Tacheometric Surveying

Why it matters

Tacheometric surveying is essential for quickly obtaining both horizontal and vertical distances, which is crucial in topographic mapping and construction projects. It allows for efficient data collection in areas where traditional methods may be challenging or time-consuming.

Key ideas

• Tacheometer: A type of theodolite used in tacheometric surveying, equipped with a stadia diaphragm.
• Stadia Method: Involves using a tacheometer to measure the angle of elevation or depression and the staff intercept to calculate distances.
• Subtense Method: Uses a fixed subtense bar and the angle subtended at the instrument to determine distances.
• Principle of Stadia Method: Based on the geometry of similar triangles, where the distance is proportional to the staff intercept.

Formulas

For a vertical staff and inclined sight, K = f/i and additive constant C:

• Horizontal distance D = Ks cos²θ + C cosθ.
• Vertical distance from instrument axis to central-hair intercept V = Ks sinθ cosθ + C sinθ.
• Staff-point elevation RL_Q = RL_P + instrument height + V − central staff reading r. At θ = 0, D = Ks + C. Keep instrument height above station separate from its elevation above datum.

Worked example

Given K = 20, C = 0.3 m, staff intercept s = 2.5 m, θ = +5°, RL_P = 100 m, instrument height 1.5 m and central reading r = 2.0 m: D = 50 cos²5° + 0.3 cos5° = 49.919 m. V = 50 sin5° cos5° + 0.3 sin5° = 4.367 m. RL_Q = 100+1.5+4.367−2.0 = 103.867 m.

Reference: NPTEL inclined stadia measurements.

Common mistakes

• Incorrectly reading the staff intercept, leading to errors in distance calculation.
• Neglecting the instrument constant C in calculations.
• Misinterpreting the angle of elevation or depression.

For GATE CE

Questions often involve calculating horizontal distances and elevations using given tacheometric data. Practice problems that require understanding the stadia method and applying the formulas correctly.

Quick check

1. What is the primary instrument used in tacheometric surveying?
2. Name one method used in tacheometric surveying.
3. What is the role of the stadia diaphragm in a tacheometer?

Answers: 1. Tacheometer 2. Stadia Method 3. It helps in measuring the staff intercept.