horizontal alignment 2010

8/8/2019 Horizontal Alignment 2010

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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.
http://www.pdfcomplete.com/cms/hppl/tabid/108/Default.aspx?r=q8b3uige22http://www.pdfcomplete.com/cms/hppl/tabid/108/Default.aspx?r=q8b3uige22


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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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ReverseCurves

Simple Curves

Properties of Circular Curve Properties of Circular Curve


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Horizontal Curve Fundamental Horizontal Curve Fundamental

Sight Distance on Horizontal Curves SSD on Horizontal Curve


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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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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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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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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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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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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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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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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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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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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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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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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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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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THANK YOU.

horizontal alignment 2010

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