--- title: "Setback with overtaking, deflection 70 degrees" subject: "Transportation Engineering I" chapter: 3 key: "semester_6/transportation_engineering_i:n-81a-setback-overtaking" source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-81a-setback-overtaking site: BCT Engineering --- # Setback with overtaking, deflection 70 degrees Transportation Engineering I · Chapter 3: Geometric Design of Highway - Asked in: 2081 Ashwin, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-81a-setback-overtaking - Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3 ## Question A Two-lane highway was designed with super elevation of 6% and coefficient of lateral friction of 0.15. The design speed of curve is 75 kmph. The stopping sight distance required is 115 m. Determine set back distance required for this curve for providing reasonable opportunities of overtaking as there not enough space to provide full overtaking opportunities, provided that the deflection angle is 70°. ## Short answer For a two-lane highway with 75 km/h design speed, 6% superelevation, 0.15 friction, and 70° deflection angle, radius is 210.9 m. Intermediate sight distance (2×SSD = 230 m) is used since full overtaking distance is not feasible. With sight line at 1.75 m from centre, setback distance from centre line is calculated as 32.6 m using m = R - (R-d)cos(α/2) where α = S/(R-d). ## Answer **Given:** two-lane road, $e = 6\%$, $f = 0.15$, $V = 75$ km/h, SSD $= 115$ m, deflection angle $\Delta = 70^\circ$. **Assumptions:** lane width $w = 3.5$ m, so the line of sight runs along the centre of the inner lane at $d = 1.75$ m from the road centre line. Since there is not enough space for full overtaking sight distance, the **intermediate sight distance** is provided: $ISD = 2\times SSD$. #### Step 1: Radius of the curve (centre line) $$ R = \frac{V^2}{127\,(e+f)} = \frac{75^2}{127\,(0.06+0.15)} = \frac{5625}{26.67} = 210.9\ \text{m} $$ #### Step 2: Sight distance and length of curve $$ S = ISD = 2\times115 = 230\ \text{m} $$ Length of curve $L_c = R\Delta = 210.9\times\dfrac{70\pi}{180} = 257.7$ m. Since $S = 230$ m $< L_c = 257.7$ m, the sight line lies fully within the curve (Case $S < L_c$). #### Step 3: Setback $$ \alpha = \frac{S}{R-d} = \frac{230}{210.9 - 1.75} = 1.0996\ \text{rad} = 63.0^\circ $$ $$ \begin{aligned} m &= R - (R-d)\cos\frac{\alpha}{2} \\ &= 210.91 - 209.16\cos(31.5^\circ) \\ &= 210.91 - 178.34 = 32.58\ \text{m} \end{aligned} $$ **Answer: setback distance from the centre line of the road $m \approx 32.6$ m** (about 33 m) for intermediate sight distance of 230 m. *For comparison, SSD only (115 m) would need $m \approx 9.6$ m.* ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. When there is not enough space for full overtaking sight distance, which sight distance is provided? A. Stopping sight distance only B. Intermediate sight distance = 2 x SSD C. Overtaking sight distance = 3 x SSD D. Headlight sight distance Answer: B. ISD = 2 x SSD = 230 m is used when full overtaking opportunities cannot be provided. (Key point: Sight distance when overtaking space is limited) 2. What is the radius for V = 75 km/h, e = 0.06 and f = 0.15? A. About 118 m B. About 351 m C. About 211 m D. About 421 m Answer: C. R = V^2/(127(e+f)) = 5625/(127 x 0.21) = 5625/26.67 = 210.9 m. (Key point: Radius of the curve) 3. Lc = R x Delta = 257.7 m and S = 230 m. Which case applies? A. S > Lc, so the sight line extends onto the tangents B. S < Lc, so the sight line lies within the curve C. S = Lc exactly D. No setback is needed Answer: B. Since 230 m < 257.7 m, use alpha = S/(R-d) and m = R - (R-d)cos(alpha/2). (Key point: Choice of setback case) 4. With d = 1.75 m and alpha = 63.0 degrees, what is the setback m? A. About 9.6 m B. About 32.6 m C. About 26.4 m D. About 178 m Answer: B. m = 210.91 - 209.16 cos(31.5 deg) = 210.91 - 178.34 = 32.6 m (9.6 m would be for SSD only). 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