1. **Problem Statement:** (a) State four obstacles encountered in curve ranging. (b) A circular curve of radius 539.65 m connects two straight tangents deflecting through an angle of 26° 34' 25". The chainage of the second tangent point is 2024.726 m. The curve is to be set out by the method of chords produced using standard chord lengths of 25 m. Tabulate the setting out data. 2. **Part (a) - Obstacles in Curve Ranging:** - Obstacle 1: Dense vegetation or trees blocking the line of sight. - Obstacle 2: Buildings or structures obstructing the survey line. - Obstacle 3: Water bodies like rivers or lakes. - Obstacle 4: Uneven or steep terrain making measurement difficult. 3. **Part (b) - Curve Setting Out by Chords Produced:** - Given: - Radius, $R = 539.65$ m - Deflection angle, $\Delta = 26^\circ 34' 25'' = 26.5736^\circ$ (converted to decimal degrees) - Chainage of second tangent point, $C_{TP2} = 2024.726$ m - Standard chord length, $L = 25$ m 4. **Formulas and Important Rules:** - Length of curve, $L_c = \frac{\pi R \Delta}{180}$ - Number of chords, $n = \frac{L_c}{L}$ (round up to nearest whole number) - Deflection angle for each chord, $\delta = \frac{\Delta}{2n}$ - Chainage of first tangent point, $C_{TP1} = C_{TP2} - L_c$ 5. **Calculations:** - Convert $\Delta$ to decimal degrees: $$26^\circ + \frac{34}{60} + \frac{25}{3600} = 26.5736^\circ$$ - Calculate length of curve: $$L_c = \frac{\pi \times 539.65 \times 26.5736}{180} = 249.99 \text{ m (approx)}$$ - Number of chords: $$n = \frac{249.99}{25} = 10 \text{ chords (rounded)}$$ - Deflection angle per chord: $$\delta = \frac{26.5736}{2 \times 10} = 1.3287^\circ$$ - Chainage of first tangent point: $$C_{TP1} = 2024.726 - 249.99 = 1774.736 \text{ m}$$ 6. **Tabulate Setting Out Data:** | Chord No. | Chainage (m) | Deflection Angle (°) | |-----------|--------------|---------------------| | 1 | 1774.736 | 1.3287 | | 2 | 1799.736 | 2.6574 | | 3 | 1824.736 | 3.9861 | | 4 | 1849.736 | 5.3148 | | 5 | 1874.736 | 6.6435 | | 6 | 1899.736 | 7.9722 | | 7 | 1924.736 | 9.3009 | | 8 | 1949.736 | 10.6296 | | 9 | 1974.736 | 11.9583 | | 10 | 1999.736 | 13.2870 | - Note: Deflection angle for chord $k$ is $k \times \delta$. 7. **Summary:** - The curve length is approximately 250 m. - The curve is divided into 10 chords of 25 m each. - Deflection angles increase by 1.3287° per chord. - Chainages start from 1774.736 m at the first tangent point and increase by 25 m per chord. This completes the setting out data using the method of chords produced.