4. Surveying-II
• The lines of a triangulation system form a network tying
together the triangulation stations at the triangles.
• If it were possible to measure one side and all angles in a
triangulation system with absolute precisions, no further
linear measurement would be necessary.
• Unavoidable errors in the field measurement, however,
make it describe that the length of two or more lines in
each system be measured as a means of checking the
computed distances. The lines whose lengths are
measured are called base lines.
5. Surveying-II
• The arrangements of triangles in most system afford many
different geometrical figures, each of which theoretical
value of included angles is know. Also, the sum of angles
about any station should be equal 360o, and in any
triangle the length of the sides should be proportional to
the sines of the angle opposite. These known conditions
serve as a measure of the precision of the angle
measurements and as a means of adjusting the errors so as
to secure the most probable values of the measured
quantities.
6. Surveying-II
• If two angles of any triangle are measured, the value of
the third can be readily computed. This procedure
however does not permit the application of the known
conditions as a measure of the precisions of the
measurements or as a means of adjusting the errors;
therefore, it is customary to measure all angles.
7. Surveying-II
• Triangulation may be used for a simple topographic
survey covering but a few acres, or it may be used to
extend control of the highest order across the continent.
The relative merits of the triangulation method are based
upon the character of the area to be surveyed and not upon
the degree of precision to be attained. If favorable routes
are available, the method of traversing is superior to the
method of triangulation, but if the terrain offers many
obstacles to traverse work (such as hills, vegetation, or
marsh) triangulation is superior.
8. Surveying-II
STEPS OF TRIANGULATION SURVEY
The work of triangulation consists of the following steps:
1. Reconnaissance, (To select the location of station).
2. Erection of signals and, in some cases, tripods or towers
for elevating the signals or the instrument.
3. Measurement of angles between the sides of triangles.
9. Surveying-II
STEPS OF TRIANGULATION SURVEY
4. In the cases, astronomical observations at one or more
triangulation stations, in order to determine the true
meridian to which azimuths are referred.
5. Measurement of base line.
6. Computation, including the adjustment of the
observations, the computation of the length of each
triangle side, and the computation of the coordinates of
stations.
10. Surveying-II ROUTINES OF TRIANGULATION
SURVEYING
The entire triangulation surveying may b divided into two
stages i.e,
(i). Field works.
(ii). Computation of triangulation data.
11. Surveying-II
Keeping in mind the above stages the triangulation
survey can be consisted of the following operations.
1. Reconnaissance.
2. Erection of signals and towers.
3. Measurement of base lines.
4. Measurement of horizontal angles.
5. Measurement of vertical angles.
6. Astronomical observation to find azimuth of the sides of
triangles at regular intervals.
7. Computation of triangulation data.
12. Surveying-II
RECONNAISSANCE
Preliminary field inspection of the area to be surveyed is
known as “Reconnaissance”. The reconnaissance survey
is very important in all types of surveys and required great
skill, experience and judgment for the survey party chief.
As the economy and accuracy of the whole triangulation
system depends upon the efficiency of reconnaissance.
The following operations are required in reconnaissance.
13. Surveying-II
1. Pre examination of country terrain to be surveyed.
2. Selection of best site for base line.
3. Selection of suitable positions of triangulation station.
4. Determination of indivisibility and heights of stations.
5. Selection of well defined natural points.
6. Collection of information for communication of water,
food, laborers and guides etc.
14. Surveying-II
When the topographical maps of the area are available the
reconnaissance can be done effectively in the office. Moss
iced vertical aerial photograph can also be used to make
the general study of the area. If maps and photographs are
not available then a rapid preliminary survey for
reconnaissance is carried out to ascertain the general
location of schemes of triangulation suitable for that
country. By selecting well conditioned triangles, proper
identification of points can be judged by the accurate
bisection of intersected points. The essential features of
the topography should be sketched. The relative strength
and cast of various triangulation schemes are studies and a
final scheme is selected.
15. Surveying-II
INSTRUMENTS USED
As the reconnaissance, is a rapid survey the instruments
are used as follows:
1. Small theodolite and sextant for measurement of angles.
2. Prismatic compass for measurement of bearing.
3. A barometer for ascertaining the elevation.
4. A steel tape.
5. A powerful filed glass or a good telescope.
6. Miscellaneous items such as ladders, ropes & creepers
etc, for climbing trees.
16. Surveying-II
Examination of country Terrain
The country terrain should be properly examined by the
chief of the survey party to know the several topography
of the country terrain. The places of importance such as
undulation, hills, valleys, mineral quarries etc, the nature
of people, their traditions, labor available, sources of
drinking water, food, etc, the means of transportation
should be studied.
17. Surveying-II ELECTION OF BEST SITE FOR BASE LINE
The site, selected for base line, should be best from the all
consideration of survey work. The site should be free
from undulations, woods, etc. Means of transportation
should be available.
18. Surveying-II SELECTION OF TRIANGULATION
STATION
The following points should be considered while selecting
the stations for triangulation work:
1. The triangulation stations should be inter-visible. The
inter-visibility of stations can be made by placing the
stations upon the most elevated ground such as tops of
hills etc., so that they should not be disturbed by
atmosphere.
2. The stations should be accessible to instruments. The
supplies of food, water etc., should be available. Camping
site should be available.
19. Surveying-II SELECTION OF TRIANGULATION
STATION
3. The triangles formed by the stations should be well
conditioned as far as possible. No angle should be less
than 30o and more than 120o.
4. The stations selected should provide good intersection
for various points and detailed survey of the area.
5. Extensive distance stations should be avoided. The
station’s distance should be neither too small nor too
lager. The small sight will have errors due to centering &
bisection while large line of sight (on distance station)
will make the signal too indistinct for accurate
bisections.
20. Surveying-II SELECTION OF TRIANGULATION
STATION
6. The station should be commanding stations so that they
can be used for controlling subsidiary stations and for
future extension of survey work. The subsidiary
triangulation stations should be selected such that they
are most useful for detailed survey work.
7. Grazing lines of sights should be avoided. No line of
sight should pass over industrial areas to be Avoid
irregular atmosphere refraction.
8. In a wooded country, stations should be so located that
the cost of clearing, cutting of wood should be
minimum.
21. Surveying-II
MEASUREMENT OF BASE LINE
Equipment required:
1. Theodolite.
2. Ranging Rod.
3. Steel tape.
4. Thermometer.
5. Spring Balance.
6. Trusses.
7. Levels.
8. Staff Rod.
22. Surveying-II Correction applied to the measurement of base
line with a steel tape:
Correction due to absolute length:
Ca = Lc / l
Where;
Ca = correction due to absolute length.
L = measured length.
C = error in one length of the tape.
l = nominal length of the tape.
23. Surveying-II
Correction due to temperature:
CT = α (T – To) L
Where;
CT = correction due to change in temperature.
α = coefficient of thermal expansion.
T = Temperature during the measurement.
To = Temperature at which the tape is standardized.
L = measured length of line.
24. Surveying-II
Correction due to steep of slope (negative):
C slope = L – l
= L – (L2 – h2)1/2
= L – L (1 – h2/L2)1/2
= L – L [1 – (h/L) 2]1/2
= L –L [1 – h2/2L]
C slope = h2/2L
Therefore; Slope = h2/2L
25. Surveying-II
If θ is given then:
Slope = L –l
= L -Lcos θ
= L (1-cos θ)
= L (2sin2 θ/2)
= 2L sin2 θ/2
26. Surveying-II
Problem
A line is measured with the help of a steel tape which is
standardized at 65oF and was found to be 1571ft. Find
the length of the line. Even that the tape during
measurement was 85oF.
α = change in unit length per degree change or rise in
temperature.
27. Surveying-II
Solution:
Given data:
To = 65o. T = 85oF L = 1571ft
α = 0.0000065 /o F
Calculations:
Since; CT = α (T – To) L
= 0.0000065 × (85 o – 65 o) × 1571
= 0.204
True length = CT + L = 0.204 + 1571 = 1571.204ft
as required.
28. Surveying-II
Problem
A line measured with the help of a steel tape which is
standardized at 88o F and was found to be 1571ft. Find the
true length of line. Given that the temperature during
measurement was 75o F and coefficient of thermal
expansion is 0.00000625/o F.
29. Surveying-II
Solution
Given Data:
To = 88o F L = 1571 ft T = 75o F
α = 0.00000625/o F
Calculations:
Since CT = α (T – To) L
= 0.00000625 × (75o – 88o) × 1571
= -0.1276
True length = L + CT = 1571 + (-0.1276)
= 1570.8724ft as required.
30. Surveying-II
Problem
A line is measured with the help of a steel tape which is
standardized at 30 lbs and was found to be 280ft. Find
true length of the line? Given that the pull applied during
measurement was 20 lbs and A =0.004 inch2 and E =
30×106 psi
31. Surveying-II
Solution:
Given Data:
Po = 30 lbs P =20 lbs L = 1280ft
• A = 0.004 inch2 E = 30 ×106 psi
Calculations:
Cp = [(P – Po) × L] /AE
= [(20 – 30) × 1280] / [0.004 × 30×106] = -0.106ft
True length = L + Cp = L + Cp
= 1280 + (– 0.106) = 1279.893ft
32. Surveying-II
Problem
A line was measured with the help of a 100ft steel tape at
65o F and pull of 20 lbs and was found to be 875ft. Find
the true length of the line? Given that standard
temperature and pull for the tape is 75o F and 10 lbs
respectively.
α = 0.0000065/oF A = 0.005 inch2
E = 29 ×106 psi
Also given that weight of the tape is 1.5 lbs
33. Surveying-II Solution:
Given Data:
T = 65o F
P = 20 lbs
To = 75o F
Po = 10 lbs
L = 875ft
α = 0.0000065/oF
A = 0.005 inch2
E = 29 × 106 psi
Weight of tape is 1.5 lbs.
35. Surveying-II
**NOTE:
n = 875 / 100 = 8.75
w = W / l = 1.5 / 100 = 0.015 lbs/ft
True length = L + CT + Cp – C sag
= 875 + (-0.057) + 0.60 – 0.205
= 874.798ft
**Units = (lbs × ft) ÷ (inch2 × lbs / inch2) = ft
If area is given in ft2 then it will have to be converted into
inch2. In above case it is completely justified without
converting the units as shown above.
36. Surveying-II
Problem
A steel tape was exactly 100ft long at 64oF when
supported through its length under a pull of 100 lbs. A line
was measured with this tape under pull of 200 lbs at 84oF
and found to be 2406 ft. Assuming the tape to be
supported at every 100ft. Compute the true length of the
line; given that weight of one cubic inch of steel is
0.0000065/oF. Modulus of elasticity is 30×106 & psi &
total weight of the tape is 4.0 lbs.
37. Surveying-II
Solution:
Given Data:
P = 20 lbs
Po = 10 lbs
T o = 64oF
T = 84oF
l = 100ft
E = 30×106 psi
α = 0.0000065/oF
Specific weight of steel = γ = 0.28 lbs/inch3
Total weight of tape = 40 lbs
True length =?
39. Surveying-II
**Note:
n = 2406 / 100 = 24.06 w = 4 lbs / 100 ft = 0.04 lbs/ft
**To calculate ‘A’:
Suppose X-section area = A inch2
Length of tape = 100 ft = 1200 inch
Volume = 1200 × A × 0.28
A = 4 / (0.28 × 1200) inch2
A = 0.0119 inch2
Now;
True length = 2406 + 0.313 + 0.0674 – 4.01
= 2402.37 ft
40. Surveying-II
Problem
During the measurement of base line of four bays, the
following information was obtained.
Bay No. Measured
Length
‘l’ ft
Temperature oF
‘T’
Difference
of level
‘h’
Pull
applied
‘P’
1 98.25 60 + 0.25 20
2 99.50 59 + 0.64 15
3 95.75 62 - 0.90 10
4 35.80 64 + 0.40 20
41. Surveying-II
The tape weigh 0.0088 lbs/ft run and has X-sectioned area
0.0025 inch2. It was standardized 64oF under a pull of 10
lbs. α = 0.00000625 /o F; E = 30×106 psi. Compute the
true length of base line.
