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Trigonometrical Levelling

Trigonometrical leveling is a surveying method to determine elevations of points using angles measured by a theodolite and distances measured by a tape or chain. Elevations are calculated using trigonometric functions of the measured angles and distances. Common equipment includes a theodolite, staff, tape or chain, ranging rod and plumb bob.

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Abir Mahmud
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76 views11 pages

Trigonometrical Levelling

Trigonometrical leveling is a surveying method to determine elevations of points using angles measured by a theodolite and distances measured by a tape or chain. Elevations are calculated using trigonometric functions of the measured angles and distances. Common equipment includes a theodolite, staff, tape or chain, ranging rod and plumb bob.

Uploaded by

Abir Mahmud
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Trigonometrical Leveling is the process of

determining the differences of elevations of


objects from observed angles (Theodolite) and
known distances (Chain / Tape).

Distance between the points observed is not large


so that either the effect of curvature and refraction
may be neglected or proper correction may be
applied linearly.
1. Determine the elevations of particular points.
2. Determine the distance between particular points.
3. Determine the aerial distances.

1. Theodolite with tripod stand


2. Staff
3. Tape/Chain
4. Ranging Rod
5. Plumb bob
N

M
H
Q

h1

R
C

A D

P
Q1

S2.
S1.

B.M.
CALCULATION

For ΔPRQ1,

PQ1 PR
= Sin {1800-(θ1+ θ2)}
Sin θ2 B

θ2
D1 b R
= Sin θ2
= Sin (θ1+ θ2)
b
A
θ1 `
Q1
P
D1
D1 = b Sin θ2/Sin (θ1+ θ2)
CALCULATION

For ΔPRQ1,

PQ1 PR
= Sin {1800-(θ θ )}
Sin θ2 1+ 2 B

θ2
D1 b R
= Sin θ2 = Sin (θ1+ θ2)
b A
`
θ1 Q1
P
D1
D1 = b Sin θ2/Sin (θ1+ θ2)
For ΔACQ,

QC h1 Q
tan β1 = =
AC D1

h1
h1 = D1 tan β1
β1
C
A D1
P

R.L. of Q = R.L. of B.M. +s1+h1

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