Chapter II: Tacheometry

1. Definitions

• Tacheometer: A measurement instrument derived from two Greek roots:

  • Tacheo-: meaning "rapid"

  • -meter: meaning "measurement"

• Purpose: Enables rapid and precise measurements.

• Historical Context:

  • Term appeared in the mid-19th century.

  • Initially referred to a theodolite with stadimeter capabilities.

• Modern Definition:

  • A tacheometer is properly designated when it can self-measure distances.

• Distance Measurement:

  • Conducted using an infrared sighting rangefinder integrated into the tacheometer and a tetrahedral reflecting prism.

  • Prism is placed vertically over the measurement point with a circular level.

  • Measurement can also occur using laser technology, with or without reflectors, facilitating data collection from inaccessible points.

• Modern Equivalent: The tacheometer is now termed a total station.

  • Capable of storing field measurements on memory cards for computer processing in formats such as DXF, DWG, or others using CAD software or spreadsheets.

  • Advanced models may include remote controls with radio links for single-person operation and integrated GPS systems.

• Tacheometric Survey:

  • Refers to operations measuring angles, distances, and height differences employing a tacheometer and accessories.

  • Classified as a type of topographic survey.

  • Based on instruments for measuring angles and indirect measuring of distances and height differences, utilizing traversing and radiation methods.

2. Field Work

• Survey Team: A team, referred to as a “brigade,” typically includes:

  • Team leader

  • Sketcher

  • Operator

  • Note-keeper (recorder)

  • Staff holders or prism holders (one or more)

• Team Composition:

  • This is the maximum team size but may be reduced based on the survey's importance.

  • Each team member has defined tasks.

2.1. Team Leader

• Responsibilities:

  • Organizes all work and is responsible for the project.

  • Chooses methods and determines points for surveying.

2.2. Sketcher (Drafter)

• Roles and Tasks:

  • Prepares a sketch of the survey area.

  • Directs field operations and ensures staff holders are at stations.

  • Numbers points and takes additional measurements.

  • Maintains communication with the operator, conveying important operations for note-taking.

2.3. Operator

• Procedure:

  • Centers and sets up the tacheometer over a traverse point.

  • Measures trunnion height and communicates it to the prism holder (instrument height equals target point height).

  • Observes the main traverse by:

  • Orienting the traverse towards a known distant point.

  • Observing angles at polygon vertices.

  • Taking readings on the horizontal circle and stadimetric readings (distances, height differences).

  • Surveying detail points as indicated by the sketcher’s instructions.

  • Returning to the initial reference point to ensure the instrument’s stability.

2.4. Note-Keeper (Recorder)

• Duties:

  • Records readings announced by the operator, repeating them for accuracy.

  • Must focus on instructions from the sketcher, especially concerning point numbering consistency in field books.

3. Methods

• Measurements aim to position objects and points by:

  • Rectangular or polar coordinates.

  • Elevations.

• Measurements include:

  • Horizontal and vertical angles.

  • Inclined and horizontal distances.

4. Field Sketch

• Purpose:

  • Used to prepare layouts, identify campsites, or illustrate exploration reports.

• Requirements:

  • The sketch must be clear and adhere to established rules, indicating:

  • Location of the site (ideally with Lambert coordinates).

  • Direction of North.

  • Scale.

5. Office Work

5.1. Calculations

• Objective:

  • To interpret the sketch, leading to calculations for project needs such as perimeters and areas, along with necessary checks.

5.2. Plan

• Final Drawing:

  • The report leads to producing a plan which represents the ultimate goal of any topographic operation.

  • Possible return to the field for operations like property subdivision, road layout, and setting out structures may be necessary.

• Geodetic Calculations:

  • Includes computations of horizontal distances, rectangular coordinates, and elevations.

  • Results are graphically represented in a drawing using conventional symbols and a fixed scale.

6. Types of Tacheometry

• Diagram Tacheometer:

  • An older mechanical model used with specific staffs.

  • Expected accuracy for distance measurement is approximately ±14 cm for a distance of 50 m.

• Electronic Tacheometer:

  • A combination of a theodolite with an electronic distance-measuring instrument.

7. Tacheometric Measurement Method

7.1. Distance Measurement

• Types of Instruments:

  • Delta and RDS with differing reticles (crosshairs).

• Delta Method for Horizontal Distance:

  1. Using the upper stadia line:

  • $D<em>1 = riangle H</em>1 imes 100 = (L<em>{sup}-L</em>{med}) imes 100$

    • Where $riangle H_1$ is the reading from the reference line to the upper stadia line.

  1. Using the lower stadia line:

  • $D<em>2 = riangle H</em>2 imes 200 = (L<em>{med}-L</em>{inf}) imes 200$

    • Where $riangle H_2$ is the reading from the reference line to the lower stadia line.

• RDS Method for Horizontal Distance:

  • $D = (L<em>{sup} - L</em>{inf}) imes 100$

7.2. Measurement of Height Differences (Elevations)

• Delta Method for Height Differences:

  • $riangle H = (L<em>{niv} - L</em>{med}) imes P$

• RDS Method for Height Differences:

  • $riangle H = (L<em>{med} - L</em>{inf}) imes 100 imes Coeff$

• Notes:

  • Coeff represents a coefficient related to measurement accuracy.