Lecture 1

Leveling - Theory, Methods, and Equipment

• Objectives:
  • Understanding leveling terminology
  • Understanding differences in vertical datums
  • Understanding the effects of curvature and refraction on leveling
  • Understanding how to correct for the effects of curvature and refraction in differential leveling

Work Required

• Read sections 4.1 through 4.5.2
• Complete problems 4.1, 4.2, using distances of 850 feet, 1387 feet, and 2100 feet, and problem 4.6.

4.1 Introduction

• Leveling is a process for determining elevations of points or differences in elevation
• Used for mapping, engineering design, and construction
• Applications include highway, railroad, canal, and water system design; earthwork calculations; and land evaluation
• Leveling involves various processes to establish vertical datum

4.2 Definitions

• Vertical Line: A line following the local direction of gravity (plumb line)
• Level Surface: A curved surface perpendicular to the local vertical line at every point; a body of still water is a close approximation
• Level Line: A line within a level surface
• Horizontal Plane: A plane perpendicular to the local vertical line
• Horizontal Line: A line within a horizontal plane
• Vertical Datum: A reference level surface (e.g., average sea level) from which elevations are measured
• Elevation: The vertical distance from a vertical datum to a point or object

4.3 North American Vertical Datums (NGVD29 and NAVD88)

• NGVD29: A previous vertical datum based on mean sea level at specific locations
• NAVD88: A more accurate vertical datum, adjusted to account for improved data and changes in sea level and Earth's crust
• Based on a single benchmark in Canada

4.4 Curvature

• A level surface is curved due to the Earth's curvature.
• An instrument's line of sight is horizontal, not a level surface due to curvature effects.
• Corrections need to be applied to measurements involving significant horizontal distances

4.4 (a) Curvature (c)

• Equation for curvature correction (c) using horizontal distance (M) in miles: c = 0.667(M)²
• Equation using horizontal distance in thousands of feet (F): c = 0.0239(F)².
• Correction must be subtracted to obtain accurate results.

4.4 (b) Curvature and Refraction

• Refraction causes light rays (and thus the instrument's line of sight) to bend toward the Earth's surface.
• Combined effect of curvature and refraction (c+r) for horizontal distances (M) in miles to the level rod: c+r = 0.574(M)²
  • Correction must be subtracted from initial rod reading to compensate for curvatures and refractions effects

4.5 Measuring Vertical Distances (Taping/Electronic Methods)

• Measures a vertical line using taping or EDM techniques
• Typically used for shorter distances or when precision is not as critical

4.5.2 Differential Leveling

• Method to measure differences in vertical elevation between two or more points.
• Uses a level instrument and rod
• Establish a benchmark with a known elevation and measures the elevation from the instrument.
• Requires taking multiple measurements to create a "loop" for verifying calculations and accuracy of the data.

Example Differential Leveling Notes

• Data recording format for differential leveling
• Includes columns for Station, Backsight (BS), Height of Instrument (HI), Foresight (FS), Intermediate Foresight (IFS), Elevation, and Corrected Elevation
• Describes procedures of using Backsight (BS), Foresight (FS), and Height of Instrument (HI) for calculating elevations of unknown points for differential levelings