MEASURING AND
CALCULATING SLOPES
Roadway Slopes:
Roadway grade and travel way,
shoulder, and ditch line slopes affect the removal of a road's greatest enemy
water.
Some slope
enables water to flow away from the roadway,
but too much creates erosion.
Table 1 contains the recommended
slopes for roads cross section, shoulders, and ditches for paved and unpaved
roads. Slopes are described by the vertical
rise or fall per unit of horizontal distance.
For example,
the recommended slope for a paved road cross section is a 14 inch rise from shoulder to crown for each foot of
horizontal road width.
This is expressed as "14 inch to 1" or "2
percent." Steeper slopes are usually expressed as a proportion.
For example, A 1:4 slope, pronounced "1
to 4," has a 1 foot rise (or fall)
for every 4 feet of horizontal distance.
The Pop-level:
The most accurate instruments for
measuring slope are theodolites and transits.
A "pop" or hand
level is accurate enough for most maintenance work.
Figure 1 shows the elements of a
typical eye level. The operator holds the
instrument in his/her hand, and steadies it
against a temporary, non-bending pole.
Another person is needed to help
measure vertical and horizontal distance.
A leveling rod works well for
vertical distance.
Determining the Slope:
The slope is the incline or decline between two points.
It is the usual practice to call these points "A"
and "E." The procedure begins with
positioning the eye level (or theodolite or transit) where the operator can
read the level rod at each of the two points. The operator then reads the
elevation of each point on the level rod, and subtracts the values. This is the
difference in elevation between points "A"
and "B." The crew then measures
the horizontal distance between the two points. It is sometimes convenient to
position the instrument at one of the points. In Figure 2,
the instrument is placed over Point A. One
measures the height of the transit or eye level as the elevation of Point A.
The slope is calculated by the
dividing the elevation difference by the horizontal distance. The following
examples illustrate slope calculation.
Note the need to carefully consider the
units of measure.
Cross Section Slope
Elevation of
Shoulder 4 feet-11inches
Elevation of
Crown 4
feet-8 inches
Difference
in Elevation 0
feet-3 inches
Horizontal
Distance 12 feet
Slope
expressed as inches per foot:
3 inches/12 feet =1/4" per foot
Slope
expressed as a percent:
[3 inches/ (12
feet x 12 inches/foot)] xl00%
= [3
inches/144 inches] xl00%=2%
Ditch Front Slope
Elevation of
slope Top feet-11inches
Elevation of
Ditch Bottom 5 feet-5 inches
Difference
in Elevation 1 foot-6 inches
Horizontal
Distance 6 feet
To express
as a proportion, both measure must be
The same
units.
1 foot-6
inches =1.5 feet or 18 inches
6 feet =72
inches
1.5 feet:6
feet = 1:4 or 18 inches:72 inches = 1:4
Comparing these results to Table 1 shows that the cross section would be
adequate if the road was paved, but too low for a gravel road.
The 1:4 ditch slopes is a minimum
slope for either type road. Knowing how to calculate roadway slopes helps
municipal road crews effectively remove water without incurring erosion from
water run-off. Whether using a transit or pop level, crews can determine if
slopes are sufficient to carry water away from the road but not so great that
water will erode road surfaces and road sides.
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