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Princípios básicos da topografia
Neste guia, apresentamos os princípios básicos da Topografia, os instrumentos básicos e as operações mais utilizadas.
Instrument Errors in the Total Station
Ideally, the total station should meet the following conditions:
- a) The line of sight (ZZ axis) must be perpendicular to the tilt axis (KK axis).
- b) The tilt axis (KK axis) must be perpendicular to the vertical axis (VV axis).
- c) The vertical axis (VV axis) must be perfectly vertical.
- d) The vertical circle reading must exactly show zero when pointing at the zenith.
If these conditions are not met, the following terms are used to describe each specific error:
- a) Line of sight error or collimation error c (deviation from the right angle between the line of sight and the tilt axis).
- b) Tilt axis error a (deviation from the right angle between the tilt axis and the vertical axis).
- c) Vertical axis tilt (angle formed between the plumb line and the vertical axis).
The effects of these three errors on horizontal angle measurements increase as the height difference between the points being measured increases. Line of sight and tilt axis errors can be eliminated by taking measurements in both telescope positions.
Line of sight error (and also tilt axis error in high-precision total stations, which is usually very small) can be determined and recorded. When measuring an angle, these errors are automatically considered, so measurements made can be considered practically error-free, even when reading with only one telescope position.
The determination and recording of these errors are described in detail in the corresponding user manual. Vertical axis tilt is not considered an instrument error but occurs when the instrument is not leveled properly, and it is not eliminated even by taking measurements in both telescope positions. The influence of this error on vertical and horizontal angle measurements is automatically corrected using a two-axis compensator.
d) Vertical index error i (the angle formed between the zenith direction and the vertical circle zero reading, i.e., the vertical circle reading when using a vertical line of sight), which is not 100 gon (90°) but rather 100 gon + i. The vertical index error can be determined and recorded.
This error is eliminated by taking measurements in both telescope positions. Note: Instrument errors vary depending on temperature, resulting from considerable vibrations or after long periods of transportation. If you want to perform measurements with only one telescope position, you should first determine the instrument errors and record them.
How to Align from a Central Point
If it is necessary to align intermediate points relative to a measurement line where the end points are not visible to each other, proceed as follows:
- Select two points, 1 and 2 (approximately along the alignment), from which the end points A and E are visible. Use plumb rods to mark the points.
- From point 1, align point 2 with the straight line 1 – A.
- From point 2, align point 3 with the straight line 2 – E.
- From point 3, align point 4 with the straight line 3 – A. Continue with the same procedure to eliminate the lateral deviations of the two intermediate points.
Basic Surveying Measurements
How to Measure Slopes
If you need to set out or measure slopes in percentage terms, for example, to determine ditches, foundations, or pipeline layouts, you can apply one of the two following methods:
- With a level. Measure the height difference and distance (either optically with a leveling rod or with a tape). The slope is calculated as follows: 100 ΔH / D = slope in %.
- With a theodolite or a total station. Position the instrument at a point along the line whose slope needs to be measured and place a leveling rod at a second point along the line.
Using the telescope, determine the height i of the instrument with the leveling rod. The horizontal circle reading (which measures the zenith angle in gons or degrees) can be configured to provide values in percentage (refer to the user manual), so the slope value can be read directly as a percentage. The distance is irrelevant.
Instead of using a leveling rod, you can use a prism pole. Extend the pole to the instrument height i and aim the telescope at the center of the prism.
How to Measure Right Angles
The most accurate way to measure a right angle is by using a theodolite or a total station. Place the instrument on a point along the line where the right angle is to be measured, point the telescope at the far end of the line, set the horizontal circle to zero (refer to the user manual), and rotate the total station until the horizontal circle reading indicates 100 gon (90°).
For measuring a right angle in applications where high precision is not required (for example, in small constructions or when determining longitudinal or transverse profiles), the horizontal circle of a level can be used. Using a plumb bob suspended from the central tripod fixing screw, place the level over a point along the line where the right angle is to be measured. Manually rotate the horizontal circle in the direction of the line to be measured or the longitudinal profile until it shows zero. Finally, rotate the level until the horizontal circle index indicates 100 gon (90°).
A sighting board is the best solution for orthogonal surveying of a point on a line or vice versa, as well as for determining right angles over short distances. The light beam from the point is deflected 90° by a pentaprism so that it reaches the observer. The sighting board consists of two superimposed pentagonal prisms, whose field of view is directed to the right and left, respectively. Between the two prisms, there is an unobstructed view of the point to be measured. The observer can stand on the line (marked by two vertical rods) and move perpendicularly to the line until the image of the two rods overlaps.
The observer then moves along the line until the point to be measured and the two images of the rods coincide.
Application Programs
Area Calculation
- Place the total station at a point on the ground from which the entire area to be measured is visible. It is not necessary to position the horizontal circle.
- Measure the boundary points of the area sequentially, in a clockwise direction. You should always measure the distances.
- By pressing a key, the area is automatically calculated, and the value is displayed on the screen.
Setting Out
- Place the instrument at a known point and set the horizontal circle (refer to the "Instrument Setup" section in the user manual).
- Manually enter the coordinates of the point to be set out. The program automatically calculates the direction and distance (the two parameters needed for any setting out).
- Rotate the total station until the horizontal circle reading indicates zero.
- Place the reflector at this point (point "P").
- Measure the distance. The difference ΔD from point P will be displayed automatically. Alternatively, you can manually transfer the point coordinates from the computer to the total station in the office. In this case, to carry out the setting out, you only need to enter the identifiers of the points.
Remote Heights
- Place a reflector vertically beneath the point whose height is to be determined. The total station can be placed anywhere.
- Measure the distance to the reflector.
- Aim the telescope at the point whose height is unknown.
- The height difference H between the ground point and the point of interest is calculated with a single key press, and the value is displayed on the screen.
Link Distances
This program determines the distance and height difference between two points.
- Place the total station at any point.
- Measure the distance to each of the two points A and B.
- With a single key press, the distance D and height difference H values are displayed on the screen.
Free Stationing
This program calculates the position and height of the instrument station, as well as the orientation of the horizontal circle, from the measurement of at least two known coordinate points.
The coordinates of the reference points can be entered manually or transferred to the instrument in advance. In large projects where measurements or setting out are required, free stationing has the great advantage that the operator can choose the most convenient instrument location. This way, the operator is no longer obligated to place the instrument at a known coordinate point with a suboptimal location.
The measurement options and procedures are described in detail in the user manuals. Note: When performing surveying tasks that involve determining or setting out heights, always keep in mind the height of the instrument and the height of the reflector.
Available Application Programs
- Point Recording
- Orientation and Dragging Heights
- Inverse Intersection
- Link Distances
- Setting Out
- Remote Heights
- Free Stationing
- Reference Line
- Hidden Points
- Area Calculation
- Angle Measurement
- Polygonation
- Local Inverse Intersection
- COGO Functions
- Automatic Recording
- Surface Measurement
- Digital Terrain Models
- Offset
GPS Surveying
Surveying
GPS surveying uses signals transmitted by artificial satellites whose orbits allow the position of any point on the Earth's surface to be determined at any time, regardless of atmospheric conditions.
The accuracy with which point positions are determined depends on the type of GPS receiver used and the post-processing technique applied. Compared to using a total station, GPS surveying offers the advantage that the points to be measured do not need to be visible to each other. Today (as long as there are no significant obstructions, such as dense foliage or tall buildings that block satellite signals), GPS technology can be applied to many diverse surveying tasks that were previously only possible with electronic total stations.
The new GPS antennas from Leica Geosystems allow various surveying tasks to be carried out with centimeter-level accuracy – whether mounted on a tripod or a plumb rod, aboard boats, vehicles, or construction sites, using static and kinematic surveying methods.
