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Understanding Interpolation and Slope in Contour Mapping

This chapter delves into the principles of interpolation and slope in topographic mapping, with emphasis on visualizing contours and understanding contour characteristics. Key concepts include plotting contours using grid patterns, computing elevations, and calculating slope as the ratio of vertical change to horizontal distance. This guide covers essential techniques for drawing contour lines, interpolating values between known elevations, and recognizing the importance of slope in landscape architecture. Mastering these skills enables efficient and precise mapping of landforms.

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Understanding Interpolation and Slope in Contour Mapping

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  1. CE 276Site Design Wes Marshall, P.E. University of ConnecticutJanuary 2007 Chapter 2 – Interpolation & Slope

  2. Chapter 2Interpolation & Slope

  3. What did we talk about last class? • Visualizing Contours • Contour Characteristics • continuous and closed • never cross & never divide or split • steepest slope is perpendicular to contour line • Types of Landform Ridge Depression Concave Slopes Valley Uniform Slope Gap Summit Convex Slopes Saddle • How to Draw a Section

  4. Contours A contour is an imaginary lineconnecting points of equal elevation (Booth, Basic Elements of Landscape Architecture)

  5. Continuous & Closed • Contours are continuous lines creating closed figures • Contour lines never cross except in rare circumstances

  6. Slope • The steepest slope is perpendicular to the contour line • This is because it has the greatest vertical change in the shortest horizontal distance • Thus, water flows perpendicular to contour lines

  7. Interpolation & Slope • Last section was about… Visualizing Contours • This section is about the basic mathematical equations of contours • Enables us to plot & manipulate contours

  8. Plotting of Contours • Topographic data typically collected with a grid pattern • The size of the grid depends upon: • The variation in slope • The extent of the area • Purpose of the survey

  9. Plotting of Contours • For more complex sites: • Apply the same basic principles with a grid geometry applicable to the site • High or low points may need to be located between grid points

  10. Plotting of Contours • After finding all the necessary elevations (i.e. at each grid point)… • Plot them on a scaled plan • Interpolate whole number elevations • Begin drawing the contour lines

  11. Interpolation • What is interpolation? • Interpolation is the process of computing intermediate values between two related & known values • With contours, interpolation is done to whole number elevations

  12. Interpolation d/D = e/E d = horizontal distance from one grid intersection to an intermediate point D = total horizontal distance between grid intersections e = elevation change between initial grid elevation and intermediate point E = total elevation change between grid intersections

  13. Interpolation Examples

  14. Sample Interpolation

  15. Sample Interpolation

  16. Contour Interpolation Cross Section Method

  17. Contour Interpolation Cross Section Method

  18. Contour Interpolation • To begin, draw a series of evenly spaced lines above the line of elevations to be interpolated.

  19. Contour Interpolation • Label these corresponding to the range of spot elevations provided in the problem.

  20. Contour Interpolation • Next, extrapolate those spot elevations to their proper elevation on your lines.

  21. Contour Interpolation • Now, connect these spot elevations with straight lines, representing the slope between the spot elevations.

  22. Contour Interpolation • Where these slope lines intersect the elevation lines will be where the contours hit the line of interpolation on the grid below.

  23. Contour Interpolation • Plot these intersection points on the line of interpolation.

  24. Contour Interpolation • Then repeat this process for all rows and columns in your interpolation grid.

  25. Contour Interpolation • Once completed, solving the interpolation should be a matter of connecting the dots.

  26. Interpolation Between Contour Lines • Interpolation: • Can also be used to find elevation of points between contour lines contourinterval elevationdistance distance from point to contour line x = total distance between contour lines

  27. Interpolation Between Contour Lines contourinterval elevationdistance distance from point to contour line x = total distance between contour lines 4’ x 1’ = 0.4’ 10’

  28. Interpolation Between Contour Lines contourinterval elevationdistance distance from point to contour line x = total distance between contour lines 13 m x 0.5 m = 0.2241 m 29 m

  29. Interpolation • Keep in mind that interpolation is only accurate when we have a constant slope • This is true for interpolation between contours and between spot elevations

  30. Slope • Slope refers to: • Any ground whose surface makes an angle with the horizontal plan • The vertical change in elevation, fall or rise (in feet or meters), in a horizontal distance • Can also be called grade or gradient

  31. Calculating Slope • Slope is the rise or fall in 100 units of horizontal distance • It can be expressed as a percentage or a decimal • 8% slope = 0.08 slope The units must be consistent!

  32. Calculating Slope S = DE/L = Rise / Run S = Slope (or gradient) DE = Difference in elevation between the end points of a line L = Horizontal distance Rise Run

  33. Calculating Slope • Be Careful with calculating Run, L • A common mistake is to measure the length parallel to surface • L represents the true horizontal distance

  34. 3 Types of Slope Calculations • Given: elevations & distance between two pointsFind: slope • Given: difference in elevation between two points & slopeFind: horizontal distance • Given: percentage of slope & horizontal distanceFind: difference in elevation

  35. Slope Examples

  36. Other Ways to Express Slope • Slope is often described as a ratio such as 2:1 • This equates to 2 units of horizontal distance for every 1 units of vertical elevation • Slope can also be shown in degrees, minutes, and seconds

  37. Slope as a Ratio (Booth, Basic Elements of Landscape Architecture)

  38. Slope as a Percentage (Booth, Basic Elements of Landscape Architecture)

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