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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.

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slide1

Surveying I.

Lecture 4.

slide2

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.
slide3

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.
slide4

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
slide5

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.

slide6

Systematic errors of angle measurements

Collimation error

The line of sight is not perpendicular to the transit axis.

slide7

Systematic errors of angle measurements

The effect of collimation error on the horizontal readings:

slide8

Systematic errors of angle measurements

since:

and:

When the angles are small:

and:

Thus:

slide10

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

slide11

Systematic errors of angle measurements

Excentricity of the telescope

The line of sight do not intersect the standing axis.

Readings in two faces!

slide12

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”

slide13

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.

slide14

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!

slide15

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.

slide16

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°.

slide17

The Horizontal Reading

BUT: Systematic errors exist - like the collimation error

The effect has opposite sign in the FL and FR reading.

slide18

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’’

slide19

The Zenith Angle

In theory the sum of the FL and FR readings should be 360°.

slide20

The Zenith Angle

What happens, when the index is not in the vertical direction?

slide21

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