---
title: "Combined curve table, R=300 m, Ls=60 m"
subject: "Surveying II"
chapter: 6
key: "semester_4/surveying_ii:combined-curve-transition-60m-r300"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/combined-curve-transition-60m-r300
site: BCT Engineering
---

# Combined curve table, R=300 m, Ls=60 m

Surveying II · Chapter 6: Curves

- Asked in: 2073 Bhadra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/combined-curve-transition-60m-r300
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6

## Question

It is proposed to insert a circular curve of 300 m radius with a transition curve of length 60 m long each end of the circular curve. Prepare necessary data for setting out the combined curve in tabular form. Deflection angle between two alignments of road is 45° and chainage of intersection point is 2000 m. Peg interval for transition and circular curve are 20 m and 30 m respectively. Take chainage at multiple of peg interval.

## Short answer

Compute shift s, spiral angle θs, tangent length Ts, circular length Lc. Ts = 154.47 m, Lc = 175.62 m. Chainages: TS = 1845.53 m, SC = 1905.53 m, CS = 2081.15 m, ST = 2141.15 m. Set out transitions with α = 573l²/(RLs) min and circular curve with δ = 1718.87c/R min.

## Answer

Given $\Delta = 45^\circ$, $R = 300$ m, $L_s = 60$ m, chainage of IP = 2000 m, peg interval 20 m on transitions and 30 m on the circular curve.

#### Curve elements
$$
\begin{aligned}
s &= \frac{L_s^2}{24R} = \frac{60^2}{24\times 300} = 0.500\ \text{m}\\
\theta_s &= \frac{L_s}{2R}\ \text{rad} = 5.730^\circ\\
T_s &= (R+s)\tan 22.5^\circ + \frac{L_s}{2} = 154.47\ \text{m}\\
L_c &= \frac{\pi R}{180}(\Delta-2\theta_s) = 175.62\ \text{m}
\end{aligned}
$$

| Point | Chainage (m) |
|---|---|
| TS = 2000 − 154.47 | 1845.53 |
| SC = TS + 60 | 1905.53 |
| CS = SC + 175.62 | 2081.15 |
| ST = CS + 60 | 2141.15 |

#### First transition (set from TS): $\alpha = 573\,l^2/(RL_s)$ minutes
| Point (chainage, m) | l from TS (m) | α (min) | α (° ′ ″) |
|---|---|---|---|
| 1845.53 | 0.00 | 0.00′ | 0°00′00″ |
| 1860.00 | 14.47 | 6.67′ | 0°06′40″ |
| 1880.00 | 34.47 | 37.83′ | 0°37′50″ |
| 1900.00 | 54.47 | 94.45′ | 1°34′27″ |
| 1905.53 | 60.00 | 114.60′ | 1°54′36″ |

Check: at SC, $\alpha = \theta_s/3 = 1.9099^\circ = 1^\circ54'36''$.

#### Circular curve (set from SC): $\delta = 1718.87\,c/R$ minutes
| Point (chainage, m) | Chord c (m) | δ = 1718.87c/R | Cumulative deflection |
|---|---|---|---|
| 1905.53 | - | - | 0°00′00″ |
| 1920.00 | 14.47 | 1°22′55″ | 1°22′55″ |
| 1950.00 | 30.00 | 2°51′53″ | 4°14′48″ |
| 1980.00 | 30.00 | 2°51′53″ | 7°06′41″ |
| 2010.00 | 30.00 | 2°51′53″ | 9°58′34″ |
| 2040.00 | 30.00 | 2°51′53″ | 12°50′28″ |
| 2070.00 | 30.00 | 2°51′53″ | 15°42′21″ |
| 2081.15 | 11.15 | 1°03′52″ | 16°46′13″ |

Check: last cumulative deflection $= (\Delta - 2\theta_s)/2 = 16.7704^\circ$ = 16°46′13″. The second transition is set out from ST in the same way, using $l$ measured back from ST.

**Answer:** $T_s = 154.47$ m, $L_c = 175.62$ m, TS = 1845.53, SC = 1905.53, CS = 2081.15, ST = 2141.15 m.

## Check yourself

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

1. Shift is
   A. Ls^2/(24R) = 0.5 m
   B. Ls^2/(8R)
   C. Ls/(2R)
   D. Ls^2/R
   Answer: A. 60^2/7200 = 0.5. (Key point: Shift)

2. theta_s equals
   A. Ls/R = 11.46 deg
   B. Ls/(2R) = 5.73 deg
   C. Ls/(6R)
   D. 2Ls/R
   Answer: B. 60/600 rad = 0.1 rad = 5.73 deg. (Key point: Spiral angle)

3. Lc is
   A. pi R Delta/180 = 235.6 m
   B. pi R (Delta + 2 theta_s)/180
   C. pi R (Delta - 2 theta_s)/180 = 175.62 m
   D. R Ls
   Answer: C. Transitions consume 2 theta_s. (Key point: Circular arc)

4. Deflection of transition at SC is
   A. theta_s
   B. 2 theta_s/3
   C. theta_s/6
   D. theta_s/3 = 1 deg 54' 36"
   Answer: D. alpha = phi/3. (Key point: Check at SC)

## Related in Surveying II

- [Transition curve R=300 m, deflection 40°](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-curve-80kmph-radius-300) — Surveying II, chapter 6
- [Transition curve 6°, Ls=90 m, chainage 13+700](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atransition-t1v-t2v-chainage-13700) — Surveying II, chapter 6
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