4.2 Horizontal Alignments - An-Najah National Universitymoodle.najah.edu/pluginfile.php/235882/mod_resource/content/0... · 4.2 Horizontal Alignments TRANSPORTATIONSYSTEMENGINEERING1,61360

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4.2 Horizontal Alignments

TRANSPORTATION SYSTEM ENGINEERING 1 , 61360

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• Horizontal alignment consists of straight sectionsof the road, known as tangents, connected byhorizontal curves.

• The design of the horizontal alignment containsthe determination of:– Minimum radius– Length of the curve,

– Horizontal offsets from thetangents to the curve tofacilitate Locating the curvein the field

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• Types of Horizontal curves:1. Simple2. Compound3. Reversed4. Spiral (transition)


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• The curves are usually segments of circles• The minimum radius of a horizontal curve depends

on:– Design speed– Superelevation (e),– Coefficient of side fictions (fs)

• The minimum radius corresponds to the maximumrecommended superelevation rate which depend on:– Location of the highway– Weather conditions (e.g., the occurrence of snow),– Distribution of slow-moving vehicles.


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• Assuming that the SSD is unobstructed, then thedesign of the curve is as follows.

Point ofCurvature

Point ofTangency

Point of Intersection

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• A simple circular curve is described either by its– Radius– Degree of the curve: the angle subtended at the center by

a circular arc of 30m (100 ft) (Highway Engineering)

• There are two ways to define degree of the curveD, based on– 30m (100 ft) of arc length

(Highway Practice)– 30m (100 ft) chord length

(Railroad Practice)

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• If θ is the angle in radians subtended at the center by anarc of a circle, the length of that arc is given by:

Da Dc

RL

USCustomary

SI

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• Formulas for Simple Curves


Intersection angle

MC

L

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• Field Location of a Simple Horizontal Curve.– Simple horizontal curves are

usually set out in the fieldby staking out points on thecurve using:

– Deflection anglesmeasured from thetangent at the point ofcurve (PC)

– Lengths of the chordsjoining consecutive wholestations.


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• Field Location of a Simple Horizontal Curve.


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• Previously we assumed that there are noconstraints on the design of horizontal curves– At a horizontal curve if an object is located near the inside edge

of the road, this may interface with the view of the driver, whichwill result in a reduction of the driver's sight distance ahead.

• It is necessary to design the curve so that the availablesight distance is at least equal to the safe SSD.


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An object at B

Line of Sight isthe chord AT

Horizontal distancetraveled by thevehicle is the arc AT

R R


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m is called HSOHorizontal Sightline Offset


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• Compound curves consist of two or more curvesin succession, turning in the same direction, withany two successive curves having a commontangent point.

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• These curves are used mainly in obtainingdesirable shapes of the horizontal alignment,particularly at:– at-grade intersections, ramps of interchanges, and– highway sections in difficult topographic areas.

• To avoid abrupt changes in the alignment, theradii of any two simple curves that form acompound curve should not be widely different.– AASHTO recommends that the ratio of the flatter radius to the

sharper radius at intersections should not be greater than 2:1.

• To provide smooth transition from a flat curve to a sharpcurve, the length of each curve should not be too short.


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• Reverse curves usually consist of two simple curves with:– equal radii– turning in opposite directions– with a common tangent.

• They are generally used to changethe alignment of a highway.

• Reverse curves are seldomrecommended because‒ sudden changes to the alignment

make it difficult for drivers to keepin their lanes.

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• Transition curves are placed between tangents andcircular curves or between two adjacent circular curveshaving substantially different radii, in order to avoid asudden change from a tangent with infinite radius to acurve of finite radius, or between curves of different radii.

• If the transition curve isa spiral, the degree ofcurve between thetangent and the circularcurve varies from 0 attangent end to thedegree of the circularcurve Da at curve end.

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• The minimum length of a spiral transition curve shouldbe the larger of the these two values:

indicates the level of comfortand safety involved.

SI

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• The minimum length of a spiral transition curve shouldbe the larger of the these two values:

indicates the level of comfortand safety involved.


USCustomary

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• In practice, many highway agencies do not use transitioncurves, since drivers will usually guide their vehicles intocircular curves gradually.

• A practical alternative for determining the minimumlength of a spiral is to use the length required forsuperelevation runoff.

Important


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• The tangent is joined directly with the main circular curvecalled “tangent-to-curve transition”.

• If the curve is superelevated at a rate of e, an appropriatetransition length must be provided.

• This superelevation transition length is composed of:– superelevation runoff– tangent runout


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• Superelevation runoff : is defined as the distance overwhich the pavement cross slope on the outside lanechanges from zero (flat) to full superelevation of thecurve (e)

• For highways where :– rotation is about any pavement reference line– the rotated width has a common superelevation,

• The superelevation can be calculated by:


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• Minimum recommended superelevation runoff length:

Two-laneMultilane

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• Theoretically, superelevation runoff should be placedentirely on the tangent section thus providing fullsuperelevation between the PC and PT.

• In practice, sharing the runoff between tangent andcurve:– Reduces peak lateral acceleration and its effect on side friction.– Motorists tend to adjust their driving path by steering a

“natural spiral” thus supporting the observation that some ofthe runoff length should be on the curve.


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• Tangent runout : consists of the length of roadwayneeded to accomplish a change on the outside-lane crossslope from normal (i.e., 2 percent) to zero, or vice versa

• The minimum length of tangent runout:

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• AASHTO recommends that when spiral curves are used intransition design,– Superelevation runoff should be achieved over the length of the

spiral curve.

Length of spiral curve = Length of superelevation runoff


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• The change from a crowned cross section to asuperelevated one be achieved without causing anydiscomfort to motorists or creating unsafe conditions.

• There are four methods:1. Crowned pavement is rotated about the centerline.2. Crowned pavement is rotated about the inside edge.3. Crowned pavement is rotated about the outside

edge.4. A straight cross-slope pavement is rotated about the

outside edge.

* Refer to the Multimedia CD of the courseTRANSPORTATION SYSTEM ENGINEERING 1 , 61360

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Crowned pavement is rotated about the centerline

* Refer to the Multimedia CD of the courseTRANSPORTATION SYSTEM ENGINEERING 1 , 61360

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• Superelevation on divided highways can be achievedthrough one of the following methods :– Method 1 involves superelevating the whole cross section,

including the median, as a plane section.• Rotation is done about the centerline of the median.• Only for narrow medians and moderate superelevation rates

– Method 2 involves rotating each pavement separately aroundthe median edges, while keeping the median in a horizontalplane.

• When median width is 30 ft or less,

– Method 3 treats the two pavements separately, resulting invariable elevation differences between the median edges

• When median width is 40 ft or greater.


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4.2 Horizontal Alignments - An-Najah National Universitymoodle.najah.edu/pluginfile.php/235882/mod_resource/content/0... · 4.2 Horizontal Alignments TRANSPORTATIONSYSTEMENGINEERING1,61360