Introduction to Leveling

Introduction to Leveling

• Leveling is a surveying operation to determine elevations, elevation differences, and control grades.
• Point elevation is the vertical distance above or below a reference level, usually mean sea level.
• Determining point elevations is vital for road, railway, drainage, and canal construction.
• Leveling quantifies earthwork and calculates water storage in reservoirs or dams.

Key Terms

• Vertical Line: A line parallel to gravity, represented by a plumb bob.
• Level Line: A curved line where all points have equal elevation, perpendicular to gravity.
• Horizontal Line: A straight line tangent to a level line at a given point.
• Level Surface: A surface of constant elevation, perpendicular to a plumb line at every point, like still water unaffected by tides.
• Horizontal Surface (Plane): A plane tangent to a level plane or perpendicular to gravity
• Difference in Elevation: Vertical distance between level surfaces through different points.
• Reduced Level (RL): The level of a point from a reference datum and indicates the height or depth relative to the assumed datum.
• Bench Mark (BM): A permanent or semi-permanent point with known elevation, serving as a starting point.
• Back Sight (BS): The initial sight after setting up the instrument, often on a benchmark or known elevation point, used to determine the Height of Instrument (HI).
• Height of Instrument (HI): The elevation of the line of sight for a level instrument setup.
• Fore Sight (FS): The final sight before relocating the instrument.
• Intermediate Foresight (IFS): A reading taken between the back sight and foresight with a similar instrument height.

Methods of Leveling

• Three main methods exist: spirit, trigonometric, and barometric leveling.
• Spirit Leveling (Direct Leveling): Measures vertical distances relative to a horizontal line to calculate elevation differences. A spirit level establishes the telescope's line of sight as the assumed horizontal line.
• Trigonometric Leveling: Measures horizontal distances and vertical angles to compute elevation differences, suitable for inaccessible points like mountain peaks.
• Barometric Leveling: Determines elevations by measuring air pressure changes, using aneroid barometers (altimeters) for approximate measurements within 5–10 feet. Requires at least three barometers to account for pressure, temperature, and humidity variations.

Leveling Instruments

• Each level instrument consists of a high-powered telescope with a spirit level, where a centered bubble indicates a horizontal line of sight.
• Purposes include fixing the line of sight and magnifying objects.
• The telescope has an objective lens, an eyepiece, and a reticle (cross-hairs).
• Leveling instruments (spirit levels) include Wye, Dumpy, Builder's, self-leveling, tilting, and laser levels, each with type-dependent functionality.
• Leveling Rods:Graduated from zero, can be one-piece (3m), telescoping (4m), or hinged (4m) wood. Self-reading rods are read through the telescope. Target rods use a sliding target set by the rodman
• Telescope has three main parts: objective lens, eyepiece, and reticle (cross-hairs).

Temporary Adjustments

• Adjustment involves three steps at each station:
  • Setting up the instrument over a station
  • Leveling the instrument
  • Focusing to avoid parallax
• To set up the instrument, use firm ground and an approximately horizontal tripod head.
• On softer ground, use supports like stakes or a platform for the tripod legs.
• Level the instrument via a three-foot screw, turning the telescope until the bubble tube is parallel to two screws, centering the bubble by turning the screws in opposite directions. For the second step the telescope is turned so that the bubble tube is perpendicular to a line through screws 1 and 2, centering the bubble by turning screw 3.
• Repeat the steps until the bubble remains centered when the telescope is turned back and forth.
• Focusing eliminates parallax by carefully focusing the objective lens until the image and crosshair remain stationary relative to each other when the eye moves.

Equipment Care

• Tripod setup should be firm and horizontal before the instrument is removed from its box.
• Handle the instrument by its base and carefully screw it onto the tripod.
• Avoid setting up on smooth, hard surfaces without securing the tripod points.
• Clean dusty lenses with a camel's hair brush or lens paper.
• Leveling screws should turn easily with fingertips; excessive force indicates a problem.
• Loosen screws and clamps during storage to prevent damage from temperature changes.
• Level rods should not be dragged, and their metal base should avoid impacts to prevent wear and measurement errors.

Theory of Spirit Leveling

• After setup and leveling at point B, the sight line aligns with the level rod held by the rodman at a known elevation.
• This sight is called the back sight (BS).
• Add the back sight to the benchmark elevation to determine the height of the instrument (HI).
• Use the known HI to determine the elevation of other points by placing the level rod and taking a reading.

Continuing Leveling

• After reading, a foresight (FS) is subtracted from the HI to define further elevation for a point.
• Readings between the back sight reading and the last station are intermediate points foresight (IFS) readings.
• The last reading from an instrument is the foresight (FS).
• To continue leveling, the level shifts to a temporary turning point (TP).
• A back sight reading (BS) is taken at the new position on the rod which has been turned to the telescope side.
• HI is determined for the new setup to continue operation.

Instrument Adjustment

• The line of collimation should be the line of sight through optical center and cross-hairs.
• Perfect adjustment is required for horizontal line of sight when leveled; the height of collimation equals instrument height.
• Collimation is not horizontal when the leveling sight is not the true horizontal line.
• Errors associated with this phenomenon is the collimation error.
• The existence of incorrect collimation can be checked with two-peg test.

Equations

• el of B = HI - FS = el of A + BS - FS
• True el of B = el of A + BS + e1 - FS - e2
• If the instrument is mid way between A and B
  • Δh AB = BS + e1 - FS - e2
  • b/c e1=e2
  • Δh AB = BS – FS

Types of Spirit Leveling

• Spirit leveling types: simple, differential, profile, cross-section, trigonometric, and reciprocal.
• Differential Leveling: Used for elevation differences between distant points, requiring multiple instrument setups. Back sight readings are required to BM or TP and FS reading to a point in question for each setup.
• Height of Instrument (HI) Method of Reducing Level
  • Desired elevation found by:
    • Adding BS to BM to find height
    • Subtracting FS from height

Arithmetic Check

• Equation: BS-FS = Last RL-First RL

Rise and Fall Method

• The ground surface rise or fall between successive readings is computed to determine point elevations.
• Ground surface fall is subtracted, and rise is added to elevation difference.

Inverted Sights

• Used when leveling points above the line of collimation, such as soffits or tunnel roofs.
• The staff is held upside down, adding the FS reading to the height of the instrument.
• The back sight (BS) taken on the point is subtracted from the elevation of the point to determine the height of instrument (HI).

Leveling Examples

• Reduction of Leveling and Arithmetic Check Calculations

Effects of Earth’s Curvature and Atmospheric Refraction

• Leveling measurements in vertical planes are influenced.
• These effects must be considered because of their impacts on the vertical direction.
• Refraction occurs when light rays pass through air strata of different densities.
• It is greatest with large temperature differences, causing variation in air densities.
• Combined correction = 0.0785 L2* (6/7) = 0.0673 L2 (m) where L in km
• With smaller sight lengths (<100m) and if the instrument has mid-way set up between BS and FS reading stations can ignore errors.

Reciprocal Leveling

• Levels across deep bodies of water is necessary to transfer level sight.
• When long errors are required, these become apparent due to collimation, the earth's curvature, atmospheric refraction, rod reading errors plus instrumentation.
• By means of reciprocal levelling, avoid corrections need for curvature and refractions.
• Equation - H = ((a1 – b1) + (a2 – b2)) / 2; 2 similar instruments in correct measurement are required

Uses of Profile Leveling

• Decide what gradient fits the quantity of fill and cat
• Determine what earthwork to embark on
• Record and locate places to decide drainage lines.

Cross Section Leveling

• Profile leveling helps provide info about the level of a provided route only along a centerline, ground details aren’t helpful on either side of a line. Ground character has little change.
• This helps provide data on terrain at right angles as it connects to centerlines.
• Provide transverse at 20m to 30m and add to points where route changes

Uses

• Economical level to work with, or decide what level to work in
• Helps embankments
• Trigonometric leveling is next

Sources of Errors

• Instrumental errors are an important source.
• Line of sight should be parallel to bubble tube, and will proportion to line of sight. Maintain equal fore and backwards sights,
• Lenses should be focused
• Stabilize everything, ensure nothing is lose on tripod
• Staff graduations should be error free

Handling of Equipment

• When handling equipment be sure bubbles align
• Always keep staff vertical
• When equipment displaces or is altered it may change
• Always have turning/change points.
• Never touch the staff unless its been checked
• If there are issues with reading or booking, read staff through scope
• When the wind blows its hard to hold steady.
• Heat messes of instruments and you may have sun in the scope
• Always remember your basic practices