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Geodesy

An overview of the basic concepts of geodesy and topography, a detailed exploration of the methods and tools used in topographic surveying.

Geodesy and Topography

Meaning of Geodesy

Geodesy, strictly speaking, is the science that studies the Earth with the purpose of defining the Earth’s surface in terms of its shape and dimensions. In a broader sense, it also includes the study of specific physical phenomena such as the Earth’s gravitational field, crustal movement, pole displacement, and tides.
The ultimate goal of geodesy is to acquire knowledge about the entire globe.

Geodesy and Topography

Topography is a branch of geodesy that generally deals with the study and measurement of portions of the Earth’s surface. It specifically focuses on determining the positions of points on the Earth’s surface based on a point defined by its coordinates, using measurements of distances, elevations, angles of direction, azimuth angles, and zenith angles.

Difference between Geodesy and Topography

The difference between geodesy and topography is as follows: geodesy is concerned with the shapes and dimensions of the Earth, while topography is the graphical and numerical representation of a limited portion of the Earth’s surface.

Topography: Topographic Surveying

What is Topography: Definition

Topography is a discipline that, through its methods and tools, allows for the graphical representation of parts of the Earth’s surface on geometrically-based maps that enable measurements to be made.
Topographic maps can be classified based on the scale of representation and the level of detail depicted:

  • Plats (scale ranging from 1/100 to 1/1000)
  • Maps (scale ranging from 1/1000 to 1/5000)
  • Topographic maps (scale ranging from 1/5000 to 1/100,000)
Topographic Surveying

Topographic surveys encompass the operations necessary for the graphical representation of a portion of the Earth’s surface, and the applications of topographic discipline are diverse in nature.

In civil engineering, topographic surveys are employed:

  • For the testing or structural monitoring phase
  • In the construction of facades
  • In preliminary tests for the elevation plan of masonry works
  • In quarries, landfills, bridges, roads, tunnels, and galleries
  • For metal structures and industrial buildings
  • In the analysis of riverbeds or basins (bathymetry)

In addition to civil engineering, topographic surveys have found extensive applications in other sectors such as architecture, to define the dimensional, geometric, and structural characteristics of a building, or archaeology, for the documentation of remains or as a preliminary analysis before excavation.

Topographic surveys can be planimetric, altimetric, or planimetric-altimetric.
Planimetric surveys enable the determination of the position of a point by projecting it onto a reference surface, using x and y coordinates calculated from field measurements.
Altimetric surveys allow for the measurement of the distance between a point P and the reference surface.

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Definition of Topographic Field

The Earth’s surface is irregular, and for this reason, in topographic discipline, a theoretical reference surface called the “geoid” is assumed.
The shape of the geoid is a complex, mathematically undefinable form, conventionally approximated to a rotating ellipse called an ellipsoid. The ellipsoid is characterized by slight undulations known as geoidal undulations, which are generated by variations in the Earth’s gravitational field.
In essence, the ellipsoid is a mathematical model of the Earth that allows the identification of point positions and their representation on a flat surface.

Therefore, the topographic field refers to the surface area around a point within which it is assumed that the ellipsoid coincides with the horizontal plane tangent to the point itself.

Definition of Topographic Distance

The distance between two points in the topographic field is referred to as the topographic distance.
The definition of topographic distance is the length of the segment that connects the two points projected onto the reference surface.
In topographic distances, the concept of spherical error must be considered, which is the limit within which the reference surface can be considered flat.

Coordinate Systems in Topography

In ambito topografico i sistemi di coordinate servono a stabilire la posizione dei punti per poi procedere

In topography, coordinate systems are used to establish the position of points and perform measurements relative to them.
Let’s now examine how polar coordinates and Cartesian coordinates are defined and employed in topography.

Polar Coordinates

Polar coordinates are a two-dimensional coordinate system that describes the position of a point using an angle and a distance from a fixed point called the pole.

Cartesian Coordinates

In topography, Cartesian coordinates are based on an orthogonal system of axes, x and y, and the position of a point is determined by the intersection of the two axes.

Topographic Polygonalization

Il rilievo topografico, come abbiamo avuto già modo di dire in precedenza, è l’insieme di operazioni necessarie alla rappresentazione grafica e numerica di una porzione di territorio.
La prima fase del rilievo topografico consiste in quello che viene definito inquadramento geometrico genera

Topographic surveying, as mentioned earlier, involves a set of operations necessary for the graphical and numerical representation of a portion of the territory.
The first phase of topographic surveying is the general geometric framing of the surface under examination, which consists of a limited series of interconnected points covering the entire surface and forming the so-called base network.
This is followed by the densification of the points in the base network and the detailed surveying phase.

Depending on the method chosen to connect the points in the base network, the following terms are used:

  • Triangulation
  • Intersections
  • Polygonization

These are complementary methods that are used in a mixed formula in topographic surveying, and in the case of large territories, they may be used simultaneously.
If the points in the framing network are connected pairwise, a network of triangles with a common side is created, resulting in triangulation. On the other hand, if the points are connected by a series of line segments, polygonization is performed.

Therefore, in topography, polygonals refer to a series of points connected by line segments.
During the densification of the framing network for detailed surveying, the method of intersections is used to represent isolated points, i.e., points not connected to each other. Intersections are obtained using lines originating from known points.

Trilateration in Topography

The method of trilateration in topography allows for determining the position of a point by measuring the distance from two other known points.
It is employed when defining an irregular space characterized by the absence of right angles or when locating a point with a complex position that is challenging to determine.

Topographic Instruments

Topographic instruments refer to all the tools used in topographic surveying for the direct or indirect measurement of points, angles, and elevations.
In particular, we will delve into the use of the total station in topography and topographic surveying with a total station.

La stazione totale è lo strumento topografico più utilizzato perché caratterizzato da una tecnologia aThe total station is the most commonly used topographic instrument due to its advanced technology, which includes a theodolite (for measuring horizontal and vertical angles) and an EDM (electronic distance measuring device that uses infrared or laser beams). Topographic surveying with a total station allows for the measurement of angles and distances of a series of points and their positioning in space relative to a predefined coordinate system.

Architectural surveying with a total station and archaeological surveying with a total station are examples of the high precision and effectiveness of this instrument, which has found numerous applications. Among the technologies employed, we must also mention the method of topographic surveying with GPS (Global Positioning System), although it has been surpassed and replaced by more modern GNSS receivers that utilize signals from satellites of all constellations (GPS, GLONASS, Galileo, BeiDou, IRNSS, QZSS, SBAS) in orbit to determine the absolute position of points on the Earth’s surface.

Stazioni totali, sistemi GPS e ricevitori GNSS sono strumenti avanzati che consentono ai professionisti Total stations, GPS systems, and GNSS receivers are advanced instruments that allow professionals in the field to efficiently perform topographic monitoring because they enable the acquisition of real-time reliable data that can be stored.

Metrology and Topography

In this overview of the fundamental concepts that we will delve into in our articles, we also wanted to focus on the relationship between topography and metrology as the science of measurement and its applications.
LaTopography is a discipline that originated in ancient times as a need to measure the surrounding reality, such as agricultural lands, and even after centuries, the ultimate purpose of this science remains the understanding of the territory.
PSpeaking of metrology emphasizes the issue of measurement, the connection between instruments and measurement, and the necessity for these tools to ensure effective measurement for professionals in the field.

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