RTA Road Design Guide

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ROADS AND TRAFFIC AUTHORITY OF NSW

ROAD DESIGN GUIDE

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WITHDRAWN - September 2003 - (If information required on this SECTION – Contact sender)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

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SECTION 2 ROAD GEOMETRY

CONTENTS 2.1 SIGHT DISTANCE 2.2 HORIZONTAL ALIGNMENT 2.3 VERTICAL ALIGNMENT

2.4 CO-ORDINATION OF HORIZONTAL AND

VERTICAL ALIGNMENT

Roads and Traffic Authority Road Design Guide

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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

(106)

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 development b. Procedure

c. Rate of Rotation d. Relative grade

e. Length of superelevation development to satisfy relative grade

2.2.19 Plan transition a. Clothoid spiral b. Cubic parabola 2.2.20 Lane widening 2.2.21 Compound curves a. Radii b. Length

2.2.22 Broken back curves

2.2.23 Reverse curves

(107)

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

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2.4

CO-ORDINATION OF HORIZONTAL AND VERTICAL ALIGNMENT

(This subject is more fully covered in Section 6)

Page No.

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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).

(110)

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).

(111)

RTA of NSW Section 2 - Road Geometry

Road Design Guide June, 95 1

Issue 1.0

2.1 SIGHT DISTANCE

2.1.1 General

A principal aim in road design is to ensure that a driver has sufficient sight distance to be able to perceive any road hazards in sufficient time to take action to avoid mishap. A driver's sight distance should be as long as practicable, but it is often restricted by crest vertical curves, horizontal curves in cutting, roadside vegetation and buildings at intersections. These restrictions can make manoeuvres such as overtaking unsafe due to the sight restriction.

The provision of adequate sight distance therefore requires a determination of the length of crest vertical curves and radius of horizontal curves to suit the desired sight distance. Where the desired radius of horizontal curve cannot be achieved, it becomes necessary to determine the extent to which the inside of the curve should be cleared to allow the driver to see the required distance along the road.

2.1.2 Sight Distances

In design there are three sight distance requirements to be met :

(i) Stopping Sight Distance

At all times a driver must be provided with sufficient visibility to see an object in the lane of travel and stop before striking it. This is known as the "stopping" sight distance.

(ii) Overtaking Sight Distance

At reasonable intervals a driver should have sufficient visibility to detect oncoming vehicles in sufficient time to allow safe and uninterrupted overtaking of a vehicle with minimal risk of collision with oncoming traffic. This is known as the "overtaking" sight distance.

(iii) Intermediate Sight Distance

Although the provision of overtaking sight distance is desirable, the cost of construction to achieve it can be prohibitive. The provision of "intermediate" sight distance enables a driver to travel a road in comfort with reasonably safe overtaking opportunities.

Calculations to obtain the distance needed to stop or to overtake are made on the assumption that the driver is travelling at a speed consistent with the alignment of the road. In practice, the actual speed adopted by a driver is influenced by geometric features of the road layout rather than the sight distance provided.

2.1.3 Constants Assumed for Determination .of Sight Distances

The following values are used in calculating stopping distances and sight distances (see

Figure 2.1.1).

Reaction Time -- 1.5 secs for design speeds ≤100 km/hr

-- 2.5 secs where design speed is ≥ 100 km/hr and access is controlled.

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

-- 0.2m Stationary object on road.

-- 0.6m Vehicle tailstop light.

2.1.4 Stopping Sight Distance

Stopping sight distance is the minimum distance required by an average driver of a vehicle travelling at a given speed to react and stop before reaching an object in the vehicle path. Stopping sight distance is measured along the line of travel from a point 1.15m high (representing the height of a driver's eye), to a point 0.2m high (representing a stationary object on the roadway).

The length of vertical curve required at crests increases significantly as the object cut off value approaches zero and therefore the general figure adopted which produces satisfactory designs is 200mm. However, zero should be used in the case of intersections where it is necessary to see road markings, or on the approaches to causeways and floodways where water or sand left by floods, or washouts may occur (see Figure 2.3.3).

Stopping sight distance has two components, the distance travelled during total reaction time and the distance travelled during braking time.

Reaction distance (dr)

=

R v

=

R V

t t

3 6

.

Braking distance (d)

=

v

=

gf

V

f

l l 2 2

2

254

Stopping Sight Distance (Ds)

=

R V

+

V

f

t l

3 6

254

2

.

Where:

dr= distance travelled during reaction time

d= distance travelled during braking time

Ds= 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 throughout the braking period (see Table 2.1.1).

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

The stopping sight distance to be used for various speeds on level bituminous or concrete

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2 16/09/98 Road Design Guide

Issue 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 COMPONENTS

Figure 2.1.1

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

DISTANCE (m) TRAVELLED DURING* DESIGN CO-EFFICIENT OF REACTION TIME Rr BRAKING TOTAL STOPPING DISTANCE (m) SPEED (km/h) V LONGITUDINAL FRICTION DEMAND fl

1.5 Secs 2.5 Secs 1.5 Secs 2.5 Secs

50 0.50 20 25 45 60 0.47 25 35 60 70 0.45 30 50 80 80 0.43 35 65 100 90 0.41 40 80 120 100 0.39 45 70 105 150 175 110 0.37 75 135 210 120 0.35 85 165 250 130 0.33 90 210 300

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

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Issue 1.0 2.1.5 Effect of Grade on Braking

Distance

The distance a vehicle travels while being braked is longer on downhill grades and shorter on uphill grades. The braking distance component of the stopping sight distance formula (Section 2.1.4) when adjusted to take into account the effect of grade is

:-d

V

f

_l

G

=

±

2

254 (

0 01

.

)

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

longitudinal friction demand for design speed (see Table 2.1.1).

G = longitudinal grade per cent

(+ uphill, - downhill)

2.1.6 Overtaking Sight Distance

Overtaking sight distance is measured along the line of travel between two points each 1.15m above the road pavement. It is equal in length to the minimum distance between two opposing vehicles which will permit a safe overtaking manoeuvre.

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

Table 2.1.2 Overtaking Sight Distances

DESIGN SPEED (km/h) OVERTAKING SIGHT DISTANCE (m) 1.15m-1.15m 50 250 60 300 70 350 80 450 90 600 100 750 110 900 120 1100 130 1400

When applying the overtaking sight distances given in Table 2.1.2, the following factors should also be considered :

(i) Frequency

The frequency at which overtaking sight distance should be provided is related to the travel speed, traffic volume, traffic composition,

terrain and cost of construction. It is an essential safety measure and to a large degree will influence both the location and design of a road. In undulating or flat country, it should occur frequently or continuously; at other locations minor modifications to alignment or grading may provide the sight distance necessary at little or no additional cost. As a general rule if overtaking sight distance cannot be economically provided at least once in each 2km of road, (depending on road type and volume), consideration should be given to the installation of auxiliary lanes in accordance with

Section 8.1.

(ii) Length of continuing overtaking sight

distance

Isolated sections of roadway that have only minimum overtaking sight distance, are of little value if oncoming traffic prevents the utilisation of any overtaking opportunity provided. After overtaking sight distance has been established, it needs to be maintained continuously along a length of roadway to maximise overtaking opportunities and to enable an overtaking manoeuvre, once commenced, to be either completed or abandoned with safety. This length should be as long as economically practicable, and on roads with high traffic volumes should be equal to at least half the overtaking sight distance for the design speed.

(iii) Vertical alignment

The provision of minimum overtaking sight distance at crests is usually uneconomical and may not be used since many drivers are reluctant to overtake in these circumstances. Shorter crest curves with stopping sight distance often result in longer sections with overtaking sight distance.

(iv) Auxiliary lane option

The provision of overtaking sight distance at some locations on two lane roads may not be cost effective and in these cases, a section of auxiliary lane construction with stopping sight distance is generally more economical than two lanes with overtaking sight distance.

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Issue 1.0 2.1.7 Intermediate Sight Distance

Cases occur where it is not economically practicable to provide overtaking sight distance at reasonable intervals. The model for overtaking sight distance is based on one set of conditions, that is, the overtaking of a vehicle travelling at a lesser speed than the general travel speed on the section of road. In practice there is a wide range of conditions where a sight distance shorter than overtaking sight distance would be useful. For example, a much shorter sight distance is suitable to overtake a slow-moving truck.

Where overtaking sight distance cannot be obtained and the introduction of an auxiliary lane is not warranted, the provision of intermediate sight distance may meet some overtaking needs by providing sight distance sufficient to complete or abort an overtaking manoeuvre before reaching an opposing vehicle which is just out of sight and travelling towards the first vehicle at the 85th percentile speed . The intermediate sight distances for various speeds are shown in Table 2.1.3

Table 2.1.3 Intermediate Sight Distances. DESIGN SPEED (km/h) INTERMEDIATE SIGHT DISTANCE (m) [1.15m-1.15m] 50 140 60 180 70 220 80 260 90 300 100 380 110 450 120 530 130 600

2.1.8 Summary of Sight Distances

Table 2.1.4. summarises the sight distances as discussed for level bituminous or concrete pavements.

Table 2.1.4 Sight Distances on Level Bituminous or Concrete Pavements DESIGN SPEED (km/h) STOPPING SIGHT DISTANCE (m) INTER-MEDIATE SIGHT DISTANCE (m) OVER-TAKING SIGHT DISTANCE (m) 50 45 140 250 60 60 180 300 70 80 220 350 80 100 260 450 90 120 300 600 100 150/175 380 750 110 210 450 900 120 250 530 1100 130 300 600 1400

2.1.9 Sight Distance at Night

Unless roadway lighting is installed, sight distance at night is confined to the range of a vehicle's headlight beam. The distance of a driver's visibility is therefore limited regardless of which standard sight distance has been incorporated into the road's horizontal and vertical alignments for daylight driving. The limitations of vehicle headlights restrict the sight distance that can be safely assumed for visibility of an object on a roadway, to between 120m and 150m.This corresponds to satisfactory stopping distance up to 100km/h on a sealed road and less for a gravel surface.

The criterion for headlight sight distance does not apply to roads which have street lighting to the standards prescribed by the S.A.A. Public Lighting Code, AS 1158, or on roads with high traffic volumes where it is necessary to keep headlights on dipped beam for a relatively high percentage of the travel time.

2.1.10 Sight Distance at Vertical Sags

Sag vertical curves may be designed to provide acceptable standards of comfort or to allow adequate headlight sight distance, with the latter usually being the governing criterion.

Where a sag vertical curve is on a straight,

Figure 2.3.7 (page 2-37) gives the length of

vertical curve which provides for headlight sight distance (to a maximum of 150m) with an angle of beam 1° above the horizontal axis.

2.1.11 Sight Distance at Vertical Crests

The minimum sight distance to be provided at vertical crests is stopping sight distance for the specified design speed and an object height of 0.2m. The provision of overtaking sight distance at vertical crests is usually uneconomical and a

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Issue 1.0

more satisfactory option is the adoption of intermediate sight distance.

Figures 2.3.3 and 2.3.4 (pages 2-33 & 2-34) give the length of vertical curve required to obtain stopping sight distance for eye height of 1.15m to zero pavement level and to an object height of of 0.2m for given design speeds and algebraic differences in grade.

Figures 2.3.5 and 2.3.6 (pages 2-35 & 2-36) give the length of vertical curve required to obtain overtaking and intermediate sight distances (1.15m to 1.15m) for given design speeds and algebraic differences in grade.

2.1.12 Sight Distance at Horizontal Curves

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

The relation of a drivers line of sight to the sight distance measured around the curve and the curve radius is shown as Figure 2.2.6 (page 2-26). Also shown are the formulae to calculate the offset distance required from the pavement centreline to the line of sight obstruction and the minimum radius which avoids benching. Table 2.2.2 gives calculated offsets for stopping and intermediate sight distances for various curve radii.

2.1.13 Benching for Visibility on Horizontal Curves

Benching is the widening of the inside of a cutting on a curve to obtain the specified sight distance. It usually takes the form of a flat table or bench over which a driver can see an approaching vehicle or an object on the road. In plan view, the benching is fixed by the envelope formed by the lines of sight. The driver and the object being approached are assumed to be in the inner lane. The sight distance is measured around a line 1.5m from the driver's side of the lane line and is the path the vehicle would follow in braking. Benching adequate for inner lane traffic satisfies visibility requirements for the outer lane (see Section 2.1.12).

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

0.3m under the sight line to allow for obstructions such as small boulders and grass growth.

Where a horizontal and crest vertical curve overlap, the line of sight between approaching vehicles may not be over the top of the crest but to one side and in part may be off the formation. Cutting down the crest on the pavement will not increase visibility if the line of sight is clear of the pavement, and the bottom of the bench may be 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 radius curve so that the line of sight remains within the formation. This will increase the 85th percentile speed and an iteration is necessary to ensure that stopping sight distance requirements are met.

2.1.14 Sight Distance at Combined Horizontal & Vertical Curves

Where sag and crest vertical curves are combined with horizontal curves, the sight distance requirements of Sections 2.1.10,

2.1.11 & 2.1.12 should be amalgamated to

ensure continuous provison of the appropriate sight distance.

2.1.15 Sight Distance at Intersections

(To be read in conjunction with Section 4.3.2) At all intersections, the following sight distance requirements should be satisfied:

(i) Stopping sight distance (1.15m to zero), should be available on each approach of the intersection, so that drivers may appreciate the layout of the intersection by having clear visibility to pavement markings and channel?isation.

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

(iii) Vehicles in the major road should have sufficient sight distance (1.15m to 1.15m) to observe a vehicle from the minor road move into 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 observation time (3 secs) plus,

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

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Issue 1.0 2.1.16 Sight Distance on Undivided

Roads

The minimum sight distance to be provided at all points in a two-lane or multi-lane road is stopping distance.

Where barrier lines are to be avoided and cost associated with heavy earthworks is not a primary consideration, intermediate sight distance may be used. It satisfies many overtaking requirements though it does not comply with all the requirements assumed for overtaking sight distance.

In undulating country where overtaking opportunities are few, and auxiliary lanes for overtaking are inappropriate, consideration should be given to providing intermediate sight distance at regular intervals.

In cases where barrier lines are necessary at crests, shoulders should be wide enough for a stationary vehicle to stand well clear of the pavement, so that moving vehicles are not forced to cross the centreline of the road (see

Section 3).

Care should be taken to avoid dips in the roadway which could hide an opposing vehicle and cause an overtaking driver an unexpected hazard.

2.1.17 Sight Distance on Divided Roads

At least stopping sight distance is to be provided at all points on a divided road. Generally intermediate sight distance should be adopted where economically practicable.

2.1.18 Sight Distance through Underpasses

Where economically feasible, overtaking sight distance should be maintained as the highway passes under a structure. If this cannot be achieved, intermediate sight distance will suffice. The absolute minimum sight distance which must be provided at underpasses is stopping sight distance.

2.1.19 Sight Distance at Interchanges

Mutual sight must be available between the drivers of converging vehicles at interchanges. This is particularly important at the merge of onload ramps and beneath grade separations where piers or abutment walls may obscure visibility.

2.1.20 Other Restrictions to Visibility

There are other minor constraints on sight distance that must be kept in mind by the designer:

• In avenues of trees, visibility can be curtailed at a sag owing to the line of sight being interrupted by the foliage. The same may happen where a bridge crosses a sag and the line of sight is cut by the structure.

• Guard fencing, bridge handrails, median kerbs and similar obstructions can restrict the visibility available at horizontal and vertical curves.

• There is a considerable difference between the sight distance available to a driver depending on whether the curve ahead is to the left or to the right.

2.1.21 Effect of No-Overtaking Zone Markings

Reference is made the Department's publication, "Interim Guide to Signs and Markings", Section 7.4, for the practices of marking no-overtaking zones on two lane roads.

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Issue 1.0

2.2 HORIZONTAL ALIGNMENT

(To be read in conjunction with Section 6)

2.2.1 General

The speed adopted on an open road is affected more by the driver's perception of the horizontal alignment of the road than by any other single design feature. For this reason, whenever curves are used to change the direction of travel or to suit the topography, the radii must be large enough to permit travel speeds commensurate with those expected on adjoining straights or along the whole of the section being designed. Generally, the adopted alignment should be as direct as possible, with curve radii as large as practicable.

An alignment without straight sections is described as curvilinear. Curvilinear alignment is suitable for dual carriageway roads but is undesirable for two-lane, two-way roads, as it does not provide sufficient length for overtaking. As with other elements of design, horizontal alignment should generally provide for safe and continuous operation at a uniform travel speed. Sudden reductions in standard, such as isolated curves of small radius (particularly at the end of long straights), introduce an element of surprise to the driver and should be avoided.

Where physical restrictions on curve radius cannot be overcome and it becomes necessary to introduce curvature of lower standard than the design speed of the project, the design speed of successive geometric elements should not change by more than 10km/h (on two way roads both directions of travel need to be considered).

2.2.2 Straight Alignment

The tangent or straight section is the most common element of horizontal alignment. It provides clear orientation, but at the same time is visually uninteresting unless aimed at some landmark. Being totally predictable, with a view which appears static, it causes driver monotony and encourages the undesirable combination of fatigue and excessive speed. At night, opposing headlights can cause problems.

Straights of suitable length are desirable on two lane roads to facilitate overtaking manoeuvres and should be provided as frequently as the terrain permits. Straights are too long if they encourage drivers to travel well in excess of the design speed and should therefore be avoided. Straights which are too short to provide adequate separation between adjoining curves, should also be avoided.

In flat country, long straights on roads may have to be accepted. If curves are deliberately introduced into the design to break the monotony, they

should have long arc lengths or else they will look like kinks. Unless the change in alignment is considerable, oncoming headlights will remain a nuisance to drivers.

2.2.3 Curved Alignment

The second element of horizontal alignment is the curve. Properly designed curves are appreciated by drivers because they provide interest by presenting a changing panorama while arousing a sense of anticipation of what is beyond the curve. The most advantageous property of a curving roadway is that it provides a visual appreciation of the driver's position and speed in relation to roadside objects and other traffic.

It is preferable that the radii of horizontal curves be the largest attainable. Isolated small radii curves in an otherwise free flowing horizontal alignment and small radii curves at the end of long straights, on steep down grades and over crests are unsafe and must be avoided.

General details of curve elements are given in

Tables 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 be less than the range quoted in Table 2.2.1

Table 2.2.1 Minimum Radii for Horizontal Curves Design Speed (km/h) Radii (m) 50 50 or more 60 90 or more 70 150 or more 80 240 or more 90 340 or more 100 460 or more 110 600 or more 120 800 or more 130 1000 or more

Accident records suggest that curves with radii between 300m and 440m should be avoided for design speeds greater than 70km/h. They are deceptive to the driver as it appears that they can be safely travelled at higher speeds than is actually possible. Wherever possible, curves are to be selected to give stopping sight distance for the adopted design speed, with the line of sight contained within the formation (see Section

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2 June, 95 Road Design Guide

Issue 1.0 90 ₁₀₀ ₁₁₀ ₁₂₀ ₁₃₀ ₁₄₀ 60 100 7 0.6 60 40 0.6 160 180 200 220 70 Speed Curve Radius (m) Curve TS-TS Super % (km/h) (m) Relative Grade % Super Trans (m) Plan _Trans. 2 (m) C'line Offset (m) Relative Grade % Super Trans (m) Plan _Trans. 2 (m) Pavement Widening 3

for Nominal Lane Width

(m) of 4 C'line Offset (m) Relative Grade % Super Trans. (m) Plan _Trans. 2 (m) C'line Offset (m) Sight Distances 5 (m) Benching Offset (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 80 ₁₀₀ ₁₁₀ ₁₂₀ ₁₃₀ ₁₃₀ V R Lh E 0.9 80 60 1.3 1.3 80 60 1.3 0.9

NOTES: 1. For design speeds grater than 70 km/h, curve radii within the shaded box are only to be used in exceptional circumstances. 2. A Plan transition (Lp) is not required if the calculated maximum offset (S) from the base control line is less than 300mm. 3. Lane widening is not required if the calculated widening is less than 200mm. 4. Adoption of 2.8, 3.0 and 3.25m lane widths is not recommended for design speeds of 80, 90 and 100 km/h respectively. 5. S.S.D, I.S.D, O.S.D = Stopping, Intermediate and Overtaking Sight Distances. # Use is optional. * For transition and widening offsets, see Table 2.2.3. A 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 and control on the centreline of the basic two lanes. C Multi-lane roadway with more than two lanes between the control and the edge of the travelled way.

HORIZONTAL ALIGNMENT Table 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 60 180 300 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 7 0.6 60 40 0.4 0.9 80 60 0.8 1.2 90 60 0.8 0.8 0.6 0.5 0.3 0.2 80 220 350 180 7 0.5 80 60 0.5 0.8 90 60 0.6 1.0 110 80 0.9 0.7 0.5 0.4 0.2 100 260 450 80 230 6 0.4 80 60 0.4 0.7 90 60 0.4 0.9 110 80 0.7 0.7 0.4 0.3 120 200 600 280 6 0.4 80 60 0.3 0.7 90 60 0.3 0.9 110 80 0.5 0.6 0.4 0.3 150 380 750 340 5 0.4 80 0.7 90 0.8 110 80 0.4 0.6 0.4 0.3 210 450 900 400 4 0.3 80 470 3 0.3 80 0.5 90 0.6 110 0.5 0.3 0.2 300 600 1400 1100 530 250 0.3 0.4 0.6 0.3 80 110 0.7 90 0.6 Gr Le Lp S Gr Le Lp S Gr Le Lp S

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Issue 1.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 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 -3.0 0.3 -3.0 0 0 0 0 0 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 Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 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 -3.0 0.3 -3.0 0 0 0 0 0 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 Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 10 0 10 20 30 40 50 60 80 Cross-fall % Outside of Control 70 90 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 10 0 10 20 Cross-fall % Outside of Control

Widening Not Required 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 0 0 0 0 0 .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 90 TP 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 0 0 0 0 .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 OFFSETS

TYPE A

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

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Issue 1.0 Radius 460m - 550m SS TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Widening Not Required

30 40 50 60 70 80 90 TP 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 0 0 0 0 .01 .12 .07 .05 .06 .23 .13 .10 .20 .35 .20 .15 .34 .47 .27 .20 .39 .58 .33 .25 .40 .70 .40 .30 Radius 600m - 700m SS TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 .10 .07 .05 .20 .13 .10 .30 .20 .15 .40 .27 .20 .50 .33 .25 .60 .40 .30 Offset Not Required

Radius 750m - 900m SS TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True 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 -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 0 0 0 .10 .07 .05 .20 .13 .10 .30 .20 .15 .40 .27 .20 .50 .33 .25 .60 .40 .30 Offset Not Required

* To be used in exceptional circumstances only

TABLE 2.2.3 (Continued)

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Issue 1.0 5.3Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 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 0 0 0 0 0 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 -6.7 1.30 .90 .70 .60 .40 .30 7.0 -7.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 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 0 0 0 0 0 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 _SC Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 10 0 10 20 30 40 50 60 80 Cross-fall % Outside of Control 70 90

Widening Not Required -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 -7.0 0 0 0 0 0 .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 90 5.8 -5.8 1.27 .75 .58 .50 .33 .25 4.5 -4.5 1.11 .60 .47 .40 .27 .20 80 90 6.7 -6.7 .60 .20 .50 .80 .30 .80 5.8 -5.8 .50 .17 .42 .78 .25 .67 100 5.9 -5.9 .59 .58 .42 .33 .17 Radius 340m - 440m SS TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 0 .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 TABLE 2.2.3 (Continued)

TYPE B

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

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Issue 1.0 Radius 460m - 550m SS TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 0 .01 .10 .07 .05 .04 .20 .13 .10 .15 .30 .20 .15 .26 .40 .27 .20 .30 .60 .40 .30 100 5.0 -5.0 .29 .50 .33 .25 -3.0 Radius 600m - 700m SS TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True 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 0 0 0 .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 Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

100 -1.2 -3.0 100 4.0 -4.0 100 -1.7 -3.0

* To be used in exceptional circumstances only

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Issue 1.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 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 0 0 0 0 0 0 3.3 -3.3 .65 .45 .35 .30 .20 .15 4.5 -4.5 1.11 .60 .47 .40 .27 .20 5.8 -5.8 1.27 .75 .58 .50 .33 .25 6.7 -6.7 1.30 .90 .70 .60 .40 .30 7.0 -7.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 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 0 0 0 0 0 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 Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Nominal Width 2.8 3.0 3.25 3.5 3.7* 10 0 10 20 30 40 50 60 80 Cross-fall % Outside of Control 70 90 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

Widening Not Required Widening Not Required -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 0 0 0 0 0 .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 90 TP 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 0 0 0 0 .15 .26 .15 .11 .35 .35 .20 .15 .55 .44 .25 .19 .65 .53 .30 .23 .69 .61 .35 .26 .70 .40 .30 80 90 0.8 -3.0 -3.0 2.0 .03 .15 .10 .07 .05 .12 .19 .30 .23 .20 .13 .10 80 90 100 2.5 -3.1 .12 .27 .20 .17 .10 .07 1.4 -3.0 .02 .13 .10 .08 .05 .05 -0.8 -3.0 .80 100 110 120 0.6 -3.0 .01 .09 .06 .05 .02 1.5 -3.0 .06 .17 .12 .10 .05 -1.2 -3.0 100 110 120 6.0 -6.0 .70 -3.0 1.1 .05 .17 .10 .07 -3.0 0.3 .01 .09 .05 .04 -1.4 -3.0 TABLE 2.2.3 (Continued)

TYPE C

(Control on multilane road, refer Table 2.2.2)

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Issue 1.0 Radius 460m - 550m _SS _TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 0 .11 .22 .15 .11 .25 .30 .20 .15 .39 .38 .25 .19 .47 .45 .30 .23 .49 .53 .35 .26 .60 .40 .30 100 110 120 6.0 -6.0 .50 -3.0 1.1 .03 .15 .10 .07 -3.0 0.3 .01 .07 .05 .04 -1.4 -3.0 Radius 600m - 700m _SS _TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 0 .08 .22 .15 .11 .20 .30 .20 .15 .32 .38 .25 .19 .37 .45 .30 .23 .39 .53 .35 .26 .60 .40 .30 100 110 120 5.0 -5.0 .40 -3.0 0.6 .03 .15 .10 .07 -3.0 -0.1 .01 .07 .05 .04 -1.5 -3.0 Radius 750m - 900m _SS _TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 0 .06 .22 .15 .11 .15 .30 .20 .15 .24 .38 .25 .19 .28 .45 .30 .23 .29 .53 .35 .26 .60 .40 .30 100 110 120 4.0 -4.0 .30 -3.0 0.6 .02 .15 .10 .07 -3.0 -0.5 .01 .07 .05 .04 -1.7 -3.0 Radius 1000m - 3000m _SS _TS -3.0 -3.0 Distances from SS Super Transition Plan Transition and Widening Widening Per Lane Inside of Control Offset to True Control

30 40 50 60 70 80 90 TP 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 0 0 0 .19 .11 .07 .25 .15 .10 .31 .19 .13 .38 .23 .15 .44 .26 .18 .50 .30 .20 100 110 120 3.0 -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)

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Issue 1.0 2.2.5 Length of Curved Roadway

Length of curved roadway is the sum of the length of circular arc on the true control line and the lengths of the plan transitions which connect the shifted circular arc to the tangents, or the length of the pegged base control line if plan transitions are not required (see Section

2.2.19). The total length should provide a

pleasing appearance by avoiding the impression of a "kink" in the horizontal alignment. Also, the shifted circular arc should be sufficiently long, in relation to the lengths of the spiral transitions, to avoid the appearance of a "hump" in the outer pavement edge due to superelevation.

The appropriate minimum length of curved roadway is a function of aesthetics and is therefore subjective. However, a convenient measure which satisfies this aesthetic function, is the adoption of a minimum length of at least three times the length of plan transition or desirably the distance travelled by a vehicle during one second for each 10 km/h of design speed. The latter is calculated with the following formula:

L

_h

= ×

V

1000

×

V

=

V

3600

10

36

2

Where:

L

_h

=

length of horizontal curve (m)

V

=

design speed (km/h)

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

2.2.6 Circular Arc

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

2.2.7 Deflection Angle

The minimum deflection angle (∠°) required to contain the desirable length of pegged circular arc may be derived with the formula:

∠°=Length of Pegged Circular Arc 0.01745R

2.2.8 Vehicular Movement on a Circular Path

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

For a given radius and speed, a set force is required to maintain the vehicle in this path. In road design, this is provided by the transverse friction demand, developed between tyre and pavement, and by superelevation.

For small values of superelevation, the following approximation may be accepted:

e

f

v

gR

or

V

R

+

=

2 2

127

Where:

e = pavement superelevation (m/m or tangent of angle). This is taken as positive if the pavement falls towards the centre of the curve

f = assumed value of transverse friction demand between vehicle tyres and road pavement. (Table 2.24) Taken as positive if the frictional force on the 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 of the centripetal force is exerted by the super-elevation. This condition can occur on large radius curves with positive superelevation or for slow moving vehicles on curves of any radius. At low speeds, f can be negative, and the curve is then over-superelevated for that speed. Curves are generally designed, so that a positive f is obtained for the range of vehicle speeds likely to occur.

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

2.2.9 Transverse Friction

The value of the transverse friction factor is a function of the type and condition of the road surface, the behaviour of the vehicle and the type and condition of the tyres. It is therefore variable and the least determinable of the elements 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. As horizontal curves are designed to avoid skidding, with a margin of safety, the assumed transverse friction factor, (f) adopted for design purposes, (friction demand) is substantially less than this upper limit.

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Issue 1.0 10 9 8 7 6 5 4 3 2 1 0 50 60 70 80 90 100 110 120 130 140 60 70 80 90 100 120 140 160 180 200 250 300 350 400 500 600 700 800 900 1000 ₁₁₀₀ 1200 1300 V f 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

SPEED / RADIUS / SUPERELEVATION RELATIONSHIP

(FOR SEALED RURAL ROADS)

E

Curve Radius (m)

Speed (km / h)

Note:

The grey boxed areas define the recommended "E" to be adopted

for the ranges of radii indicated. For "E" less than 3%, adopt 3%.

%

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Issue 1.0

A driver's attitude, when driving, varies in relation to the road environment, terrain, surface conditions and the traffic density on the road. For instance, drivers will use higher values of transverse friction when traffic density is low and/or the road surface is dry, than when the opposite conditions apply.

The maximum values of assumed transverse friction demand (f) to be adopted for the design of horizontal curves, for various conditions, are given in Table 2.2.4; they are a guide for average conditions and should be used cautiously.

Table 2.2.4Maximum Assumed Values of Transverse Friction Demand

DESIGN SPEED (km/h) BITUMEN AND CONCRETE PAVEMENTS GRAVEL AND UNSURFACED ROADS* 50 0.30 0.14 60 0.24 0.13 70 0.19 0.12 80 0.16 0.11 90 0.13 0.10 100 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 be reuced on the basis of assumed values of transverse friction demand.

2.2.10 Superelevation - General

Horizontal curves are superelevated to balance the effects of centrifugal force. The amount of superelevation will depend on vehicle speed, curve radius and pavement surface characteristics. The rate to be adopted is chosen for the aspects of safety, comfort and appearance.

Curves of 3000m radius and over may be superelevated but this is not generally necessary except for appearance reasons. Superelevation gives the curve a more natural appearance in certain situations, especially in flat open terrain, and helps define the outer edge of pavement

2.2.11 Desirable Superelevation

Values of desirable superelevation are shown in

Table 2.2.5.

Table 2.2.5 Desirable Superelevation

radius superelevation 50-330 7% 330-550 6% 550-750 5% 750-950 4% >950 3%

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

2.2.12 Maximum Superelevation Values

The maximum value of superelevation is limited by heavily laden or slow moving vehicles and by conditions of ice and snow. In rural areas the maximum value of superelevation to be adopted is 10% with the desirable maximum being 7%. In certain situations it may be desirable to increase the superelevation to the maximum as an additional safety feature. The development of a steep superelevation may create difficulties with drainage on the inside of a curve and it may be necessary to slightly increase the grade. In urban areas superelevation exceeding 4% is undesirable because of pedestrian traffic.

2.2.13 Minimum Superelevation Values

The minimum value of superelevation should not be less than the slope of the normal crossfall adopted for the adjacent straight road alignment. This is normally 3% but can be 4% in flat country areas where near level longitudinal alignment is unavoidable.

In urban situations, although 3% is the recommended minimum superelevation, lower superelevation values may be adopted in difficult circumstances.

2.2.14 Adverse Crossfall

In rural situations all curves under 3000m radius should be superelevated. However, to improve pavement drainage on very flat longitudinal grades, or in the design of temporary roadways, sidetracks and temporary connections, consideration may be given to the use of up to 3% adverse crossfall.

The curve radius with adverse crossfall can be calculated with the same formula used for positive crossfall (See Section 2.2.8). However the e value for superelevation is negative and the f value for the assumed transverse friction demand is 2/3 of the rural values listed in Table

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Issue 1.0

In urban situations where drivers are more adaptable to changes in radius, superelevation and transverse friction, the use of adverse crossfall on small radii curves is tolerable.

2.2.15 Superelevation on Bridges

Where a bridge structure is proposed near a horizontal curve and intrusion of the normal application of the superelevation transition onto the deck is unavoidable, it is preferable to maintain a uniform section on the bridge deck by continuing the rate of curve superelevation along the full length of the bridge.

2.2.16 Superelevation on Steep Grades

The adoption of the maximum values of super?elevation on very steep grades may increase the longitudinal grade on the outer lanes unacceptably . Usually the superelevation is the only geometric element which can be varied and it sometimes becomes necessary to either reduce the superelevation or extend the length of the eases at the end of the superelevation development .

It is recommended that designers profile the outer edges of pavement to ensure acceptable drainage 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 of Pavement Inner Edge of Pavement 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 curve 3. 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 PROFILES

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

SECTION 2

ROAD GEOMETRY

2.1

SIGHT DISTANCE

2.2

HORIZONTAL ALIGNMENT

Page No.

2.3

VERTICAL ALIGNMENT

Page No.

2.4

SECTION 2

NOTATION

2.1 SIGHT DISTANCE

=

R v

=

R V

3 6

.

=

v

=

gf

V