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Which of the following relation between radius and degree of curve for 20m length?

$1146 / D$

$1720 / D$

Both A and B

None of the above

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey

Option A

$1146 / D$

Quick Summary:

In surveying, the degree of a curve ( $D$ ) can be defined either by the arc definition or the chord definition. For a 20 m length (arc or chord), the relation between the radius of the curve ( $R$ ) and the degree of curve ( $D$ ) is given by $R = \frac{1146}{D}$ meters, where $D$ is in degrees.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$R = \frac{180 \times S}{\pi D}$ — General expression relating radius $R$ , arc length $S$ , and degree of curve $D$

$R = \frac{1146}{D}$ — Formula for a 20m chain or arc length

$R = \frac{1719}{D} \approx \frac{1720}{D}$ — Formula for a 30m chain or arc length

⚙️ Working Principle

The degree of a curve $D$ is defined as the angle subtended at the center by an arc or chord of specified length $S$ . From the fundamental circular geometry relation $S = R \times \theta$ (where $\theta$ is in radians), converting $\theta$ from degrees ( $D°$ ) to radians yields $S = R \times \left(\frac{D \pi}{180}\right)$ , which gives $R = \frac{180 S}{\pi D}$ . Substituting $S = 20\text{ m}$ results in $R = \frac{3600}{\pi D} \approx \frac{1146}{D}$ .

📌 Key Points

▸
Degree of curve ( $D$ ) is the angle subtended at the center by a standard arc or chord length.
▸
For a 20 m standard length, $R = \frac{1145.92}{D} \approx \frac{1146}{D}$ meters.
▸
For a 30 m standard length, $R = \frac{1718.87}{D} \approx \frac{1720}{D}$ meters.

✅ Advantages

▸
Allows rapid calculation of curve radius directly from degree in field operations without trigonometric tables.
▸
Simplifies setting out of simple circular curves using standard chain lengths.

❌ Disadvantages / Limitations

▸
Arc and chord definitions introduce slight discrepancies for very sharp curves (large $D$ ).
▸
Formula approximation introduces minor rounding error if exact precision is required.

🛠️ Applications / Uses

▸
Route surveying for railways and highways.
▸
Field setting out of circular curves using chains or tapes.

🔄 Comparison Table

Feature	20 m Chain	30 m Chain
Standard Arc/Chord Length ( $S$ )	20 meters	30 meters
Exact Formula	$R = \frac{1145.92}{D}$	$R = \frac{1718.87}{D}$
Approximate Formula	$R = \frac{1146}{D}$	$R = \frac{1720}{D}$

📄 Additional Information

▸
Option B ( $1720 / D$ ) is the standard formula used for a 30m chain length, not a 20m chain length.
▸
Option C is incorrect because $1720 / D$ applies specifically to 30m chain lengths.

📊 Diagram / Illustration

✅

A is correct — For a 20m length, the formula derived from geometry gives $R = \frac{1146}{D}$ meters.

Core Concepts Used

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Degree of Curve Arc and Chord Definition Circular Curves in Surveying

💡 EXAM TIP

Always check the specified chain length in the question: use $1146/D$ for 20m and $1720/D$ for 30m. If specified in feet (100 ft chain), the relation is $5730/D$ .

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