--- title: "Elements of transition curve" subject: "Surveying II" chapter: 6 key: "semester_4/surveying_ii:transition-curve-elements" source: https://www.bctengineer.com/q/semester_4/surveying_ii/transition-curve-elements site: BCT Engineering --- # Elements of transition curve Surveying II · Chapter 6: Curves - Asked in: 2070 Magh, 6 marks - Video: [Transition Curve | Elements of Transition Curve | Advantage | Prashant YT | Surveying | BE/Diploma](https://www.youtube.com/watch?v=k4IiiB17yfA) — Prashant YT - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/transition-curve-elements - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6 ## Question Describe elements of transition curve. ## Short answer Key elements are transition length Ls = v³/(CR), shift s = Ls²/(24R), spiral angle θs = Ls/(2R), and tangent length Ts = (R+s)tan(Δ/2)+Ls/2. Chainages: TS, SC, CS, ST; deflection angle from TS is α = 573l²/(RLs) minutes; SC coordinates x≈Ls, y=Ls²/(6R). ## Answer A combined (composite) curve consists of a circular arc with a transition curve at each end. The elements are: ```text V (IP) / \ / \ / \ TS / \ ST o___.___.___o SC CS ``` | Element | Meaning / formula | |---|---| | $L_s$ | Length of transition curve, $L_s = v^3/(CR)$ | | TS, ST | Tangent–spiral and spiral–tangent points (start and end of the composite curve) | | SC, CS | Spiral–circular and circular–spiral junction points | | $\theta_s$ | Spiral (tangent) angle at SC, $\theta_s = L_s/(2R)$ rad | | $s$ | Shift of the circular curve, $s = L_s^2/(24R)$ | | $T_s$ | Total tangent length, $T_s = (R+s)\tan(\Delta/2) + L_s/2$ | | $\Delta$ | Total deflection angle between the straights | | $L_c$ | Length of circular arc, $L_c = R(\Delta - 2\theta_s)$ (θ in radians) | | $\alpha$ | Deflection angle at TS to a point at distance $l$: $\alpha = 573l^2/(RL_s)$ min | | $\alpha_s$ | Deflection angle at SC from TS, $\alpha_s = \theta_s/3$ | | $x, y$ | Coordinates of SC: $x \approx L_s$, $y = L_s^2/(6R)$ | | Total length | $2L_s + L_c$ | **Chainages:** TS = IP − $T_s$; SC = TS + $L_s$; CS = SC + $L_c$; ST = CS + $L_s$. The shift $s$ is the distance by which the circular curve is moved inward from the original tangents so that the transition can fit; it equals the perpendicular distance between the tangent and the shifted circular arc. The rate of change of radial acceleration $C$ and the design speed $v$ decide $L_s$; the super-elevation is attained over $L_s$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What do SC and CS denote? A. Shift and chord points B. Spiral-to-circular and circular-to-spiral junction points C. Starting chainage and curve start D. Start and end of the whole composite curve Answer: B. TS and ST are the ends of the composite curve; SC and CS are the junctions with the circular arc. (Key point: Junction points) 2. What is the shift s of the circular curve? A. s = Ls/(2R) B. s = Ls^2/(24 R), the inward movement of the circular arc from the tangent C. s = Ls/3 D. s = R Delta Answer: B. The shift s = Ls^2/(24R) is the amount the circular curve is moved inward so the spiral can fit. (Key point: Shift) 3. What is the spiral angle thetas at SC and the deflection angle alpha_s at SC from TS? A. thetas = 2Ls/R; alpha_s = thetas/3 B. thetas = Ls/R; alpha_s = thetas/2 C. thetas = Ls/(2R); alpha_s = thetas D. thetas = Ls/(2R); alpha_s = thetas/3 Answer: D. thetas = Ls/(2R) radians and the deflection at TS to SC is one third of it. (Key point: Spiral angle) 4. How is the length of circular arc Lc found? A. Lc = R(Delta - thetas) B. Lc = R Delta C. Lc = R(Delta - 2 thetas), with angles in radians D. Lc = 2 Ls + R Delta Answer: C. The two spirals use up 2 thetas of the deflection, leaving Delta - 2 thetas for the arc. 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