Surveying I. Lecture 2.

Outline Levelling Structure of levels Adjustment of levels Error sources Procedure of levelling

Levelling MSL - Mean Sea Level Level line - a line with constant height (a curved line) Horizontal line - a tangential to the level line at the instrument

Levelling Over short distances the horizontal line and level line coincide. For a distance of 100m the effect of the curvature is less than 1 mm. The levelling device (called level) must be set up so, that the line of sight is perpendicular to the gravity vector (plumb line). -> the line of sight is horizontal.

Levelling

Levelling

Levelling - Bookkeeping Rise and fall method:

Levelling - Bookkeeping Height of Collimation method:

Elements of Surveyor’s level How to set the line of sight to be exactly horizontal? More general: how to set anything to be exactly horizontal? The bubble tube

The bubble tube The radius determines the sensitivity of the bubble tube:

The bubble tube The determination of sensitivity:

The Surveyor’s telescope Object Eyepiece Object lens Virtual image Note that the virtual image is magnified and inverted!

The Surveyor’s telescope The diaphragm (cross-hairs) To provide visible horizontal and vertical reference lines in the telescope. Line of collimation With adjustment screws the diaphragm can be moved in the telescope to adjust the line of collimation.

The Surveyor’s telescope Parallax When focusing the telescope, the real image formed by the objective lens is made to coincide with the diaphragm. What is the parallax? When viewing two distant objects approximately along a straight line, and the eye is moved to one side, then the more distant object moves relative to the other in the same direction. This can lead to observation errors (wrong reading, wrong targeting). If the real image formed by the objective lens does not coincide with the diaphragm a parallax is observed -> the reading depend on the position of the eye! diaphragm image

The Surveyor’s telescope Focusing the telescope External focusing Variable length Focusing lens Internal focusing Fixed length

The Surveyor’s level Tilting level Bubble tube Diaphragm Tilting screw Circular bubble Tilting axis Levelling head Clamping screw - to fix the telescope in one vertical plane Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis

The Surveyor’s level Tilting level How can we view the bubble tube? Using a mirror (older instrument) Prismatic coincidence reader (modern instruments) Prism Bubble tube Bubble tube is tilted Bubble tube is horizontal (leveled)

The Surveyor’s level Setting up the level 1. Fix the level on a tripod 2. Center the circular bubble by adjusting the foot screws. (to approximately level the instrument) Primary axis Secondary axis 3. Sight the levelling staff, and eliminate the parallax. 4. Adjust the sensitive bubble tube by the tilting screw.

The Surveyor’s level Automatic level We must adjust the bubble tube before every reading when using the tilting level -> takes a lot of time, may cause blunders An automatic level contains an optical device, which compensates the tilting of the telescope - called compensator.

The Surveyor’s level Operation of the compensator Advantage: faster observations, elimination of a possible reason of blunders Disadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator

The levelling staff

Adjusting the level The two-peg test Collimation error - the line of collimation is not horizontal, when the level is levelled The effect of collimation error cancels, if d1=d2. Thus the height difference is:

Adjusting the level The two-peg test From the previous configuration:

Systematic errors in levelling The effect of curvature Solution: the instrument should be set up exactly in the middle between two points.

Systematic errors in levelling The refraction The air has different optical properties everywhere. Air pressure, humidity etc. Have an impact on the refractivity. Thus the light does not propagate along a straight line, but along a curve:

Systematic errors in levelling Solution: the instrument should be set up exactly in the middle between two points, thus the effect of curvature is the same for the backsight and foresight.

Systematic errors in levelling The effect of collimation error Solution: the instrument should be set up exactly in the middle between two points and the collimation error must be constant, thus the effect is eliminated

Systematic errors in levelling Tilting of the staff Depends on the: tilting angle reading (the higher the reading is, the bigger the error is) Solution: staffs should be equipped with circular bubbles

Systematic errors in levelling Settlement of the tripod Solution: the reading should be taken in both order, and the mean value of the height differences should be computed Orders: backsight - foresight foresight - backsight

Systematic errors in levelling Settlement of the staff Solution: all lines should be run twice in the opposite directions.

Procedure of levelling 1. The instrument must be set up in the middle between two staffs. 2. The bubble tube must be levelled before each reading. 3. You must not use the parallax screw between the backsight and foresight readings 4. The bubble tube must not be affected by strong heat. 5. Readings must be taken 30-50 cm above the ground. 6. Staff should be set up vertically. 7. A change plate should be used to place the staff on the ground. 8. Levelling must be done in two opposite directions.

Procedure of levelling 9. All the observations should be made with a constant speed. 10. Observations should be made only in suitable weather: cloudy sky, constant temperature, early morning, or late afternoon. 11. Staff should be calibrated. 12. If there are three hairs in the diaphragm, one should use all of them to take a reading.

Thanks for the Attention!