2 Setting up a theodolite Setting up the tripod (the head of the tripod should be approximately horizontal) above the control pointFix the instrument on the tripod.Sight the control point in the optical plummet using the footscrews of the instrument.Level the instrument by adjusting the length of the legs of the tripod using the circular bubble.Find the normal point of the bubble tube.
3 Setting up a theodolite Level the instrument accurately using the bubble tube and the three levelling screws.Finally loosen the instrument on the tripod, and slide it above the control point on the head of the tripod.Fix the instrument on the tripod.
4 Systematic errors of angle measurements Systematic errors can be caused by:structural failures or misalignments of the instrumentthe observerexternal 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 procedurescomputing the effect of the error, and correcting the observations
5 Systematic errors of angle measurements Let’s suppose that the systematic errors are independent -> can be treated separately.Diaphragm is tiltedWe have to use the same point to sight a target.Intersection of the crosshairs.
6 Systematic errors of angle measurements Collimation errorThe line of sight is not perpendicular to the transit axis.
7 Systematic errors of angle measurements The effect of collimation error on the horizontal readings:
8 Systematic errors of angle measurements since:and:When the angles are small:and:Thus:
9 Systematic errors of angle measurements Readings in two faces!
10 Systematic errors of angle measurements The transit axis is not adjustedThe transit axis is not perpendicular to the standing axis.From the OP’P1’ triangle:From the P’P1P1’ triangle:sinceReadings in two faces!then
11 Systematic errors of angle measurements Excentricity of the telescopeThe line of sight do not intersect the standing axis.Readings in two faces!
12 Systematic errors of angle measurements Excentricity of the horizontal circleThe center of the horizontal circle do not coincide with the standing axis.Sine theorem:Readings in two facesorusing two indices!Dangerous error source: r=14cm, (d)=10-6m, w=90 -> (d)=14,4”
13 Systematic errors of angle measurements Tilting of the horizontal circleThe 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.
14 before each repetition! Systematic errors of AM - Setting up errorsCentering errorThe extension of the standing axis does not go through the station.Centering should becheckedbefore each repetition!
15 Systematic errors of AM - Ext. conditions Deformation of the tripodFL and FR readingsin the opposite order!The tripod may revolve due to direct and uneven sunlight.Experience show that the speed of revolution is constant.Effect of refractionThe light does not propagate along a straight line.Majority of the impact is on the vertical angle measurements.Will be discussed later.
16 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?In theory the difference between FL and FR reading should be exactly 180°.
17 The Horizontal Reading BUT: Systematic errors exist - like the collimation errorThe effect has opposite sign in the FL and FR reading.
18 The Horizontal Reading ExampleFL:FR:The difference should be 180°, but it is 180°00’29’’.2d = 29’’ -> d = 14,5’’Horizontal Reading = FL + d = 88° 05’ 40’’
19 The Zenith AngleIn theory the sum of the FL and FR readings should be 360°.
20 The Zenith AngleWhat happens, when the index is not in the vertical direction?
21 The Zenith Angle How can we compute the zenith angle? FL: 68-15-22 FR:2d=360°-FL-FR=18’’d=9’’Z = FL+d =