Tacheometric surveying is an angular surveying method that uses a tachometer to measure horizontal and vertical distances between two points. This technique eliminates the need for chain or tape surveying, making it faster and more efficient. Tacheometry is particularly useful in challenging terrains such as ravines, swamps, and water bodies. The accuracy of this method ranges from 1/1000 to 1/10,000, making it a reliable tool in various surveying applications.
Principle of Tacheometric Surveying
The principle of tacheometric surveying is based on the geometric property of isosceles triangles: the ratio of the base length to its distance from the apex remains constant.
Using this principle, the following formulas are derived:
- Horizontal Distance Formula:
H=K⋅s⋅cos2θH = K \cdot s \cdot \cos^2 \theta - Vertical Distance Formula:
V=K⋅s⋅sin2θ2V = \frac{K \cdot s \cdot \sin 2\theta}{2} or V=H⋅tanθV = H \cdot \tan \theta
Here:
- ss is the staff intercept (Top Reading – Bottom Reading).
- KK is the multiplying constant (typically 100).
- θ\theta is the vertical angle measured by the theodolite.
These values help calculate the reduced level (R.L.) of a point, ensuring accurate measurements in both elevation and distance.
Procedure for Tacheometric Surveying
Tacheometric surveying follows a systematic process:
- Instrument Setup: Place the instrument at the specified station and level it accurately.
- Zero Setting: Set the vertical circle’s vernier to zero and measure the instrument’s height either manually or using the stadia rod.
- Orientation: Align the instrument using reference meridians:
- For a magnetic meridian, align the compass needle to north.
- For a real meridian, adjust the vernier to the known bearing of a reference point.
- Readings on Benchmark: Record readings for the top, bottom, and axial hairs with respect to a benchmark or temporary benchmark.
- Observation of Points: Identify and record data for representative locations in the area of interest.
- Transition to Another Station: Move to the next station, repeat setup, and take back sight readings to ensure accuracy.
- Cross-Verification: Sight each station twice to validate distances and elevations within acceptable limits.
Methods of Tacheometric Surveying
Tacheometric surveying calculates distances and elevations using angular observations. The methods are classified into two main categories:
1. Stadia Method of Tacheometry
The stadia method is the most commonly used technique for determining horizontal distances and elevations.
- Fixed Hair Method:
This method employs a telescope with two fixed stadia hairs equidistant from the central hair. The intercept seen through the telescope is used to calculate distances. It is the most widely adopted approach in tacheometric surveying. - Movable Hair Method:
Here, the cross-hairs are adjustable, allowing the stadia interval to vary based on the staff position. This method also uses fixed-distance targets for accurate measurement.
2. Tangential Method of Tacheometry
This method requires two observations between the staff and instrument stations. The horizontal distance and elevation differences are calculated based on angular measurements. While it allows the use of a standard transit theodolite, the tangential method is less preferred due to its slower pace.
Errors and Precautions in Tacheometric Surveying
Despite its efficiency, tacheometric surveying is prone to certain errors:
- Instrumental Errors:
Faulty instrument adjustments or incorrect graduations on the stadia rod can lead to inaccuracies. - Manipulation and Sighting Errors:
These errors result from improper centering, leveling, or inaccurate readings, depending on the surveyor’s expertise. - Natural Causes:
Wind, visibility issues, and unequal refraction can distort measurements, with refraction being the most significant concern.
Precautions such as regular instrument calibration and careful observation can mitigate these errors.
Advantages of Tacheometric Surveying
Tacheometric surveying offers several benefits, making it a preferred method in many scenarios:
- Speed: Surveys are conducted quickly, even in challenging terrains.
- Efficiency: Eliminates the need for tapes and chains, reducing time and effort.
- Cost-Effectiveness: The method is affordable and requires minimal equipment.
- Accuracy: Provides sufficient precision for topographic mapping, hydrological surveys, and cross-checking measurements.
Conclusion
Tacheometric surveying combines speed, accuracy, and cost-efficiency, making it an invaluable method in modern surveying practices. Its principle, derived from geometry, and systematic procedure allow for reliable measurements even in difficult terrains. Despite potential errors, proper precautions ensure the method remains a cornerstone of surveying techniques worldwide.