Leveling and Surveying Principles

• Leveling is determining the relative heights and depths of objects on the Earth's surface, involving measurements in a vertical plane.

Key Definitions

• Level Surface: A curved surface perpendicular to the direction of gravity at every point.
• Level Line: A line lying within a level surface.
• Horizontal Surface: A plane tangential to the level surface. The line within this plane is a horizontal line.
• Datum: Is a level surface (imaginary) used as a reference to measure vertical distances.
• The Indian datum is based on the Mean Sea Level (MSL) at Karachi.
• Reduced Level (Elevation): The height or depth of a point relative to a datum.
• Benchmark: A fixed reference point with a known elevation (RL).

Types of Benchmarks

• G.T.S. Benchmark: Established by the Great Trigonometrical Survey of India with high precision relative to the MSL at Karachi.
• Permanent Benchmark: Established by government agencies like PWD between GTS benchmarks for survey facilitation.
• Arbitrary Benchmark: Assumed RL of a well-defined reference point in small leveling operations.
• Temporary Benchmark: Reference points set when work is interrupted and cannot be completed at once.

Leveling Instruments

• A leveling instrument consists of:
  • Leveling head with three-foot screws to center the bubble.
  • Telescope to provides line of sight.
  • Bubble tube to make the line of sight horizontal.
  • Tripod for instrument support.

Components of Dumpy Level

• Key parts include:
  • Telescope
  • Bubble tubes
  • Vertical spindle
  • Tribrach screws
  • Foot screws
  • Leveling head

Telescope Functions

• Used for observing distant objects by providing a line of sight.
• The telescope rotates with the vertical spindle.

Telescope Parts in Dumpy Level

• Eyepiece
• Objective lens
• Diaphragm
• Focusing screw
• Ray shade

Part Details

• Eyepiece: Contains a magnifying glass to view distant objects and crosshairs for accurate readings; erecting eyepieces view normal images.
• Objective Lens: Located at the opposite end of the telescope with two parts: a convex lens in front and a concave lens in the back.
• Images obtained from the objective lens are always inverted.
• Diaphragm: Located in front of the eyepiece, containing perpendicular crosshairs for bisecting objects.
• Focusing Screw: Adjusts focus for crosshair and enhances image clarity, including eyepiece magnification.
• Bubble Tubes: Two bubble tubes check the instrument's level, arranged perpendicularly on top.

Achieving Perfect Instrument Position

• The instrument is in perfect position when the bubbles in both tubes are centered.
• Vertical Spindle: Located at the instrument's center, allowing horizontal telescope rotation, connected to the tripod using the vertical spindle.
• Tribrach: Parallel to the leveling head (or trivet), connected via leveling screws to adjust the plate and achieve horizontal level.
• Foot Screws: Foot screws regulate the tribrach to level the instrument, using the bubble tube for observation and adjustment.

Leveling Head

• Also called as trivet, it holds two parallel triangular plates.
• Grooves at the corners support the foot screws.

Types of Levels

• Dumpy Level: Solid construction with the vertical spindle and telescope barrel cast as one piece; simple, stable, and compact.
• The telescope is fixed and cannot rotate or be removed.
• Wye Level: The telescope is supported by two vertical wye supports with curved clips that allow rotation or removal.
• Modern Tilting Level: Allows slight vertical motion via a tilting screw, enabling leveling without using foot screws.
• Automatic Level: Achieves automatic leveling using a tilting compensator suspended like a pendulum in the path of light rays, providing high precision and speed.

Leveling Staff

• They area graduated rod for measuring vertical distances
• Sop with Telescopic Staff: The most common type, it has three telescopic sections extending to 4m.
• Top section length 1.25m, slide into the central box of 1.25m and a bottom box of 1.5m length with smallest division on this staff being 0.005m.
• Folding Metric Staff: Is a 4m staff which are arranged in two 2m sections connected at the middle, for folding or detachment.
• Aluminum Telescopic Staff: Made from special anticorrosive aluminum alloy with a push-button locking system and provided with a canvas bag.

Definitions

• Line of Collimation: An imaginary line from the intersection of crosshairs to the optical center of the objective lens.
• Also known as the line of sight.
• Axis of Telescope: An imaginary line connecting the eyepiece center and the optical center of the objective lens.
• Axis of Bubble Tube: The imaginary line tangential to the bubble tube at its midpoint.
• Vertical Axis: The axis perpendicular to the line of collimation or line of sight.
• Back sight (BS): Which is the first staff reading taken on a benchmark (known RL) after setting up the level.
• It is considered positive.
• Fore sight (FS): It is a staff reading to determine the RL, where the last reading taken before moving the level and considered negative.
• Intermediate sight (IS): Any staff reading between BS and FS on a point with unknown RL.
• Height of Instrument (HI): Reduced level of the line of collimation when the instrument is level; the height from the datum to the line of sight.
• Staff Station: The point where the staff is held for reading during leveling.
• Change Point (CP): An intermediate station where FS and BS are taken to change the instrument's position.
• Focusing: Adjusting the eyepiece and the object glass to have a clear vision of the object.
• Parallax: Condition when the image is not in the plane of the crosshairs, which can be adjusted by focusing.

Adjustments of Level

• Temporary adjustments
• Permanent adjustments

Permanent Adjustments

• Ensure long-term accuracy based on the instrument type.
  • The axis of bubble tube should be perpendicular to the vertical axis.
  • The line of sight should be parallel to the axis of bubble tube.
  • The horizontal crosshair should be perpendicular to the vertical axis

Temporary Adjustments

• Made at each setup before taking readings
• Setting up the instrument.
• Leveling the instrument.
• Focusing:
  • Secure the level on the tripod by rotating the lower section.
  • Initially, level the instrument using its legs. Fine-tune by using the foot screws. Position the bubble tube parallel to each pair of foot screws, then bring the bubble to the midpoint by turning both screws equally, either inward or outward.
  • Focus the eyepiece by pointing the telescope toward the sky or a piece of white paper, then adjust the eyepiece until there's a clear sight of the crosshairs.
  • Focus the target by pointing it toward the staff, and turn the focusing screw until the graduation is clear

Field Note in Leveling (Level Book)

• Leveling field notes are recorded in a level book, which has a tabular structure for entering and reducing levels.
• Height of instrument method
• Rise and fall method

Height of Instrument Method

• HI is derived by adding BS to the RL of the BM and the RI of intermediate points, change point from HI.
• When the process is repeated until all the RL of the pointe are taken.
• HI changes when the instrument is moved.
• Arithmetic Check: ΣBS - ΣFS = Last RL - First RL.

Rise and Fall Method

• Calculate the difference between consecutive readings; smaller readings indicate a rise and larger readings indicate a fall.
• RL is determined by adding a rise or subtracting a fall from the preceding point's RL.
• Arithmetic Check: ΣBS - ΣFS = ΣRise - ΣFall = Last RL - First RL

Comparison of HI and Rise and Fall Methods

Errors in Leveling

• Instrumental errors:
  • Imperfect permanent adjustment: Misalignment of the line of collimation.
  • Defective Bubble Tube: When there's defect with tube so the the axis may not be horizontal.
  • Incorrect Graduations of Staff: Graduations should be checked with measuring tape when staff is new.
• Personal errors
  • Careless leveling of instrument
  • The bubble not being level at the time of taking reading
  • Imperfect focusing
  • The staff is not being held vertically
• Natural errors
  • Curvature and refraction of earth: Objects appear higher/ in reality the sight is lower.
  • Sun and Wind: Bright sun can effect staff, and high winds can move the tripod.
  • Tripod and staff settlement: Possibility to settle if soil is not firm

Curvature and Refraction

• For sights ≥ 200m, needed effects of curvature/refraction.
• Effects of earth here show that the observed reading is more than the reading provided by the earth

Calculations

• Correction for curvature (C) = 0.0785d², (d = distance in km; C in meters).
• True staff reading = Observed staff reading - 0.0785d²
• Correction for refraction (Cᵣ) = (1/7)C = 0.0112d²
• True staff reading = Observed staff reading + 0.0112d²
• Combined Correction = C = 0.06728d² = C - Cᵣ
• True staff reading = Observed staff reading - 0.06728d²

Bubble Tube Sensitivity

• Sensitivity is the angular value of one division on the tube.
• Sensitivity indicates more division movement at the same angle change.
• Sensitivity can be increased by:
  • Increasing the internal radius of the tube
  • Increasing the tube diameter
  • Increasing the length of the bubble
  • Decreasing the wall roughness
  • Decreasing the liquid viscosity

Explore level surfaces, datums, and leveling equipment components such as eyepieces and objective lenses. Understand benchmarks and instrument adjustments for accurate surveying. Learn about leveling operations.