---
title: "Transition curve from spiral angle 8.35"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-69bh-tc-spiral"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-69bh-tc-spiral
site: BCT Engineering
---

# Transition curve from spiral angle 8.35

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2069 Bhadra, 8 marks
- Video: [Spiral Curves for Highway Alignment](https://www.youtube.com/watch?v=CCpi0eNks94) — Daniel Findley
- 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-69bh-tc-spiral
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

The angle of intersection between two straights is 137.23°. The spiral angle for each transition curve is 8.35°. Calculate the length of transition curve, combined length of curves and length of tangent if the radius of the curve is 325 m.

## Short answer

Deflection angle = 180° − 137.23° = 42.77°. Transition length Ls = 2Rθs (θs in rad) = 94.7 m. Combined curve length = circular arc (147.9 m) + 2Ls = 337.3 m. Tangent length Ts = (R+s) tan(Δ/2) + Ls/2 = 175.1 m.

## Answer

#### Reading of the data
The angle of intersection 137.23° is the interior angle between the two straights, so the deflection angle is $\Delta=180^\circ-137.23^\circ=42.77^\circ$. Radius $R=325$ m, spiral angle $\theta_s=8.35^\circ$.

#### Length of transition curve
For a spiral, $\theta_s=\dfrac{L_s}{2R}$ (radians), so

$$
L_s=2R\theta_s=2(325)(0.14573)=94.73\ \text{m}
$$

#### Combined length of curve
- Shift: $s=\dfrac{L_s^2}{24R}=\dfrac{94.73^2}{24(325)}=1.150$ m
- Central angle of the circular arc: $\Delta_c=\Delta-2\theta_s=42.77-2(8.35)=26.07^\circ$
- Circular arc length: $L_c=R\Delta_c=325(0.45501)=147.88$ m

$$
L=L_c+2L_s=147.88+2(94.73)=337.33\ \text{m}
$$

#### Length of tangent (from PI to the start of the transition)

$$
T_s=(R+s)\tan\frac{\Delta}{2}+\frac{L_s}{2}=(326.150)\tan(21.39^\circ)+47.36=175.08\ \text{m}
$$

**Answer:** $L_s=94.7$ m; combined curve length = 337.3 m; tangent length $T_s=175.1$ m.

(If the given angle were instead the deflection angle, $\Delta=137.23^\circ$, the same $L_s$ results with $\Delta_c=120.53^\circ$, total length 873.1 m and $T_s=880.2$ m.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The angle of intersection is 137.23° (interior angle). What deflection angle is used?
   A. 137.23°
   B. 42.77°
   C. 68.6°
   D. 317.23°
   Answer: B. Deflection = 180° - interior angle = 42.77°. (Key point: Deflection angle)

2. How is the spiral length found from the spiral angle?
   A. Ls = R θs = 47.4 m
   B. Ls = θs / 2R
   C. Ls = 2 R θs (θs in radians) = 94.73 m
   D. Ls = 4 R θs
   Answer: C. θs = Ls/(2R), so Ls = 2Rθs. (Key point: Spiral length)

3. What central angle is left for the circular arc?
   A. Δ - 2θs = 26.07°
   B. Δ - θs = 34.42°
   C. Δ + 2θs = 59.47°
   D. θs = 8.35°
   Answer: A. Two spirals each use θs of the deflection, so the arc angle is Δ - 2θs. (Key point: Circular arc angle)

4. Which expression gives the tangent length from PI to the start of the spiral?
   A. R tan(Δ/2) only
   B. (R + s) tan(Δ/2) - Ls/2
   C. (R - s) tan Δ
   D. (R + s) tan(Δ/2) + Ls/2
   Answer: D. The shifted circle has tangent (R+s)tan(Δ/2), and the spiral adds Ls/2 along the tangent. (Key point: Tangent length)

## Close variants set in other exams

- [Transition curve length from spiral angle 10.32](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-73bh-tc-spiral) — Transportation Engineering I, chapter 3, asked 2×

## Related in Transportation Engineering I

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