---
title: "Tape corrections for 66 m in three spans"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-66m-three-equal-spans"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-66m-three-equal-spans
site: BCT Engineering
---

# Tape corrections for 66 m in three spans

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2074 Chaitra, 6 marks
- Video: [Surveying Tape Correction Numerical 1](https://www.youtube.com/watch?v=VKh33kzPV38) — Studyclass 247
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/tape-66m-three-equal-spans
- 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 30.008 m. This tape was used to measure a distance of 66 m in three equal spans in catenary conditions at a pull of 5 kg. The weight of tape was 30 gm/m. Apply necessary tape correction for the measured length of line.

## Short answer

Add sag at standardisation (0.0405 m) to 30.008 m to get true tape length 30.0485 m. Apply tape length correction (+0.1067 m) and sag correction for three 22 m spans (-0.0479 m) to 66 m, yielding corrected length 66.0588 m.

## Answer

**Method.** The tape was standardised in catenary, so the sag in its standard length is added back to find the true tape length. Then the sag for the three 22 m spans is applied.

#### Data
- $w = 0.03$ kg/m; $P = 5$ kg (same as standard); $L = 66$ m in three equal spans of 22 m
- Standard length of the 30 m tape in catenary $= 30.008$ m

#### 1. Tape length
Sag at standardisation: $\dfrac{0.03^{2}\times 30^{3}}{24\times 5^{2}} = 0.0405$ m.
True tape length $= 30.008 + 0.0405 = 30.0485$ m.

$$
C_a = 66\times\frac{30.0485 - 30}{30} = +0.1067\ \text{m}
$$

#### 2. Sag correction
Each span: $\dfrac{0.03^{2}\times 22^{3}}{24\times 5^{2}} = 0.015972$ m.

$$
C_s = -3\times 0.015972 = -0.0479\ \text{m}
$$

#### 3. Corrected length
$$
L_{true} = 66 + 0.1067 - 0.0479 = 66.0588\ \text{m}
$$

**Answer: corrected length of the line $= 66.0588$ m.**

## Check yourself

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

1. Why is 0.0405 m added to 30.008 m?
   A. The tape was standardised in catenary, so its true length is longer than the stated length
   B. Because the pull is increased
   C. Because temperature is raised
   D. To remove slope
   Answer: A. Sag in the standard is included in the stated length. (Key point: Standard sag add-back)

2. What span length is used in the sag correction?
   A. 30 m
   B. 22 m (66/3)
   C. 66 m
   D. 33 m
   Answer: B. Three equal spans of 22 m. (Key point: Span length)

3. Why is C_a positive (+0.1067 m)?
   A. Tape is shorter than 30 m
   B. Sag is positive
   C. True tape length (30.0485 m) is longer than 30 m so the line measured is too short
   D. Pull is above standard
   Answer: C. A long tape reads too small, so the correction is added. (Key point: Tape length sign)

4. The total sag correction for the line is
   A. -0.0405 m
   B. -0.1067 m
   C. -0.0160 m
   D. 3 x 0.015972 = -0.0479 m
   Answer: D. Three spans each give 0.015972 m, subtracted. (Key point: Total sag)

## Close variants set in other exams

- [Tape correction for 24.726 m distance](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-24-726-m-catenary) — 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 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×
- [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: 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: 23 m span](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-catenary-span-23m) — Surveying I, chapter 2