---
title: "Simple curve by offsets from long chord"
subject: "Surveying II"
chapter: 6
key: "semester_4/surveying_ii:simple-curve-offsets-long-chord"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/simple-curve-offsets-long-chord
site: BCT Engineering
---

# Simple curve by offsets from long chord

Surveying II · Chapter 6: Curves

- Asked in: 2073 Bhadra, 4 marks
- Video: [Solved Example on Setting out of Simple Circular Curve by taking Offsets from the Long Chord](https://www.youtube.com/watch?v=7GWzhSxyQ9k) — 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/simple-curve-offsets-long-chord
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6

## Question

Explain the setting out of simple circular curve by offsets from long chord.

## Short answer

The curve is set out by measuring perpendicular offsets from the long chord joining T₁ and T₂. Offset at distance x from the midpoint is O_x = √(R² − x²) − (R − O0), where O0 = R(1 − cos(Δ/2)) is the mid-ordinate. The method requires only tape and cross-staff, and is suitable for short, accessible curves.

## Answer

**Offsets from the long chord** is a chain-and-tape method (no theodolite needed) in which the curve is located by perpendicular offsets measured from the long chord joining the two tangent points T₁ and T₂. It is used for short curves.

```text
        T1 ______________ T2   <- long chord
          \  |  |  |  |  /
           \ |  |  |  | /     offsets O_x
            '-.__.__.-'
```

#### Principle
Let $O$ be the centre, $R$ the radius, $\Delta$ the deflection angle.

- Long chord: $LC = 2R\sin\dfrac{\Delta}{2}$
- Mid-ordinate (at the middle of the long chord): $O_0 = R\left(1-\cos\dfrac{\Delta}{2}\right)$
- Offset at a distance $x$ from the middle of the long chord:

$$
O_x = \sqrt{R^2 - x^2} - (R - O_0)
$$

The term $R - O_0 = R\cos(\Delta/2)$ is the distance from the centre to the long chord, so $O_x$ is the height of the curve above the chord at that point.

#### Procedure
1. Locate T₁ and T₂ by measuring the tangent length $T = R\tan(\Delta/2)$ from the IP; join them to get the long chord.
2. Measure the long chord, mark its mid point M.
3. Divide the long chord on both sides of M at equal intervals (say 5 or 10 m): $x = 0, 5, 10, \dots$.
4. Compute $O_x$ for each $x$; the offsets are symmetrical on both sides of M.
5. Set out each offset perpendicular to the long chord (using a cross-staff or optical square) and fix the curve pegs.
6. The offsets at T₁ and T₂ are zero; the offset at M is the mid-ordinate $O_0$ (check).

**Use:** short curves where the chord is accessible and level; accuracy is limited by the perpendicular setting.

## Check yourself

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

1. What does this method need?
   A. Only chain/tape and optical square or cross-staff
   B. A theodolite
   C. A total station
   D. A level
   Answer: A. Offsets are perpendicular to the long chord. (Key point: Equipment)

2. Long chord equals
   A. 2R cos(Delta/2)
   B. 2R sin(Delta/2)
   C. R tan(Delta/2)
   D. R Delta
   Answer: B. It joins T1 and T2. (Key point: Long chord)

3. Offset at x from the middle is
   A. sqrt(R^2 + x^2) - R
   B. R - sqrt(R^2 - x^2)
   C. sqrt(R^2 - x^2) - (R - O0)
   D. x^2/(2R)
   Answer: C. R - O0 = R cos(Delta/2) is the centre-to-chord distance. (Key point: Offset formula)

4. Best suited for
   A. Long curves
   B. Curves over water
   C. Curves with transitions
   D. Short curves with accessible, level chord
   Answer: D. Accuracy is limited by perpendicular setting. (Key point: Use)

## Related in Surveying II

- [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
- [Rankine's data, 8° curve, 187.62 m long chord](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-8deg-18762-long-chord) — Surveying II, chapter 6
- [Simple circular curve by deflection angle method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-deflection-angle-method-sketch) — Surveying II, chapter 6
- [Short note: Setting out vertical curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-setting-out-note) — Surveying II, chapter 6
- [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
- [Elements of simple circular curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-circular-curve-elements) — Surveying II, chapter 6

## Related in other subjects

- [Simple circular curve elements and chainages](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-64s-simple-curve) — Transportation Engineering I, chapter 3
- [Setting out of a building](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Asetting-out-building) — Building Technology, chapter 2