CE 276 Site Design

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)