--- title: "Contour terms and interpolation methods" subject: "Surveying II" chapter: 4 key: "semester_4/surveying_ii:contour-terms-interpolation-methods" source: https://www.bctengineer.com/q/semester_4/surveying_ii/contour-terms-interpolation-methods site: BCT Engineering --- # Contour terms and interpolation methods Surveying II · Chapter 4: Contouring - Asked in: 2077 Chaitra, 3+4 marks; 2073 Bhadra, 8 marks (asked 2 times) - Video: [CONTOURING PART-2 |METHODS OF LOCATING CONTOURS |INTERPOLATION METHODS FOR PLOTTING THE CONTOURS||](https://www.youtube.com/watch?v=lMCVxKcUypU) — CIVIL SHOTS - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/contour-terms-interpolation-methods - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-4 ## Question Define terms contour interval, horizontal equivalent and index contour. Explain methods of contour interpolation. ## Short answer Contour interval is the constant vertical distance between successive contours; horizontal equivalent is the horizontal distance between consecutive contours, varying with slope; index contour is every fifth contour, thicker and labeled. Interpolation locates intermediate contours between known points by estimation, proportional calculation x = d*(h_c - h1)/(h2 - h1), or graphical methods like tracing paper with parallel lines. ## Answer #### Definitions - **Contour interval (CI)** is the constant vertical distance between two consecutive contours, for example 1 m or 5 m. It is the same over one map. - **Horizontal equivalent (HE)** is the horizontal distance between two consecutive contours. It varies with the slope of the ground: small on steep ground and large on gentle ground. $HE = \dfrac{CI}{\tan\alpha}$, where $\alpha$ is the ground slope angle. - **Index contour** is every fifth contour (for example every 5th line when CI = 2 m, giving 10 m, 20 m, 30 m ...) drawn as a thicker line and labelled with its RL, so that the map can be read quickly. The other contours are called **intermediate (minor) contours**. #### Methods of contour interpolation **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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the horizontal equivalent (HE), and how does it vary? A. The vertical distance between contours; constant B. The horizontal distance between consecutive contours; small on steep ground, large on gentle ground C. The distance between index contours; constant D. The map scale ratio Answer: B. HE = CI / tan(alpha), so it decreases as the slope angle increases. (Key point: Horizontal equivalent) 2. What does contour interpolation assume between two plotted points? A. The ground slope is uniform B. The ground is level C. The slope is steepest at the middle D. The two points are at the same RL Answer: A. Contour positions are located by proportion, assuming a uniform slope between the two points. (Key point: Interpolation assumption) 3. With RLs h1 < h2 and plotted distance d, the distance from the lower point to a contour h_c is? A. (h_c - h1)/(h2 - h1) × d B. (h2 - h_c)/(h2 - h1) × d C. (h_c + h1)/(h2 + h1) × d D. d × (h2 - h1)/h_c Answer: A. By proportion, the fraction of the height difference from h1 to h_c gives the same fraction of distance d. (Key point: Arithmetical formula) 4. Which interpolation method is recommended for large volumes of work? A. Estimation by eye B. Arithmetical calculation C. Tracing paper method D. Direct measurement on the ground Answer: C. The tracing paper method is quick, simple and accurate enough for large volumes. (Key point: Preferred method) ## Related in Surveying II - [Contour interval, index contour, why never cross](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acontour-interval-index-plotting-never-cross) — Surveying II, chapter 4 - [Contour interval, index contour, contouring methods](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acontour-interval-direct-indirect-methods) — Surveying II, chapter 4 - [Contour gradient, index contour, interval factors](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acontour-gradient-index-interval-factors) — Surveying II, chapter 4 - [Contour interval, index contour, plotting, uses](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acontour-interval-index-plotting-procedure-uses) — Surveying II, chapter 4 - [Contour interpolation, method for large work](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acontour-interpolation-methods-large-work) — Surveying II, chapter 4 - [Contour interpolation and uses of contour maps](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Acontour-interpolation-uses) — Surveying II, chapter 4