance can be more practica
l.
Stadia are still used for small topographic and preliminary su
rveys for projects of limited extent.
The method used for horizontal distance measurement dep
ends on the accuracy of the work, cost of operation and oth
er conditions.
Cont….
.

Figure 2.1: Taping equipment and accessories

 Method of Ranging
Direct Ranging
The process of laying out a straight line between point
s is known as ranging.
When the end stations are inter-visible, ranging is bei
ng carried out directly.
 The intermediate points are placed at distances havin
g interval less than one tape length.
Cont…..

Indirect Ranging
 When the end stations between which a straight line is to be
laid, are not inter-visible, indirect method of ranging is bein
g adopted.
Figure below shows the field operations involved in reciprocal
ranging. Let A and B are the two end points whose distance is
required to be found and are not inter visible. To fix the inter
mediate points in a straight line between these points, two mo
re points say C and D are chosen in such a way that D & B ar
e visible from C and C & A from D. Then, direct ranging is b
eing carried out alternatively along DCA and CDB for a num
ber of times so that ACDB lie in a straight line
2.3.2. Miscellaneous Taping and Ranging opera
tions.

1. Angle measurement:
When angle-measuring instruments like transit or theodolite are not available tapes
can be used to determine the angle between two lines within 5 to 10 minutes of arc.

2. Use of right angled triangle.

Erecting a line perpendicular to survey line at B and connecting the point with point on
other side on the survey line.
B’

A Pond C D
B
 Cont…..
Taping around the obstruction is possible
 During measurement of distance, various obstacles may be
encountered in the field.
 5.3. Systematic errors in taping
Sources of errors
The principal systematic errors in linear measurement
s made with a tape are:
1.Incorrect length of tape
2.Tape not horizontal;
3.Variation in temperature;
4.Incorrect tension or pull;
5.Sag in tape;
6.Incorrect a alignment of tape and;
Cont…..

 Random errors introduced in taping measurements are bec

ause of:
 Error in determining temperature of tape;
 Failure to apply the proper tension;
 Wind deflecting the plumb bob.
 Taping pin not set exactly where the plumb bob touched
the ground.
 Inability of the observer to estimate the last place in readi
ng between graduations.
 Inability of the tape man to steady the plumb bob.
 5.3.1. Corrections for errors in tape measurement

1.Incorrect length of tape

 The length of steel tape may vary when it is kinked, worn and i
mperfectly repaired after breaks. So, in order to reduce (eliminat
e) the variation in length, it should be checked with the standar
d.
 The correction to be applied to any measurement made with the
tape in order to account for the deviation is called the absolut
e correction Ca.
Ca= true length-nominal length
 The true length is the value determined by calibration under spec
ific conditions. Tape too long add correction, tape too short subt
ract correction.
Cont…..

Example
A distance is measured with a 50m steel tape and is fo
und to be 1357.40m. Later the tape is standardized an
d is found to have an actual length of 49.96m. What is
the correct distance measured? 
Solution: Ca=true length-nominal length
= 49.96-50=-0.04/ tape length
Corrected distance=1357.40+ (1357.40*-0.04)
50
= 1357.40-1.08592=1356.3141m
Cont…..

2.Malalignment of Tape
 If the tape is assumed to be on a survey line, it may be
misaligned out of survey line and an error is introduce
d. This malalignment may be at the end of the tape or
at the middle of the tape
 If the end of the tape is out of line by an amount h in a
length L, the error will be
h

L
e=h2/2L and the correction C = - h 2/2L
 The distance that is measured along the slope is
always greater than the horizontal distance. This
makes the correction to be subtractive.
 Cont…..
3.Change in Temperature:
 When a taping instrument is made, it is standardized for diffe
rent conditions, temperature, pull and support. When the fiel
d temperature differs considerably from the standard, a meas
urement made with a take will also vary considerably because
of the thermal expansion of the material to which the tape is
made. So, possible corrections are necessary for the variation
in length of the tape by the equation. 
Ct=L (T-Ts)
  Where Ct =temperature correction (m)
 = Coefficient of thermal expansion (for steel
=11.5*10-6/C0)
L = Length of tape actually used
T = Temperature at which measurement is made (0C)
Ts= Temperature at which tape was standardized (0C)
Cont.…..

Example
A traverse line is 152.4 m long. If the tape used in the field
is 50.0m when standardized at 170c, what correction mu
st be applied if the temperature at the time of measurem
ent is 230c? ( =11.2*10-6/0c)
 
Solution: Ct=L (T-Ts)
= 50*11.2x10-6(23-17)
= 3.36 x10-3 m/length
Total correction = 152.4* 3.36 x10-3 =+0.010m
50
Corrected Distance=152.4+0.010=152.41m
 Cont.…..
4. Correction for tension (CT)
 If a tape is used in the field under a tension different from the standard t
ension used in calibration, the tape will change its length a slight amoun
t according to the relation ship between stress and strain. The amount of
correction to be added or subtracted for the measured length is a functio
n of the measured length, tension during taping, the standard tension, cr
oss sectional area of the tape, and the modulus of elasticity of which the
tape is made. 
Correction for pull (incorrect tension)
CP= (P-Ps)L
AE
Where Cp is the correction per tape length (m)
P is the tension applied (kg)
Ps standard tension (kg)
L the length (m)
A is the cross-sectional area of tape (cm2)
E is the modulus of elasticity of the steel tape
Modules of Elasticity of steel is 2,100,000kg/cm2
Cont.…..

Example
A 30m tape weighing 0.90kg has cross-sectional area of 0.04
85 cm2. The tape measures 29.94m when it is pulled under a t
ension of 45kg. The tape was standardized under a tension of
10kg and modulus of elasticity of the tape is 2.1x106 kg/cm2.
Determine the correct distance measured. 
Solution: Using the above equn (correction for pull)
CP= (P-Ps)L
AE
Cp= (45-10)30 =0.010m
0.0485* 2.1x106
The correct distance =29.94+0.010= 29.95m
Cont.…..
5. Correction for sag:
 A tape supported only at the ends will sag in the center b
y an amount that is related to its weight and the pull (ten
sion). If the tape is standardized for a flat a negative corr
ection is required for sag because the chord distance is al
ways less than the curved distance along the sag which is
given by:-
Cg = - w2 L3 , Where Cg = Correction for sag
24P2 L = Length of the tape b/n supports
w = Weight of the tape per unit length (N/M)
P = Pull applied in the field.
If the total weight of the tape (W) is used, the formula will be.
Cs = - W2L
 24P2
Where Cs= Correction between points of support, m
W=weight of tape, kg/m
L= distance between support, m
P= applied tension, kg
Cont.…..

Example
Calculate the sag correction for a 30m steel tape un
der a pull of 100N if the weight of the tape was 0.
17 N/m.

Cg = w2 L3 = - (0.17)2 (30)3 = - 0.003m

24P2 (24) (100)2
Cont.…..
6. Tape not horizontal
 In surveying it is essential that horizontal lengths are determined.
When a distance lies along a uniform slope and when the differenc
e in height between the two end points has been determined it may
be preferable to measure the distance directly. After wards the hori
zontal distance can be by applying the following correction:-
 Case I. If the elevation difference of the two extreme ends known
Cs= v2
2s
where V = elevation difference
S = measured slope distance
Cs = Correction for slope
 Case II. If the slope angle ፀ is known
Cs = S(1 - cos ፀ )
Cont.…..

Example
A distance measured with a hundred meter steel tape along an uneve
n ground and found to be 238. 40m. if the elevation difference b/n
the end pts is 2.75m (or ,the slope angle is 0 0 39’39”) what’s the res
pective measured horizontal distance.
Given – S-238.40m V= 2.75m (ፀ= 00 39’39”)
Refld - H distance
Slop – (1) Cs = V2 = ( 2.75)2 = 0.02
2S (2x238.40)
Or
(2) Cs = S(1 – Cos 00 39’39”) = 238.40 (1.00 39’39”)
= 0.02M
H distance = S - Cs = 238.40 – 0.02
= 238.38m
 5.4. Electromagnetic distance measurement

a surveying instrument for measuring distance electronically be



tween two points through electromagnetic waves.

method of determining the length between two points, using p



hase changes, that occur as electromagnetic energy waves trave

ls from one end of the line to the other end.

Methods of measuring distance

1.DDM or Direct distance measurement - This is mainly done

by chaining or taping.
 Cont.…..

2.ODM or Optical distance measurement - This measurement is

conducted by tacheometry, horizontal subtense method or telemetric

method. These are carried out with the help of optical wedge

attachments.

3.EDM or Electromagnetic distance measurement - The method of

direct distance measurement cannot be implemented in difficult

terrains. When large amount of inconsistency in the terrain or large

obstructions exist, this method is avoided.

Types of Electronic Distance Measurement Instrument
1.Microwave instruments
2.Infrared wave instruments
Cont.…..
1.Microwave instruments:-These instruments make use of mi
crowaves. Wadley and named them as Tellurometers. The instr
ument needs only 12 to 24 V batteries.
2.Infrared wave instruments:-In this instrument amplitude mo
dulated infrared waves are used. Prism reflectors are used at th
e end of line to be measured. These instruments are light and e
conomical and can be mounted on theodolite. With these inst
ruments accuracy achieved is ± 10 mm. The range of these ins
truments is up to 3 km. These instruments are useful for most
of the civil engineering works.
3.Light wave instruments:-These instruments rely on propaga
tion of modulated light waves. This type of instrument was fir
st developed in Sweden and was named as Geodimeter. Durin
g night its range is up to 2.5 km while in day its range is up to
3 km. Accuracy of these instruments varies from 0.5 mm to 5
mm/km distance. These instruments are also very useful for ci
 Cont.…..

5.5. Trigonometric Leveling

In this type of leveling, horizontal distance and vertical angles are measured and used to compute
elevations differences. D

S B

H
C
HI

If S or H and  are known, hAB can be obtained

 hAB=HI+CD-BD BD is rod reading
 hAB=HI+S sin  -BD
Q&A

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