---
title: "Horizontal length for 120.0 m recorded"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-29-995-120m"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-29-995-120m
site: BCT Engineering
---

# Horizontal length for 120.0 m recorded

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2065 Shrawan, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/tape-29-995-120m
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

A tape standardised as 29.995 m in catenary at 110 N and 15°C temperature is used in the field with a tension of 90 N and 22°C mean temperature. Calculate the horizontal length if the recorded length is 120.0 m. Assume mass of the tape = 0.0312 kg/m, Young's modulus of elasticity = $2.1\times10^{6}$ kg/cm², cross-sectional area of tape = 0.03 cm², linear expansion of tape = $11\times10^{-6}$ per °C.

## Short answer

Standardized in catenary; true tape length after adding sag is 30.00371 m. Corrections: standardization +0.0148 m, temperature +0.0092 m, pull -0.0039 m, sag -0.0520 m. Horizontal length = 119.968 m.

## Answer

**Method.** The tape is standardised in catenary, so the sag in its stated length is added back. In the field it is used in catenary in 30 m spans (120 m $=$ 4 tapes). $g = 9.81$ m/s$^2$.

#### Data
- $w = 0.0312\times 9.81 = 0.30607$ N/m
- Standard: 29.995 m at $15^\circ$C and $P_0 = 110$ N (catenary); field: $T = 22^\circ$C, $P = 90$ N, $L = 120.0$ m
- $A = 0.03$ cm$^2$, $E = 2.1\times 10^{6}$ kg/cm$^2$, so $AE = 0.03\times 2.1\times 10^{6}\times 9.81 = 618{,}030$ N
- $\alpha = 11\times 10^{-6}$/$^\circ$C

#### 1. Tape length
Sag at standardisation: $\dfrac{0.30607^{2}\times 30^{3}}{24\times 110^{2}} = 0.008710$ m.
True tape length $= 29.995 + 0.00871 = 30.00371$ m.

$$
C_a = 120\times\frac{30.00371 - 30}{30} = +0.0148\ \text{m}
$$

#### 2. Temperature
$$
C_t = 11\times 10^{-6}\times(22 - 15)\times 120 = +0.0092\ \text{m}
$$

#### 3. Pull
$$
C_p = \frac{(90 - 110)\times 120}{618{,}030} = -0.0039\ \text{m}
$$

#### 4. Sag
Per tape: $\dfrac{0.30607^{2}\times 30^{3}}{24\times 90^{2}} = 0.013011$ m; $C_s = -4\times 0.013011 = -0.0520$ m.

#### 5. Horizontal length
$$
D = 120.0 + 0.0148 + 0.0092 - 0.0039 - 0.0520 = 119.9682\ \text{m}
$$

**Answer: horizontal length $= 119.968$ m.**

## Check yourself

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

1. Why is the pull correction negative?
   A. Field pull 90 N is less than standard 110 N
   B. Pull is more
   C. Temperature is low
   D. Because sag
   Answer: A. P < P0. (Key point: Pull sign)

2. The 29.995 m is adjusted by
   A. subtracting sag
   B. adding the standard sag 0.00871 m
   C. no adjustment
   D. adding pull
   Answer: B. Catenary standard includes sag. (Key point: Standard in catenary)

3. Sag in field uses pull
   A. 110 N
   B. 20 N
   C. 90 N
   D. 200 N
   Answer: C. Field pull. (Key point: Field sag)

4. 120 m with 30 m spans means
   A. 3
   B. 12
   C. 30
   D. 4 tapes
   Answer: D. 120/30. (Key point: Number of tapes)

## Related in Surveying I

- [Horizontal length of 16 m, 29.8850 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-29-8850-16m-fully-supported) — Surveying I, chapter 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: 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
- [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×

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