---
title: "Horizontal length of 16 m, 29.8850 m tape"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-29-8850-16m-fully-supported"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-29-8850-16m-fully-supported
site: BCT Engineering
---

# Horizontal length of 16 m, 29.8850 m tape

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2059 Chaitra, 10 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-29-8850-16m-fully-supported
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

A tape of nominal length 30 m is standardized in catenary at 40 N tension and found to be 29.8850 m. If the mass of the tape is 0.015 kg/m, calculate the horizontal length of 16 m in fully supported condition.

## Short answer

Add sag at standardisation (0.0152 m) to get true tape length 29.9002 m. Apply tape-length correction to 16 m: -0.0532 m. No field sag. Horizontal length = 15.9468 m.

## Answer

**Method.** The tape was standardised in catenary at 40 N, so its true (fully supported) length is found by adding back the sag in the standard. It is then used fully supported at the same tension (40 N), so there is no sag in the field.

#### Data
$w = 0.015\times 9.81 = 0.14715$ N/m, $P = 40$ N, standard length $= 29.8850$ m, $L = 16$ m.

#### 1. Sag at standardisation (30 m)
$$
\frac{w^{2}\,l^{3}}{24\,P^{2}} = \frac{0.14715^{2}\times 30^{3}}{24\times 40^{2}} = 0.015225\ \text{m}
$$
True tape length $= 29.8850 + 0.015225 = 29.9002$ m.

#### 2. Tape length correction
$$
C_a = 16\times\frac{29.9002 - 30}{30} = -0.0532\ \text{m}
$$

#### 3. Horizontal length
Fully supported, so the sag correction is zero:
$$
D = 16 - 0.0532 = 15.9468\ \text{m}
$$

**Answer: horizontal length of the 16 m $= 15.9468$ m.**

## Check yourself

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

1. Add sag to 29.8850 because
   A. standardised in catenary
   B. field in catenary
   C. temperature
   D. pull
   Answer: A. Standard includes sag. (Key point: Why add sag)

2. Field sag correction is
   A. -0.015
   B. zero
   C. +0.015
   D. computed for 16 m
   Answer: B. Fully supported. (Key point: Field sag)

3. Sag at 30 m, 40 N
   A. 0.15
   B. 0.0015
   C. 0.015225 m
   D. 0.5
   Answer: C. Computed. (Key point: Sag size at standard)

4. Horizontal length
   A. 16.0532
   B. 16.0
   C. 15.9
   D. 15.9468 m
   Answer: D. 16 - 0.0532. (Key point: Result)

## Related in Surveying I

- [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
- [Horizontal length of 30 m span, 50 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-50m-span-30m-26c) — Surveying I, chapter 2
- [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
- [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×

## Related in other subjects

- [Suspension 150 m: SF, BM at 30 m, tension, length](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Asuspension-150m-dip15-180-150-dead-7-5) — Theory of Structures I, chapter 7, asked 2×
- [Suspension 150 m: BM and SF at 30 m, tension, length](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Asuspension-150m-dip15-180-120-dead-5) — Theory of Structures I, chapter 7, asked 2×