--- title: "Contour interpolation, method for large work" subject: "Surveying II" chapter: 4 key: "semester_4/surveying_ii:contour-interpolation-methods-large-work" source: https://www.bctengineer.com/q/semester_4/surveying_ii/contour-interpolation-methods-large-work site: BCT Engineering --- # Contour interpolation, method for large work Surveying II · Chapter 4: Contouring - Asked in: 2070 Magh, 6 marks - Video: [Locating Contour Lines by Interpolation](https://www.youtube.com/watch?v=G-esV7tB_5s) — Fech - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/contour-interpolation-methods-large-work - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-4 ## Question What is mean by contour interpolation? Which method do you suggest for contour interpolation in large volume of work and how would you applied it? ## Short answer Contour interpolation locates contour positions between plotted spot heights assuming uniform slope. For large work, the tracing paper method is recommended: equidistant parallel lines on transparency numbered with contour values, placed to align end RLs, and crossing points pricked. Then equal-value points are joined; every fifth thickened as index. ## Answer **Contour interpolation** is the process of locating the positions of contours of required values between two plotted points of known RL. It assumes the ground slope is uniform between the two points. **Methods of interpolation** 1. **Estimation:** The positions of contours are estimated by eye between the two points. It is quick but rough. 2. **Arithmetical calculation:** The distance from the lower point to the contour is found by proportion: $$ x = \frac{h_c - h_1}{h_2 - h_1}\times d $$ where $h_1, h_2$ are the RLs of the two points ($h_2 > h_1$), $h_c$ is the contour value and $d$ is the plotted distance between the points. It is accurate but slow. 3. **Graphical methods** - *Tracing paper (transparent sheet) method:* Parallel equidistant lines are drawn on tracing paper and numbered with the contour values. The paper is turned and moved until the lines for the two end RLs pass through the two points. The crossing of line AB with the lines of the paper marks the contours. It is quick and common. - *Perpendiculars (similar triangles) method:* At A and B, perpendiculars to AB are drawn with lengths proportional to their heights above a convenient datum (to a scale of levels), and their ends A' and B' are joined. Lines parallel to AB are drawn at the contour levels; where they cut A'B', perpendiculars dropped back to AB give the contour points. The tracing paper method is quick, simple and accurate enough, so it is recommended for a large volume of work. **Application of the tracing paper method for a large area** 1. Plot all spot levels on the sheet, with their RLs written beside each point. 2. For CI = 1 m (say), draw equally spaced parallel lines on tracing paper (or use a ruled transparent sheet) and number them with consecutive levels (50, 51, 52, ... 60). 3. To interpolate between A (RL 52.4) and B (RL 57.8), place the paper so that the line for 52.4 passes through A (estimate between lines 52 and 53) and the line 57.8 passes through B. 4. Prick the points where AB crosses the lines 53, 54, 55, 56, 57 on the sheet. 5. Repeat for all pairs of neighbouring points, then join the equal values by smooth curves and thicken every fifth contour. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does contour interpolation do? A. Locates contours of required values between two plotted points of known RL B. Measures the RL of each point directly with a level C. Joins contours of different values into one line D. Fixes the contour interval for the map Answer: A. Interpolation finds where contours of given values fall between plotted points of known RL, assuming uniform slope between them. (Key point: Meaning of interpolation) 2. What is the basic assumption in contour interpolation? A. The ground is level between the points B. The ground slope is uniform between the two points C. The ground slope changes at the midpoint D. The two points are at the same RL Answer: B. Positions are found by proportion, which is valid only if the slope between the two points is uniform. (Key point: Uniform slope assumption) 3. In the arithmetical method, x = (hc - h1)/(h2 - h1) x d gives: A. The contour interval B. The distance from the higher point to the contour C. The distance from the lower point to the contour of value hc D. The slope of the ground Answer: C. h1 is the lower RL, so x is the distance from the lower point to the contour hc, found by proportion of the level difference. (Key point: Arithmetical formula) 4. Which method is recommended for a large volume of interpolation work, and why? A. Estimation, because it is the fastest B. Arithmetical calculation, because it is the most accurate C. Tracing paper method, because it is quick, simple and accurate enough D. Similar triangles method, because it needs no drawing Answer: C. The tracing paper method balances speed and accuracy, so it suits large areas; calculation is accurate but slow, and estimation is rough. 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