RTA Road Design Guide

ROADS AND TRAFFIC AUTHORITY OF NSW

ROAD DESIGN GUIDE

TABLE OF CONTENTS GLOSSARY OF TERMS December 1989 SECTION 1: BASIC DESIGN CRITERIA August 1991 Amended August 1996 SECTION 2: ROAD GEOMETRY March 1988 SECTION 3: CROSS SECTION Issue 1.0 June 1999 Revision 1.1 Feb 2000 SECTION 4: INTERSECTIONS AT GRADE Issue 1.0 May 1999 Revision 1.1 Jan 2000 SECTION 5: DRAFT DESIGN OF EARTH STRUCTURES February 1989 WITHDRAWN - September 2003 - (If information required on this SECTION – Contact sender) SECTION 6: SAFETY BARRIERS FOR ROADS AND BRIDGES May 1996 SECTION 7: DRAFT DRAINAGE September 1991 SECTION 8: EROSION AND SEDIMENTATION April 1993 SECTION 9: MISCELLANEOUS 9.1 Auxiliary Lanes August 1988

SECTION 2

ROAD GEOMETRY

CONTENTS

2.1 SIGHT DISTANCE2.2 HORIZONTAL ALIGNMENT2.3 VERTICAL ALIGNMENT2.4 CO-ORDINATION OF HORIZONTAL AND

VERTICAL ALIGNMENT

Roads and Traffic AuthorityRoad Design GuideMarch 1988

2.1 SIGHT DISTANCE Page No.

2.1.1 General

2.1.2 Sight Distances

2.1.3 Constants assumed for determination of sight distances

2.1.4 Stopping sight distance

2.1.5 Effect of grade on braking distance

2.1.6 Overtaking sight distance

2.1.7 Intermediate sight distance

2.1.8 Summary of sight distances

2.1.9 Sight distance at night

2.1.10 Sight distance at vertical sags

2.1.11 Sight distance at vertical crests

2.1.12 Sight distance at horizontal curves

2.1.13 Benching for visibility on horizontal curves

2.1.14 Sight distance at combined horizontal and vertical curves

2.1.15 Sight distance at intersections

2.1.16 Sight distance on undivided roads

2.1.17 Sight distance on divided roads

2.1.18 Sight distance through underpasses

2.1.19 Sight distance at interchanges

2.1.20 Other restrictions to visibility

2.1.21 Effect of no-overtaking zone markings

2.2 HORIZONTAL ALIGNMENT Page No.

2.2.1 General

2.2.2 Straight alignment

2.2.3 Curved alignment

2.2.4 Horizontal curve radius

2.2.5 Length of curved roadway

2.2.6 Circular arc

2.2.7 Deflection angle

2.2.8 Vehicular movement on a circular path

2.2.9 Transverse friction

2.2.10 Superelevation - general

2.2.11 Desirable superelevation

2.2.12 Maximum values of superelevation

2.2.13 Minimum values of superelevation

2.2.14 Adverse crossfall

2.2.15 Superelevation on bridges

2.2.16 Superelevation on steep grades

2.2.17 Superelevation at road junctions

2.2.18 Superelevation development

a. Length of superelevation developmentb. Procedurec. Rate of Rotationd. Relative gradee. Length of superelevation development to satisfy relative grade

2.2.19 Plan transition

a. Clothoid spiralb. Cubic parabola

2.2.20 Lane widening

2.2.21 Compound curves

a. Radiib. Length

2.2.22 Broken back curves

2.2.23 Reverse curves

2.2.24 Sight distance on horizontal curves

2.3 VERTICAL ALIGNMENT Page No.

2.3.1 General

2.3.2 Grading

2.3.3 Grading at intersections

2.3.4 Vertical curves

2.3.5 Length of vertical curves for appearance

2.3.6 Length of vertical curves for comfort

2.3.7 Length of vertical curves for sight distance requirements

2.3.8 Sight line constant for crest curves

2.3.9 Length of crest curves

2.3.10 Sag vertical curves

2.3.11 Sight line constant for sag curves

2.3.12 Determination of lengths for sag curves

2.3.13 Overhead obstruction at sag curves

2.3.14 Vertical curves on undivided roads

2.3.15 Vertical curves on divided roads

2.3.16 Calculation of parabolic vertical curves

2.4 CO-ORDINATION OF HORIZONTAL AND VERTICAL ALIGNMENT(This subject is more fully covered in Section 6)

Page No.

2.4.2 General

SECTION 2 NOTATION

A Algebraic difference of vertical grades (%).

a Vertical component of acceleration (m / sec2).

B Benching offset (m).

C Sight line constant for vertical curves.

Ca Length of circular arc (m).

Cl Lateral clearance between vehicles in adjacent lanes (m).

CL Base control line.

Dh Headlight illumination distance (m).

Dm Intermediate sight distance (m).

Do Overtaking sight distance (m).

Ds Stopping sight distance (m).

d Braking distance (m).

dr Distance travelled during reaction time (m).

E Superelevation (%).

e Superelevation (m / m or tangent of angle).

f Assumed value of transverse friction demand.

fl Assumed coefficient of longitudinal friction demand.

G Longitudinal grade (%).

Gr Relative grade (%).

g Acceleration due to gravity (9.8m / sec2).

H Clearance of overhead obstructions (m).

h Mounting height of headlight (m).

h1 Height of eye above road (m).

h2 Object cutoff height above road (m).

K Measure of vertical curvature.

L Length of vertical curve (m).

Le Length of superelevation development (m).

Lh Length of horizontal curve (m).

Lp Length of plan transition (m).

SECTION 2 NOTATION (continue)

Lr Length of crossfall rotation (m).

Lx Length of a vehicle between its rear axle and the limit of its front overhang (m).

n Normal crossfall (%)

P Spiral transition factor

p Spiral transition offset (m).

Q Rate of change of grade per unit length (% / m).

R Horizontal curve radius (m).

Rt Reaction time (secs).

S Maximum plan transition offset for cubic parabola (m).

S.C. Spiral curve, common point of spiral and circular curve.

S.S. Start of superelevation transition.

T.P. Tangent point, common point of tangent and circular curve.

T.S. Tangent spiral, common point of tangent and spiral.

V Speed (km / h).

v Speed (m / sec).

Vm Distance between adjacent T.S. points on broken-back or reverse curves (m).

W Lane widening (m).

Wa Distance rear wheels track inside front wheels on curve (m).

Wb Extra width allowance for difficulty of driving on curve (m).

Wd Additional width of front overhang on curve (m).

We Distance from inside lane line to driver position (m).

Wl General lane width (m).

Wn Width of pavement on tangent (m).

Wr Width from axis of rotation to outside edge of running lanes (m).

Ws Width of inner travel lane and adjacent shoulder (m).

x Distance of offset from either the T.S. or S.C. end of plan transition (m).

y Intermediate offsets of plan transition (m).

θ Elevation angle of headlight beam (+ø upwards).

∠° Deflection angle (degrees).

RTA of NSW Section 2 - Road Geometry

Road Design Guide June, 95 1Issue 1.0

2.1 SIGHT DISTANCE

2.1.1 General

A principal aim in road design is to ensure that adriver has sufficient sight distance to be able toperceive any road hazards in sufficient time totake action to avoid mishap. A driver's sightdistance should be as long as practicable, but itis often restricted by crest vertical curves,horizontal curves in cutting, roadside vegetationand buildings at intersections. These restrictionscan make manoeuvres such as overtakingunsafe due to the sight restriction.The provision of adequate sight distancetherefore requires a determination of the lengthof crest vertical curves and radius of horizontalcurves to suit the desired sight distance. Wherethe desired radius of horizontal curve cannot beachieved, it becomes necessary to determinethe extent to which the inside of the curveshould be cleared to allow the driver to see therequired distance along the road.

2.1.2 Sight Distances

In design there are three sight distancerequirements to be met :

(i) Stopping Sight DistanceAt all times a driver must be provided with

sufficient visibility to see an object in the lane oftravel and stop before striking it. This is knownas the "stopping" sight distance.

(ii) Overtaking Sight DistanceAt reasonable intervals a driver should

have sufficient visibility to detect oncomingvehicles in sufficient time to allow safe anduninterrupted overtaking of a vehicle withminimal risk of collision with oncoming traffic.This is known as the "overtaking" sight distance.

(iii) Intermediate Sight DistanceAlthough the provision of overtaking sight

distance is desirable, the cost of construction toachieve it can be prohibitive. The provision of"intermediate" sight distance enables a driver totravel a road in comfort with reasonably safeovertaking opportunities.Calculations to obtain the distance needed tostop or to overtake are made on the assumptionthat the driver is travelling at a speed consistentwith the alignment of the road. In practice, theactual speed adopted by a driver is influencedby geometric features of the road layout ratherthan the sight distance provided.

2.1.3 Constants Assumed forDetermination .of Sight Distances

The following values are used in calculatingstopping distances and sight distances (seeFigure 2.1.1).

Reaction Time -- 1.5 secs for design speeds≤100 km/hr-- 2.5 secs where design speedis ≥ 100 km/hr and access iscontrolled.

Driver Eye Height -- 1.15m Passenger Car.-- 1.8m Commercial Vehicle.

Object Height -- 1.15m Approaching Vehicle.-- 0.2m Stationary object onroad.-- 0.6m Vehicle tailstop light.

2.1.4 Stopping Sight Distance

Stopping sight distance is the minimum distancerequired by an average driver of a vehicletravelling at a given speed to react and stopbefore reaching an object in the vehicle path.Stopping sight distance is measured along theline of travel from a point 1.15m high(representing the height of a driver's eye), to apoint 0.2m high (representing a stationary objecton the roadway).The length of vertical curve required at crestsincreases significantly as the object cut off valueapproaches zero and therefore the generalfigure adopted which produces satisfactorydesigns is 200mm. However, zero should beused in the case of intersections where it isnecessary to see road markings, or on theapproaches to causeways and floodways wherewater or sand left by floods, or washouts mayoccur (see Figure 2.3.3).Stopping sight distance has two components,the distance travelled during total reaction timeand the distance travelled during braking time.

Reaction distance (dr) = =R vR V

tt

36.

Braking distance (d) = =vgf

Vfl l

2 2

2 254Stopping Sight Distance (Ds)

= +RV Vf

t

l36 254

2

.Where:

dr= distance travelled during reaction timed= distance travelled during braking timeDs= stopping sight distance (m)Rt= reaction time (secs)v = speed (m/s)V = speed (km/h)fl= assumed coefficient of longitudinal

friction demand (regarded as constant throughoutthe braking period (see Table 2.1.1).

g= acceleration due to gravity (9.8m/sec2)

The stopping sight distance to be used forvarious speeds on level bituminous or concretesurfaces are shown in Table 2.1.1.


2 16/09/98 Road Design GuideIssue 1.0

Sight Distance

Eye height (1.15m)

Object height (0.2m)

CREST

Vertical Clearance

Eye height (1.8m)

Bridge Tail - light height (0.6m)

Sight Distance

SAG

SIGHT DISTANCE COMPONENTSFigure 2.1.1

Table 2.1.1 Stopping Sight Distances on Level Bituminous or Concrete Surfaces.

DISTANCE (m) TRAVELLEDDURING*

DESIGN CO-EFFICIENT OF

REACTION TIMERr

BRAKING

TOTAL STOPPINGDISTANCE

(m)

SPEED(km/h)

V

LONGITUDINALFRICTION DEMAND

fl1.5 Secs 2.5 Secs 1.5 Secs 2.5 Secs

50 0.50 20 25 4560 0.47 25 35 6070 0.45 30 50 8080 0.43 35 65 10090 0.41 40 80 120100 0.39 45 70 105 150 175110 0.37 75 135 210120 0.35 85 165 250130 0.33 90 210 300

Total Distances given are approximately 5m to 8m longer than calculated distances to provide extra distance for stationary betweenvehicle and object.



2.1.5 Effect of Grade on BrakingDistance

The distance a vehicle travels while beingbraked is longer on downhill grades and shorteron uphill grades. The braking distancecomponent of the stopping sight distanceformula (Section 2.1.4) when adjusted to takeinto account the effect of grade is :-

dV

f Gl

=±

2

254 0 01( . )

Where:d = braking distance (m).V = speed (km/h).fl = assumed coefficient of

longitudinal friction demand for design speed (seeTable 2.1.1).

G = longitudinal grade per cent(+ uphill, - downhill)

2.1.6 Overtaking Sight Distance

Overtaking sight distance is measured along theline of travel between two points each 1.15mabove the road pavement. It is equal in length tothe minimum distance between two opposingvehicles which will permit a safe overtakingmanoeuvre.

The overtaking sight distance figures for variousspeeds are shown in Table 2.1.2.

Table 2.1.2 Overtaking Sight Distances

DESIGN SPEED(km/h)

OVERTAKINGSIGHT DISTANCE

(m)1.15m-1.15m

50 25060 30070 35080 45090 600100 750110 900120 1100130 1400

When applying the overtaking sight distancesgiven in Table 2.1.2, the following factorsshould also be considered :

(i) Frequency

The frequency at which overtaking sightdistance should be provided is related to thetravel speed, traffic volume, traffic composition,

terrain and cost of construction. It is an essentialsafety measure and to a large degree willinfluence both the location and design of a road.In undulating or flat country, it should occurfrequently or continuously; at other locationsminor modifications to alignment or grading mayprovide the sight distance necessary at little orno additional cost. As a general rule ifovertaking sight distance cannot beeconomically provided at least once in each2km of road, (depending on road type andvolume), consideration should be given to theinstallation of auxiliary lanes in accordance withSection 8.1.

(ii) Length of continuing overtaking sightdistance

Isolated sections of roadway that have onlyminimum overtaking sight distance, are of littlevalue if oncoming traffic prevents the utilisationof any overtaking opportunity provided. Afterovertaking sight distance has been established,it needs to be maintained continuously along alength of roadway to maximise overtakingopportunities and to enable an overtakingmanoeuvre, once commenced, to be eithercompleted or abandoned with safety. This lengthshould be as long as economically practicable,and on roads with high traffic volumes should beequal to at least half the overtaking sightdistance for the design speed.

(iii) Vertical alignment

The provision of minimum overtaking sightdistance at crests is usually uneconomical andmay not be used since many drivers arereluctant to overtake in these circumstances.Shorter crest curves with stopping sight distanceoften result in longer sections with overtakingsight distance.

(iv) Auxiliary lane option

The provision of overtaking sight distance atsome locations on two lane roads may not becost effective and in these cases, a section ofauxiliary lane construction with stopping sightdistance is generally more economical than twolanes with overtaking sight distance.



2.1.7 Intermediate Sight Distance

Cases occur where it is not economicallypracticable to provide overtaking sight distanceat reasonable intervals. The model forovertaking sight distance is based on one set ofconditions, that is, the overtaking of a vehicletravelling at a lesser speed than the generaltravel speed on the section of road. In practicethere is a wide range of conditions where a sightdistance shorter than overtaking sight distancewould be useful. For example, a much shortersight distance is suitable to overtake a slow-moving truck.

Where overtaking sight distance cannot beobtained and the introduction of an auxiliarylane is not warranted, the provision ofintermediate sight distance may meet someovertaking needs by providing sight distancesufficient to complete or abort an overtakingmanoeuvre before reaching an opposing vehiclewhich is just out of sight and travelling towardsthe first vehicle at the 85th percentile speed .

The intermediate sight distances for variousspeeds are shown in Table 2.1.3

Table 2.1.3 Intermediate SightDistances.

DESIGN SPEED(km/h)

INTERMEDIATESIGHT DISTANCE

(m)[1.15m-1.15m]

50 14060 18070 22080 26090 300100 380110 450120 530130 600

2.1.8 Summary of Sight Distances

Table 2.1.4. summarises the sight distances asdiscussed for level bituminous or concretepavements.

Table 2.1.4 Sight Distances on LevelBituminous or ConcretePavements

DESIGNSPEED(km/h)

STOPPINGSIGHT

DISTANCE(m)

INTER-MEDIATE

SIGHTDISTANCE

(m)

OVER-TAKINGSIGHT

DISTANCE(m)

50 45 140 25060 60 180 30070 80 220 35080 100 260 45090 120 300 600100 150/175 380 750110 210 450 900120 250 530 1100130 300 600 1400

2.1.9 Sight Distance at Night

Unless roadway lighting is installed, sightdistance at night is confined to the range of avehicle's headlight beam. The distance of adriver's visibility is therefore limited regardlessof which standard sight distance has beenincorporated into the road's horizontal andvertical alignments for daylight driving. Thelimitations of vehicle headlights restrict the sightdistance that can be safely assumed for visibilityof an object on a roadway, to between 120mand 150m.This corresponds to satisfactorystopping distance up to 100km/h on a sealedroad and less for a gravel surface.

The criterion for headlight sight distance doesnot apply to roads which have street lighting tothe standards prescribed by the S.A.A. PublicLighting Code, AS 1158, or on roads with hightraffic volumes where it is necessary to keepheadlights on dipped beam for a relatively highpercentage of the travel time.

2.1.10 Sight Distance at Vertical Sags

Sag vertical curves may be designed to provideacceptable standards of comfort or to allowadequate headlight sight distance, with the latterusually being the governing criterion.

Where a sag vertical curve is on a straight,Figure 2.3.7 (page 2-37) gives the length ofvertical curve which provides for headlight sightdistance (to a maximum of 150m) with an angleof beam 1° above the horizontal axis.

2.1.11 Sight Distance at Vertical Crests

The minimum sight distance to be provided atvertical crests is stopping sight distance for thespecified design speed and an object height of0.2m. The provision of overtaking sight distanceat vertical crests is usually uneconomical and a



more satisfactory option is the adoption ofintermediate sight distance.

Figures 2.3.3 and 2.3.4 (pages 2-33 & 2-34)give the length of vertical curve required toobtain stopping sight distance for eye height of1.15m to zero pavement level and to an objectheight of of 0.2m for given design speeds andalgebraic differences in grade.

Figures 2.3.5 and 2.3.6 (pages 2-35 & 2-36)give the length of vertical curve required toobtain overtaking and intermediate sightdistances (1.15m to 1.15m) for given designspeeds and algebraic differences in grade.

2.1.12 Sight Distance at HorizontalCurves

Where an obstruction off the pavement (such asa bridge pier, building, batter or natural growth)restricts sight distance, the minimum radius ofcurvature is determined by the stopping sightdistance for the adopted design speed. On two-lane, two-way roads however, it is preferable toprovide for intermediate sight distance so as tominimise the use of barrier lines.

The relation of a drivers line of sight to the sightdistance measured around the curve and thecurve radius is shown as Figure 2.2.6 (page 2-26). Also shown are the formulae to calculatethe offset distance required from the pavementcentreline to the line of sight obstruction and theminimum radius which avoids benching. Table2.2.2 gives calculated offsets for stopping andintermediate sight distances for various curveradii.

2.1.13 Benching for Visibility onHorizontal Curves

Benching is the widening of the inside of acutting on a curve to obtain the specified sightdistance. It usually takes the form of a flat tableor bench over which a driver can see anapproaching vehicle or an object on the road. Inplan view, the benching is fixed by the envelopeformed by the lines of sight. The driver and theobject being approached are assumed to be inthe inner lane. The sight distance is measuredaround a line 1.5m from the driver's side of thelane line and is the path the vehicle would followin braking. Benching adequate for inner lanetraffic satisfies visibility requirements for theouter lane (see Section 2.1.12).

Where sight benches in cuttings are required onhorizontal curves or on combinations ofhorizontal and vertical curves, the extent ofsight benching is best obtained graphically. Thelevel of the sight bench should be fixed at least

0.3m under the sight line to allow forobstructions such as small boulders and grassgrowth.

Where a horizontal and crest vertical curveoverlap, the line of sight between approachingvehicles may not be over the top of the crest butto one side and in part may be off the formation.Cutting down the crest on the pavement will notincrease visibility if the line of sight is clear ofthe pavement, and the bottom of the bench maybe lower than the shoulder level. In these cases,as well as in the case of sharp horizontal curves,a better solution may be to use a larger radiuscurve so that the line of sight remains within theformation. This will increase the 85th percentilespeed and an iteration is necessary to ensurethat stopping sight distance requirements aremet.

2.1.14 Sight Distance at CombinedHorizontal & Vertical Curves

Where sag and crest vertical curves arecombined with horizontal curves, the sightdistance requirements of Sections 2.1.10,2.1.11 & 2.1.12 should be amalgamated toensure continuous provison of the appropriatesight distance.

2.1.15 Sight Distance at Intersections(To be read in conjunction with Section 4.3.2)

At all intersections, the following sight distancerequirements should be satisfied:

(i) Stopping sight distance (1.15m tozero), should be available on each approach ofthe intersection, so that drivers may appreciatethe layout of the intersection by having clearvisibility to pavement markings andchannel?isation.

(ii) A driver stopped in the minor roadshould have sufficient sight distance (1.15m to1.15m) to react to an acceptable gap, start upand enter or cross the major traffic stream,without causing major disruption.

(iii) Vehicles in the major road shouldhave sufficient sight distance (1.15m to 1.15m)to observe a vehicle from the minor road moveinto the intersection, and in the event of a stall,be able to decelerate to a stop prior to collision.This sight distance is numerically equal to:

• the distance travelled during the observationtime (3 secs) plus,

• the stopping distance of the vehicles on themajor road (see Section 4.3.2).



2.1.16 Sight Distance on UndividedRoads

The minimum sight distance to be provided atall points in a two-lane or multi-lane road isstopping distance.

Where barrier lines are to be avoided and costassociated with heavy earthworks is not aprimary consideration, intermediate sightdistance may be used. It satisfies manyovertaking requirements though it does notcomply with all the requirements assumed forovertaking sight distance.

In undulating country where overtakingopportunities are few, and auxiliary lanes forovertaking are inappropriate, considerationshould be given to providing intermediate sightdistance at regular intervals.

In cases where barrier lines are necessary atcrests, shoulders should be wide enough for astationary vehicle to stand well clear of thepavement, so that moving vehicles are notforced to cross the centreline of the road (seeSection 3).

Care should be taken to avoid dips in theroadway which could hide an opposing vehicleand cause an overtaking driver an unexpectedhazard.

2.1.17 Sight Distance on Divided Roads

At least stopping sight distance is to be providedat all points on a divided road. Generallyintermediate sight distance should be adoptedwhere economically practicable.

2.1.18 Sight Distance throughUnderpasses

Where economically feasible, overtaking sightdistance should be maintained as the highwaypasses under a structure. If this cannot beachieved, intermediate sight distance willsuffice. The absolute minimum sight distancewhich must be provided at underpasses isstopping sight distance.

2.1.19 Sight Distance at Interchanges

Mutual sight must be available between thedrivers of converging vehicles at interchanges.This is particularly important at the merge ofonload ramps and beneath grade separationswhere piers or abutment walls may obscurevisibility.

2.1.20 Other Restrictions to Visibility

There are other minor constraints on sightdistance that must be kept in mind by thedesigner:

• In avenues of trees, visibility can becurtailed at a sag owing to the line of sightbeing interrupted by the foliage. The samemay happen where a bridge crosses a sagand the line of sight is cut by the structure.

• Guard fencing, bridge handrails, mediankerbs and similar obstructions can restrictthe visibility available at horizontal andvertical curves.

• There is a considerable difference betweenthe sight distance available to a driverdepending on whether the curve ahead is tothe left or to the right.

2.1.21 Effect of No-Overtaking ZoneMarkings

Reference is made the Department'spublication, "Interim Guide to Signs andMarkings", Section 7.4, for the practices ofmarking no-overtaking zones on two lane roads.



2.2 HORIZONTAL ALIGNMENT(To be read in conjunction with Section 6)

2.2.1 General

The speed adopted on an open road is affectedmore by the driver's perception of the horizontalalignment of the road than by any other singledesign feature. For this reason, whenevercurves are used to change the direction of travelor to suit the topography, the radii must be largeenough to permit travel speeds commensuratewith those expected on adjoining straights oralong the whole of the section being designed.Generally, the adopted alignment should be asdirect as possible, with curve radii as large aspracticable.

An alignment without straight sections isdescribed as curvilinear. Curvilinear alignmentis suitable for dual carriageway roads but isundesirable for two-lane, two-way roads, as itdoes not provide sufficient length for overtaking.

As with other elements of design, horizontalalignment should generally provide for safe andcontinuous operation at a uniform travel speed.Sudden reductions in standard, such as isolatedcurves of small radius (particularly at the end oflong straights), introduce an element of surpriseto the driver and should be avoided.

Where physical restrictions on curve radiuscannot be overcome and it becomes necessaryto introduce curvature of lower standard thanthe design speed of the project, the designspeed of successive geometric elements shouldnot change by more than 10km/h (on two wayroads both directions of travel need to beconsidered).

2.2.2 Straight Alignment

The tangent or straight section is the mostcommon element of horizontal alignment. Itprovides clear orientation, but at the same timeis visually uninteresting unless aimed at somelandmark. Being totally predictable, with a viewwhich appears static, it causes driver monotonyand encourages the undesirable combination offatigue and excessive speed. At night, opposingheadlights can cause problems.

Straights of suitable length are desirable on twolane roads to facilitate overtaking manoeuvresand should be provided as frequently as theterrain permits. Straights are too long if theyencourage drivers to travel well in excess of thedesign speed and should therefore be avoided.Straights which are too short to provideadequate separation between adjoining curves,should also be avoided.

In flat country, long straights on roads may haveto be accepted. If curves are deliberatelyintroduced into the design to break themonotony, they

should have long arc lengths or else they willlook like kinks. Unless the change in alignmentis considerable, oncoming headlights will remaina nuisance to drivers.

2.2.3 Curved Alignment

The second element of horizontal alignment isthe curve. Properly designed curves areappreciated by drivers because they provideinterest by presenting a changing panoramawhile arousing a sense of anticipation of what isbeyond the curve. The most advantageousproperty of a curving roadway is that it providesa visual appreciation of the driver's position andspeed in relation to roadside objects and othertraffic.

It is preferable that the radii of horizontal curvesbe the largest attainable. Isolated small radiicurves in an otherwise free flowing horizontalalignment and small radii curves at the end oflong straights, on steep down grades and overcrests are unsafe and must be avoided.General details of curve elements are given inTables 2.2.2 and 2.2.3

2.2.4 Horizontal Curve Radius

For a given speed, and under normal conditions,the radius for a horizontal curve should not beless than the range quoted in Table 2.2.1

Table 2.2.1 Minimum Radii for HorizontalCurves

Design Speed(km/h)

Radii(m)

50 50 or more60 90 or more70 150 or more80 240 or more90 340 or more100 460 or more110 600 or more120 800 or more130 1000 or more

Accident records suggest that curves with radiibetween 300m and 440m should be avoided fordesign speeds greater than 70km/h. They aredeceptive to the driver as it appears that theycan be safely travelled at higher speeds than isactually possible. Wherever possible, curves areto be selected to give stopping sight distance forthe adopted design speed, with the line of sightcontained within the formation (see Section2.2.24).


2 June, 95 Road Design GuideIssue 1.0

90 100

110

120

130

140

6010

07

0.6

6040

0.6

160

180

200

220

70

Spe

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Rad

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(m)

Cur

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Sup

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%(k

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(m)

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(m)

C'li

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(m)

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Sig

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(m)

Ben

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(m)

240

260

280

300

320

340

360

380

400

420

440

460

500

550

600

650

700

750

800

900

1000

2000

3000

over

3000

80 100

110

120

130

130V

RLh

E

0.9

8060

1.3

1.3

8060

1.3

0.9

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if th

e ca

lcul

ated

wid

enin

g is

less

than

200

mm

.

4.

Ado

ptio

n of

2.8

, 3.0

and

3.2

5m la

ne w

idth

s is

not

reco

mm

ende

d fo

r des

ign

spee

ds o

f 80,

90

and

100

km/h

resp

ectiv

ely.

5

. S

.S.D

, I.S

.D, O

.S.D

= S

topp

ing,

Inte

rmed

iate

and

Ove

rtaki

ng S

ight

Dis

tanc

es.

#

U

se is

opt

iona

l.

*

For

tran

sitio

n an

d w

iden

ing

offs

ets,

see

Tab

le 2

.2.3

.

A

Nor

mal

two-

lane

road

way

with

con

trol o

n ce

ntre

line.

B

Two-

lane

road

way

with

con

trol a

long

one

edg

e.

Fo

ur-la

ne ro

adw

ay w

ith c

ontro

l on

cent

relin

e.

Tw

o-la

ne ro

adw

ay w

ith c

limbi

ng la

ne a

nd c

ontro

l on

the

cent

relin

e

of

the

basi

c tw

o la

nes.

C

Mul

ti-la

ne ro

adw

ay w

ith m

ore

than

two

lane

s be

twee

n th

e co

ntro

l

an

d th

e ed

ge o

f the

trav

elle

d w

ay.

HO

RIZ

ON

TAL

ALI

GN

ME

NT

Tabl

e 2.

2.2

A*

B*

C*

43.5

39.9

36.8

34.1

31.8

29.8

38.2

34.4

31.2

28.6

36.1

33.5

31.3

29.4

27.7

34.2

32.5

30.9

29.4

28.1

26.9

40.3

37.3

34.1

43.3

40.2

37.5

48.0

45.1

40.3

46.3

24.0

16.5

470

3#3#

80#

0.5#

90#

0.6#

110#

0.5

0.3

0.2

300

600

1400

0.7

0.6

0.4

0.3

6018

030

0

S.S

.D.I

.S.D

.S

.S.D

.O

.S.D

.I.S

.D.

2.8

3.0

3.25

3.5

3.7

6.6

6.1

5.7

5.3

5.0

4.8

6.6

6.0

5.6

5.2

6.8

6.4

6.0

5.7

5.5

6.8

6.5

6.3

6.0

5.8

5.6

7.7

7.2

6.7

10.7

10.0

9.4

12.0

11.3

10.2

12.8

7.2

5.3

140

70.

660

400.

40.

980

600.

81.

290

600.

80.

80.

60.

50.

30.

280

220

350

180

70.

580

600.

50.

890

600.

61.

011

080

0.9

0.7

0.5

0.4

0.2

100

260

450

8023

06

0.4

8060

0.4

0.7

9060

0.4

0.9

110

800.

70.

70.

40.

312

020

060

0

280

60.

480

600.

30.

790

600.

30.

911

080

0.5

0.6

0.4

0.3

150

380

750

340

50.

480

0.7

900.

811

080

0.4

0.6

0.4

0.3

210

450

900

400

40.

380

470

30.

380

0.5

900.

611

00.

50.

30.

230

060

014

00

1100

530

250

0.3

0.4

0.6

0.3

8011

00.

790

0.6

Gr

L eL p

SG

rL e

L pS

Gr

L eL p

S



Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control

Offset to True Control

NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 70

Cross-fall %

Outside of Control

Radius 90m - 140m

Radius 160m - 220m

Radius 240m - 320m

Radius 340m - 440m

SS TS TP SC

-3.0-3.0

-2.7-3.0

-1.3

-3.00.3-3.0

00000

0

2.0

-3.3.04.22.17.15.10.07

3.7

-4.3.30.45.35.30.20.15

5.3-5.7

.56

.67

.53

.45

.30

.23

6.7

-6.7.60.90.70.60.40

.30

7.0

-7.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 70

Cross-fall %

Outside of Control

SS TS TP SC

-3.0-3.0

-2.7-3.0

-1.3

-3.00.3-3.0

00000

0

2.0

-3.3.03.20.15.12.07.05

3.7

-4.3.20.40.30.25.15.10

5.3-5.7

.37

.60

.45

.38

.23

.15

6.7

-6.7

.60

.20

.50

.40

.30

7.0

-7.0

SS TS TP SC

SS TS

-3.0

-3.0

.80

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 80

Cross-fall %

Outside of Control70 90

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control

Widening Not Required


-3.0

-3.0

-2.7

-3.0

-1.8 -0.5 0.8 2.0 3.3 4.5 5.8 6.7 7.0

-3.0-3.0-3.0-3.0 -3.3 -4.5 -5.8 -6.7 -7.0

00000

.01

.12

.08

.07

.03

.07

.23

.17

.13

.07

.25

.35

.25

.20

.10

.43

.47

.33

.27

.13

.49

.58

.42

.33

.17

.50

.70

.50

.40

.20

30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -1.9

-3.0 -3.0 -3.0 -3.0 -3.0

-0.8 0.4 1.5 2.6 3.7 4.9 5.8 6.0

-3.2 -3.9 -4.9 -5.8 -6.0

0000

.01

.12

.07

.05

.06

.23

.13

.10

.20.35.20.15

.34

.47

.27

.20

.39

.58

.33

.25

.40

.70

.40

.30

TABLE 2.2.3 TRANSITION AND WIDENING OFFSETSTYPE A (Control other than centreline of normal two-lane roadway, refer Table 2.2.2)

* To be used in exceptional circumstances only



Radius 460m - 550mSS TS

-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -1.9

-3.0 -3.0 -3.0 -3.0 -3.0

-0.8 0.4 1.5 2.6 3.7 4.9 5.8 6.0

-3.2 -3.9 -4.9 -5.8 -6.0

0000

.01

.12

.07

.05

.06

.23

.13

.10

.20.35.20.15

.34

.47

.27

.20

.39

.58

.33

.25

.40

.70

.40

.30


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.0

-3.0 -3.0 -3.0 -3.0 -3.0

-1.0 0.0 1.0 2.0 3.0 4.0 4.8 5.0

-3.0 -3.3 -4.0 -4.8 -5.0

000

.10

.07

.05

.20

.13

.10

.30.20.15

.40

.27

.20

.50

.33

.25

.60

.40

.30

Offset Not Required


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.1

-3.0 -3.0 -3.0 -3.0 -3.0

-1.2 -0.4 0.5 1.4 2.2 3.1 3.8 4.0

-3.0 -3.2 -3.5 -3.8 -4.0

000

.10

.07

.05

.20

.13

.10

.30.20.15

.40

.27

.20

.50

.33

.25

.60

.40

.30

Offset Not Required


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.3

-3.0 -3.0 -3.0 -3.0 -3.0

-1.5 -0.8 0.0 0.8 1.5 2.3 2.8 3.0

-3.0 -3.0 -3.0 -3.0 -3.0

000

.08

.05

.03

.17

.10

.07

.25.15.10

.33

.20

.13

.42

.25

.17

.50

.30

.20

Offset Not Required


TABLE 2.2.3 (Continued)

TYPE A (Control other than centreline of normal two-lane roadway, refer Table 2.2.2)



5.3Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 70

Cross-fall %

Outside of Control

Radius 90m - 140m

Radius 160m - 220m

SS TS TP SC

-3.0-3.0

-2.7

-3.0

-1.8

-3.0-0.5-3.0

00000

0

0.8

-3.0.03.15.12.10.07.05

2.0

-3.0.19.30.23.20.13.10

3.3-3.3

.65

.45

.35

.30

.20

.15

6.7

-6.71.30.90.70.60.40

.30

7.0

-7.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 70

Cross-fall %

Outside of Control

SS TS TP SC

-3.0-3.0

-2.7-3.0

-1.8

-3.0-0.5-3.0

00000

0

0.8

-3.0.02.13.10.08.05.03

2.0

-3.0.12.27.20.17.10.07

3.3-3.3

.40

.40

.30

.25

.15

.10

4.5

-4.5

.40

.13

.33

.68

.20

7.0

-7.0

.53

Radius 240m - 320m SS TS TP SCDistances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 80

Cross-fall %



-3.0

-3.0

-2.7

-3.0

-1.9 -0.8 0.3 1.4 2.5 3.7 4.8 6.7 7.0

-3.0-3.0-3.0-3.0 -3.1 -3.7 -4.8 -6.7 -7.000000

.01

.12

.08

.07

.03

.09

.23

.17

.13

.07

.30

.35

.25

.20

.10

.51

.47

.33

.27

.13

.60

.70

.50

.40

.20

80 905.8-5.8

1.27.75.58

.50

.33

.25

4.5-4.5

1.11.60.47

.40

.27

.20

80 906.7

-6.7

.60

.20

.50

.80

.30

.80

5.8

-5.8

.50

.17

.42

.78

.25

.67

1005.9

-5.9.59.58.42

.33

.17


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.0

-3.0 -3.0 -3.0 -3.0

-1.0 0.0 1.0 2.0 3.0 4.0 5.8 6.0

-3.0 -3.2 -4.0 -5.8 -6.0

0000

.01

.12

.07

.05

.06.23.13.10

.20

.35

.20

.15

.34

.47

.27

.20

.40

.70

.40

.30

100

5.0

-5.0.39.58.33.25

-3.0


TYPE B (Control other than centreline of normal two-lane roadway, refer Table 2.2.2)





-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.0

-3.0 -3.0 -3.0 -3.0

-1.0 0.0 1.0 2.0 3.0 4.0 5.8 6.0

-3.0 -3.2 -4.0 -5.8 -6.0

0000

.01

.10

.07

.05

.04.20.13.10

.15

.30

.20

.15

.26

.40

.27

.20

.30

.60

.40

.30

1005.0

-5.0.29.50.33.25

-3.0


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90

TP SC

-3.0

-3.0

-2.8 -2.1

-3.0 -3.0 -3.0 -3.0 -3.0

0.3 0.6 1.4 2.3 3.2 4.1 4.8 5.0

-3.0 -3.3 -4.1 -4.8 -5.0

000

.10

.07

.05

.20

.13

.10

.30

.20

.15

.40

.27

.20

.50

.33

.25

.60

.40

.30

Offset Not Required


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.2

-3.0 -3.0 -3.0 -3.0 -3.0

-1.4 -0.7 0.1 0.9 1.7 2.4 3.2 3.8

-3.0 -3.0 -3.2 -3.5 -3.8

000

.10

.07.05

.20

.13

.10

.30.20.15

.40

.27.20

.50

.33

.25

.60

.40

.30

Offset Not Required

Radius 1000m - 3000m SS TS

-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.3

-3.0 -3.0 -3.0 -3.0 -3.0

-1.0 -0.3 0.3 1.0 1.7 2.3 2.8 3.0

-3.0 -3.0 -3.0 -3.0 -3.0

000

.08

.05

.03

.17

.10

.07

.25.15.10

.33

.20

.13

.42

.25

.17

.50

.30

.20

Offset Not Required

100-1.2

-3.0

100

4.0

-4.0

100-1.7

-3.0



TYPE B (Control other than centreline of normal two-lane roadway, refer Table 2.2.2)



Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 70

Cross-fall %

Outside of Control

Radius 90m - 140m

Radius 160m - 220m

SS TS TP SC

-3.0-3.0

-2.7-3.0

-1.8

-3.0-0.5-3.0

00000

0

3.3

-3.3.65.45.35.30.20

.15

4.5

-4.51.11.60.47.40.27.20

5.8-5.8

1.27.75.58

.50

.33

.25

6.7

-6.71.30.90.70.60.40

.30

7.0

-7.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 70

Cross-fall %

Outside of Control

SS TS TP SC

-3.0-3.0

-2.7-3.0

-1.9

-3.0

0.3-3.0

00000

0

3.7

-3.7.40.40.30.25.15.10

4.8

-4.8.68.53.40.33.20.13

5.9-5.9

.78

.67

.50

.42

.25

.17

6.7

-6.7

.60

.20

.50

.30

7.0

-7.0

.80

Radius 240m - 320m

Radius 340m - 440m

SS TS TP SC

SS TS

-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20 30 40 50 60 80

Cross-fall %


Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control



-3.0

-3.0

-2.8

-3.0

-2.1 -0.3 2.5 3.4 4.3 5.2 6.1 6.8 7.0-3.5-3.1-3.0-3.0 -4.3 -5.2 -6.1 -6.8 -7.0

00000

.19

.26

.19

.15

.07

.45

.35

.25

.20

.10

.71

.44

.31

.25

.13

.84

.53

.38

.30

.15

.89

.61

.44

.35

.18

.90

.70

.50

.40

.20

30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.2

-3.0 -3.0 -3.0 -3.0 -3.1-0.5 1.9 2.7 3.5 4.4 5.2 5.8

-3.6 -4.4 -5.2 -5.8

0000

.15

.26

.15

.11

.35

.35

.20

.15

.55.44.25.19

.65

.53

.30

.23

.69

.61

.35

.26

.70

.40

.30

80 900.8-3.0 -3.0

2.0

.03

.15

.10.07.05

.12

.19

.30.23.20.13.10

80 90 1002.5

-3.1.12.27.20.17.10.07

1.4

-3.0.02.13.10.08.05.05

-0.8

-3.0.80

100 110 1200.6

-3.0

.01

.09

.06

.05

.02

1.5

-3.0.06.17.12.10.05

-1.2-3.0

100 110 1206.0

-6.0.70

-3.0

1.1

.05

.17

.10

.07

-3.0

0.3

.01

.09

.05

.04

-1.4-3.0


TYPE C (Control on multilane road, refer Table 2.2.2)





-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.2

-3.0 -3.0 -3.0 -3.0 -3.1-0.5 1.9 2.7 3.5 4.4 5.2 5.8

-3.6 -4.4 -5.2 -5.8

0000

.11

.22

.15

.11

.25

.30

.20

.15

.39.38.25.19

.47

.45

.30

.23

.49

.53

.35

.26

.60

.40

.30

100 110 1206.0

-6.0

.50

-3.0

1.1

.03

.15

.10

.07

-3.0

0.3

.01

.07

.05

.04

-1.4-3.0


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.3

-3.0 -3.0 -3.0 -3.0 -3.0-0.8 1.4 2.1 2.8 3.5 4.3 4.8

-3.1 -3.7 -4.3 -4.8

0000

.08

.22

.15

.11

.20

.30

.20

.15

.32.38.25.19

.37

.45

.30

.23

.39

.53

.35

.26

.60

.40

.30

100 110 1205.0

-5.0

.40

-3.0

0.6

.03

.15

.10

.07

-3.0

-0.1

.01

.07

.05

.04

-1.5-3.0


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.4

-3.0 -3.0 -3.0 -3.0 -3.0-1.1 0.8 1.5 2.1 2.7 3.4 3.8

-3.0 -3.2 -3.6 -3.8

0000

.06

.22

.15

.11

.15

.30

.20

.15

.24.38.25.19

.28

.45

.30

.23

.29

.53

.35

.26

.60

.40

.30

100 110 1204.0

-4.0

.30

-3.0

0.6

.02

.15

.10

.07

-3.0

-0.5

.01

.07

.05

.04

-1.7-3.0


-3.0

-3.0

Distances from SS

SuperTransition

PlanTransition

andWidening

WideningPer

Lane

Inside of Control


NominalWidth

2.83.03.253.53.7*

10 0 10 20

Cross-fall %

Outside of Control


30 40 50 60 70 80 90TP SC

-3.0

-3.0

-2.8 -2.5

-3.0 -3.0 -3.0 -3.0 -3.0-1.4 0.3 0.8 1.4 1.9 2.5 2.8

-3.0 -3.0 -3.0

000

.19

.11

.07

.25

.15

.10

.31.19.13

.38

.23

.15

.44

.26

.18

.50

.30

.20

100 110 1203.0

-3.0-3.0

-0.3

.12

.07

.05

-3.0

-0.8

.06

.04

.02

-1.9-3.0 -3.0

Offset Not Required


TYPE C (Control on multilane road, refer Table 2.2.2)




2.2.5 Length of Curved Roadway

Length of curved roadway is the sum of thelength of circular arc on the true control line andthe lengths of the plan transitions which connectthe shifted circular arc to the tangents, or thelength of the pegged base control line if plantransitions are not required (see Section2.2.19). The total length should provide apleasing appearance by avoiding the impressionof a "kink" in the horizontal alignment. Also, theshifted circular arc should be sufficiently long, inrelation to the lengths of the spiral transitions, toavoid the appearance of a "hump" in the outerpavement edge due to superelevation.

The appropriate minimum length of curvedroadway is a function of aesthetics and istherefore subjective. However, a convenientmeasure which satisfies this aesthetic function,is the adoption of a minimum length of at leastthree times the length of plan transition ordesirably the distance travelled by a vehicleduring one second for each 10 km/h of designspeed. The latter is calculated with the followingformula:

L V V Vh = × × =1000

3600 10 36

2

Where:Lh = length of horizontal curve (m)

V = design speed (km/h)

Appropriate lengths of curved roadway forvarious radius curves are given in Table 2.2.2.

2.2.6 Circular Arc

The approximate length of circular arc on thebase control line is the difference between thelength of curved roadway and the sum of halfthe lengths of the plan transitions.

2.2.7 Deflection Angle

The minimum deflection angle (∠°) required tocontain the desirable length of pegged circulararc may be derived with the formula:

∠°=Length of Pegged Circular Arc0.01745R

2.2.8 Vehicular Movement on aCircular Path

As a vehicle travels on a circular curve, acentripetal force must be applied to balance theinertial forces associated with the circular path.

For a given radius and speed, a set force isrequired to maintain the vehicle in this path. Inroad design, this is provided by the transversefriction demand, developed between tyre andpavement, and by superelevation.

For small values of superelevation, the followingapproximation may be accepted:

e fvgR

orV

R+ =

2 2

127Where:e = pavement superelevation (m/m or tangent of

angle). This is taken as positive if the pavementfalls towards the centre of the curve

f = assumed value of transverse friction demandbetween vehicle tyres and road pavement. (Table2.24) Taken as positive if the frictional force onthe vehicle acts towards the centre of the curve.

g = acceleration due to gravity (9.8m/sec2)v = speed (m/sec)V = speed (km/h)R = radius (m)

Where f equals zero in the formula, the whole ofthe centripetal force is exerted by the super-elevation. This condition can occur on largeradius curves with positive superelevation or forslow moving vehicles on curves of any radius.At low speeds, f can be negative, and the curveis then over-superelevated for that speed.Curves are generally designed, so that apositive f is obtained for the range of vehiclespeeds likely to occur.

Figure 2.2.1 illustrates the relationship of speed,radius and superelevation based on theassumed coefficients of transverse frictiondemand listed in Table 2.2.4.

2.2.9 Transverse Friction

The value of the transverse friction factor is afunction of the type and condition of the roadsurface, the behaviour of the vehicle and thetype and condition of the tyres. It is thereforevariable and the least determinable of theelements adopted to determine the "safe speed"of a horizontal curve.

The upper limit of the transverse friction factor(friction supply) is the point of impending skid. Ashorizontal curves are designed to avoidskidding, with a margin of safety, the assumedtransverse friction factor, (f) adopted for designpurposes, (friction demand) is substantially lessthan this upper limit.



10 9 8 7 6 5 4 3 2 1 050

6070

8090

100

110

120

130

140

6070

8090

100

120

140

160

180

200

250

300

350

400

500

600

700

800

900

1000

1100 1200

1300

Vf

50 60 70 80 90 100

110

120

0.30

0.24

0.19

0.16

0.13

0.12

0.12

130

0.11

0.11

SP

EE

D /

RA

DIU

S /

SU

PE

RE

LEV

ATI

ON

RE

LATI

ON

SH

IP(F

OR

SE

ALE

D R

UR

AL

RO

AD

S)

E

Cur

ve R

adiu

s (m

)

Spe

ed (k

m /

h)

Not

e: T

he g

rey

boxe

d ar

eas

defin

e th

e re

com

men

ded

"E"

to b

e ad

opte

d

fo

r the

rang

es o

f rad

ii in

dica

ted.

For

"E

" le

ss th

an 3

%, a

dopt

3%

.

%

Figu

re 2

.2.1



A driver's attitude, when driving, varies inrelation to the road environment, terrain, surfaceconditions and the traffic density on the road.For instance, drivers will use higher values oftransverse friction when traffic density is lowand/or the road surface is dry, than when theopposite conditions apply.

The maximum values of assumed transversefriction demand (f) to be adopted for the designof horizontal curves, for various conditions, aregiven in Table 2.2.4; they are a guide foraverage conditions and should be usedcautiously.

Table 2.2.4 Maximum Assumed Values ofTransverse Friction Demand

DESIGNSPEED(km/h)

BITUMENAND

CONCRETEPAVEMENTS

GRAVEL ANDUNSURFACED

ROADS*

50 0.30 0.1460 0.24 0.1370 0.19 0.1280 0.16 0.1190 0.13 0.10100 0.12 -110 0.12 -120 0.11 -130 0.11 -

* extrapolated from 1945 D.M.R. Data Book

NOTE: Desirable of superelevation (Table 2.2.5) must not bereuced on the basis of assumed values of transverse frictiondemand.

2.2.10 Superelevation - General

Horizontal curves are superelevated to balancethe effects of centrifugal force. The amount ofsuperelevation will depend on vehicle speed,curve radius and pavement surfacecharacteristics. The rate to be adopted is chosenfor the aspects of safety, comfort andappearance.

Curves of 3000m radius and over may besuperelevated but this is not generallynecessary except for appearance reasons.Superelevation gives the curve a more naturalappearance in certain situations, especially inflat open terrain, and helps define the outeredge of pavement

2.2.11 Desirable Superelevation

Values of desirable superelevation are shown inTable 2.2.5.

Table 2.2.5 Desirable Superelevation

radius superelevation50-330 7%

330-550 6%550-750 5%750-950 4%

>950 3%

Figure 2.2.1 illustrates typical combinations ofsuperelevation, curve radii and friction demand.

2.2.12 Maximum Superelevation Values

The maximum value of superelevation is limitedby heavily laden or slow moving vehicles and byconditions of ice and snow. In rural areas themaximum value of superelevation to be adoptedis 10% with the desirable maximum being 7%.In certain situations it may be desirable toincrease the superelevation to the maximum asan additional safety feature. The developmentof a steep superelevation may create difficultieswith drainage on the inside of a curve and itmay be necessary to slightly increase the grade.

In urban areas superelevation exceeding 4% isundesirable because of pedestrian traffic.

2.2.13 Minimum Superelevation Values

The minimum value of superelevation shouldnot be less than the slope of the normalcrossfall adopted for the adjacent straight roadalignment. This is normally 3% but can be 4% inflat country areas where near level longitudinalalignment is unavoidable.

In urban situations, although 3% is therecommended minimum superelevation, lowersuperelevation values may be adopted indifficult circumstances.

2.2.14 Adverse Crossfall

In rural situations all curves under 3000m radiusshould be superelevated. However, to improvepavement drainage on very flat longitudinalgrades, or in the design of temporary roadways,sidetracks and temporary connections,consideration may be given to the use of up to3% adverse crossfall.

The curve radius with adverse crossfall can becalculated with the same formula used forpositive crossfall (See Section 2.2.8). Howeverthe e value for superelevation is negative andthe f value for the assumed transverse frictiondemand is 2/3 of the rural values listed in Table2.2.4.



In urban situations where drivers are moreadaptable to changes in radius, superelevationand transverse friction, the use of adversecrossfall on small radii curves is tolerable.

2.2.15 Superelevation on Bridges

Where a bridge structure is proposed near ahorizontal curve and intrusion of the normalapplication of the superelevation transition ontothe deck is unavoidable, it is preferable tomaintain a uniform section on the bridge deckby continuing the rate of curve superelevationalong the full length of the bridge.

2.2.16 Superelevation on Steep Grades

The adoption of the maximum values ofsuper?elevation on very steep grades mayincrease the longitudinal grade on the outerlanes unacceptably . Usually the superelevationis the only geometric element which can bevaried and it sometimes becomes necessary toeither reduce the superelevation or extend thelength of the eases at the end of thesuperelevation development .

It is recommended that designers profile theouter edges of pavement to ensure acceptabledrainage design and aesthetics.

20m Ease(min)

Control

n

E

E

20m Ease(min)

20m Ease(min)

Relative grade

Axis of Rotation

Not to Scale

Superelevation Development Le

Plan Transition Lp

20m Ease(min)

Outer Edge ofPavement

Inner Edge ofPavement

S.S. T.S. T.P. S.C.

Notes 1. T.S. = Tangent Spiral, common point of tangent and spiral.2. T.P. = Tangent Point, common point of tangent and curve3. S.S. = Start of Superelevation Transition.4. S.C. = Spiral Curve, common point of spiral and circular curve

7. All longitudinal measurements are made along the pegged control line.8. All lateral measurements are made at right angles to pegged control line.

5. n = Normal crossfall (%)6. E = Superelevation (%)

SUPERELEVATION PROFILESFigure 2.2.2



2.2.17 Road Junction Superelevation

Where a side road junctions on the outside of asmall radius curve, a compromise is necessarybetween adequate superelevation on thethrough road and safe conditions for vehiclesturning against the adverse crossfall. Thesituation worsens if the curve is located on asteep grade. If the intersection cannot berelocated, the superelevation should bemodified to ensure safe turning conditions.

Generally, if the side road is important or thecurve has a steep longitudinal grade over 5%,the superelevation should not exceed 4% andshould preferably be limited to 3%. The sameproblem does not exist where the junction is onthe inside of the curve as the super?elevationthen favours the turning movements.

2.2.18 Superelevation Development

A profile of a typical superelevationdevelopment is shown on Figure 2.2.2.

It can be seen from the diagram that thesuperelevation development is introducedahead of the Plan Transition to ensure that adriver does not have to cope with adversecrossfall when beginning to turn.

60 - 70 percent of the super?elevationdevelopment is normally located in advance ofthe tangent point. This is regardless of thepresence of a plan transition.

(a) Length of Superelevation Development

The desirable length of superelevationdevelopment is the length required to uniformlyrotate the crossfall from normal to fullsuperelevation with adjustment for therequirements of relative grade.

The length of superelevation development [fromnear normal crossfall at the S.S. point to nearfull superelevation at the S.C. point (withallowance made for eases as described below)]should be adequate to give satisfactory ridingqualities and to ensure good appearance. Thehigher the design speed or wider thecarriageway the longer the superelevationdevelopment.

To improve the appearance a 20m minimumease is provided that spans the start and end ofthe superelevation development.

(b) Procedure

The procedure to be adopted to determine therequired superelevation development for acurve is as follows:

(i) Calculate the required length forrotation development (Lr ) [see (c) over].

(ii) Calculate the relative grade (Gr )[see (d) over].

(iii) If calculated value of Gr is lessthan the values given in Table 2.2.6 (over), thecalculated figure should be adopted. If it isgreater, the tabulated figure should be used.

(iv) The selected value of Gr should besubstituted in the formula given in (e) over, tocalculate the length of super-elevationdevelopment (Le) required to satisfy the relativegrade criterion.

(v) In most cases the length ofsuperelevation development required for therelative grade criteria (Le) will be the oneadopted, however if the length of rotationdevelopment (Lr) exceeds Le then Lr should beselected. Superelevation is applied as shown onFigure 2.2.3.

(c) Rate of Rotation

Satisfactory riding quality is determined by thedistance required to uniformly rotate thecrossfall from normal to full superelevation.

In low speed environments or in mountainousterrain where design speed of the alignment isless than 80km/h, the rate of rotation adopted is3.5% per second of design travel time.

For design speeds of 80km/h or more thedesirable rate of rotation should not exceed2.5% per second of design travel time.

Length of Rotation CalculationDesign Speed <80km/h:

LE E E E V

r =×

=− −( ). .

( ).

1 2 1 2

3 5 3 6 12 6

Design Speed ≥80km/h:

LE E V E E V

r = −×

= −( ). .

( )1 2 1 2

2 5 3 6 9Where:Lr = Length of rotation (m)E1,E2 = Crossfall at ends of superelevationdevelopment (%)V = Design Speed (km/h)



The length of rotation and length ofsuperelevation development are similar,howeverthe latter incorporates the consideration ofrelative grade [See (e) below].

(d) Relative Grade

Good appearance in relation to superelevationdevelopment refers to a satisfactory relativegrade. Relative Grade is the difference in gradebetween the grade of the outside edge ofpavement and the grade of the axis of rotation.The axis of rotation, or control line, is usuallythe centre line but may be the inner edge ofpavement.

Note: The transitions as shown, refer to a cubic parabola. In computer aided design, the plan transition is usually a clothoid spiral, set out without reference to a Pegged Base Control Line (See Section 2.2.19b)

Outer edge of pavement

Inner edge of pavement

LeSuperelevation Development ( )

LpPlan Transition ( )

S.S. T.S. T.P.

S.C.

Offset(S)

True Control Line

Pegged Base Control LineNot to Scale

FullSuperelevation (E)

at end of ease

NormalCrossfall (n)

at start ofease

DIAGRAM OF TRANSITIONSFigure 2.2.3



Relative Grade Calculation

Relative Grade as derived from the formulas forLength of Rotation is:

Design Speed < 80km/h:

GW

Vrr= 12 6.

Design Speed ≥ 80km/h:

GWVr

r= 9

Where:Gr = Relative Grade (%)Wr = Width from axis of rotation to outside

edge of running lanes (m)V = Design speed (km/h)

A reasonably smooth appearance of thesuperelevation development will result if therelative grade is not more than the valuesshown in Table 2.2.6 These values aresubjective and should not be regarded asprecise criteria.

Table 2.2.6 SuperelevationDevelopment Maximum Relative GradeValues for Appearance Criterion.

DESIGN RELATIVE SPEED (%)SPEED(km/h)

A*One lane

B*Two Lanes

C*More ThanTwo Lanes

40 or under 0.9 1.3 1.760 0.6 1.0 1.380 0.5 0.8 1.0

100 0.4 0.7 0.9120 or over 0.4 0.6 0.8A* normal two-lane roadway with control on centreline

B* two-lane roadway with control along one edge,four-lane roadway with control on centreline,two-lane roadway with climbing lane andcontrol on centreline of basic two lanes.

C* multi lane roadway with more than lanes betweenthe control and the edge of the running lanes.

(e) Superelevation DevelopmentLength to Satisfy Relative Grade

The length of superelevation development tosatisfy relative grade requirements is derivedfrom the following formula:

LW E E

Ger

r

= −( )1 2

Where:Le =Length of superelevation

development (m)E1, E1 =Crossfall at ends ofsuperelevation development (%)(E1 - E1) =Algebraic difference incrossfallGr =Relative grade as calculatedor from Table 2.26 (%)Wr =Width from axis of rotation tooutside edge of running lanes (m)

2.2.19 Plan Transition

The curve inserted to transition from a straightto a circular arc is known as a Plan Transition.The general arrangement of a plan transitionand its relationship to superelevationdevelopment is shown on Figure 2.2.3. Theradius reduces from infinity at the end of thestraight to that of the circular curve at thebeginning of the arc.

The plan transition curve provides a uniformrate of change of radial acceleration for avehicle travelling from a straight to a circularcurve and vice versa. It also serves to improvethe appearance in approach to the curve byeliminating the abrupt change of direction whichwould otherwise be present at the tangent pointof smaller radii curves. If a plan transition is notprovided, some drivers will cut into adjoininglanes to enter and leave curves. The provisionof a plan transition reduces this tendency.

The plan transition, if provided, should bepositioned equally on each side of the T.P. andshould occupy that portion of the superelevationdevelopment (see Section 2.2.18) from the T.S.point, to the S.C. point, where fullsuperelevation is reached (see Figure 2.2.3).

The length of plan transition is therefore relatedto the length of the superelevation developmentand is calculated using the following formula,which is based on rate of rotation (see Section2.2.18)

LL E

E Epe=−( )1 2

Where:Lp = Length of plan transition (m)Le = Superelevation development length (m)

(E1-E2) = Algebraic difference in crossfall (%)E = Superelevation (%)

Two types of plan transition may be used; theclothoid spiral, and an approximation of thecubic parabola.



(a) Clothoid Spiral

A clothoid (or Euler) spiral has the intrinsicproperty that its curvature (or the reciprocal ofthe radius) varies at a uniform rate along thecurve. As such, it closely approximates theaction of steering a vehicle from a straight to acircular curve. The use of this form of transitionis usually restricted to computer aided designdue to the complexity of the mathematicsinvolved.

Transition curves formed by clothoid spirals areset out as a single control line without referenceto a pegged base control.

Clothoid spiral transition curves are generallynot required for curve radii larger than 1000m,with normal superelevation.

(b) Cubic Parabola

The cubic parabola has been the traditionalmeans of providing a plan transition. It has beenextensively used, primarily due to the ease ofcalculation by manual methods.

The transition is set out using offsets to a truecontrol line from a pegged base control line, asshown on Figure 2.2.4.

These offsets may be calculated using thefollowing formulae:

(i) Maximum Offset to True Control line

The maximum offset (S) from the pegged basecontrol line to the true control line, occurs overthe length of constant superelevation betweenS.C. and C.S., on the circular curve. Its value isgiven approximately by:

SL

Rp=

2

24

Where:Lp = Length of plan transition (m)R = Radius of circular curve (m)S = Maximum plan transition offset (m)

Where the calculated maximum offset is lessthan 300mm, it may be omitted because thecontribution by the transition to positioning ofvehicles or to appearance is negligible.

Recommended lengths of plan transition areshown in Table 2.2.2, for recommendedtransition offsets see Tables 2.2.3

(ii) Plan Transition Offset

The following approximation of the cubicparabola formula may be used to calculate thecurve offsets:

y xRLp

=3

6Where:

y = Intermediate offsets (m)x = distance of offset from either the T.S. or

S.C. end of the transition (m)R = Curve Radius (m)p = Length of transition (m)

The transition offsets may be applied by eitherof the two methods detailed on Figure 2.2.4.

The factors required to establish the offsets tobe applied for the more common lengths of plantransition, as measured from the T.S., aregiven in the table on Figure 2.2.4.

Transition offsets on curves of various radii aregiven in Tables 2.2.3



R = Radius of Base Control Line (m)

LP = Length of Plan Transition (m)S = Maximum Plan Transition (m)y = Intermediate offset (m) [Method 1]x1 = Distance of offset from T.S. (m)x2 = Distance of offset from S.C.P = Offset adjustment factor from Table below

p = Transition offset (m) [Method 2]

Where:

x1

p

T.S. T.P.

S.C.

2LP

2LP

x2

y

Ry

S2

True control line

S (p maximum)

Pegged basecontrol line

Factors for Calculating Offsets for Cubic Parabola Transitions [Method 2]LENGTH OF FACTOR P AT DISTANCE x1 FROM START OF TRANSITION (T.S.)TRANSITION

(LP )10 20 30 40 50 60 70 80

40 4 33 62 6650 3 26 78 101 10460 3 22 75 128 147 15070 2 19 64 140 185 202 20480 2 17 56 133 210 249 264 266

Application of Offset

Method 1The offsets (y) as calculated in Section 2.2.19(b), are measured from the tangent between the T.S.andT.P., and from the extension of the true control line between the S.C. and T.P.

Method 2The offsets (p), between the base and control lines (rounded to nearest 0.01m), may be established bydividing the factor (P) from the table by the radius of the circular curve (R).

Notes:1. The transition is equally spaced (Lp /2) about the tangent point (T.P.)2. The offset at the T.P. is S/2

OFFSETS FOR A CUBIC PARABOLA PLAN TRANSITIONFigure 2.2.4



2.2.20 Lane Widening

Widening is required on horizontal curves to:

• provide for the greater width required by aturning vehicle,

• allow for inaccuracies in steering a vehiclearound a curve, particularly at high speed,

• cater for vehicle slippage

When a vehicle turns on a horizontal curve, itsrear wheels track inside the front wheels (seeFigure 2.2.5). Each travel lane must thereforebe widened, firstly by a distance which equals:

R R Lx− −2 2

Where:R = Radius (m)Lx = Length of a vehicle between its

rear axle and the limit of front overhang (m)

At the same time it is desirable for a vehicle tomaintain a clearance to each edge of its travellane and a lateral clearance between vehicles(see Figure 2.2.5). The appropriate value of Clwhich is used with varying lane widths (Wl) isgiven in Table 2.2.8:

Table 2.2.8 Lateral Clearance (CL )

Wl(m) Cl(m)3.0 0.6

3.25 0.73.5 0.83.7 0.9

The lateral clearances in Table 2.2.8 assumethat a vehicle, travelling at speed, canaccurately negotiate the curved travel way. Asthis is not usual, further widening of the lane isrequired to allow for inaccuracies which occur insteering. These inaccuracies increase withspeed of travel and the additional width iscalculated with the formula:

WV

Rb =19

Where:R = Radius (m)V = Speed (km/h)

Although semi-trailers require most lanewidening, the dimensions of the NAASRAsingle unit vehicle (S.U.), given in Table 2.2.9,have been assumed for the purpose ofdetermining optimum lane widening.

Table 2.2.9 S.U. Vehicle DimensionsDIMENSION (m)

Vehicle 2.5Overall Length 11.0

Length Between Axles 7.3Front Overhang 1.0

The width of lane widening on horizontal curvesis therefore calculated with the formula:-

W R R CV

RWl l= − − + + + = −2 69 2 5

19.

Where:R = Radius (m)Cl = Lateral clearance between vehicles in

adjacent lanes (m)V = Speed (km/h)Wl = Lane width (m)

The calculated widening is applied to each lane.The total widening may be applied on the insideof plain circular curves, in which case the sameeffect as a plan transition is achieved. Forcurves with a radius of 30m or less, the actualpaths of articulated vehicles should bedetermined from templates or vehicle pathcomputer programs. If the calculated widening isless than 200mm per lane, it need not beapplied.

The transition to the widened curve is uniformand coincides with the plan transition. Wherethere is no plan transition, about half thewidening is developed before the tangent point;the total widening being fully developed by theS.C.

See Table 2.2.2 for recommended values ofpavement widening for various lane widths andvarious radii of curves, and Table 2.2.3 forrecommended widening offsets.

2.2.21 Compound Curves

(a) Radii

Compound curves are curves of the samedirection having a common tangent point.Compound curves which have radii <1000m areundesirable and should be considered only incases of very difficult location where otheralternatives, such as a simple curve, are notavailable. When their use is unavoidable in lowspeed design, the ratio of the larger radius to thesmaller should not exceed 1:0.5, the moredesirable ratio being 1:0.75.For high speed design, the design speed criteriagiven in Section 2.2.4 and not curve ratiosshould be satisfied.



Wa

Wd

Wb

Cl

+

R

W

W

0.5C

l

0.5C

l

Cl

7.3

1.0

2.5

Wl

Wl

W=

RR

2-

69-

++

+C

l2.

5V

R19

-W

l

W

= L

ane

Wid

enin

g (m

).W

a=

Wid

th b

etwe

en fr

ont a

nd r

ear

whee

l tra

cks

on c

urve

(m).

Wb

= W

idth

allo

wanc

e fo

r di

fficu

lt of

dri

ving

on

curv

e (m

).W

d=

Wid

th b

etwe

en tr

acks

of f

ront

whe

el a

nd fr

ont o

verh

ang

of v

ehic

le o

n cu

rve

(m).

Wl

= L

ane

widt

h (m

).

Cl

= l

ater

al c

lear

ance

bet

ween

veh

icle

s in

adj

acen

t lan

es (m

) (Re

fer

Tabl

e 2.

2.8)

.

R =

Rad

ius

of c

entr

elin

e of

two-

lane

(m).

V =

Des

ign

spee

d fo

r cu

rve

radi

us (k

m/h

).

Whe

re:

LAN

E W

IDE

NIN

G O

N C

UR

VE

SFi

gure

2.2

.5



2.2.21 Compound Curves (continued)

Curves with radii >1000m may be compoundedat sites where existing controls (a bridge, utilityservice, adverse topography) make theprovision of a single radius curve impracticable(see Section 2.4).

A series of more than two compound curves ofdiminishing radii should not be used.

(b) Length

The combined length of compound curve shouldbe at least equal to the desirable lengthsrecommended by Section 2.2.5 with the lengthof the smaller radius curve being at least twothirds the length of the larger radius curve.

2.2.22 Broken Back Curves

Broken back curves are adjacent curves of thesame direction which are separated by a shortlength of straight. On these curves lanediscipline is poor, they are unsightly and shouldbe avoided where possible. In most instancestwo similar curves can be replaced by a singlecurve, or if need be, a compound curve.

When broken back curves cannot be avoidedthe minimum length of straight between theends of the adjacent plan transitions should beequal to the Design Speed expressed as metres(Vm). For example, for a Design Speed of80km/h, the minimum length of straight wouldbe 80m. The direction of superelevation appliedto the curves may be retained on the straightsection.

2.2.23 Reverse Curves

Reverse curves are where adjacent curves arein the opposite direction. It is essential fordriving comfort and safety that a length ofstraight alignment be provided between the twocurves. The desirable minimum lengthmeasured between adjacent T.S. points shouldbe equal to the Design Speed expressed asmetres (Vm).

Where location is difficult, reverse curves mayhave a common T.S. point, in which case thepavement at the common T.S. will be level.Where T.S. points are not common to bothcurves, and a section of straight alignment mustbe used which is less than 0.66 Vm , it will benecessary to design special superelevationtransitions.

2.2.24 Sight Distance on HorizontalCurves (See Section 2.1.12)

Driver visibility on a horizontal curve may belimited by an obstruction off the pavement. Theextent to which the curve should be adjusted, orthe obstruction removed to provide adequatesight distance, is determined by the driver's lineof sight while travelling the curve.

Figure 2.2.6 illustrates drivers line of sight andthe formula used to calculate the required offsetdistance. The sight distances adopted for thecalculation should be at least Stopping SightDistance and preferably Intermediate SightDistance so as to avoid the necessity ofproviding barrier lines. Fig 2.2.6 also shows theformula used to calculate the required minimumcurve radius to avoid obstruction to drivervisibility.

Section 2.1 gives the sight distances to beadopted for various design speeds and Table2.2.2 provides calculated offsets for variouscurve radii.



Obstruction

Line of Sight

Ds

BWs

Lane / Centre line

R

We

Formula to determine outer radius ofinner travel lane:

R (approx) =D

Ws

s

2

8 15( . )−

Formula to determine offset for line of sight:

α (Radians) =D

Rs

− 15.

B = R R− −( . ) cos1512α

Where:α = Angle subtended by line of sight (degrees)R = Outer radius of inner travel lane (m)B = Offset distance from radius R to the line of sight obstruction (m)Ds = Sight distance measured around the curve between two points 1.5m from the lane line (m)We = Distance from lane line to driver position (adopted as 1.5 metres)Ws = Width of inner travel lane and adjacent shoulder (m)

LINE OF SIGHT FOR HORIZONTAL CURVESFigure 2.2.6



2.3 VERTICAL ALIGNMENT

2.3.1 General

The elevation of the control line of a roadway isreferred to as its vertical alignment, or moresimply as its 'grading'. It is made up of straightsand curves which are referred to as 'verticalcurves' to distinguish them from horizontalcurves. As an aid to calculations, these curvesare usually parabolic, although more complexpolynomial curves can be used. Six possiblevariations of vertical curve are shown on Figure2.3.1.

+G1

+G2

L2

L

+G1-G2

-G2

-G1

A

Crest VerticalCurves

-G1+G2

-G1

-G2+G1

+G2

Sag Vertical Curves

Where:G1 and G2 = tangent grades (%)A = algebraic difference in grade (%)L = length of vertical curve (m)

TYPES OF VERTICAL CURVESFigure 2.3.1

As with horizontal alignment, the grading of aroad affects travelling speeds, road safety andthe appearance of the road. The travel speed ofcars is usually governed more by the horizontalalignment than the vertical grading andtherefore in assessing likely travel speeds theeffect of the grading can usually be ignored.However, for heavy vehicles the reverse is thecase.

Grading at crests affects the sight distancesavailable to the driver and thus contributes tothe safety of the road. Consequently, the primeaim in grading a new road, or regrading anexisting road should be to provide a verticalalignment with sight distances as long aspracticable. The lengths of crest curves shouldensure that the sight distance ahead is neverless than the stopping sight distance required tostop a vehicle travelling at the likely travelspeed, (as assessed from consideration of thehorizontal alignment). The lengths of sagcurves may be fixed by the requirements ofcomfort, as related to vertical acceleration, bydrainage requirements, headlight performanceor overhead restrictions to the line of sight.

When designing the grade line, compound andbroken back curves should be avoided. Hiddendips should also be avoided. Where thehorizontal alignment contains straights longenough to allow overtaking, the grading shouldnot contain minor humps or hollows which wouldobstruct continuous overtaking sight distance.

2.3.2 Grading

The values listed in Table 2.3.1 are thedesirable maximum grades that should beadopted for sealed roads.

Table 2.3.2 Desirable MaximumGrades for Sealed Surfaces. (%) (a)

DESIGNSPEED

TERRAIN

(km/h) FLAT ROLLING MOUNTANOUS60 6-8 7-9 9-11(b)

80 4-6 5-7 7-9100 3-5 4-6 6-8120 3-5 4-6 --

(a) Values closer to the lower figures are desirable(b) Grades over 10% should be used with caution.(c) For unsealed surfaces, the above values should be

reduced by 1%.

Grades on roads in cuttings and at the super -elevation transition of horizontal curves shouldbe adequate for proper drainage of table drains(except at summits of vertical curves) should be0.5%. If grades less than 0.5% areunavoidable, special design or treatment of thetable drains is necessary to ensure efficiency.

In very flat urban areas, it is preferable to designlevel or near level grades and provide additionalgully pits or other gutter outlets rather thanintroduce artificial undulations in order toprovide self draining gutters. This lattertechnique can result in unsightly appearance,suggesting faulty construction, particularlywhere the horizontal alignment is straight ornearly straight.



2.3.3 Grading at Intersections

At intersections on roads with moderate to steepgrades, the grades through the intersectionshould not normally exceed 3%, although indifficult terrain 5% may have to be accepted.

It should be noted that the grading of both roadsthrough the intersection should be carefullychecked for comfort, particularly wheremovements can take place at speed. This isvery important at channelised intersectionswhere opposing directions of travel may be wellseparated.

2.3.4. Vertical Curves

There are various curve forms suitable for useas vertical curves; the parabola has beentraditionally used due to its constant rate ofchange of grade and the ease of manualcalculation. Other forms, particularly thosemore suited to computer calculation are equallysatisfactory.

Due to the properties of a simple parabola, therate of change of grade per unit length is aconstant:

AL

Q=The reciprocal:-

LA

K=

is the horizontal distance in metres which resultsin a 1% change in grade

Where:-L =Length of vertical curveA =Algebraic difference of vertical

grades %K =Length of vertical curve (m) for 1%

change of grade(m/unit%)Q =Rate of change of grade per unit

length (% / m)

Figure 2.3.2 illustrates the K value concept andSections 2.3.7 and 2.3.8 show how to calculateK for various distances and sight lines.

The K value concept is a simple and convenientmethod for measuring a vertical curve. Foreach design speed and sight line configuration asingle value of K covers all combinations of Aand L.

For design purposes the K value concept alsohas the advantage of easily determining theapproximate radius of large parabolic verticalcurves:

R K= 100

Table 2.3.2 shows that K also facilitatesselection of appropriate curve templates forvarious combinations of horizontal and verticalscales.

Table 2.3.2 Selection of Curve TemplatesSCALES RADIUS

OFHorizontal Vertical TEMPLATE

(mm)1:2000 1:200 5 x K1:1000 1:100 10 x K1:500 1:50 20 x K1:500 1:100 40 x K

2.3.5 Length of Vertical Curve forAppearance

At very small changes of grade, a vertical curvehas little effect except to the appearance of theprofile and may be omitted. At any significantchange of grade, short vertical curves detractfrom the appearance. This is particularlyevident on high standard roads and on sagcurves.

Table 2.3.3 gives minimum vertical curvelengths for satisfactory appearance; longercurves are preferred where they can be usedwithout conflict with other design requirements,such as sight distance for overtaking. As thevalues in the table are subjective, the lack ofprecision is intentional. General ranges, notprecise values, are relevant.

Table 2.3.3 Vertical Curve AppearanceCriterion

DESIGNSPEED(Km/h)

MAXIMUMGRADE

CHANGEWITHOUTVERTICAL

CURVE(%)

MINIMUMLENGTH OFVERTICAL

CURVE FORSATISFACTORY

APPERANCE

40 1.0 20-3060 0.8 40-5080 0.6 60-80

100 0.4 80-100120 0.2 100-150



K= 62.5

R=100K (Approx.)

L = 250

Q=0.016% per metre

1 1

(i) For a simple parabola, the rate of change of grade per unit length is a constant:

A / L = Q ( % / m )

(ii) The reciprocal is the horizontal distance in metres which results in a one percent change in grade:

L / A = K (m / unit % )

AA = 1G G 2- = 4.0%

1%

G2 = - 15%1G = + 2.5%

INSET

EXAMPLE

QAL

= = =4 0250

0 016%.

. per metre

KLA

= = =2504 0

62 5.

. metres per 1% change in grade

L KA= = × =62 5 4 250. metre vertical curve

Approx. radius of circular curve: R K= =100 6250 metres

PARABOLIC VERTICAL CURVES K MEASURES OF CURVATUREFigure 2.3.2



2.3.6 Length of Vertical Curve forComfort

Discomfort is felt by a human when subjected torapid changes in vertical acceleration. Whenpassing from one grade to another, it is usual tolimit the vertical acceleration generated on avertical curve to a value less than 0.05g, (whereg is the acceleration due to gravity). On lowstandard roads, and at intersections, a limit of0.10g may be used.

The vertical component of acceleration normalto the curve, when traversing the path of aparabolic vertical curve at uniform speed isgiven by:

av A

Lv

KV

K= = =

2 2 2

100 100 1300

Where:a =Vertical component of acceleration

(m/sec2)v =Speed (m/sec)V =Speed (km/h)A =Algebraic difference of vertical

grading (m)L =Length of vertical curve (m)K =Measure of vertical curvature

Values for K for specific design speeds andvertical accelerations of 0.05g and 0.10g areshown in Table 2.3.4. As this is a subjectivecriterion, values have been rounded.

Table 2.3.4 Vertical Curve ComfortCriterion

DESIGNSPEED(km/h)

K=LENGTH (m) OFVERTICAL CURVE FOR1% CHANGE IN GRADE*a g= 0 05. a g= 010.

40 3 1.560 6 380 10 5

100 16 8120 23 12

g = acceleration due to gravity (9.8 m/ sec2)

* Values rounded as they are subjective approximations andshould not be rgarded as having any precise basis.

2.3.7 Length of Vertical Curve for SightDistance Requirements

The length of a vertical curve for a given sightdistance is given by the following expressions:

Where length of curve is less than the sightdistance:

L DCAs= −2 (1)

Where length of curve is greater than the sightdistance:

LD A

Cs= ×( )2

(2)

Where:L =Length of vertical curve (m)Ds =Stopping sight distance (m)A =Algebraic difference of vertical

grading (%)C =Sight line constant for vertical

curves (See Sections 2.3.8, 2.3.11 and 2.3.13)

In equation (2) the vertical curve parameter

Kmay be substituted for LA to give:

KDC

s=2

(3)

which is constant for a given sight distance andis a method of defining the sight line.

The calculated length of vertical curve is usuallyrounded, and may be modified to comply withthe subjective criteria of Sections 2.3.5 and2.3.6.

While equation (1) will always result in a lower Kvalue than equation (2), it is often convenient touse the expression L KA= to determine thelength of the curve in all situations, with Kderived from equation (3). This is notappropriate in the case of overtaking provisionswhere the sight distance being used may belonger than individual vertical curves.



2.3.8 Sight Line Constant for CrestCurves

For crest curves, the sight line constant C to beused with the expressions in Section 2.3.7 isgiven by :

C h h= +200 1 22( )

Where:h1 = height of eye above road (m)h2 = object cut off height above road

(m)

Values for C , for an eye height of 1.15m (h1)and selected values of h2, are given in Table2.3.5

Table 2.3 5 Sight Line Constants for CrestCurves.

EYE HEIGHT (1.15m)[h1]

OBJECT CUT OFFHEIGHT (m)

[h2]

SIGHT LINECONSTANT

C0.0 2300.2 461

1.15 920

2.3.9 Length of Crest Curves

For a particular design speed, the requiredlength of crest curve is usually governed bysight distance requirements. However, for smallchanges of grade, appearance considerations(Section 2.3.5.) may require larger values. Ontwo lane roads, extremely long crest curvesover 750m, should be avoided for drainagereasons. Additionally, many drivers refuse topass on such curves despite adequate sightdistance. It is often more economical to useauxiliary lane construction on a short verticalcurve than to obtain overtaking sight distance bythe use of a long vertical curve. Further, theprovision of a short vertical curve in conjunctionwith longer approach and departure grades willresult in more usable overtaking opportunities.

Values of K determined for the various sightdistance design situations are given in Table2.3.6.

The K Value relationship to length of verticalcurve and change in grade % for C values of230, 461 and 920 are shown on Figures 2.3.3,2.3.4, 2.3.5 and 2.3.6.

2.3.10 Sag Vertical Curves

On sag vertical curves, sight distance is notrestricted by vertical alignment unless anoverhead obstruction is present. At night onunlit roads, a vehicle's headlights, with the angleof beam 1? above the horizontal axis, limits thesight distance to between 120m and 150m,which is adequate for stopping sight up to100km/h.

On high standard roads not likely to be providedwith roadway lighting, consieration should begiven to providing 150m of headlight sightdistance on sag vertical curves. Adjoining sagand crest curves should be provided with similarheadlight sight distances. The resulting verticalalignment will provide near consistent nightdriving conditions on unlit roads.

However, when the sag is combined withhorizontal curvature which would cause theheadlight beam to shine off the pavement(assuming a 3? lateral spread each way), little isgained by flattening the sag vertical curve.

Figure 2.3.7 gives minimum lengths of sagvertical curve for stopping distance withinheadlight beam.

When sag vertical curves cannot be flattened toprovide desirable headlight stopping distance,they should be designed to provide adequateriding comfort based on the criterion of 0.05gvertical acceleration, although 0.10g may beadopted in difficult terrain.

Figure 2.3.8 gives length of sag vertical curvefor adequate riding comfort.



Table 2.3.6 K Values for Crest Curves - Sight Distance Criteria.

STOPPING REQUIREMENTS OVETAKING REQUIREMENTS( . , . , )h h C1 215 115 920= = =

DESIGNSPEED(km/h)

STOPPINGSIGHT

DISTANCE(m)

K( .

.)

hhC

1

2

1150 2461

===

K( .

.)

hhC

1

2

1150 2230

===

INTERMEDIATESIGHT

DISTANCE

OVERTAKINGSIGHT

DISTANCE

(a) (b) (c) SIGHTDISTANCE

(m)

K SIGHTDISTANCE

(m)

K

(1) (2) (3) (4) (5) (6) (7) (8)50 45 4.4 8.8 140 25 200 4560 60 7.8 15.7 180 35 300 10070 80 13.9 27.8 220 55 350 14080 100 22.0 43.5 270 80 450 22090 120 32.0 63.0 330 120 600 400100 150/175 49.0 / 66.0 98.0 /133.0 400 180 750 620110 210 95.0 190.0 490 260 900 880120 250 135.0 270.0 580 370 1100 1320130 300 195.0 390.0 700 540 1400 2130

(a) Normal minimun sight distance. However, K values in design should be between values in columns (3) and (4).(b) In cases where zero object height may be considered appropriate, e.g at intersections, values in column (4) apply.(c) Intermediate values are those below which barrier line marking is normally required. When intermediate sight distances cannotbe achieved economically, stopping sight distance, is to be adopted. Sight distance between intermediate and stopping may be adoptedonly when necessary to retain critical pre-determined grade levels.

2.3.11 Sight Line Constant for SagCurves

To satisfy headlight sight distance, the sight linevalue C to be used with the expression inSection 2.3.7, is given by:

C h Ds= +200( tan )θ

Where:h = Mounting height of headlight (m)Ds = Stopping sight distance (max 150m)θ = Elevation angle of headlight beam

(+° upwards )

A mounting height of 0.75m and an angle ofbeam 1° above the horizontal axis gives thesight C values shown in Table 2.3.7.

Table 2.3.7 K and C Values for SagCurves Headlight Criterion

DESIGNSPEED(km/h)

SIGHTDISTANCE

(m)

CVALUE K

50 45 307 6.660 60 359 10.070 80 429 14.980 100 499 20.090 120 569 25.3

100 150 673 33.4110 150* 673 33.4120 150* 673 33.4130 150* 673 33.4

* maximum length of headlight beam

2.3.12 Determination of Length for SagCurves

For a given design speed, the length of a sagvertical curve will be determined by either thecomfort criterion (Table 2.3.4), or the sightdistance for headlight requirements ( up to150m ) shown in Table 2.3.7. These values arebrought together in Table 2.3.8 and Figures2.3.7 and 2.3.8.



Table 2.3.8 K Values for Sag Curves Comfort and Headlight Criteria

DESIGNSPEED(km/h)

K = LENGTH OF VERTICAL CURVE(m) FOR 1% CHANGE INGRADE

COMFORTCONSIDERATIONS

*

HEADLIGHTCONSIDERATIONS

KGeneralDesigna=0.05

g

KSpecialCases

a=0.10g

SightDistance

(m)

K a

50 4 2 45 6.6 0.03g60 6 3 60 10.0 0.03g70 8 4 80 14.9 0.03g80 10 5 100 20.0 0.02g90 13 7 120 25.3 0.02g

100 16 8 150 33.4 0.02g110 19 10 150 33.4 0.03g120 23 12 150 33.4 0.03g130 150 33.4 0.04g

* As these are subjective values and theefore only considered as general approximation, exact values for every design speed are notgiven.

2.3.13 Overhead Obstructions at SagCurves

Overhead obstructions, such as road or railoverpasses, sign gantries or even overhangingtrees, may limit the sight distance available onsag vertical curves ( see Figure 2.1.1 )

The sight line constant C for this situation isgiven by:

C H h H h= − + −200 1 22( )

Where :H = Height of overhead

obstructionh1 = eye heighth2 = object cut off height

Using an eye height of 1.8m and an objectheight of 0.6m (commercial vehicle eye heightto vehicle tail-light height), the sight lineconstants for a range of vertical clearances aregiven in Table 2.3.9. Intermediate values maybe interpolated. The length of vertical curverequired to give a particular sight distance maybe found from Section 2.3.7. Generally 5.3m isto be used as the vertical clearance.

Table 2.3.9 Sight Line Constant forOverhead Obstructions

VERTICAL CLEARANCE(m)

SIGHT LINECONSTANT

C4.0 22004.5 26004.6 27005.0 30005.3 32605.5 34006.0 4400



Lengthof

VerticalCurve

inMetres

(L)

Algebraic Difference in Grade (A%)


Figure 2.3.3

KEY

V Velocity (km/h)m Stopping Sight DistanceK K valueM.O. Mid OrdinateR.T. Reaction Time

Stopping Sight Distance Ds

Zero Object Height

C = 230

1.15(Where Sight Distance is measured between twopoints 1.15 above the travelled way and zero)

LENGTH OF CREST VERTICAL CURVE FOR STOPPING SIGHT DISTANCE

1000

950

900

850

800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

130V300m390K2.5RT

120V250m270K2.5RT

110V210m190K2.5RT

100V175m133K2.5RT

100V150m98K1.5RT

90V120m63K1.5RT

80V100m43.5K1.5RT

70V80m27.8K1.5RT

60V60m15.7K1.5RT

56V45m8.8K1.5RT

M.O. = 1m

2m

4m

6m

8m

M.O. = 10m



Lengthof

VerticalCurve

inMetres

(L)



Figure 2.3.4

KEY

V Velocity (km/h)m Stopping Sight DistanceK K valueM.O. Mid OrdinateR.T. Reaction Time

Stopping Sight Distance Ds

Object 0.2m high

C = 461

1.15

(Where Sight Distance is measuredbetween two points 1.15 and 0.2m above the travelled way)


1000

950

900

850

800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

130V300m195K2.5RT

120V250m135K2.5RT

110V210m95K2.5RT

100V175m66K2.5RT

100V150m49K1.5RT

90V120m32K1.5RT

80V100m22K1.5RT

70V80m13.9K1.5RT

60V60m7.8K1.5RT

50V45m4.4K1.5RT

M.O. = 1m

2m

4m

6m

8m

M.O. = 1m



Lengthof

VerticalCurve

inMetres

(L)



Figure 2.3.5

KEY

V Velocity (km/h)m Stopping Sight DistanceK K valueM.O. Mid Ordinate

C = 920

(Where Sight Distance is measured between two points 1.15 above the travelled way)


2000

1900

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Overtaking Sight Distance Do( )

1800

1700

1600

1500

1400

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

1.15m

100V750m620K

90V600m400K

80V450m220K

70V350m140K

130V1400m2130K

120V1100m1320K

110V900m880K

60V300m100K

M.O. = 20m

50V200m45K

M.O. = 1m

2m

4m

6m

8m

10m

15m



Lengthof

VerticalCurve

inMetres

(L)



Figure 2.3.6

KEY

V Velocity (km/h)m Stopping Sight DistanceK K valueM.O. Mid Ordinate

C = 920

(Where Sight Distance is measured between two points 1.15 abovethe travelled way.)


2000

1900

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Intermediate Sight Distance Dm( )

1800

1700

1600

1500

1400

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

1m

1.15m

2m

4m

6m

100V380m160K

110V450m220K

120V530m310K

130V600m400K

8m 10m 15m M.O. = 20m

90V300m100K

80V260m75K

70V220m55K

60V180m35K

50V140m25K



Lengthof

VerticalCurve

inMetres

(L)



Figure 2.3.7

LENGTH OF SAG VERTICAL CURVE FOR HEADLIGHT REQUIREMENTS

1

0.75m

(Maximum illumination distance = 150m)

Stopping Sight Distance Ds [<100km/h]Headlight Illumination Distance Dh150m

KEYV Velocity (km/h)C Sight line valuem Stopping Sight DistanceK K valueg Acceleration due to gravityM.O. Middle ordinate

400

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

2m

3m

4m

M.O. = 1m

100V673C150m33.4K0.02g

90V569C120m25.3K0.02g

80V499C100m20.0K0.02g

70V429C80m14.9K0.03g

60V359C60m10K0.03g

50V307C45m.3K0.02g



Lengthof

VerticalCurve

inMetres

(L)

Figure 2.3.8

Desirable Riding Comfort - 0.05gMinimum Riding Comfort - 0.10g

LENGTH OF SAG VERTICAL CURVE FOR ADEQUATE RIDING COMFORT



400

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

2m

3m

4m 110V

100V

90V

80V

80V

70V

60V

60V

70V90V

KEY

Vertical acceleration of 0.05gfor V (km/h)Vertical acceleration of 0.10gfor V (km/h)

M.O. Middle ordinate (m)

M.O.=1m