---
title: "True length of 680 m line, 20 m tape"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-20m-680m-line"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-20m-680m-line
site: BCT Engineering
---

# True length of 680 m line, 20 m tape

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2068 Baisakh, 8 marks
- Video: [Find the correct length of the line|correction for chain length|length correction](https://www.youtube.com/watch?v=zrthvZDi3VM) — Hamro Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/tape-20m-680m-line
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

A steel tape was exactly 20 m long at 10°C when supported throughout its length under a pull of 5 kg. A line measured with this tape under a pull of 16 kg and at a mean temperature of 22°C was found to be 680 m long. Assuming the tape is supported at every 10 m, find the true length of the line. Given that the cross-sectional area of the tape = 0.03 sq.cm, $E = 2.1\times10^{6}$ kg/sq.cm, $\alpha = 11\times10^{-6}$ per °C, weight of tape = 10 gm/cu.cm.

## Short answer

Apply temperature, pull, and sag corrections. Temperature: +0.0898 m, pull: +0.1187 m, sag: -0.0100 m. True length = 680.1985 m.

## Answer

**Assumption.** Standardised fully supported at $10^\circ$C and 5 kg, so there is no standard sag to add back.

#### Data
- $L = 680$ m; supports every 10 m (68 spans)
- $P_0 = 5$ kg, $P = 16$ kg; $T_0 = 10^\circ$C, $T = 22^\circ$C
- $A = 0.03$ cm$^2$, $E = 2.1\times 10^{6}$ kg/cm$^2$, $\alpha = 11\times 10^{-6}$/$^\circ$C
- Weight per metre $= A\times\rho = 0.03\ \text{cm}^2\times 10\ \text{g/cm}^3 = 0.3$ g/cm $= 0.03$ kg/m

#### 1. Temperature
$$
C_t = 11\times 10^{-6}\times(22 - 10)\times 680 = +0.0898\ \text{m}
$$

#### 2. Pull
$$
C_p = \frac{(16 - 5)\times 680}{0.03\times 2.1\times 10^{6}} = +0.1187\ \text{m}
$$

#### 3. Sag
Per 10 m span: $\dfrac{0.03^{2}\times 10^{3}}{24\times 16^{2}} = 0.000146$ m.

$$
C_s = -68\times 0.000146 = -0.0100\ \text{m}
$$

#### 4. True length
$$
L = 680 + 0.0898 + 0.1187 - 0.0100 = 680.1985\ \text{m}
$$

**Answer: true length of the line $= 680.1985$ m.**

## Check yourself

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

1. Weight per metre equals
   A. A x density = 0.03 cm^2 x 10 g/cm^3 = 0.3 g/cm = 0.03 kg/m
   B. 0.3 kg/m
   C. 0.03 g/m
   D. 10 g/m
   Answer: A. Multiply area by unit weight, then convert. (Key point: Weight per metre)

2. The pull correction uses
   A. (16 + 5)
   B. (16 - 5) x 680/(A E)
   C. (16-5)/680
   D. 16 x 680/AE
   Answer: B. Difference of pulls over AE. (Key point: Pull correction)

3. The temperature difference is
   A. 22 - 20
   B. 10 C
   C. 22 - 10 = 12 C
   D. 32 C
   Answer: C. Standard temperature is 10 C. (Key point: Temperature)

4. The sag correction is small because
   A. Spans are long
   B. Pull is small
   C. Weight is large
   D. pull is large and spans only 10 m
   Answer: D. Sag varies with l^3 and 1/P^2. (Key point: Sag size)

## Close variants set in other exams

- [True length of 780 m line, tape 0.693 kg](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-30m-780m-line) — Surveying I, chapter 2, asked 2×
- [True length of 1020 m line, 20 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-1020m-line) — Surveying I, chapter 2, asked 2×

## Related in Surveying I

- [True length: tape found 2.5 cm too long](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-825-plus-750-m) — Surveying I, chapter 2
- [Tape corrections for 86 m, 10 kg pull](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-86m-pull-10kg) — Surveying I, chapter 2, asked 3×
- [Tape corrections for 86 m, 15 kg pull](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-86m-supports-10m-15kg) — Surveying I, chapter 2, asked 3×
- [Correction per tape length (kg data, 58)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-base-line-correction-per-tape-58) — Surveying I, chapter 2, asked 2×
- [True length of 358.650 m line](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-358-650-m-line) — Surveying I, chapter 2
- [True length of base line AB (four bays)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-base-line-four-bays) — Surveying I, chapter 2