Surveying I. Lecture 4.

Setting up a theodolite Setting up the tripod (the head of the tripod should be approximately horizontal) above the control point Fix 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.

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.

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: and: When the angles are small: and: 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. From the OP’P1’ triangle: From the P’P1P1’ triangle: since Readings in two faces! then

Systematic errors of angle measurements Excentricity of the telescope The line of sight do not intersect the standing axis. Readings in two faces!

Systematic errors of angle measurements Excentricity of the horizontal circle The center of the horizontal circle do not coincide with the standing axis. Sine theorem: Readings in two faces or using two indices! Dangerous error source: r=14cm, (d)=10-6m, w=90 -> (d)=14,4”

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 circle Could be neglected for modern instruments. However repeated measurements should be taken by rotating the horizontal circle with 180°/# of repetitions.

before each repetition! Systematic errors of AM - Setting up errors Centering error The extension of the standing axis does not go through the station. Centering should be checked before each repetition!

Systematic errors of AM - Ext. conditions Deformation of the tripod FL and FR readings in the opposite order! The tripod may revolve due to direct and uneven sunlight. Experience show that the speed of revolution is constant. 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.

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°.

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 FL: 88-05-26 FR: 268-05-55 The difference should be 180°, but it is 180°00’29’’. 2d = 29’’ -> d = 14,5’’ Horizontal Reading = FL + d = 88° 05’ 40’’

The Zenith Angle 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?

The Zenith Angle How can we compute the zenith angle? FL: 68-15-22 FR: 291-44-20 2d=360°-FL-FR=18’’ d=9’’ Z = FL+d =68-15-31

Thank You for Your Attention!