--- title: "Simple circular curve by deflection angle method" subject: "Surveying II" chapter: 6 key: "semester_4/surveying_ii:simple-curve-deflection-angle-method-sketch" source: https://www.bctengineer.com/q/semester_4/surveying_ii/simple-curve-deflection-angle-method-sketch site: BCT Engineering --- # Simple circular curve by deflection angle method Surveying II · Chapter 6: Curves - Asked in: 2078 Chaitra, 4 marks - Video: [Deflection Angle Method/Rankine's Method of Setting out of Simple Circular Highway Curve](https://www.youtube.com/watch?v=am3MYbQApz8) — CIVIL Solved - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/simple-curve-deflection-angle-method-sketch - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6 ## Question Explain about the setting out procedures of horizontal simple circular curve by deflection angle method with supporting sketch. ## Short answer A simple circular curve is set out by the deflection angle method from the tangent point T1. Chords are measured and cumulative deflection angles (half the subtended central angle) are turned with a theodolite; each peg is fixed by swinging the chord from the previous peg onto the line of sight. The final cumulative angle equals Δ/2, providing a check at T2. ## Answer A simple circular curve is set out by the **deflection angle (Rankine's) method** from the tangent point T1, using a theodolite and a tape. The angle between the tangent and the chord to any point on the curve is half the angle subtended by that chord at the centre. ```text IP / \ / \ / \ / \ T1 T2 ' . . ' 1 2 3 (deflection angles d1, d2, ... are turned at T1 from the line T1-IP) ``` #### Basic formulas For a chord $c$ and radius $R$, the tangential (deflection) angle is $\dfrac{c}{2R}$ rad: $$ \delta = \frac{1718.9\,c}{R}\ \text{minutes} $$ #### Elements of the curve - Tangent length: $T = R\tan\dfrac{\Delta}{2}$ - Length of the curve: $L_c = \dfrac{\pi R\Delta}{180^\circ}$ - Chainage of T1 = chainage of IP − $T$; chainage of T2 = T1 + $L_c$ #### Procedure 1. Locate the IP and find T1 and T2 by measuring $T$ along the two straights from the IP. 2. Find the chainage of T1. The first peg is at the next full chainage, so the first chord $c_1$ is a sub-chord. The last chord $c_n$ is also a sub-chord. All other chords are normal (full) chords $C$ (20 m or 30 m). 3. Compute the deflection angles: $\delta_1 = \dfrac{1718.9\,c_1}{R}$, $\delta_2 = \delta_1 + \dfrac{1718.9\,C}{R}$, and so on. Each is a cumulative angle measured from the tangent T1-IP. 4. Set up the theodolite at T1 and sight the IP with the horizontal circle reading zero. 5. Turn the telescope through $\delta_1$ and measure $c_1$ from T1 along the line of sight to fix peg 1. Then set the angle $\delta_2$ and, holding the zero end of the tape at peg 1, swing the chord length $C$ until its end lies on the line of sight; this fixes peg 2. Continue in the same way. 6. **Check:** the last cumulative deflection angle must equal $\Delta/2$, and the last peg must fall on T2. The method is accurate and is widely used for long curves on open ground, where all the pegs can be seen from T1. Because each peg is fixed from the previous one, errors accumulate along the curve. If the line of sight is blocked, the theodolite is shifted to a peg already set on the curve and the work continues from there. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the tangential (deflection) angle for a chord c on a curve of radius R? A. c/R radians B. 2c/R radians C. c/(2R) radians, i.e. 1718.9 c/R minutes D. c/(4R) radians Answer: C. The angle between tangent and chord is half the central angle subtended by the chord: δ = c/(2R) rad = 1718.9 c/R minutes. (Key point: Deflection angle formula) 2. Why are the first and last chords usually sub-chords? A. T1 and T2 are rarely at full-station chainages, so pegs at full stations make the end chords shorter B. To reduce the number of pegs C. Because the theodolite cannot read large angles D. Because the tape is too short Answer: A. The first peg is set at the next full chainage after T1, and the curve ends at T2, so the first and last chords are shorter than the normal chord. (Key point: Sub-chords) 3. How is the theodolite set at T1? A. Zero reading on the centre of the curve B. Zero reading on T2 C. Zero reading on the IP (the tangent), then turn the cumulative angles D. Reading of Δ/2 on the IP Answer: C. The deflections are measured from the tangent T1-IP, so the back-sight on the IP is taken at zero. (Key point: Back-sight at T1) 4. What is the check at the end of the curve? A. Last cumulative deflection equals Δ and peg falls at IP B. Last cumulative deflection equals Δ/2 and the last peg falls on T2 C. Sum of chords equals tangent length D. Last deflection equals 1718.9 c/R Answer: B. The total deflection from the tangent to T2 is Δ/2, and the final peg must coincide with T2. (Key point: Check of the work) ## Related in Surveying II - [Setting out simple curve by Rankine's method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-rankine-method-sketch) — Surveying II, chapter 6 - [Composite curve by deflection angle method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acomposite-curve-deflection-angle-method) — Surveying II, chapter 6, asked 5× - [Curve by tangential angle, deflection 48°30'](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atangential-angle-curve-radius-r-48) — Surveying II, chapter 6 - [Transition deflection angle derivation and laying out](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-deflection-angle-derive-laying-out) — Surveying II, chapter 6 - [Short note: Setting out vertical curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-setting-out-note) — Surveying II, chapter 6 - [Setting out right hand side composite curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aright-hand-composite-curve-setting-out) — Surveying II, chapter 6 ## Related in other subjects - [Simple circular curve elements and chainages](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-64s-simple-curve) — Transportation Engineering I, chapter 3 - [Setting out of a building](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Asetting-out-building) — Building Technology, chapter 2 - [Composite curve with 48 degree deflection](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-72m-composite-60) — Transportation Engineering I, chapter 3 - [Vertical curve with horizontal curve, 45 degrees](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-77c-vc-horizontal) — Transportation Engineering I, chapter 3