Question Not Found | Examoogle

Back to Practice Questions

CivilAdvanced Survey

Prev Next

Mid-ordinate is also known as __________

Apex distance

Versed sine

Both A and B

In A or B

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey

Option B

Versed sine

Quick Summary:

In simple circular curve geometry, the mid-ordinate (also known as the versed sine) is the distance from the midpoint of the long chord to the midpoint of the curve · It represents the maximum distance between the curve and its long chord, measured along the central radial line · The apex distance (or external distance), by contrast, is the distance from the intersection point to the apex of the curve.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$M = R \left(1 - \cos\left(\frac{\Delta}{2}\right)\right)$ — Mid-ordinate (Versed Sine) 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 Length $L$

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

⚙️ Working Principle

The term 'versed sine' originates from classical trigonometry, where $\text{versin}(\theta) = 1 - \cos(\theta)$ . For a circular curve with radius $R$ and deflection angle $\Delta$ , the central angle subtended by half the curve is $\Delta/2$ . The distance from the center of the curve to the long chord is $R \cos(\Delta/2)$ , making the mid-ordinate equal to $R - R \cos(\Delta/2) = R(1 - \cos(\Delta/2))$ , which directly uses the versed sine function.

📌 Key Points

▸
Mid-ordinate ( $M$ ) is measured from the midpoint of the long chord to the apex of the curve.
▸
It is mathematically equivalent to the versed sine of half the deflection angle multiplied by the radius.
▸
Apex distance ( $E$ ) is measured from the intersection point ( $V$ ) to the apex of the curve ( $C$ ).
▸
Long chord length ( $L$ ) is given by $L = 2R \sin(\Delta/2)$ .

✅ Advantages

▸
Useful in setting out simple circular curves by the method of offsets from the long chord.
▸
Provides a quick field check for curve symmetry and alignment accuracy.

❌ Disadvantages / Limitations

▸
Setting out curves using mid-ordinates is suitable only for short curves or small radii.
▸
Errors in measuring the long chord propagate directly into the calculated mid-ordinate.

🛠️ Applications / Uses

▸
Setting out circular curves in road and railway survey work.
▸
Determining sight distances and clearances on horizontal highway curves.

🔄 Comparison Table

Feature	Mid-ordinate (Versed Sine)	Apex Distance (External Distance)
Definition	Distance from midpoint of long chord to apex of curve	Distance from point of intersection (PI) to apex of curve
Formula	$M = R(1 - \cos(\Delta/2))$	$E = R(\sec(\Delta/2) - 1)$
Measurement Line	Lies between chord and arc along radial line	Lies between vertex and arc along radial line

📄 Additional Information

▸
Apex distance (Option A) is the external distance ( $E$ ), which is the distance from the intersection point ( $V$ ) to the summit/apex of the curve ( $C$ ).
▸
Options C and D are incorrect because mid-ordinate is strictly synonymous with versed sine, not apex distance.

📊 Diagram / Illustration

✅

B is correct — Mid-ordinate is defined as the distance from the midpoint of the long chord to the midpoint of the curve, which mathematically corresponds to the versed sine of half the central angle.

Core Concepts Used

Click any tag to open in AI Tutor

Simple Circular Curve Geometry Versed Sine Function Curve Setting Out Methods

💡 EXAM TIP

Remember for competitive exams: Versed sine $= 1 - \cos\theta$ , so Mid-ordinate $= R \cdot \text{versin}(\Delta/2)$ . Don't confuse it with External Distance (Apex Distance), which uses $\sec(\Delta/2) - 1$ .

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)