Question Not Found | Examoogle

CivilAdvanced Survey

Calculate the value of K and C, if the measurements are taken between two points of 50m and 130m distance apart and the stadia readings will be 0.024m, 0.824m respectively.

100, 0

47.6 100, 47.6

47.6, 100

0, 100

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey

Option B

47.6

100, 47.6

Quick Summary:

In tacheometric surveying, the horizontal distance $D$ between the instrument station and the staff station is given by the distance equation $D = Ks + C$ , where $K$ is the multiplying constant ( $f/i$ ) and $C$ is the additive constant ( $f + d$ ). Using the two given conditions with staff intercept $s$ and distance $D$ , simultaneous equations are solved to determine $K = 100$ and $C = 47.6\text{ m}$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$D = Ks + C$ — General tacheometric distance equation

$K = \frac{f}{i}$ — Multiplying constant

$C = f + d$ — Additive constant

$K = \frac{D_2 - D_1}{s_2 - s_1}$ — Formula to derive $K$ from two observation points

⚙️ Working Principle

Tacheometry relies on the principle of isosceles triangles, where the ratio of the distance from the vertex to the base and the length of the base remains constant. The stadia hair readings give the staff intercept $s$ , which when multiplied by the multiplying constant $K$ and added to the additive constant $C$ yields the horizontal distance $D$ .

📌 Key Points

▸
The multiplying constant $K$ is typically equal to $100$ in an ideal tacheometer equipped with an anallactic lens.
▸
The additive constant $C$ varies according to telescope design, but reduces to $0$ when an anallactic lens is fitted.
▸
Subtracting equation (i) from equation (ii) yields $130 - 50 = K(0.824 - 0.024) \Rightarrow 80 = K(0.800) \Rightarrow K = 100$ .
▸
Substituting $K = 100$ into equation (i): $50 = 100(0.024) + C \Rightarrow 50 = 2.4 + C \Rightarrow C = 47.6\text{ m}$ .

✅ Advantages

▸
Allows direct determination of horizontal distance without using physical measuring tapes.
▸
Particularly suitable for steep, rough, or inaccessible terrains.

❌ Disadvantages / Limitations

▸
Accuracy depends strongly on precise staff intercept measurements.
▸
Observational errors in staff reading lead directly to distance inaccuracies.

🛠️ Applications / Uses

▸
Contour mapping and topographic surveying.
▸
Preliminary route location surveys for roads, railways, and canals.

📄 Additional Information

▸
Option A (100, 0) represents an anallactic telescope where the additive constant $C = 0$ .
▸
Option C (47.6, 100) reverses the values of $K$ and $C$ , which is incorrect.
▸
Option D (0, 100) is invalid as $K$ cannot be zero for meaningful distance measurement.

📊 Diagram / Illustration

✅

B is correct — Solving $50 = 0.024K + C$ and $130 = 0.824K + C$ simultaneously yields $K = 100$ and $C = 47.6\text{ m}$ .

Core Concepts Used

Click any tag to open in AI Tutor

Tacheometric Surveying Multiplying and Additive Constants Stadia Hair Method

💡 EXAM TIP

Remember that if an anallactic lens is provided in the tacheometer telescope, $K = 100$ and $C = 0$ directly, eliminating the additive term.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)