---
title: "Tape correction for 24.726 m distance"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-24-726-m-catenary"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-24-726-m-catenary
site: BCT Engineering
---

# Tape correction for 24.726 m distance

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2072 Chaitra, 6 marks
- Video: [Surveying | Corrections in Tape Part 1 of 2](https://www.youtube.com/watch?v=MdHdzGSSz7Q) — the Engineer's Insight
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/tape-24-726-m-catenary
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

A 30 m steel tape was standardized in catenary condition under a pull of 5 kg and found to be 30.015 m. The tape was used to measure a distance of 24.726 m in catenary conditions at a pull of 5 kg. The weight of the tape was 30 gm/m. Apply necessary tape correction.

## Short answer

Find true tape length by adding sag at standardisation (0.0405 m) to 30.015 m, giving 30.0555 m. Correct 24.726 m for tape length (+0.0457 m) and sag (-0.0227 m) to obtain 24.7491 m.

## Answer

**Method.** The tape was standardised in catenary (30 m span), so the sag in its stated length is added back to give the true tape length. The 24.726 m is measured as one catenary span at the same pull.

#### Data
$w = 0.03$ kg/m, $P = 5$ kg, standard length $= 30.015$ m (catenary), $L = 24.726$ m.

#### 1. Tape length
Sag at standardisation: $\dfrac{0.03^{2}\times 30^{3}}{24\times 5^{2}} = 0.0405$ m.
True tape length $= 30.015 + 0.0405 = 30.0555$ m.

$$
C_a = 24.726\times\frac{30.0555 - 30}{30} = +0.0457\ \text{m}
$$

#### 2. Sag correction
$$
C_s = -\frac{0.03^{2}\times 24.726^{3}}{24\times 5^{2}} = -0.0227\ \text{m}
$$

#### 3. Corrected length
$$
L_{true} = 24.726 + 0.0457 - 0.0227 = 24.7491\ \text{m}
$$

**Answer: corrected length $= 24.7491$ m.**

## Check yourself

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

1. Why is the sag at standardisation added to 30.015 m?
   A. Catenary standard length includes sag, so the true tape length is longer
   B. The tape stretches
   C. Temperature is higher
   D. To account for slope
   Answer: A. Sag shortens the span, so adding it back gives the tape length. (Key point: Why add sag)

2. Which length is used in the sag at standardisation?
   A. 24.726 m
   B. 30 m
   C. 5 m
   D. 60 m
   Answer: B. The tape was standardised over its full 30 m. (Key point: Sag span)

3. The field sag correction uses
   A. 30 m
   B. 12.363 m
   C. 24.726 m as a single span
   D. two equal spans
   Answer: C. It is measured as one catenary span. (Key point: Field sag)

4. The corrected length 24.7491 m is
   A. Shorter than measured
   B. Equal to measured
   C. Cannot be compared
   D. longer than measured, since tape-length gain exceeds sag loss
   Answer: D. +0.0457 outweighs -0.0227. (Key point: Result)

## Close variants set in other exams

- [Tape corrections for 66 m in three spans](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-66m-three-equal-spans) — Surveying I, chapter 2, asked 2×

## Related in Surveying I

- [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×
- [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 standardized in catenary: 24 m span](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-catenary-span-24m) — Surveying I, chapter 2, asked 2×
- [Tape standardized in catenary: 20 m span](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-catenary-span-20m) — Surveying I, chapter 2, asked 2×
- [Tape standardized in catenary: 23 m span](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-catenary-span-23m) — Surveying I, chapter 2
- [Tape corrections for 86 m, supports at 15 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-30m-86m-supports-15m) — Surveying I, chapter 2, asked 3×