--- title: "Setting out simple curve by Rankine's method" subject: "Surveying II" chapter: 6 key: "semester_4/surveying_ii:simple-curve-rankine-method-sketch" source: https://www.bctengineer.com/q/semester_4/surveying_ii/simple-curve-rankine-method-sketch site: BCT Engineering --- # Setting out simple curve by Rankine's method Surveying II · Chapter 6: Curves - Asked in: 2080 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-rankine-method-sketch - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6 ## Question Illustrate the methods (including sketch) of setting out of simple circular curve by Rankine's method. ## Short answer Rankine’s method sets a curve from T1 using a theodolite. After sighting the IP, cumulative deflection angles and chord lengths from the previous peg locate successive points. The last cumulative angle must equal Δ/2, and the final peg must coincide with T2. ## Answer **Rankine's method** sets out a circular curve by deflection angles measured at the first tangent point T₁ with a theodolite, and chord lengths measured with a tape. ```text V (IP) /\ / \ / .. \ T1 o' 3 4 'o T2 1 2 ``` #### Principle Each deflection angle is the angle between the tangent at T₁ and the chord from T₁ to the point, which equals half of the central angle of the arc: $$ \delta = \frac{1718.87\,c}{R}\ \text{minutes},\qquad \Delta_n = \delta_1+\delta_2+\dots+\delta_n $$ #### Procedure 1. Compute $R$, $T$, $L$ and the chainages of T₁ and T₂. 2. Find the sub-chord $c_1$ (T₁ to the first full peg), the full chords $c$ and the last sub-chord $c_n$. 3. Compute the deflection angle for each chord and the cumulative angles. 4. Set the theodolite at T₁ with the plates at zero, sight V. 5. Set the first angle $\delta_1$ and measure $c_1$ from T₁ to fix point 1. 6. Set the next cumulative angle $\Delta_2$; with the tape zero at point 1 and length $c$, swing until it meets the line of sight to fix point 2. Continue to T₂. 7. The final angle must equal $\Delta/2$ and the final point must coincide with T₂. **Merit:** accurate; only one instrument station is needed. **Limitations:** errors accumulate and there is no check except at the end; the whole curve must be visible from T₁. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In Rankine's method each deflection angle is A. measured at the IP B. the full central angle C. measured at the previous peg D. half the central angle subtended by the chord, measured at T1 from the tangent Answer: D. The tangent-chord angle equals half the central angle, δ = 1718.87c/R minutes. (Key point: Principle) 2. Where is the theodolite set and what is the initial sight? A. At T1, zero set, sighting the IP B. At the IP sighting T1 C. At the centre of curve D. At T2 sighting centre Answer: A. All points are fixed from T1 with the plates at zero on the IP. (Key point: Instrument setup) 3. How is point 2 fixed? A. Measure radius from centre B. Turn to cumulative angle and swing a chord length from point 1 until it meets the line of sight C. Measure from T1 the full distance to point 2 D. Offset from the long chord Answer: B. Intersection of the line of sight at cumulative angle and the chord tape from the previous point fixes the peg. (Key point: Fixing a point) 4. A limitation of the method is A. it cannot give checks at all points and is inaccurate B. it needs two instruments C. errors accumulate and the whole curve must be visible from T1 D. it needs the radius unknown Answer: C. Each point depends on the previous one so errors accumulate, and everything must be visible from T1. (Key point: Limitations) ## Related in Surveying II - [Short note: Rankine's method of curve setting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Arankine-method-circular-curve) — Surveying II, chapter 6 - [Simple circular curve by deflection angle method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-deflection-angle-method-sketch) — 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 - [Elements of simple circular curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-circular-curve-elements) — Surveying II, chapter 6 - [Composite curve design by Rankine's method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acomposite-curve-rankine-design-2079j) — Surveying II, chapter 6, asked 2× ## 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 - [Simple Rankine plant 2 MPa / 20 kPa: efficiency, power](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Arankine-2mpa-20kpa-50kgs) — Fundamental of Thermodynamics & Heat Transfer, chapter 6 - [Setting out of a building](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Asetting-out-building) — Building Technology, chapter 2 - [Car on circular curve, angular rate](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Acar-circular-curve-constant-speed) — Applied Mechanics (Dynamics), chapter 1