# Calculate (to the nearest integer) the length of the curve of 15 chains radius with a deflection angle of 50° 30’, when the length of chain is 20 m.

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Calculate (to the nearest integer) the length of the curve of 15 chains radius with a deflection angle of 50° 30’, when the length of chain is 20 m.
1. 300 m
2. 250 m
3. 264 m
4. 270 m

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Correct Answer - Option 3 : 264 m

Concept:

$\text{Length of Curve} = R × δ×\frac{\pi}{180}$

Where,

R = radius of curve, $\delta$ = deflection angle

Calculation:

Given,

Length of chain = 20 m,

R = 15 chains = 15 × 20 = 300 m,

deflection angle ($\delta$) = 50°30' = 50.50° (∵ 1° = 60', So, 30' = 0.5°)

∵ We know that, $\text{Length of Curve} = R × δ×\frac{\pi}{180}$

⇒ $\text{Length of Curve} = 300 × 50.50×\frac{\pi}{180}$

Length of curve = 264.28 m

The degree of curve is given as,

• For 20 m chain length, $D_a = \frac{1146}{R}$
• For 30 m chain length, $D_a = \frac{1718}{R}$

Where,

Da = degree of curve and R = radius of the curve