Geodesy vs. Topography: Surveying and Mapping Explained

Posted on Nov 9, 2024 in Physics

Geodesy vs. Topography

Geodesy

Geodesy is the science concerned with determining the Earth’s true form. It uses a mathematical model called the ellipsoid of revolution to measure the Earth’s sphericity and is applied to large land areas and high-precision engineering works like tunnels and dams. Geodesy offers greater precision than topography.

Geodetic work involves three areas:

  • Earth’s Surface: Where measurements are taken.
  • Ellipsoid Surface: Where mathematical calculations of x and y coordinates are performed.
  • Geoid Surface: The projection of the sea level onto the continent. It represents zero elevation, from which we measure heights and depths. The geoid is an amorphous mass.

Datum Point: The intersection of the three surfaces of geodesy.

Types of Datum:

  • Local Datum: Examples include SAD-69 and SAD-56 (South American Datum with semi-major axis = 6,378,388 meters and semi-minor axis = 6,359,912 meters).
  • Global Datum: WGS-84 provides true coordinates and coincides with the Earth’s axis.

Topography

Topography, a branch of descriptive geometry, identifies points above and below a surface. It doesn’t consider the Earth’s sphericity and works on small land areas, assuming a flat Earth.

Topography involves surveying and stakeout:

  • Surveying: Data is collected in the field, processed, and plotted on a map.

Types of Surveys:

  • Planimetric Surveys: Determine the horizontal position of points (plan view).
  • Altimetric Surveys: Determine the height or elevation of points relative to a horizontal reference plane.
    • Absolute: Mean sea level.
    • Relative: A benchmark.
  • Tachymetric Surveys: Combine planimetric and altimetric measurements simultaneously. The terrain is represented by contour lines.

Contour Lines: Imaginary lines connecting points of equal elevation.

Mapping Scales and Accuracy

Scale

Scale is the ratio between a measurement on a map and the corresponding measurement on the ground.

Scale Representation:

  • Ratio/Fraction: 1/100 or 1:100
  • Equivalence: 1 cm = 10 m
  • Graphic Scale (Bar Scale): A bar segment representing a specific distance on the ground.

The numerator’s unit equals the denominator’s unit in centimeters. The numerator represents the map, and the denominator represents the ground. If a scale isn’t available, the numerator can be in centimeters, and the denominator in any linear unit.

Graphic Scale Advantage: When enlarging or reducing a map, the bar scale changes proportionally, allowing for recalculation.

Accuracy

Accuracy is the smallest unit an instrument can measure.

Topographic Telescope

Instruments like engineer’s levels, tachymeters, theodolites, and total stations use a topographic telescope.

Components:

  • Ocular Lens: Where the real, inverted image is viewed.
  • Reticle: A glass plate with perpendicular lines (horizontal and vertical crosshairs).
  • Objective Lens: Forms the real, inverted image.
  • Reticle Focusing Screw: Clarifies the crosshairs.
  • Focusing Knob: Sharpens the image.
  • Spherical Level: Ensures the instrument is level.
  • Graduated Limb: A circular scale in degrees or grads.
  • Fixed Index: Used for horizontal angle measurements.
  • Leveling Screws: Center the spherical bubble level.
  • Tangent Screw: For fine adjustments of the horizontal limb.
  • Sighting Telescope: Allows closer observation of the target.

Stadia Rods and Leveling

Stadia Rods

Graded rods used for tachymetry or leveling. Tachymeter rods are 3-4 meters long, collapsible, and painted in white, red, and black sections, graduated in centimeters and millimeters.

Leveling rods are 1.3-1.4 meters long, collapsible, and also painted with alternating colors. They are graduated in meters, decimeters, and centimeters, with millimeter precision.

Leveling

Leveling determines the elevation of points relative to a horizontal reference plane. There are three types of leveling:

  • Barometric Leveling: Uses a barometer to measure atmospheric pressure differences, which correlate to elevation differences. Accuracy is in meters, suitable for reconnaissance surveys.
  • Geometric Leveling: Uses an engineer’s level or altimeter to create horizontal planes and measure elevation differences with millimeter accuracy.
  • Trigonometric Leveling: Uses instruments like tachymeters, theodolites, and total stations to determine elevations of distant but visible points using trigonometric functions and a vertical angle.