--- title: "Linear measurement methods; sag correction" subject: "Surveying I" chapter: 2 key: "semester_3/surveying_i:methods-of-linear-measurement-sag" source: https://www.bctengineer.com/q/semester_3/surveying_i/methods-of-linear-measurement-sag site: BCT Engineering --- # Linear measurement methods; sag correction Surveying I · Chapter 2: Distance Measurements - Asked in: 2080 Bhadra, 1+2+2 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/methods-of-linear-measurement-sag - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2 ## Question What are the methods of linear measurements? Explain about sag correction. When is the sag correction considered positive and negative? ## Short answer Linear measurement methods include pacing, passometer, odometer, chaining, taping, tacheometry, subtense bar, EDM and GNSS. Sag correction Cₛ = −W²l/(24P²) is negative (subtracted) when a tape standardised on the flat is used suspended, and positive (added) when standardised in catenary and used on the flat. ## Answer #### Methods of linear measurement 1. **Pacing:** counting the paces and multiplying by the average pace length (rough, accuracy about 1/100). 2. **Passometer/pedometer and odometer or measuring wheel:** record the steps or the revolutions of a wheel (rough). 3. **Chaining or taping:** direct measurement by a chain, steel tape or invar tape (ordinary to high accuracy, 1/1000 to 1/10,000 or better). 4. **Tacheometry:** the stadia hairs of a theodolite give the distance from readings on a staff. 5. **Subtense bar** method: a bar of known length subtends a small angle at the observer. 6. **EDM/total station:** distance from the time or phase of electromagnetic waves. 7. **GNSS/GPS and photogrammetry:** distances from coordinates. #### Sag correction When a tape is suspended between two supports, it hangs in the form of a catenary (approximately a parabola), and the length measured along the curve is longer than the horizontal chord. For a span of length $l$ in which the tape weighs $W$ (weight of the tape in that span, $W = w\,l$), under a pull $P$: $$ C_s = -\frac{W^{2}\,l}{24\,P^{2}} \text{ per span} $$ or, in terms of the weight per metre $w$ and the total length $L$ in $n$ equal spans: $$ C_s = -\frac{n\,w^{2}\,l^{3}}{24\,P^{2}} = -\frac{L\,w^{2}\,l^{2}}{24\,P^{2}} $$ #### Sign of sag correction - **Negative** when the tape was standardised on the flat (fully supported) and is used suspended (in catenary), because the sagging tape reads more than the horizontal distance. The correction is subtracted. - **Positive** when the tape was standardised in catenary and is used on the flat (fully supported), because the sag effect included in its standard length must be removed. In this case it is added. - No correction is required if the standardisation and the use are under the same conditions, with the same pull and span. Sag can be reduced by applying a higher pull or by shortening the spans. The pull at which the positive pull correction exactly balances the negative sag correction is called the **normal tension**; at this pull the two effects cancel. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does a tape suspended between supports read more than the horizontal distance? A. It stretches B. It hangs in a catenary, so its length along the curve exceeds the horizontal chord C. Temperature rises D. Wind pulls it Answer: B. The curve is longer than the straight horizontal distance between supports. (Key point: Why sag exists) 2. When is sag correction negative? A. Tape standardised on the flat, used suspended B. Tape standardised in catenary, used on the flat C. Same conditions for both D. Never Answer: A. The sagging tape reads more than the horizontal distance, so the correction is subtracted. (Key point: Negative sag) 3. When is sag correction positive? A. Standardised on the flat and used in catenary B. Standardised in catenary and used on the flat C. Pull is high D. Span is short Answer: B. The sag already built into its standard length must be removed, so it is added. (Key point: Positive sag) 4. How can sag be reduced? A. Lower pull B. Higher pull or shorter span C. Longer spans D. Lighter plumb bob Answer: B. Sag varies with w^2 l^2 / P^2, so more pull or smaller span reduces it. 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