The stadia method used in tacheometric surveys generally refers to measurements taken with a ___________.

Question

Examoogle · Accepted Answer

The correct answer is Option A: tacheometer with fixed stadia hair. The stadia method is a form of tacheometric surveying where the distance and elevation are determined by observing the intercept on a graduated staff between two stadia hairs in the diaphragm of a telescope. It specifically refers to the use of a tacheometer equipped with fixed stadia hairs, where the spacing between the hairs remains constant.

Step-by-Step Solution & Concepts:
The stadia method is a form of tacheometric surveying where the distance and elevation are determined by observing the intercept on a graduated staff between two stadia hairs in the diaphragm of a telescope. It specifically refers to the use of a tacheometer equipped with fixed stadia hairs, where the spacing between the hairs remains constant.

Working Principle: The principle is based on the properties of similar triangles. As the distance to the staff increases, the intercepted portion of the staff between the fixed stadia hairs increases proportionally. By measuring this intercept $s$, the horizontal distance $D$ and vertical elevation $V$ can be calculated using the tacheometric constants $k$ (multiplying constant) and $c$ (additive constant).

Key Formulas: $D = k \cdot s + c$; $V = \frac{1}{2} k \cdot s \sin(2	heta) + c \sin(	heta)$

Key Points: The multiplying constant $k$ is typically $100$ for most standard tacheometers.; The additive constant $c$ is usually $0$ in modern anallatic lenses.; The stadia method is preferred for rapid, medium-precision topographic mapping.; The precision of stadia surveying is generally in the range of $1:1000$ to $1:2000$.

Advantages: Rapid method of data collection compared to chain and level surveying.; Ideal for inaccessible terrain where chaining is difficult.

Disadvantages: Lower precision compared to direct leveling or EDM.; Errors increase significantly with distance due to refraction and atmospheric turbulence.

Applications: Topographic surveys for highway and railway projects.; Reconnaissance surveys for large-scale engineering works.

Additional Info: Fixed stadia hairs are etched into the cross-hair glass plate at a specific distance to ensure a constant ratio.. Option B is incorrect because a fixed staff reading does not allow for distance calculation. Option D refers to subtense methods or specialized instruments not classified as standard stadia method.

Answer: A is correct — The stadia method relies on the fixed intercept provided by stadia hairs to compute distances using the property of constant multiplying ratio.

Exam Tip: Always remember that in the formula $D = ks + c$, $k$ is $f/i$ (ratio of focal length to stadia hair interval); if the telescope is anallatic, the additive constant $c$ becomes zero, simplifying the calculation.

Examoogle · Answer

Option B: fixed staff reading

Examoogle · Answer

Option C: fixed elvation of point

Examoogle · Answer

Option D: tacheometer with variable stadia hair

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)