CÓMO MEDIR UN TERRENO (2/2) | TEODOLITO Y CINTA | TOPOGRAFÍA

Calculating Coordinates in Topographic Surveys

Introduction to Coordinate Calculation

• The session focuses on calculating coordinates using the field radiation method, emphasizing its importance in topographic surveys for measuring boundaries, areas, and volumes. This is foundational for obtaining accurate coordinates.

Field Data Collection

• A comparison is made between manual calculations and spreadsheet formats used for recording data. The spreadsheet includes columns for station points, angles taken, distances from the station to vertices, and projections in x and y coordinates.

• The setup involves four vertices with a single station behind them; data is collected from the station to each vertex (1 through 4). This resembles a field record typically maintained during surveying activities.

Angle Measurements

• Angles are recorded starting from true north towards each vertex:

• Vertex 1: 17°17'00"

• Vertex 2: 78°48'

• Vertex 3: 140°

• Vertex 4: 203°

These angles are crucial as they determine the direction of measurements taken from the station.

Distance Measurements

• Distances measured from Station 1 to various vertices include:

• To Vertex 1: 11.70 m

• To Vertex 2: 22.13 m

• To Vertex 3: 21.90 m

• To Vertex 4: Approximately calculated based on previous distances.

This information will be used to calculate projections and ultimately derive coordinates.

Trigonometric Functions Application

• The sine function relates the opposite side of a triangle to its hypotenuse, while cosine relates the adjacent side:

• Sine of angle = opposite / hypotenuse

• Cosine of angle = adjacent / hypotenuse

These formulas will be applied to find projections necessary for coordinate calculation.

Calculating Projections

• Projections in x are calculated using sine functions multiplied by distance; similarly for y using cosine functions:

• For example, projection results indicate that Vertex 1 is located at (3.47 m along x-axis) and (11.17 m along y-axis) relative to Station 1.

The signs of these projections depend on their respective quadrants in which they fall (positive or negative values).

Quadrant Considerations

• Each quadrant affects whether values are positive or negative:

• North is positive; South is negative; East is positive; West is negative.

For instance, if a vertex falls into a southern quadrant, it would yield negative values for its coordinates accordingly. Understanding this helps ensure accurate plotting on maps or plans.

Finalizing Coordinates Calculation

• Initial coordinates must be established before calculating subsequent ones:

• New coordinate = initial coordinate ± projection value.

Coordinates were initially obtained via UTM (Universal Transverse Mercator), which can have slight errors but provide essential reference points for further calculations in topography surveys.

Unique vs Non-Uniqueness of UTM Coordinates

• UTM coordinates can repeat across different zones due to time zone changes affecting their representation; thus they aren't unique like latitude and longitude which provide absolute positioning globally.

Calculating Polygon Coordinates and Distances

Assigning Coordinates to Vertices

• The initial coordinates are set at 581,827, which will be assigned to Station 1. From this point, projections will be added or subtracted to determine the coordinates for vertices 1 through 4.

• For Vertex 1, the X-coordinate is calculated by adding 3.47 to the original coordinate (581,827), resulting in an X-coordinate of 582,1800. Similarly, the Y-coordinate is derived by adding 11.17.

Calculating Distances Between Vertices

• Once all vertex coordinates are established using this method, one can calculate distances from these points to other reference points such as streets.

• The distance formula used is: Distance = √((X2 - X1)² + (Y2 - Y1)²). This allows for calculating distances between any two vertices effectively.

Practical Applications of Coordinate Calculation

• The calculation can be performed in either direction (from Vertex 1 to Vertex 2 or vice versa), ensuring flexibility in determining distances regardless of starting point.

• An example shows that the distance between Vertex 1 and Vertex 2 is calculated as approximately 19.49 meters. This method proves useful when obstacles hinder direct measurement along property lines.

Comparison with Total Station Calculations

• Future discussions will compare this manual method with total station calculations that display coordinates directly on a screen using optimized methods based on sine and cosine functions.

Utilizing Excel for Efficient Calculations