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Among the following, which represents the method of observation for trigonometric levelling?
A) Direct
B) Indirect
C) Both A and B
D) None of the above
Both A and B
Trigonometric levelling is an indirect method of levelling in which the difference in elevation between two points is determined by measuring the vertical angle to a target and the horizontal or inclined distance between the stations. The observations can be conducted using either direct methods (when the instrument station and ground target are directly intervisible and reachable) or indirect/reciprocal methods (such as reciprocal observations to eliminate atmospheric refraction and earth curvature errors).
Trigonometric levelling is an indirect method of levelling in which the difference in elevation between two points is determined by measuring the vertical angle to a target and the horizontal or inclined distance between the stations. The observations can be conducted using either direct methods (when the instrument station and ground target are directly intervisible and reachable) or indirect/reciprocal methods (such as reciprocal observations to eliminate atmospheric refraction and earth curvature errors).
h=Dtan╬▒ тАФ basic height difference formula without curvature/refraction corrections
CcтАЛ=0.0785D2 тАФ correction for earth curvature in meters (D in km)
CrтАЛ=0.0112D2 тАФ correction for atmospheric refraction in meters (D in km)
CcombinedтАЛ=0.0673D2 тАФ combined curvature and refraction correction
In trigonometric levelling, the elevation difference is computed by solving a right-angled or oblique triangle formed by the observer's instrument, the height of instrument, and the target height. Vertical angles are measured using a theodolite, and distance is measured directly via tape/EDM or indirectly computed from triangulation networks.
Direct observation involves measuring vertical angles directly from a single station to a target at a known or measured horizontal distance.
Indirect observation involves determining angles or distances through auxiliary observations, such as reciprocal observations or geodetic triangulation networks.
Reciprocal observation eliminates errors due to curvature of the earth, atmospheric refraction, and collimation error.
Ideal for hilly, mountainous, or inaccessible terrains where direct spirit levelling is impractical.
Allows rapid determination of elevation differences over long distances.
Less precise compared to direct spirit levelling due to atmospheric refraction variation.
Requires accurate measurement of vertical angles and distances.
Establishing vertical control in triangulation and topographical surveying.
Determining heights of mountain peaks, towers, and inaccessible structures.
| Feature | Direct Method | Indirect Method |
|---|---|---|
Observation Setup | Single station reading to a target with known/measured distance | Observations from both ends (reciprocal) or via intermediate stations |
Refraction Error | Must be corrected using empirical formulas | Eliminated or minimized by reciprocal observations |
The direct method is used for short distances where environmental conditions are stable.
The indirect (reciprocal) method is preferred for long distances to eliminate curvature and refraction errors without needing exact refraction coefficients.
C is correct тАФ Trigonometric levelling employs both direct methods (single-station vertical angle measurement) and indirect methods (reciprocal observations and triangulation networks) to determine height differences.
For GATE/ESE exams, remember that reciprocal trigonometric levelling completely eliminates earth curvature and collimation errors, as well as atmospheric refraction errors assuming symmetric refraction conditions.