Topographical Instruments and Surveying Techniques

Concept of Slope and Gradient

The closeness of curves indicates a steep slope, while a large separation indicates a slight incline. This equidistance, whenever we have to compare the two cases, is the same. The equidistance of curves in a plane is unique.

• A series of concentric curves, where the heights rise to the center, indicates a rise or hill.
• A series of concentric curves, in which the dimensions decrease toward the center, indicates a depression or hollow.

We define slope as the ratio between the horizontal and vertical displacement, always looking from the top down. The gradient is defined as the ratio between the vertical and horizontal displacement.

Alignment

• Natural Distance (Dn): Dn is the distance traveled on the ground, following the irregularities of the terrain.
• Geometric Distance (Dg): Dg is the distance in a straight line between two points on the Earth's surface.
• Reduced Distance (Dr): Dr is the projection of the distance, both natural and geometric, onto the plane of comparison as a reference.
• Difference in Elevation: The difference in elevation between the points under consideration.
• Slope (p): The slope p of the alignment is the tangent of the angle (V1), which is the same as its horizontal projection.
• Degree of Alignment: The degree of alignment is represented on its projection in the horizontal plane of comparison, including all the spot heights.
• Module: The module of alignment is the distance measured along the projection, between two consecutive points of whole dimension.

Simple Topographical Instruments

Simple surveying instruments are those that serve to solve simple topography problems or are part of other composite tools.

Instruments Used in the Definition of Straight, Flat, Horizontal, and Vertical Lines

Bubble Level or Toric Level: It consists of a glass tube in a ring with a large radius of curvature. The tube is nearly filled with a low-viscosity liquid (alcohol), leaving an internal air bubble that occupies the top of the tube. On the glass tube, separate marks are usually made, typically 2 mm apart.

Sensitivity of the Level (S): The central angle, in seconds, corresponding to an arc of 2 mm in length, outside the level line. The sensitivity is usually expressed by manufacturers in sexagesimal seconds.

Ball Level: Built by a cylindrical container, capped by a spherical glass on which a circle is engraved. The cylinder is filled with a low-viscosity liquid with a cylindrical bubble inside.

Tools to Set Alignment

Milestones and banners, alidades with pinnules, square prisms and mirrors.

Astronomical Telescope: The elements of the telescope are the objective, ocular, and reticle.

Parallax Error: The object image is not formed on the reticle but before or after it.

Correcting the Error of Parallax

1. Aim at the sky, or place a white object in front of the objective, to see only the crosshairs.
2. Focus the crosshairs perfectly for the observer's view. Keep in mind that if the observer changes, the entire process must be repeated.
3. Perfectly focus the observed object, triggering the screw on the focus lens to see the object clearly.
4. Move the eye up and down to check that the wires do not give the feeling of moving on the observed object.

Instruments for Measuring Length

Narrow woven fabrics, synthetic and metal rules, or Invar wires.

Compound Topographical Instruments

Theodolites, distance meters, total stations, levels.