Fundamentals of Topography and Geodesy

Fundamentals of Topography

Definition of Topography

Set of methods and tools necessary to represent the ground with all its natural and artificial details.

Topographic Survey

Set of methods, measurements, and representation of any part of the earth's surface at a given level in the form of a plan or map. This part of the survey is called planimetric survey (X, y). Since the surface of the earth is three-dimensional, topographic survey also includes leveling, which is to determine the gaps between the various points of the surface represented in the plane.

Layout

Operations needed to correctly place any field project and control it during the construction process.

Units Used in Topography

• Length: Meter
• Surface: m² or Ha (10,000 m²)
• Angle: Grads

Geodesy Principles

Geodesy

Science that aims to study the shape and dimensions of the Earth.

Geoid

Equipotential surface, physical, conceptual, and irregular, obtained by extending the seas under the continents. It approximates an ellipsoid of revolution flattened at the poles.

Reference Ellipsoid

Arbitrary surface, but as regular as possible, that fits the geoid. The ellipsoid used is Hayford. In this ellipsoid, the fundamental astronomical point (the match point where the normal to the ellipsoid and the direction of gravity align) is located in Potsdam. The prime meridian and the origin parallel are Greenwich and the Equator, respectively.

Geographical Coordinates and Mapping

Geographical Coordinates

The situation of a point on the ellipsoid is defined by the intersection of a meridian and a parallel. These define the geographic coordinates called the point's latitude and longitude.

Longitude

The angle, measured in degrees, minutes, and sexagesimal seconds, formed by the plane of the Greenwich meridian and the plane of the meridian of the place. The measured longitude to the east of the Greenwich meridian is considered positive, being negative to the west.

Latitude

The vertical angle between the ellipsoid at the point considered and the level of the Equator. Points from the Equator toward the North Pole have north latitude. Those placed from this plane toward the South Pole have south latitude.

Mapping

It is the science that studies the methods to represent graphically on a plane the surface of the Earth. As the Earth's surface (geoid) is not developable, mapping and transformation laws use projection methods that allow us to transfer what is irregular on a spherical surface onto the plane. We must ensure that the map bears some resemblance to reality. To achieve this similarity, it is essential that the following quantities are equal on Earth and on the plane, maintaining the scale relationship:

• Distances between points.
• Angles between two directions.
• Surfaces between areas.

It is mathematically impossible to satisfy these equalities simultaneously, so we must decide what is most appropriate in each case. The inequality of this magnitude between Earth and the plane is called anamorphosis.