lesson 2: leveling

Definition of Terms

Vertical Control: Heighting procedures used to obtain the elevation of points of interest above or below a reference datum.

Levelling: The process of determining the height of one level relative to another.

Reduced Level: Refers to vertical heights above or below a reference datum, often referred to as the level of a point.

Basic Concepts of Levelling

Measurement: Involves measuring vertical distances relative to a horizontal line of sight.

Benchmark: Permanent marks with known elevation used as a basis for measuring the elevation of other topographical points.

Leveling Surfaces

Level Surface: A curved surface that is perpendicular to gravity or the plumb line at any point.

Level Line: Curved line in a level surface, normal to gravity and equidistant from the earth's center.

Horizontal Surface: Plane tangent to a level surface at a particular point.

Horizontal Line: Straight line within a horizontal plane, tangent to a level line.

Vertical Line: Line parallel to gravity.

Important Reference Points

Mean Sea Level: An imaginary surface of the sea midway between high and low tides.

Datum: A convenient level surface parallel with mean sea level.

Elevation: The vertical distance above or below a selected datum point.

Leveling Methods

  1. Direct/Spirit Leveling: Uses setups of leveling instruments along a route to compute elevations.

  2. Reciprocal Leveling: Determines difference in elevation between two distant intervisible points.

  3. Profile Leveling: Determines elevation differences at short intervals along a line for vertical surface plotting.

  4. Trigonometric Leveling: Uses horizontal/slope distance and vertical angles to compute elevation differences.

  5. Stadia Leveling: Computes elevation differences from observed vertical angles and intercepts on a rod.

  6. Barometric Leveling: Measures elevation by variations in atmospheric pressure.

  7. Cross-Section Leveling: Plots short profiles at right angles to the line of work, used in highway construction.

  8. Borrow Pit Leveling: Determines relative elevations in borrow pit excavations for earthwork volume calculations.

Instruments for Direct Leveling

Dumpy Level

Wye Level

Automatic Level

Transit

Laser Level

Hand Level

Differential Leveling: Determines elevation differences between points with successive setups.

Leveling Terminology

Benchmark (BM): Marks with known elevations.

Backsight (BS): Reading taken on a point with known elevation.

Foresight (FS): Reading taken on a rod whose elevation is to be determined.

Turning Point (TP): An intervening point used to continue leveling operations from a new instrument position.

Height of Instrument (HI): Line of sight elevation above or below a reference datum.

Important Equations

To calculate HI:

HI = Elev + BS

To check surveys:

Total number of BS and FS should be the same.

Sources of Error

Instrumental Errors: 2. Instrument out of adjustment.

  1. Rod not of standard length.

  2. Defective tripod.

Personal Errors: 2. Bubble not centered.

  1. Parallax.

  2. Faulty rod readings.

  3. Rod not vertical.

  4. Unequal BS and FS distances.

Natural Errors: 2. Earth's curvature and refraction, h' = 0.0675K^2; K = line of sight in km.

  1. Temperature variations, wind, settlement of instruments, faulty turning points.

Common Mistakes in Leveling

Misreading the rod.

Incorrect recording of data.

Erroneous computation.

Rod not fully extended or moving turning points.

Sample Problem Illustration

Consider Earth’s curvature and refraction for a triangle formed by points A, B, and C:

Distance from A to B is $1000m$, A to C is $2000m$.

Angles of elevation from A to B are $18°$ and B to C are $8°$.

Calculate the difference in elevation considering natural errors.

For curvature and refraction: Use formulas to adjust heights accordingly.

Summary on Curvature Effect Example:

Measured angles compute height differences adjusted for curvature and refraction, demonstrating practical application in leveling calculations.