--- title: "Short note: Setting out vertical curve" subject: "Surveying II" chapter: 6 key: "semester_4/surveying_ii:vertical-curve-setting-out-note" source: https://www.bctengineer.com/q/semester_4/surveying_ii/vertical-curve-setting-out-note site: BCT Engineering --- # Short note: Setting out vertical curve Surveying II · Chapter 6: Curves - Asked in: 2066 Magh (old course), 8 marks - Video: [Vertical Curve in Surveying/Highway Engineering | Formula Derivation + High & Low Points](https://www.youtube.com/watch?v=WQvvrnJNbdI) — 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/vertical-curve-setting-out-note - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6 ## Question Write a short note on setting out vertical curve. ## Short answer Vertical curves are parabolic arcs (summit or sag). Length L from permissible grade change rate or sight distance. BVC at IP−L/2, EVC at IP+L/2; their RLs computed from IP. Curve RL at x from BVC: RL_BVC + (g1/100)x + ((g2−g1)/(200L))x². Peg at intervals, set by offset from tangent level and checked at EVC. ## Answer Vertical curves are provided at changes of grade on roads and railways to give a smooth transition, safe sight distance and comfort. A parabola is used: the rate of change of grade is constant. #### Types - **Summit (crest) curve:** the grade changes from rising to falling or less rising. - **Sag (valley) curve:** the grade changes from falling to rising or less falling. ```text Summit curve Sag curve ___ \ / __/ \__ \_ _/ ‾‾ ``` #### Data required - Grades $g_1$ and $g_2$ (in %), chainage and RL of the intersection point. - Length $L$ of the curve, either given or found from the permissible rate of change of grade $r$: $L = \dfrac{|g_2-g_1|}{r}\times(\text{chord length})$, or from sight distance requirements. #### Computations (equal tangent parabola) 1. Chainage of BVC = IP − $L/2$, of EVC = IP + $L/2$. 2. RL of BVC $= \text{RL}_{IP} - g_1L/200$; RL of EVC $= \text{RL}_{IP} + g_2L/200$. 3. RL of any point at distance $x$ from BVC: $$ y = \text{RL}_{BVC} + \frac{g_1x}{100} + \frac{(g_2-g_1)x^2}{200L} $$ 4. Mid-ordinate (offset at the IP): $e = \dfrac{L\,|g_2-g_1|}{800}$. Level of mid-point of curve $= \text{RL}_{IP} \pm e$ (+ for sag, − for summit). 5. Turning point (highest or lowest): $x = \dfrac{g_1L}{g_1-g_2}$ from BVC. #### Setting out in the field 1. Fix the IP, BVC and EVC by measuring $L/2$ along the two tangents. 2. Peg the curve at regular intervals (usually 20 or 30 m) from BVC. 3. Compute the offsets $y_x = (g_2-g_1)x^2/(200L)$ and the tangent levels, then the curve RL (tabulated). 4. Using a level and staff, set each peg so that its top is at the computed RL (or measure the offset from the tangent level). 5. Check that the RL at EVC agrees with the computed value. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is a parabola used for a vertical curve? A. Its rate of change of grade is constant B. Its tangent length is constant C. Its radius is constant D. It is easy to draw only Answer: A. The second derivative of a parabola is constant, i.e. constant rate of change of grade. (Key point: Why parabola) 2. Which grade change gives a summit (crest) curve? A. Level to level B. Falling to rising C. Rising to falling or less rising D. Rising to more rising Answer: C. A crest occurs when the grade decreases algebraically; sag when it increases. (Key point: Types) 3. Where is the highest/lowest point of the curve from BVC? A. x = L B. x = e C. x = g1 L/(g1 - g2), where grade is zero D. x = L/2 Answer: C. Setting the slope to zero gives x = g1 L/(g1 - g2). (Key point: Turning point) 4. How is the field setting out checked? A. Mid-ordinate equals L/800 B. RL at EVC agrees with the computed value C. Offset at BVC equals e D. Number of pegs is even Answer: B. The curve must end at the computed EVC level. (Key point: Field check) ## Related in Surveying II - [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 - [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 - [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 - [Vertical curve -1% and +0.5% by parabolic method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-parabolic-neg1-pos05-ip) — Surveying II, chapter 6, asked 2× - [Vertical curve -1% and +0.5%, IP 500 m](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-falling-1-rising-05) — Surveying II, chapter 6, asked 2× - [Vertical curve table, -4.5% and +3.5%, 200 m](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-table-neg45-pos35-200m) — Surveying II, chapter 6 ## Related in other subjects - [Setting out of a building](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Asetting-out-building) — Building Technology, chapter 2 - [Vertical curve -3.5% and +4%, 250 m night](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-78b-vc-night) — Transportation Engineering I, chapter 3, asked 2× - [Vertical curve -3% and +4.5% at 320.8 m](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-68m-vc-320) — Transportation Engineering I, chapter 3, asked 2× - [Vertical curve with intermediate sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81a-vc-intermediate) — Transportation Engineering I, chapter 3