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8/8/2019 Horizontal Alignment 2010
1/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
HORIZONTAL ALIGNMENT
Reflection
How we spend our days is, of course, how we spend our
lives.
~ Annie Dillard
Love life and life will love you back. Love people and they
will love you back.
~ Arthur Rubinstein
Objectives
Identify curve types and curve components.
Learn basics of curve design.
Defined the properties of horizontal curve and itsdesign
Explained and discuss the maximum
superelevation, friction, radius and method forattaining superelevation
Horizontal Alignment
General
- necessary to established theproper relation between thedesign speedand curvature and also their joint relation withsuperelevation and side friction
Definition
o Straight segments of roadways (tangents) connected bysuitable curves (horizontal curves).
Establish
o Relationship between design speeds and curvature.
o Joint relationships with superelevation (e) and sidefriction.
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2/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Curve Types
Simple curves
o The simple curve is an arc of a circle.
o The radius of the circle determines the sharpness orflatness of the curve.
Compound curves
o Frequently, the terrain will require the use of thecompound curve.
o This curve normally consists of two simple curvesjoined together and curving in the same direction.
Curve Types
Reverse curveso Consists of two simple curves joined together, but curving
in opposite direction.
o For safety reasons, the use of this curve should beavoided when possible.
Transition/Spiral curveso A curve that has a varying radius.
o Transition or Spiral curves are placed between tangentsand circular curves or between two adjacent circularcurves with substantially different radii.
o Its purpose is to provide a transition from the tangent to asimple curve or between simple curves in a compound
curve.
C
ompoundCurves
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3/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
ReverseCurves
Simple Curves
Properties of Circular Curve Properties of Circular Curve
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4/20
8/8/2019 Horizontal Alignment 2010
5/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Horizontal Curve Fundamental Horizontal Curve Fundamental
Sight Distance on Horizontal Curves SSD on Horizontal Curve
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6/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
SSD on Horizontal Curve
Assume that the length of the horizontal curve
exceeds the required SSD,
where,
Rv - radius to the vehicles traveled path, which is alsoassumed to be the location of the drivers eyes forsight distance, and is taken as the radius to the middleof the innermost lane.
Ds - angle subtended by an arc equal to the SSD length.
vtGfg
vSSD +
=
)(2
2
we have svRSSD D=180
p
v
sR
SSD
p
180=D
L =pDR/180
SSD on Horizontal Curve
Substitute into )2
cos1(D
-= RM , gives
)90
cos1(v
vsR
SSDRM
p-=
-= -
v
svv
R
MRRSSD 1cos
90
p
where Ms = middle ordinate necessary to provideadequate stopping sight distance.
Example
A horizontal curve on a U6 highway is designedwith a 700 m radius, 3.6 m lanes, and a 100km/h
design speed. Determine the distance that must becleared from the inside edge lane to provide
sufficient sight distance for desirable and minimumSSD.
Solution
Because the curve radius is usually taken to the centerlineof the roadway, Rv = R 3.6/2 = 700 1.8 = 698.2m, whichgives the radius to the middle of the inside lane (i.e., thecritical driver location). From Appendix 1, the desirable SSDis 205m, so apply in formula
Therefore, 7.513 m must be cleared from the center of
inside lane or (7.513 1.8) = 5.713 m from the inside edgeof the inside lane. If we use minimum SSD (157 m), wemust clear 2.608m
mR
SSDRM
v
vs 513.7)2.698(
)205(90cos12.698)
90cos1( =
-=-=
pp
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7/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
HORIZONTAL ALIGNMENT
WITH AND WITHOUTTRANSITION/SPIRAL CURVES
25
Transition Curves
Basic propertieso Transition curves are normally used to join straights and
circular curves.o The purpose of transition curves are
A natural path for vehicles moving from a straight to a c ircularcurve.
A convenient means of introducing superelevation and pavementwidening.The approaching driver with improved appearance of the curveahead.
Form of transitiono The usual form of transition is the clothoid (i.e. the
curvature increases directly in proportion to the distancealong the transition.
TransitionCurves
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8/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
TS - start transition, the point at which straight and circularcurve join
SC - start circular curvePC - the point on the circular curve (extended) at which the
radius if extended would be perpendicular to the straightFs - spiral angle in degreesL - length of transition curve from TS to SCLc - length of circular curve from SC to SCA - rate of change of lateral acceleration (m/s3)x - abscissa of any pint B on the transitiony - the ordinate of any point B on the transitionp - the shift, which equals the offset from PC to the straight
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9/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Design of Spirals
Length of spiral curve:
p = tangent-circular curve offset,pmin = 0.2 m,
pmax = 1.0 m, R= radius (m), V= design speed
(km/h), C= maximum rate of change in lateral
acceleration, C= 1.2 m/s3
.
(safety)24
(comfort)0214.0
(comfort)24
maxmax,
3
min,
minmin,
RpL
CR
VL
RpL
s
s
s
=
=
=
Design of Spirals
Design Speed (km/h) Rate of change of lateral acceleration (m/s3)
50 0.60
60 0.60
80 0.45
100 0.45
120 0.30
Table: Typical design values for rate of change of lateral acceleration
Maximum Length of Spirals
Safety problems may occur when spiral curves aretoo long drivers underestimate sharpness of
approaching curve (driver expectancy)
Transition Curves
Use of Transition Curves
Desirably all curves with a design speed of 60 km/h orgreater should be transitioned except:o In hilly or mountainous terrain where there is insufficient
distanceo When R > 1800 m. However, transition curves may be
used up to R = 6000m
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10/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Superelevation
Superelevation
Superelevationrate
Max rate of superelevation usable are controlled by severalfactors such as (a) climatic conditions, (b) terrainconditions, and (c) frequency of very slow moving vehicles
Max superelevation rate of 0.10 is used for rural roads and0.06 for urban roads
Minimum Radius
The minimum radius is a limiting value for a given speedand is determined from the max rate of superelevation andthe max allowable side friction factor
)(127
2
ef
VR
s
v+
=
)('
)(
)(
),(
)(
)(
MetersinpathtraveledsvehiclethetodefinedradiusR
NewtonsinsurfaceroadwaythetonormalactingforcelcentripetaF
NewtonsinsurfaceroadwaythetoparalleiactingforcelcentripetaF
NewtonsinmassxonacceleratilateralforcelcentripetaF
NewtonsinforcefrictionalsideF
parallelweightW
normalweightW
NewtonsinVehicleofweightW
inclineofangle
v
cn
cp
c
f
p
n
=
=
=
=
=
=
=
=
=a
cpfp FFW =+
)( cnnsf FWfF +=
aaaa cos)sincos(sin22
vv
sgR
WV
gR
WVWfW =++
nd)meter/seco(inspeedvehicle
contantnalgravitatio
frictionsideoftcoefficien
=
=
=
v
g
fs
)100
(
2
efg
vR
s
v
+
=)(127
2
ef
VR
s
v+
=TheoreticalConsideration
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11/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Superelevation Example
A roadway is being designed for a speed of 120
km/h. At one horizontal curve, it s known thatthe e value is 8% and the fs is 0.09. Determinethe minimum radius of curve (measured to thetraveled path) that will provide safe vehicleoperation).
Solution
Using the equation (with 1000/3600 converting
km/h to m/s) gives
m670m457.666
)100
809.0(807.9
)3600/1000120(
)100
(
22
==+
=
+=
efg
vR
s
v
m670m975.666
)100
809.0(127
)120(
)100
(127
22
==+
=+
= efVR
s
v
OR
Example
Calculate the minimum radius of a circular curve
having a design speed of 80 km/hr and asuperelevation of 10%. Use a sideways frictionvalue of 0.14.
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12/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Solution
e = 0.1, f= 0.14, V= 80
R= 209.97~ 210 m
R
Vfe
127
2
=+
Maximum Superelevation
Superelevation cannot be too large since an
excessive mass component may push slowlymoving vehicles down the cross slope.
Limiting values emax (JKR: 0.1 rural roads, 0.06urban roads) 12 % for regions with no snow and ice conditions (higher values not
allowed),
10 % recommended value for regions without snow and iceconditions,
8% for rural roads and high speed urban roads,
4, 6% for urban and suburban areas.
Maximum Friction
Maximum side friction factoron wet concretepavements ranges from 0.45 at 100 km/h to 0.5 at30 km/h (vehicle skids).
Drivers feeling of discomfort.
Values much lower than the maximum side frictionfactors are used in design.
fV
R
e= -
2
127 100
Usedfriction
Minimum Radius
RV
ef
minmax
max( )
=
+
2
127100
where:
V= velocity (km/h)
e = superelevation
f= friction
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13/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Radius Calculation
Rmin related to max. fand max. e allowed
Rmin use max e and max f(defined by AASHTO orJKR ) and design speed
fis a function of speed, roadway surface, weathercondition, tire condition, and based on comfortdrivers brake, make sudden lane changes andchanges within a lane when acceleration around acurve becomes uncomfortable
fdecreases as speed increases (less tire
/pavement contact)
Design Speed(km/h)
Minimum Radius (m)
e = 0.06 e = 0.10
120 710 570
100 465 375
80 280 230
60 150 125
50 100 85
40 60 50
30 35 30
Minimum Radius
Max e
Controlled by 4 factors:
o Climate conditions (amount of ice and snow)
o Terrain (flat, rolling, mountainous)
o Frequency of slow moving vehicles who mightbe influenced by high superelevation rates
o Highest in common use = 10%, 12% with no iceand snow on low volume gravel-surfacedroads.8% is logical maximum to minimized
slipping by stopped vehicles
Radii Requiring Super-elevation
All curves, other than those with large radii, shouldbe super elevated.
Table (below) sets out the minimum radii ofhorizontal curves having an adverse cross-fall of 3%that need not be superelevated
Irrespective of design speed, i t is good practice tosuperelevate all curves of less than 4600 m radii.
Design Speed (km/h) Minimum Radius (meter)60 or less 90080 1300
100 2700120 4600
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14/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Method of Attaining Superelevation
3 specific methods of profile design in attainingsuperelevation are:
(a) revolving the pavement about the centreline profile
(b) Revolving the pavement about the inside edge profile
(c) Revolving the pavement about the outside edge profile
The rate of cross slope is proportional to the distance fromstart of the superelevation runoff
Except when the site condition specifically requires,method (a) shall be adopted for undivided roads
Superelevation Runoff and Tangent Runout
Normal cross section
Tangent runout= the length of highway needed to change the normal
cross section to the cross sect ion with the adverse crown removed.
Superelevation runoff= the length of highway needed to change the
cross section with the adverse crown removed to the cross section fully
superelevated.
Fully superelevated crosssection
Cross section with the adversecrown removed
Transition to Superelevation Attainment of Superelevation - General
Must be done gradually over a distance withoutappreciable reduction in speed or safety and
with comfort
Change in pavement slope should be consistent
over a distance
Methods
o Rotate pavement about centerline
o Rotate about inner edge of pavement
o Rotate about outside edge of pavement
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15/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Superelevation Transition Section
Tangent Runout Section + Superelevation Runoff
Section
Tangent Runout Section
Length of roadway needed to accomplish a change
in outside-lane cross slope from normal crossslope rate to zero
Superelevation Runoff Section
Length of roadway needed to accomplish a changein outside-lane cross slope from 0 to full
superelevation or vice versa
For undivided highways with cross-section rotated
about centerline
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
2.5 %
Normal Crown(Crowned
Section)
Normal
Crown
Inside Edge
Of
Pavement
Outside
Edge Of
Pavement
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16/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5%1.5%
Inside Edge
Of
Pavement
Outside
Edge Of
Pavement
Tangent Run
Out
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
1%
Inside Edge
Of
Pavement
Outside
Edge Of
PavementTangent Run
Out
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
0.5%
Inside Edge
Of
Pavement
Outside
Edge Of
PavementTangent Run
Out
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
0.0%
Inside Edge
Of
Pavement
Outside
Edge Of
PavementRunof
f(Adverse
Crown
Removed)
(Adverse
Crown
Removed)
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17/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
-0.5%
Inside Edge
Of
Pavement
Outside
Edge Of
Pavement
Runoff
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
-1%
Inside Edge
Of
Pavement
Outside
Edge Of
PavementRunof
f
-1.5%
Superelevation
Road Plan
View
Road Section
ViewC
L 2.5
%
Inside Edge
Of
Pavement
Outside
Edge Of
PavementRunof
f
Superelevation
Road Plan
View
Road Section
View
2.5%-2.5%C
L
Inside Edge
Of
Pavement
Outside
Edge Of
PavementRunof
f
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18/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
Superelevation
Road Plan
View
Road Section
View
6.23
%
-6.23%C
L
Inside Edge
Of
Pavement
Outside
Edge Of
Pavement
2/3
SuperelevationDeveloped
2/3
Superelevation
Developed
Superelevation
Road Plan
View
Road Section
View
9.35
%
-9.35%C
L
Inside Edge
Of
Pavement
Outside
Edge Of
Pavement
Fully
Superelevated
Fully
Superelevated
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19/20
KNS 3493 Highway Engineering Semester 1, 2010/20
Prepared by Ron Aldrino
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KNS 3493 Highway Engineering Semester 1, 2010/20
THANK YOU.
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