5_Superelevation & Transition Curves
Transcript of 5_Superelevation & Transition Curves
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Company
LOGO
Chapter 3:
Horizontal Alignment
Superelevation Application
&
Transition Curves
In the actual design of a horizontal curve, the engineer
must select appropriate values of e and fs . The value selected for superelevation, e, is critical
because high rates of superelevation can cause
vehicle steering problems on the horizontal curve, and
in cold climates, ice on the roadway can reduce fssuch that vehicles traveling at less than the design
speed on an excessively superelevated curve could
slide inward off the curve due to gravitational forces.
AASHTO provides general guidelines for the selection ofe and fs for horizontal curve design, as shown in Table3.5.
The values presented in this table are grouped by fivevalues of maximum e. The selection of any one of thesefive maximum e values is dependent on the type of road(for example, higher maximum e's are permitted on
freeways compared with arterials and local roads) andlocal design practice. Limiting values of fs are simply afunction of design speed. Table 3.5 also presentscalculated radii (given V, e, and fs) by applying Eq. 3.34.
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Transition Design Controls
The design of transition sections includes consideration
of transitions in the roadway cross slope and possible
transition curves incorporated in the horizontal
alignment.
The former consideration is referred to as superelevation
transition and
The latter is referred to as alignment transition.
Where both transition components are used, they occur
together over a common section of roadway at the
beginning and end of the mainline circular curves.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Transition Design Controls
The superelevation transition section consists of the
superelevation runoff and tangent runout sections.
The superelevation runoff section consists of the length of
roadway needed to accomplish a change in outside-lane
cross slope from zero (flat) to full superelevation, or vice
versa.
The tangent runout section consists of the length ofroadway needed to accomplish a change in outside-lane
cross slope from the normal cross slope rate to zero
(flat), or vice versa.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Transition Design Controls
These two elements are applicable to superelevation on
both simple circular curves and spiral transition curves,
but the manner of application is somewhat different for
each.
General criteria for application of runoff and terminology
for both types of curves are shown in Figure.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
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Superelevation Transition
from the 2001 CaltransHighway Design Manual
Transition Design Controls For reasons of safety and comfort, the pavement
rotation in the superelevation transition section should
be effected over a length that is sufficient to make such
rotation imperceptible to drivers. To be pleasing in
appearance, the pavement edges should not appear
distorted to the driver.
In the alignment transition section, a spiral or compound
transition curve may be used to introduce the main
circular curve in a natural manner (i.e., one that is
consistent with the drivers steered path).
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Transition Design Controls Such transition curvature consists of one or more curves
aligned and located to provide a gradual change inalignment radius.
As a result, an alignment transition introduces the lateralacceleration associated with the curve in a gentlemanner.
While such a gradual change in path and lateral
acceleration is appealing, there is no definitive evidencethat transition curves are essential to the safe operationof the roadway and,
As a result, they are not used by many agencies.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
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Transition Design Controls
When a transition curve is not used, the roadway
tangent directly adjoins the main circular curve. This
type of transition design is referred to below as thetangent-to-curve transition.
Some agencies employ spiral curves and use their length
to make the appropriate superelevation transition. A
spiral curve approximates the natural turning path of a
vehicle.
One agency believes that the length of spiral should be
based on a 4-s minimum maneuver time at the design
speed of the highway.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Transition Design Controls
Other agencies do not employ spiral curves but
empirically designate proportional lengths of tangent and
circular curve for the same purpose.
In either case, as far as can be determined, the length of
roadway to effect the superelevation runoff should be the
same for the same rate of superelevation and radius of
curvature.
Review of current design practice indicates that the
length of a superelevation runoff section is largely
governed by its appearance.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Transition Design Controls Spiral transition curve lengths as determined otherwise often
are shorter than those determined for general appearance, so
that theoretically derived spiral lengths are replaced with
longer empirically derived runoff lengths.
A number of agencies have established one or more control
runoff lengths within a range of about 30 to 200 m[100 to 650
ft], but there is no universally accepted empirical basis for
determining runoff length, considering all likely traveled way
widths.
In one widely used empirical expression, the runoff length is
determined as a function of the slope of the outside edge of
the traveled way relative to the centerline profile.
TANGENT-TO-CURVE TRANSITION
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Minimum length of superelevation runoff:
For appearance and comfort, the length of superelevation
runoff should be based on a maximum acceptable
difference between the longitudinal grades of the axis ofrotation and the edge of pavement.
The axis of rotation is generally represented by the
alignment centerline for undivided roadways;
However, other pavement reference lines can be used.
These lines and the rationale for their use is discussed
below in the section on Methods of Attaining
Superelevation.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Design Superelevation Tables
forth the basic design criteria based on design speeds for
the normal design superelevation rates of emax = 4 and 6percent as well as othervalues ranging up to 12 percent.
The criteria shown includes the minimum radius of
curvature, crown treatment and superelevation runoff
lengths (L), all of which are related to the number of
lanes to be rotated. The minimum rate of cross slope for
a traveled lane is determinedby drainage requirements.
from the 2005 WSDOTDesign Manual, M 22-01
Design Superelevation Tables
Table 3-21 to 3-25 show, in addition to length of runoff or
transition, values of R and the resulting superelevation for
different design speeds for each of five values of
maximum superelevation rate (i.e., for a full range of
common design conditions).
The minimum radii for each of the five maximum
superelevation rates were calculated from the simplified
curve formula.
from the 2005 WSDOTDesign Manual, M 22-01
Design Superelevation Tables
Under all but extreme weather conditions, vehicles can
travel safely at speeds higher than the design speed on
horizontal curves with the superelevation rates indicated
in the tables.
This is due to the development of a radius/superelevation
relationship that uses friction factors that are generally
considerably less than can be achieved.
This is illustrated in Exhibit 3-11,which compares the
friction factors used in design of various types of highway
facilities and the maximum side friction factors available
on certain wet and dry concrete pavementsfrom the 2005 WSDOTDesign Manual, M 22-01
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The term normal cross slope (NC) designates curves
that are so flat that the elimination of adverse cross
slope is not considered necessary, and thus the normalcross slope sections can be used.
The term remove cross slope (RC) designates curves
where it is adequate to eliminate the adverse cross slope
by superelevating the entire roadway at the normal
cross slope.
from the 2005 WSDOTDesign Manual, M 22-01
Design Superelevation Tables
Table 3-21.Values forDesign
ElementsRelated to
DesignSpeed andHorizontalCurvature
Table 3-21.Values for
DesignElementsRelated to
DesignSpeed andHorizontalCurvature
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Location with respect to end of curve
In the tangent-to-curve design, the location of the
superelevation runoff length with respect to the point ofcurvature (PC) must be determined.
Normal practice is to divide the runoff length between
the tangent and curved sections and to avoid placing the
entire runoff length on either the tangent or the curve.
With full superelevationattained at the PC, the runoff
lies entirely on the approach tangent, where theoretically
no superelevation is needed.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Location with respect to end of curve
At the other extreme, placement of the runoff entirely on
the circular curve results in the initial portion of the
curve having less than the desired amount of
superelevation.
Both of these extremes tend to be associated with a
large peak lateral acceleration.
Experience indicates that locating a portion of the runoff
on the tangent, in advance of the PC, is preferable, since
this tends to minimize the peak lateral acceleration and
the resulting side friction demand.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Location with respect to end of curve
Observations indicate that a spiral path results from a
drivers natural steering behavior during curve entry or exit.
This natural spiral usually begins on the tangent and ends
beyond the beginning of the circular curve.
Based on the preceding discussion, locating a portion of the
runoff on the tangent is consistent with the natural spiral pathadopted by the driver during curve entry.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Location with respect to end of curve
AASHTO does allow agencies to adopt a single value for
all design speeds and rotated widths. For simplicity,
DelDOT has adopted a runoff proportion of two-thirds in
the tangent section and one-third into the curve.
In the case of simple curves, the superelevation runoff
distance is applied with one-third on the curve itself and
two-thirds (or preferably as per Figure 5-7) on thetangent adjacent to the curve.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
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Location with respect to end of curve
Thus, full superelevation is not reached until slightly past
the P.C. and starts to reduce shortly before reaching the
P.T.
Where spiral transition curves are used, the
superelevation runoff is always coincident with the spiral
length (T.S. to S.C. or C.S to S.T.) and the designated full
superelevation is provided between the S.C. and the C.S.
The geometrics for spiral curves provide for a natural
introduction of superelevation without the compromise
necessary for circular curves.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Simple Curve
Spiral TransitionCurve
Methods of Attaining Superelevation
There are three basic methods are used to transition the
pavement to a superelevated cross section. These methods
include:
(1) revolving a traveled way with normal cross slopes
about the centerline profile,
(2) revolving a traveled way with normal cross slopes
about the inside-edge profile,
(3) revolving a traveled way with normal cross slopes
about the outside-edge profile
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Methods of Attaining Superelevation
The following figures illustrates these three methods.
The methods of changing cross slope are most
conveniently shown in the exhibit in terms of straight
line relationships,
but it is emphasized that the angular breaks between the
straight-line profiles are to be rounded in the finished
design, as shown in the figure.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
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Methods of Attaining Superelevation
In fist figure, the profile reference line corresponds to
the centerline profile. In figures second and third, the profile reference line is
represented as a theoretical centerline profile as it
does not coincide with the axis of rotation.
The cross sections at the bottom of each diagram in
Figures indicate the traveled way cross slope condition at
the lettered points.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Methods of Attaining Superelevation
The first method, as shown in following figure, revolves
the traveled way about the centerline profile. This method is the most widely used because the change
in elevation of the edge of the traveled way is made with
less distortion than with the other methods.
In this regard, one-half of the change in elevation is
made at each edge.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Methods of Attaining Superelevation Methods of Attaining Superelevation
The second method, as shown in Fig 3-37B, revolves the
traveled way about the inside-edge profile.
In this case, the inside-edge profile is determined as a
line parallel to the profile reference line. One-half of the
change in elevation is made by raising the actual
centerline profile with respect to the inside-edge profile
and the other half by raising the outside-edge profile anequal amount with respect to the actual centerline
profile.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
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from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Methods of Attaining Superelevation Methods of Attaining Superelevation
The third method, as shown in Fig. 3-37C, revolves the
traveled way about the outside-edge profile. Thismethod is similar to that shown in Exhibit 3-37B except
that the elevation change is accomplished below the
outside-edge profile instead of above the inside-edge
profile.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Methods of Attaining Superelevation
TRANSITION CURVES
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A properly designed transition curve provides a natural,
easy-to-follow path for drivers, such that the lateralforce increases and decreases gradually as a vehicle
enters and leaves a circular curve.
Transition curves minimize encroachment on adjoining
traffic lanes and tend to promote uniformity in speed.
A spiral transition curve simulates the natural turning
path of a vehicle.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
The principal advantages of transition curves
The transition curve length provides a suitable location
for the superelevation runoff. The transition from the normal pavement cross slope on
the tangent to the fully superelevated section on the
curve can be accomplished along the length of the
transition curve in a manner that closely fits the speed-
radius relationship for vehicles traversing the transition.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
The principal advantages of transition curves
The principal advantages of transition curves
Where superelevation runoff is introduced without a
transition curve, usually partly on the curve and partly
on the tangent, the driver approaching the curve may
have to steer opposite to the direction of the
approaching curve when on the superelevated tangent
portion in order to keep the vehicle within its lane.
A spiral transition curve also facilitates the transition inwidth where the traveled way is widened on a circular
curve. Use of spiral transitions provides flexibility in
accomplishing the widening of sharp curves.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
The principal advantages of transition curves
The appearance of the highway or street is enhanced by
the application of spiral transition curves.
The use of spiral transitions avoids noticeable breaks in
the alignment as perceived by drivers at the beginning
and end of circular curves.
Figure 3-32 illustrates such breaks, which are made
more prominent by the presence of superelevation
runoff.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
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Figure 3-32
illustrates such
breaks, which are
made moreprominent by the
presence of
superelevation
runoff.
from AASHTOsA Policy on Geometric Design of Highways and Streets 2001
Terminology
Types of Transition Curves
Clothoid the one
that we will examine
in more detail, most
commonly used
Lemniscate used
for large deflection
angles on high
speed roads
Cubic Parabola
unsuitable for large
deflection angles
Curvature of Transition Curve
Generally, the Euler spiral, which is also known as the
clothoid, is used in the design of spiral transition curves.
The radius varies from infinity at the tangent end of the
spiral to the radius of the circular arc at the end that
adjoins that circular arc.
By definition, the radius of curvature at any point on anEuler spiral varies inversely with the distance measured
along the spiral.
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Curvature of Transition Curve
The beginning of thetransitioncurve istangential to the alignment,
end of the transition curveis also tangential to thehorizontal curve.
At begining of thetransition curve radiusof curvature, RT=
(infinite)At end of the transitioncurve radius ofcurvature, RT=R (radius ofhorizontal curve)
Curvature of Transition Curve
The curvature of the transition curve at any point (Lx) from thestart point of the transition curve (TS );
=
=
At the end of the transition curve(SC), the curvature, k = 1 / R ;kx can be expressed as:
=
Term of (Lp.R) is constant, so this is an indication of increasedcurvature in linear
Transition Length (Lp)
In the case of a spiral transition that connects two circular
curves having different radii, there is an initial radius
rather than an infinite value.
The following equation, developed for gradual attainment
of lateral acceleration on railroad track curves, is the basic
expression used by some highway agencies for computing
minimum length of a spiral transition curve:
Transition Length (Lp)
The length of plan transition (Lp) is determined by
the rate of change of radial acceleration, and
rate of change of rotation of pavement
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Transition Length (Lp)-Radial Acceleration Method
At begining of the transition curve a=0
At end of the transition curve a=
Time of radial accelaration change t=
The radial accelaration changeover time:
=
=
Transition Length (Lp)
=
Radial acceleration will vary with design speed and design
authority.
Typical values for a lie between (0.3 -0.6 m/sec3) for V from 40-
140 km/h respectively
Lp = length of plan transition
V = design speed (km/h)
R = radius of circula r curve
a = radial acceleration
Transition Length (Lp)
If Vkm/h =
.
Lp = length of plan transition
Vp = design speed (km/hr)
R = radius of circular curve a = radial acceleration
R : Length of throw or thedistance from tangent that the
circular curve has been offset(m),
S : Chord of Clothoid (m),
: Deflection angle from TS to
SC (degree),
Geometry of Clothoid
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L : Length of clothoid (m),
X : Distance along tangent fromTS to point at right angle to SC
Y : Offset distance (right angledistance) from tangent to SC(m),
: Spiral angle from tangent toSC (raydan),
Xm, Ym : Coordinates ofhorizontal curve
Tu : Long tangent of clothoid(m),
Tk : Short tangent of clothoid
(m),
Geometry of Clothoid
=
L = Length of Plan Transition
R = radius of circular curve
A = constant of clothoid(clothoid parameter)
Geometry of Clothoid
Spiral angle from tangent to SC
(raydan) ;
=
2Distance along tangent from TS to
point at right angle to SC ;
X =
40
=
40
Offset distance (right angle
distance) from tangent to SC ;
Y =
6=
6
Geometry of Clothoid
Coordinates of horizontal curve ;
=
= +
Long tangent length of clothoid;
= Short tangent length of clothoid ;
=
Length of throw or the distance from
tangent that the circular curve has been
offset ;
= = 1
Geometry of Clothoid
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Chord of Clothoid ;
= +
Deflection angle from TS to SC (degree);
= tan
Geometry of Clothoid
R : Radius of simple curve
T : Spiral tangent distance (m),
: Angle of intersection
C : Angle of intersection of thesimple curve (degree),
Dc : Degree of simple curve.
Geometry of Clothoid
Angle of intersection of the simple
curve ;
= 2Spiral angle from tangent to SC
(raydan);
=
2Degree of simple curve ;
=2
360Spiral tangent distance ;
= + + tan
Geometry of Clothoid
In the selection of clothoid parameter, Themaximum value of radial accelaration change overtime (sademe) is taken into account in terms ofcomfort.
Clothoid parameter A that provides following
conditions are determined according to a maximumvalue of a
Then clothoid length are calculated using theparameter.
Selection of Clothoid Parameter
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Optical Requirement:
Dinamic Requirement: = 0.17
Superelevation Requirement: =
.
Selection of Clothoid Parameter
b: platform width
d : full superelevation,
q : normal crown
R: raius of the circular curve,
After determining clothoid parameter, calculate length ofclothoid by following equation ;
=
Clothoid Length should be consistent the length ofsuperelevation runoff ;
, 45
In order to application of the clothoid, the horizontal curvemust be a certain length ;
2
2
Selection of Clothoid Parameter