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

Chapter 2 Interpolation & Slope

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 DepressionConcave Slopes Valley Uniform SlopeGap Summit Convex SlopesSaddle  How to Draw a Section

Contours (Booth, Basic Elements of Landscape Architecture) A contour is an imaginary line connecting points of equal elevation

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

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

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

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

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

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

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

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

Interpolation Examples

Sample Interpolation

Contour Interpolation Cross Section Method

Contour Interpolation Cross Section Method

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

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

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

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

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

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

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

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

Interpolation Between Contour Lines  Interpolation: Can also be used to find elevation of points between contour lines distance from point to contour line total distance between contour lines contour interval elevation distance x=

Interpolation Between Contour Lines distance from point to contour line total distance between contour lines contour interval elevation distance x= 4’ 10’ 1’0.4’x=

Interpolation Between Contour Lines distance from point to contour line total distance between contour lines contour interval elevation distance x= 13 m 29 m 0.5 m mx=

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

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

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!

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

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

3 Types of Slope Calculations 1)Given:elevations & distance between two points Find:slope 2)Given:difference in elevation between two points & slope Find:horizontal distance 3)Given:percentage of slope & horizontal distance Find:difference in elevation

Slope Examples

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

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

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