surveying i. lecture 4.. setting up a theodolite 1.setting up the tripod (the head of the tripod...
TRANSCRIPT
Surveying I.
Lecture 4.
Setting up a theodolite
1. Setting up the tripod (the head of the tripod should be approximately horizontal) above the control point
2. Fix the instrument on the tripod.
3. Sight the control point in the optical plummet using the footscrews of the instrument.
4. Level the instrument by adjusting the length of the legs of the tripod using the circular bubble.
5. Find the normal point of the bubble tube.
6. Level the instrument accurately using the bubble tube and the three levelling screws.
7. Finally loosen the instrument on the tripod, and slide it above the control point on the head of the tripod.
8. Fix the instrument on the tripod.
Setting up a theodolite
Systematic errors of angle measurements
Systematic errors can be caused by:
• structural failures or misalignments of the instrument
• the observer
• external conditions during the observation (weather, etc)
Systematic errors can be eliminated by:
• eliminating the reason of the systematic error (adjustment of the instrument, following the rules - weather)
• using suitable measuring procedures
• computing the effect of the error, and correcting the observations
Systematic errors of angle measurements
Let’s suppose that the systematic errors are independent -> can be treated
separately.
Diaphragm is tilted
We have to use the same point to sight a target.
Intersection of the crosshairs.
Systematic errors of angle measurements
Collimation error
The line of sight is not perpendicular to the transit axis.
Systematic errors of angle measurements
The effect of collimation error on the horizontal readings:
Systematic errors of angle measurements
since:
tantan
''
OMcOP
MMPP and:
OP
OMc
tan
tan
When the angles are small:
cc
tan
tanand: cos
OP
OM
cos
c
tan'
tan'
OMMM
cOPPP
Thus:
Systematic errors of angle measurements
Readings in two faces!
Systematic errors of angle measurements
The transit axis is not adjusted
The transit axis is not perpendicular to the standing axis.
1
1sinPO
PP
From the OP’P1’ triangle:
11
1tanPP
PP
From the P’P1P1’ triangle: 1
11tansinPO
PP
since
1
11tanPO
PP
then
tanReadings in two faces!
Systematic errors of angle measurements
Excentricity of the telescope
The line of sight do not intersect the standing axis.
P
V=O
( )
( )
Excen
tric lin
e of s
ight
Correct lin
e of sight
d
arcsin
OPd
Readings in two faces!
Systematic errors of angle measurements
Excentricity of the horizontal circle
O
V
r
”
( )”
( )’( )”
( )’’
i’(exc)
i’(c)i”(c)
i”(exc)
The center of the horizontal circle do not coincide with the standing axis.
Sine theorem:
sinsin
r
sinarcsinr
Dangerous error source: r=14cm, ()=10-6m, =90 -> ()=14,4”
Readings in two facesor
using two indices!
Systematic errors of angle measurements
Tilting of the horizontal circle
The plane of the horizontal circle is not perpendicular to the standing axis.
Graduation error of the horizontal circleCould be neglected for modern instruments. However repeated measurements should be taken by rotating the horizontal circle with 180°/# of repetitions.
Systematic errors of AM - Setting up errors
Centering error
The extension of the standing axis does not go through the station.
V=O
d
ic
iexc
0
0
iexc
sinarcsinr
Centering should be checked
before each repetition!
Systematic errors of AM - Ext. conditions
Deformation of the tripod
The tripod may revolve due to direct and uneven sunlight.
Experience show that the speed of revolution is constant. 0tt
Effect of refraction
The light does not propagate along a straight line.
Majority of the impact is on the vertical angle measurements.
Will be discussed later.
FL and FR readingsin the opposite order!
The Horizontal Reading
Readings are taken in two faces: Face left (FL) <-> Face right (FR)
How can the horizontal reading computed from the FL and FR readings?
0
Face Left
0
Face Right
In theory the difference between FL and FR reading should be exactly 180°.
The Horizontal Reading
BUT: Systematic errors exist - like the collimation error
The effect has opposite sign in the FL and FR reading.
The Horizontal Reading
Example
0
Face Left
0
Face Right
transit axis
P
P’’
P’
M
M’
M’’
cc
FL: 88-05-26FR: 268-05-55
The difference should be 180°, but it is 180°00’29’’.
2 = 29’’ -> = 14,5’’
Horizontal Reading = FL + = 88° 05’ 40’’
The Zenith Angle
Face Left Face Right
0 0
In theory the sum of the FL and FR readings should be 360°.
The Zenith Angle
What happens, when the index is not in the vertical direction?
Face Left
0Index error
Face Right
0Index error
The Zenith Angle
How can we compute the zenith angle?
Face Left
0Index error
Face Right
0Index error
FL: 68-15-22FR: 291-44-20
2=360°-FL-FR=18’’
=9’’
Z = FL+ =68-15-31
Thank You for Your Attention!