The distance between apex point of curve to mid point of long ... | Civil MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

Back to Practice Questions

CivilAdvanced Survey

Prev Next

The distance between apex point of curve to mid point of long chord is called___

Tangent distance

Length of long chord

Mid ordinate distance

External distance

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey

Option C

Mid ordinate distance

Quick Summary:

The distance between the apex point (vertex/highest point of the curve) to the mid-point of the long chord is called the mid-ordinate distance (or versed sine of the curve) · It represents the height of the curve above its long chord at the center point.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$M = R \left(1 - \cos\frac{\Delta}{2}\right)$ — Mid-ordinate in terms of Radius ( $R$ ) and deflection angle ( $\Delta$ )

$M = R - \sqrt{R^2 - \left(\frac{L}{2}\right)^2}$ — Mid-ordinate in terms of Radius ( $R$ ) and Long Chord ( $L$ )

$E = R \left(\sec\frac{\Delta}{2} - 1\right)$ — External distance (Apex distance)

⚙️ Working Principle

In a simple circular curve, the mid-ordinate $M$ is measured along the radial line bisecting the central angle $\Delta$ . It is derived geometrically by subtracting the distance from the center of the circle to the long chord from the radius of the curve.

📌 Key Points

▸
Mid-ordinate ( $M$ ) is the distance from the apex point of the circular curve to the mid-point of the long chord.
▸
External distance ( $E$ ) is the distance from the vertex/intersection point ( $V$ ) to the apex of the curve.
▸
Long chord ( $L$ ) is the straight line joining the point of curve ( $T_1$ ) and point of tangency ( $T_2$ ).

🛠️ Applications / Uses

▸
Setting out simple circular curves in field surveying using the offset from long chord method.
▸
Designing smooth road alignments and railway curves.

📄 Additional Information

▸
Option A (Tangent distance): Distance from the vertex ( $V$ ) to the point of curve ( $T_1$ ) or point of tangency ( $T_2$ ) · Formula: $T = R \tan(\Delta/2)$ .
▸
Option B (Length of long chord): The total distance between initial tangent point ( $T_1$ ) and final tangent point ( $T_2$ ) · Formula: $L = 2R \sin(\Delta/2)$ .
▸
Option D (External distance): The distance from the intersection point ( $V$ ) to the midpoint of the circular curve along the bisector.

📊 Diagram / Illustration

✅

C is correct — Mid ordinate distance is defined as the distance between the apex point of a curve and the mid-point of its long chord.

Core Concepts Used

Click any tag to open in AI Tutor

Elements of Simple Circular Curve Mid-Ordinate Method of Curve Ranging Surveying Curves Geometry

💡 EXAM TIP

Remember that Mid-ordinate is $R(1 - \cos\frac{\Delta}{2})$ whereas External distance is $R(\sec\frac{\Delta}{2} - 1)$ ; both lie on the same bisecting line meeting at the curve's apex.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)