Download Subject: Surveying (1306o1)

SUBJECT NAME : SURVEYING
GROUP NO. 8
ENROLMENT NO.
NAME
130460106034
ARCHIT MEWADA
130460106044
ANUJ PATEL
130460106048
HARDIK M PATEL
130460106052
JAIMIN PATEL
LEVELLING
Definition:
“ Trigonometric levelling is the process of determining the
differences of elevations of stations from observed
vertical angles and known distances. ”
The vertical angles are measured by means of theodolite.
The horizontal distances by instrument
Relative heights are calculated using trigonometric functions.
Note: If the distance between instrument station and object is
small. correction for earth's curvature and refraction is not
required.
1) Direct Method:
Where is not possible to set the instrument over
the whose station whose elevation is to be
determined.
Combined correction is required.
AB’=AC=D
L ACB = 90°
Similarly,
BA´=BC´=D
L AC´B=90°
BC=D tanα
AC´=D tanβ
Distance between A & B is large
Cc & Cr required
CB´=C´A´= 0.0673 D2
True difference A-B
H=BB´
=BC+CB´
=D tanα +0.0673 D2
Depression angle B to
A
AC´=D tan β[BC´=D]
True Difference A-B
H=AA´
=BC+CB´
= D tanβ -0.0673 D2
2H = D tan α +D tan β
R.L of station B = R.L of station A + H=R.L. of
station A +D/2[tan α + tan β]
METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE:
Case 1. Base of the object accessible
Case 2. Base of the object inaccessible, Instrument stations in the
vertical plane as the elevated object.
Case 3. Base of the object inaccessible, Instrument stations not in
the same vertical plane as the elevated object.
Case 1. Base of the object accessible
B
A = Instrument station
B = Point to be observed
h = Elevation of B from the
instrument axis
D = Horizontal distance between A
and the base of object
h1 = Height of instrument (H. I.)
Bs = Reading of staff kept on B.M.
= Angle of elevation = L BAC
h = D tan 
R.L. of B = R.L. of B.M. + Bs + h
= R.L. of B.M. + Bs + D. tan 
If distance is large than add Cc & Cr
R.L. of B = R.L. of B.M. + Bs + D. tan  + 0.0673 D2
Case 2. Base of the object inaccessible, Instrument stations in
the vertical plane as the elevated object.
There may be two cases.
(a) Instrument axes at the same level
(b) Instrument axes at different levels.
1) Height of instrument axis never to the object is lower:
2) Height of instrument axis to the object is higher:
Case 2. Base of the object inaccessible, Instrument stations in the vertical plane as
the elevated object.
(a) Instrument axes at the same level
 PAP, h= D tan 1
 PBP, h= (b+D) tan 2
D tan 1 = (b+D) tan 2
D tan 1 = b tan 2 + D tan 2
D(tan 1 - tan 2) = b tan 2
R.L of P = R.L of B.M + Bs + h
(b) Instrument axes at different levels.
1) Height of instrument axis never to the object is lower:
 PAP, h1 = D tan 1
 PBP, h2 = (b+D) tan 2
hd is difference between two height
hd = h1 – h2
hd = D tan 1 - (b+D) tan 2
= D tan 1 - b tan 2 -D tan 2
hd = D(tan 1 - tan 2) - b tan 2
hd + b tan 2 = D(tan 1 - tan 2)
h1 = D tan 1
(b) Instrument axes at different levels.
2) Height of instrument axis to the object is higher:
 PAP, h1 = D tan 1
 PBP, h2 = (b+D) tan 2
hd is difference between two height
hd = h2 – h1
hd = (b+D) tan 2 - D tan 1
= b tan 2 + D tan 2 - D tan 1
hd = b tan 2 + D (tan 2 - tan 1 )
hd - b tan 2 = D(tan 2 - tan 1)
- hd + b tan 2 = D(tan 1 - tan 2)
h1 = D tan 1
In above two case the equations of D and h1 are,
D
h1
Case 3. Base of the object inaccessible, Instrument stations not in the same vertical
plane as the elevated object.
Set up instrument on A
Measure 1 to P
L BAC = 
Set up instrument on B
Measure 2 to P
L ABC = 
L ACB = 180 – (  +  )
Sin Rule:
BC=
AC=
b· sin
sin{180˚ - (+ )}
b· sin
sin{180˚ - ( + 
h1 = AC tan 1
h2 = BC tan 2
DIRECT LEVELLING ON STEEP GROUND:
Indirect levelling can be
also used where the
ground is steeper .the
following procedure is
used to determine the
difference of elevations
between A and B.
Select a suitable turning
point C.
1.Set up the instrument
at a convenient station 01
on the line AB . make the
line of collection roughly
parallel to the slope of
the ground. Clamp the
telescope .
Vertical angle θ1 to A´ .
Determine the R.L of A´ as
R.L of A´ = R.L of A + AA´
3.Take a foresight CC´ on the staff held at the C
change point without changing the vertical angle
θ1 . Measure the slope distance AC between A and
C.
R.L. of C = R.L. of A´ + AC sinθ1 – CC´
Or R.L. of C = R.L. of A + AA´ + AC sinθ1 - CC´
4.Shift the instrument to the station o2 midway
between C and B . Make the line of collimation
roughly parallel to the slope of the ground . Clamp
the telescope .
5.Take a back sight CC'‘ on the staff held at the
change point C. measure the vertical angle θ2.
6.Take a foresight BB on the staff held at the point B without
chaining the vertical θ2. measure the slope distance CB .
R.L. of B = R.L. of C + CB sinθ2- BB
Thus RL of B = ( R.L. of A + AA + AC sinθ1 – CC)+ CC+ CB
sinθ2- BB
If there are some intermediate points whose elevations are
required, the procedure is slightly different as under.
Suppose , there is an intermediate point D at slope distance
AD from A. The level of the point D can be determined
from the setting of the instrument at o1.
R.L. of D =R.L. of A´+ AD sinθ1- DD
Where DD is the intermediate sight on the staff held at D.
Same way R.L. of some intermediate points between A and
C , and also between C and B can be determined as usual
way.
YOU