1. The symbol A (Delta), or the symbol I,
represents the intersecting angle, which is the
deflection angle made by the tangents where they
2. D is the degree of curvature, or degree of
curve. It is the angle subtended by a 100-foot arc or
chord (to be discussed in chapter 11 of this TRAMAN).
3. R is the radius of the curve, or arc. The radius
is always perpendicular to the curve tangents at the
point of curvature (PC) and the point of tangency
4. T is the tangent distance, which is measured
from the PI to the PC and the PT. The PC is the beginning
of the curve, and the PT is the end of the curve.
5. L is the length of the curve measured in feet
along the curve from the PC to the PT.
A horizontal curve is generally selected to fit the
terrain. Therefore, some of the curve data will be known.
The following formulas show definite relationships
between elements and allow the unknown quantities to
1. To find the radius (R), or degree of curvature
(D), use the following formula:
2. To find the tangent distance (T), compute as
3. To find the length of curve (L), use the following
f o r m u l a :
The PC and PT are designated on the plan by a
partial radius drawn at each point and a small circle on
the center line. The station numbers of PC and PT are
noted as shown in figure 3-3. The length of the curve
(L) is added to the PC station to obtain the station of the
PT. The curve data is noted on the inside of the curve it
pertains to and is usually between the partial radii.
Since most horizontal curves have superelevation
(that is, the outside edge of the traveled way is higher
than the inside edge), there must be a transition distance
in which the shape of the road surface changes from a
normal crown to a superelevated curve. The transition
length is generally 150 feet and starts 75 feet before the
PC is reached. The same is true in leaving curves. The
transition begins 75 feet before the PT and ends 75 feet
beyond. The beginning and end of the superelevation
are noted on the plan.
A control point maybe a PT, PC, PI, or a point on
tangent (POT). Since these control points may be
destroyed during construction, you must reference them
to other points. In the field, a common practice that you
should use is to drive iron pins or other reference stakes
at right angles to the control point on each side of the
center line, and then measure and record the distance
from the pins to the control point. If room allows, these
reference points should be drawn on the road plan
opposite the control points, as shown in figure 3-3. If
not, you should show the control points and references
on a separate sheet, called a reference sheet.
The procedure used to plot road profiles is discussed
in chapter 7 of the EA3 TRAMAN. From your study of
that TRAMAN, you know that a profile is the
representation of something in outline. When applied to
roads, this means that a profile is a longitudinal-section
view of the earth along the centerline, and it is always
viewed perpendicular to the centerline.
As you know, profile-leveling procedures are used
to determine the ground elevations at each of the station
points along the center line. These elevations are
recorded in the surveyors notebook, which is used by
the draftsman to prepare the profile drawing. Generally,
the profile is drawn on the bottom portion of
plan-and-profile paper, directly below the road plan. An
example of a road profile is shown in figure 3-4.
A road grade line is also drawn on the lower portion
of the plan-and-profile paper and is represented by a
heavy solid line, as shown in figure 3-4. Like the profile,
the grade line is a longitudinal section taken along the
center line and shows the elevations to which the road
is built. The grade line is normally the center-line
elevations of the finished surface but may be the
center-line elevations of the subgrade. If the subgrade
was used, make a special note of it.
The grade lines are a series of straight lines that are
connected, where necessary, by curves (called vertical