Transcript Analysis of Parking & Street Connectivity in Terms of Town

CE 276
Site Design
Chapter 2 – Interpolation & Slope
Wes Marshall, P.E.
University of Connecticut
January 2007
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
Valley
Summit
Depression
Uniform Slope
Convex Slopes
 How to Draw a Section
Concave Slopes
Gap
Saddle
Contours
A contour is an imaginary line
connecting points of equal elevation
(Booth, Basic Elements of Landscape Architecture)
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
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 x contour = elevation
distance
total distance between contour lines interval
Interpolation Between
Contour Lines
distance from point to contour line x contour = elevation
distance
total distance between contour lines interval
4’ x 1’ = 0.4’
10’
Interpolation Between
Contour Lines
distance from point to contour line x contour = elevation
distance
total distance between contour lines interval
13 m x 0.5 m = 0.2241 m
29 m
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
Rise
S = Slope (or gradient)
DE = Difference in elevation between the end
points of a line
L = Horizontal distance
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)