Unit 2

By- MD MOZAFFAR MASUD
Assistant Professor
Department of Civil Engineering
JIT, JETGI, Barabanki

Definition of Geometric Design :
 Geometric design of highways deals with the dimensions
and layout of visible features of the highway.
 Geometric design fulfills the requirements of the driver
and the vehicle, such as comfort, efficiency and safety.
 Proper geometric design will help in the reduction of
accidents and their severity.

Goals of Geometric design :
 Maximize the comfort, safety and economy of facilities.
 Provide efficiency in traffic operation.
 Provide maximum safety at reasonable cost.
 Minimize the environmental impacts.

Geometric design
• Design factors such as gradient ,radius of curve and sight
distance also govern the final alignment of the highway.
• Gradient should be flat and less than the ruling gradient or
design gradient.
• Avoid sudden changes in sight distance, especially near
crossings
• Avoid sharp horizontal curves
• Avoid road intersections near bend
Economy
• Alignment finalised based on total cost including initial cost,
maintenance cost and vehicle operation cost.
Other consideration
• Drainage consideration, political consideration
• Surface water level, high flood level
• Environmental consideration

Highway cross section elements
• Carriageway
• Shoulder
• Roadway width
• Right of way
• Building line
• Control line
• Median
• Camber/ cross
slope
• Crown
• Side slope
• Kerb
• Guard rail
• Side drain
• Other facilities

Factors affecting geometric design
 Design speed.
 Topography.
 Traffic.
 Environmental factors.
 Economical factors.
 Vehicles properties (dimensions, weight, operating
characteristics, etc.).
 Humans (the physical, mental and psychological characteristics
of the driver and pedestrians like the reaction time).

Road alignment :
Alignment : is an arrangement in a straight line or in correct
relative positions.
 The position or the layout of the central line of the highway on
the ground is called the alignment.
 Horizontal alignment includes straight and curved paths.
 Vertical alignment includes level and gradients.

 Alignment decision is important because a bad alignment
will enhance the construction, maintenance and vehicle
operating cost. Once an alignment is fixed and
constructed, it is not easy to change it due to increase in
cost of adjoining land and construction of costly structures
by the roadside.

Types of alignment :
 Horizontal Alignment : Horizontal alignment in road design
consists of straight sections of road, known as tangents,
connected by circular horizontal curves.
 It is the design of the road in the horizontal plane.
 Consists of a series of tangents (straight lines), circular curves
and transition curves.
 Should provide safe travel at a uniform design speed.

• Vertical Alignment : Vertical alignment is the
longitudinal section (shown on the y-axis of a road, it
consists of straight grades joined by vertical curves.
• Vertical alignment specifies the elevations of points along
the roadway.

Cross-Section of road & its
elements :

Carriage way :
 The Width of pavement way on which vehicles travel is
called carriage way .

WIDTH OF
CARRIAGEWAY
SL. NO. Class of road Width of carriageway in ͚m͛
1 Single lane 3.75
2 Two lane without raised kerbs 7.0
3 Two lane with raised kerbs 7.5
4 Intermediate lane 5.5
5 Multilane pavement 3.5/lane
WIDTH OF ROADWAY OF VARIOUS CLASSES OF ROADS
SL. No. Road classification Roadway wisth
Plane and rolling terrain Mountainous and steep
terrain
1 NH & SH
a) Single lane
b) two lane
12
12
6.25
6.25
2 MDR
a) Single lane
b) two lane
9
9
4.75
4.75
3 ODR
a) Single lane
b) two lane
7.5
9
4.75
4.75
4 Village roads-single lane 7.5 4

Two lane two-way road
carriageway

Road Shoulders :
 Shoulders are provided along the road edge to serve as an
emergency lane for vehicles .
 As per IRC, the min. width of shoulder should be 2.5m.
Uses :
 Repair of broken down vehicles
 Overtaking operations
 To act as an emergency lane
 For future widening of road
 For temp. diversion of traffic during road repair etc

unTreate
d
shoulder
Treated
shoulder

Formation width :
 Formation width is the top width of the highway
embankment or the bottom width of cutting excluding the
side drain .
 Formation width = Width of Carr. Way + Width of
shoulder

Right of way :
 Right of way is the area of land acquired for the land,
along its alignment.
 It is the distance between boundary stones of road on
either side of road.

4-lane divided carriage way or dual carriage way
Median/
separator

Side drain :
 For the drainage of rain water, drains are provided on
either side of the road .
 Normally, Side drain are required for road in cutting.
For road in embankment side drain is not necessary.

Building line :
 The distance from the centre line of road on either side,
within which construction of building is not permitted is
called building line.
Purposes :
 For future widening of road
 To reduce the chance of accidents
 To relieve residents from noise pollution
 To prevent disturbance to the traffic by nearby residents

Borrow pits :
 The pits dug along the road alignment for using
excavated earth in construction of embankment are
known as borrow pits.
 Borrow pit should be dug atleast 5m from toe of
embankment.
 The small portion left undug in a borrow pit to
measure the depth of excavation is called deadman.

Kerbs :
 The boundaries between pavement and shoulders or
footpath are known as kerbs.

Mountable kerbs :
These kerbs are indicator between the boundary of a road and shoulder .
The height of the kerb is such that driver find no difficulty in crossing these kerbs
and use the shoulder incase of emergency.
Its height is kept on 10cm above the pavement edge.
Semi-barrier kerbs :
It prevents encroachment of slow speed or parking vehicles to the footpath
But at emergency vehicle can climb over and can be parked on footpath or
shoulder.
Its height is 15 to 20cm
Barrier kerbs :
They are mainly provided to cause obstruction to the vehicles leaving the carriage
way under emergency.
Its height is 23 to 45cm
Generally, such kerbs are provided on hills bridges etc.

Camber :
 Camber or cross slope is the slope provided to the
road surface in the transverse direction to drain off
rain water from the road surface.
 The rate of camber is usually designated by 1 in n (1
vertical to n horizontal)

Purposes of camber :
 To remove the rain water from the pavement surface as
quickly as possible.
 To prevent entry of water into bituminous pavement
layers.
 To prevert entry of surface water into subgrade soil
through pavement.
 To make pavement surface attractive.

Shape of the cross slope:
• Parabolic shape(fast moving vehicle)
• Straight line
• Combination of parabolic and straight line
Recommended values of camber for different types of road surface
Sl no. Type of road surface Range of camber in areas of rain
fall range
heavy light
1 Cement concrete and high type
bituminous pavement
1 in 50(2%) 1 in 60(1.7%)
2 Thin bituminous surface 1 in 40(2.5%) 1 in 50(2%)
3 Water bound macadam(WBM) and gravel
pavement
I in 33(3%) 1 in 40(2.5%)
4 Earth 1 in 25(4%) 1 in 33(3%)

Super elevation :
 It is the slope across pavement surface and is fully developed in
the circular curve.
(or)
 Super-elevation (banking) is the transverse slope provided at
horizontal curve to counteract the centrifugal force, by raising
the outer edge of the pavement with respect to the inner edge,
throughout the length of the horizontal curve.
 So super elevation helps the vehicle to over come the
centrifugal force on the curves on pavements
 The need for super-elevation on road curves, to ensure safety
against skidding and over turning with the advent of fast
moving traffic.

In the past, roads were constructed without any regard to super-elevation on
curves and had generally a cambered section for drainage purposes. It was little
realised then that a vehicle moving on a curve had to overcome a centrifugal
force to enable it to follow the curved path instead of a straight line, but, in
justice to the early designers of roads, it must be said that there was no fast
traffic in those days.

Guard rail
• It is provided at the edge of the shoulder
when the road is constructed on a fill
exceeds 3 m.
• It is also provided on horizontal curve so
as to provide a better night visibility of the
curves under the head light of the vehicle.

Road margins
Parking lane:
•These are provided on urban roads to allow kerb
parking
•As far as possible only parallel parking should be
allowed
as it is safer for moving vehicle.
•It should have sufficient width say 3m
•Lay bay:
•These are provided near the public conveniences with
guide map to enable driver to stop clear off the
carriageway.
•It has 3m width,30m length with 15m end tapers on
both sides.

Road margins
 Bus bays:
• These may be provided by recessing the kerb to avoid conflict
with moving traffic.
 It is located atleast 75m away from the intersection.
 Frontage road:
 These are provided to give access to properties along an
important highway with control access to express way or free way
 It may run parallel to the highway and are isolated by separator.
 Driveway:
 It connect the highway with commercial establishment like fuel
stations, service stations etc…
 It should be located away from the intersection.

Road margins
 Cycle track:
 It provided in urban areas when the volume of cycle traffic on the road
is very high.
 A minimum width of 2m is provided for cycle track.
 Footpath:
 These are provided in urban areas when the vehicular as well as
pedestrian traffic are heavy.
 To protect the pedestrian and decrease accident.
 Minimum width of 1.5m is provided.

Cross section of highway in hilly area

Cross section of road in built-up area

Cross section of road in cutting

Before a highway alignment is finalised in highway
project, the engineering survey are to be carried out. The
various stages of engineering surveys are
Map study (Provisional alignment Identification)
Reconnaissance survey
Preliminary survey
Final location and detailed surveys
Engineering Surveys for Highway locations

MAP STUDY
• From the map alternative routes can be suggested
in the office, if the topographic map of that area is
available.
• The probable alignment can be located on the map
from the fallowing details available on the map.
Avoiding valleys, ponds or lake
Avoiding bend of river
If road has to cross a row of hills, possibility of
crossing through mountain pass.
• Map study gives a rough guidance of the routes to
be further surveyed in the field

RECONNAISSANCE SURVEY
• To confirm features indicated on map.
• To examine the general character of the area in field
for deciding the most feasible routes for detailed studies.
• A survey party may inspect along the proposed alternative
routes of the map in the field with very simple
instrument like abney level, tangent clinometer, barometer
etc…. To collect additional details.
• Details to be collected from alternative
routes during this
survey are,
Valleys,ponds, lakes, marshy land, hill,
permanent
structure and other obstruction.
Value of gradient, length of gradient and radius of curve.

RECONNAISSANCE SURVEY cont..
 Number and type of cross drainage structures.
High Flood Level (HFL)
Soil Characteristics.
Geological features.
source of construction materials- stone quarries,
water
sources.
• Prepare a report on merits and demerits of
different alternative routs.
• As a result a few alternate alignments may be chosen
for further study based on practical considerations
observed at the site.

Preliminary survey
Objective of preliminary survey are:
•To survey the various alternative alignments proposed after
the reconnaissance and to collect all the necessary physical
information and detail of topography, drainage and soil.
•To compare the different proposals in view of the requirements
of the good alignment.
•To estimate quantity of earthwork materials and other
construction aspect and to workout the cost of the alternate
proposals.
Methods of preliminary survey:
a) Conventional approach-survey party carries out surveys
using the required field equipment, taking measurement,
collecting topographical and other data and carrying out soil
survey.

Preliminary survey cont…
• Longitudinal and cross sectional profile.
 Plain Terrain`
 Rolling Terrain
 Hilly Terrain
• Other studies
: 100 – 200m
: 50m
: 30m
 Drainage, Hydrological survey, soil survey, Traffic and
Material survey.
b) Modern rapid approach-By Aerial survey
taking the required aerial photographs for obtaining
the necessary topographic and other maps
including details of soil and geology.
• Finalize thebest alignment from all considerations by
comparative analysis of alternative routes.

Final location and detailed survey
• The alignment finalized at the design office after
the preliminary survey is to be first located on the field
by establishing the centre line.
Location survey:
• Transferring the alignment on to ground.
• This is done by transit theodolite.
• Major and minor control points are established on the
ground and centre pegs are driven, checking
the geometric design requirements.
• Centre line stacks are driven at suitable intervals, say 50m
interval in plane and rolling terrains and 20m in
hilly terrain.

Final location and detailed survey
Detailed survey:
•Temporary bench marks are fixed at intervals of about
250m and at all drainage and under pass structure.
•Earthwork calculations and drainage details are to be workout
from the level books.
•Cross sectional levels are taken at intervals of 50-100m in
Plane terrain, 50-75m in Rolling terrain, 50m in built-up area,
20m in Hill terrain.
•Detail soil survey is to be carried out.
•CBR value of the soils along the alignment may be determined
for design of pavement.
•The data during detailed survey should be elaborate and
complete for preparing detailed plans, design and estimates of
project.

Drawing and Report
 Key map
 Index map
 Preliminary survey plans
 Detailed plan and longitudinal section
 Detailed cross section
 Land acquisition plans
 Drawings of cross drainage and other retaining
structures
 Drawings of road intersections
 Land plans showing quarries etc

New highway project
• Map study
• Reconnaissance survey
• Preliminary survey
• Location of final alignment
• Detailed survey
• Material survey
• Geometric and structural design
• Earth work
• Pavement construction
• Construction controls

SIGHT DISTANCE
• Sight distance available from a point is the actual
distance along the road surface, which a driver from a
specified height above the carriageway has visibility of
stationary or moving objects. OR
 It is the length of road visible ahead to the driver at any
instance.

Types of sight distance
• Stopping or absolute minimum sight distance(SSD)
 Safe overtaking or passing sight distance (OSD)
 Safe sight distance for entering into uncontrolled
intersection.
 Intermediate sight distance
 Head light sight distance

 Stopping sight distance:
The minimum sight distance available on a highway at any
spot should be of sufficient length to stop a vehicle traveling
at design speed, safely without collision with any other
obstruction.
 Over taking sight distance:
The minimum distance open to the vision of the driver of a
vehicle intending to overtake slow vehicle ahead with safety
against the traffic of opposite direction is known as the
minimum overtaking sight distance (OSD) or the safe passing
sight distance.
 Sight distance at intersection:
Driver entering an uncontrolled intersection (particularly
unsignalised Intersection)has sufficient visibility to enable
him to take control of his vehicle and to avoid collision with
another vehicle.

 Intermediate sight distance:
This is defined as twice the stopping sight distance.
When overtaking sight distance can not be provided,
intermediate sight distance is provided to give limited
overtaking opportunities to fast vehicles.
 Head light sight distance:
This is the distance visible to a driver during night
driving under the illumination of the vehicle head
lights. This sight distance is critical at up-gradients and
at the ascending stretch of the valley curves

Stopping Sight Distance
• SSD is the minimum sight distance available on a
highway at any spot having sufficient length to enable
the driver to stop a vehicle traveling at design speed,
safely without collision with any other obstruction.
 It depends on:
Feature of road ahead
Height of driver’s eye above the road surface(1.2m)
Height of the object above the road surface(0.15m)

Criteria for measurement
•Height of driver’s eye above road surface (H)
•Height of object above road surface(h)

 Factors affecting the SSD
Total reaction time of driver
Speed of vehicle
Efficiency of brakes
Frictional resistance between road and tyre
Gradient of road
 Total reaction time of driver:
It is the time taken from the instant the object is visible
to the driver to the instant the brake is effectively
applied, it divide into types
1.Perception time
2.Brake reaction time

 Perception time:
it is the time from the instant the object comes on the
line of sight of the driver to the instant he realizes that
the vehicle needs to be stopped.
 Brake reaction time:
The brake reaction also depends on several factor
including the skill of the driver, the type of the problems
and various other environment factor.
Total reaction time of driver can be calculated by “PIEV”
theory

 Perception :
 It is the time required for the sensation received by the eyes or ears
tobe transmitted to the brain through the nervous system and
spinal chord.
 Intellection:
 It is the time required for understanding the situation.
 Emotion:
 It isthetimeelapsed during emotional sensation and
disturbancesuch as fear, anger or any other emotional feeling such
as superstition etc, with reference to the situation.
 Volition:
 It is thetime taken forthe final action
 Total reaction time of driver may be vary from 0.5 sec to 4 sec

Analysis of SSD
• The stopping sight
distance is the sum of lag
distance and the braking
distance.
 Lag distance:
It is the distance, the
vehicle traveled during the
reaction time
If ‘V’ is the design speed in
m/sec and ‘t’ is the total
reaction time of the driver
in seconds,

 Braking distance :
It is the distance traveled by the vehicle after the
application of brake. For a level road this is obtained by
equating the work done in stopping the vehicle and the
kinetic energy of the vehicle.
Work done against friction force in stopping the vehicle
is F xl = f Wl, where W is the total weight of the vehicle.
The kinetic energy at the design speed of v m/sec will be
½ m. v²
 Braking distance= v²/2gf
 SSD=lag distance + braking distance

OVERTAKING SIGHT DISTANCE
 The minimum distance open to the vision of the driver
of a vehicle intending to overtake slow vehicle ahead
with safety against the traffic of opposite direction is
known as the minimum overtaking sight
distance(OSD)or the safe passing sight distance.
The overtaking sight distance or OSD is the distance
measured along the centre of the road which a driver
with his eye level 1.2m above the road surface can see the
top of an object 1.2m above the road surface

Factors affecting the OSD
 Speeds of
overtaking vehicle
Overtaken vehicle
The vehicle coming from opposite direction, if any.
 Distance between the overtaking and overtaken
vehicles.
 Skill and reaction time of the driver
 Rate of acceleration of overtaking vehicle
 Gradient of the road

where t is the reaction time of the driver in second= 2 sec.

Overtaking Zones
 It is desirable to construct highways in such a way that the
length of road visible ahead at every point is sufficient for
safe overtaking. This is seldom practicable and there may
be stretches where the safe overtaking distance can not be
provided. But the overtaking opportunity for vehicles
moving at design speed should be given at frequent
intervals. These zones which are meant for overtaking are
called overtaking zones.
 The minimum length of overtaking zone should be three
time the safe overtaking distance i.e., 3 (d1+d2) for one-way
roads and 3(d1+d2+d3) for two-way roads.
 Desirable length of overtaking zones is kept five times the
overtaking sight distance. i.e., 5(d1+d2) for one-way roads
and 5(d1+d2+d3) for two-way roads.

Horizontal Curves
 A horizontal highway curve is a curve in plan to provide
change in direction to the central line of a road. When a
vehicle traverses a horizontal curve, the centrifugal force
acts horizontally outwards through the centre of gravity of
the vehicle.
P = W v²∕gR
Where,
P=centrifugal force, kg
W=weight of the vehicle, kg
R=radius of the circular curve, m
v=speed of vehicle, m/sec
g=acceleration due to gravity=9.8m/sec

Contd.
 P/W is known as the centrifugal ratio or the impact factor. The
centrifugal ratio is thus equal to v²∕gR
 •The centrifugal force acting on a vehicle negotiating a
horizontal curve has two effects
 Tendency to overturn the vehicle outwards about the outer wheels
 Tendency to skid the vehicle laterally, outwards
 Overturning effect
 •The equilibrium condition for overturning will occur when Ph =
Wb/2, or when P/W =b/2h. This means that there is danger of
overturning when the centrifugal when the centrifugal ratio P/W
or v²/gR attains a values of b/2h.

 Transverse skidding effect
 P = FA+ FB= f(RA+RB) =fW
 Since P = f W, the centrifugal ratio P/W is equal to ‘f ‘. In other
words when the centrifugal ratio attains a value equal to the
coefficient of lateral friction there is a danger of lateral skidding.
 Thus to avoid overturning and lateral skidding on a horizontal
curve, the centrifugal ratio should always be less than b/2h and
also ‘f’
 ‘f’ is less than b/2h.-The vehicle would skid and not overturn
 b/2h is lower than ‘f’-The vehicle would overturn on the outer
side before skidding

Super elevation
 In order to counteract the effect of centrifugal force
and to reduce the tendency of the vehicle to overturn
or skid, the outer edge of the pavement is raised with
respect to the inner edge, thus providing a transverse
slope throughout the length of the horizontal curve,
this transverse inclination to the pavement surface is
known as Superelevation or cant or banking.
 The Superelevation ‘e’ is expressed as the ratio of the
height of outer edge with respect to the horizontal
width.

Analysis of Super elevation
 The force acting on the vehicle while moving on a circular
curve of radius R meters, at speed of v m/sec are
 The centrifugal force P = Wv²/gR acting horizontal
outwards through the centre of gravity, CG
 The weight W of the vehicle acting vertically downloads
through the CG
 The frictional force developed between the wheels and the
pavement counteractions transversely along the pavement
surface towards the centre of the curve

e=rate of Super elevation=tanӨ
f = design value of lateral friction coefficient = 0.15
v = speed of the vehicle, m/sec
R = radius of the horizontal curve,
mg = acceleration due to gravity = 9.8 m/sec²

Maximum Super elevation
 In the case of heavily loaded bullock carts and trucks carrying less
dense materials like straw or cotton, the centre of gravity of the loaded
vehicle will be relatively high and it will not be safe for such vehicles to
move on a road with a high rate of Super elevation. Because of the slow
speed, the centrifugal force will be negligibly small in the case of
bullock carts. Hence to avoid the danger of toppling of such loaded
slow moving vehicles, it is essential to limit the value of maximum
allowable Super elevation.
 Indian Roads Congress had fixed the maximum limit of Super
elevation in plan and rolling terrains and is snow bound areas as 7.0
%.
 On hill roads not bound by snow a maximum Super elevation upto
10% .
 On urban road stretches with frequent intersections, it may be
necessary to limit the maximum Super elevation to 4.0 %.

Minimum Super elevation
 From drainage consideration it is necessary to have a
minimum cross to drain off the surface water. If the
calculated Super elevation is equal to or less than the
camber of the road surface, then the minimum Super
elevation to be provided on horizontal curve may be
limited to the camber of the surface.

Design of Super elevation
 Step-1:The Super elevation for 75 percent of design
speed v (m/sec/kmph) is calculated neglecting the
friction.
 Step-2: If the calculated value of ‘e’ is less than 7% or
0.07 the value so obtained is provided. If the value of
‘e’ as step-1 exceeds 0.07 then provides maximum
Super elevation equal to 0.07 and proceed with step-3
or 4.

 Step-3: Check the coefficient of friction of friction
developed for the maximum value of e =0.07 at the full
value of design speed.
If the value of f thus calculated is less than 0.15 the
Super elevation of 0.07 is safe for the design speed. If
not, calculate the restricted speed as given in step -4.
 Step-4: The allowable speed (Va m/sec. or Va Kmph)
at The curve is calculated by considering the design
coefficient of lateral friction and the maximum Super
elevation.
e+f=0.07+0.15=va²/127R

 the allowed speed, as calculated above is higher than
the design speed, then the design is adequate and
provides a Super elevation of ‘e’ equal to 0.07.
 If the allowable speed is less than the design speed, the
speed is limited to the allowed speed Va kmph
calculated above and Appropriate warning sign and
speed limit regulation sign are installed to restrict and
regulate the speed.

Attainment of super elevation
 Split-up into two parts::
Elimination of crown of the cambered section
 Rotation of pavement to attain full superelevation
Elimination of crown of the cambered section
 1st Method: Outer edge rotated about the crown
Disadvantages
Small length of road – cross slope less than
camber
Drainage problem in outer half

 2nd Method: Crown shifted outwards
1st Method: Rotation about the C/L (depressing the
inner edge and raising the outer edge each by half the
total amount of super elevation)
Disadvantages
Large negative super elevation on outer half
 Drivers have the tendency to run the vehicle along shifted
crown
Rotation of pavement to attain full super elevation

Advantages
 Earthwork is balanced
 Vertical profile of the C/L remains unchanged
Disadvantages
 Drainage problem: depressing the inner edge below the general level
2nd Method: Rotation about the Inner edge (raising both the centre as well as
outer edge – outer edge is raised by the total amount of super elevation)
Advantages-No drainage problem
Disadvantages-Additional earth filling
C/L of the pavement is also raised
(vertical alignment of the road is
changed)

Radius of Horizontal Curve
 The ruling minimum radius of the curve for ruling
design speed v m/sec. or V kmph is given by
•According to the earlier specifications of the IRC, the ruling
minimum radius of the horizontal curve was calculated from
a speed value, 16 kmph higher than the design speed i,e.,
(V+16) kmph.

Widening of Pavement on
Horizontal Curves
 On horizontal curves, especially when they are not of very large
radii, it is common to widen the pavement slightly more than the
normal width,
 Widening is needed for the following reasons :
 The driver experience difficulties in steering around the curve.
 The vehicle occupies a greater width as the rear wheel don’t track the
front wheel. known as ‘Off tracking’
 For greater visibility at curve, the driver have tendency not to follow the
central path of the lane, but to use the outer side at the beginning of
the curve.
 While two vehicle cross or overtake at horizontal curve there is
psychological tendency to maintain a greater clearance between the
vehicle for safety.

Off tracking
 An automobile has a rigid wheel base and only the
front wheels can be turned, when this vehicle takes a
turn to negotiate a horizontal curve, the rear wheel do
not follow the same path as that of the front wheels.
This phenomenon is called off tracking.
 The required extra widening of the pavement at the
horizontal curves depends on the length of the wheel
base of the vehicle ‘l’, radius of the curve ‘R’ and the
psychological factors.

Analysis of extra widening on
curves
 It is divided into two parts;
Mechanical widening (Wm): the widening required to
account for the off tracking due to the rigidity of wheel
base is called mechanical widening
Psychological widening (Wps): extra width of the
pavement is also provided for psychological reasons
such as , to provide for greater maneuverability of
steering at high speed, to allow for the extra space for
overhangs of vehicles and to provide greater clearance
for crossing and overturning vehicles on curve.
 Total widening W = Wps+ Wm

Mechanical Widening
Where, R = Mean radius of the curve in m,
n=no. of traffic lanes
l = Length of Wheel base of longest
vehicle , m ( l = 6.0 m or 6.1m for
commercial vehicles)
V= design speed, kmph

Psychological Widening
V = Design speed of the vehicle, km/h
R = Radius of the curve, m

 Total extra widening = Mechanical widening
+Psychological Widening

Method of introducing extra
widening
 With transition curve: increase the width at an approximately uniform
rate along the transition curve - the extra width should be continued
over the full length of circular curve
 Without transition curves: provide two-third widening on tangent and
the remaining one-third on the circular curve beyond the tangent point
 With transition curve: Widening is generally applied equally on both
sides of the carriageway
 Without transition curve: the entire widening should be done on inner
side
 On sharp curves of hill roads: the entire widening should be done on
inner side

Horizontal transition curves
 When a non circular curve is introduce between a
straight and a circular curve has a varying radius which
decreases from infinity at the straight end (tangent
point) to the desired radius of the circular curve at the
other end (curve point) for the gradual introduction of
centrifugal force is known as transition curve.

Objectives for providing transition
curve
 To introduce gradually the centrifugal force between the
tangent point and the beginning of the circular curve,
avoiding sudden jerk on the vehicle. This increases the
comfort of passengers.
 To enable the driver turn the steering gradually for his own
comfort and security
 To provide gradual introduction of super elevation
 To provide gradual introduction of extra widening.
 To enhance the aesthetic appearance of the road.

Type of transition curve
 spiral or clothoid
 cubic parabola
 Lemniscate
 IRC recommends spiralas the transition curve because
it fulfills the requirement of an ideal transition curve,
that is;
rate of change or centrifugal acceleration is consistent
Radius of the transition curve is infinity at the straight
edge and changes to R at the curve point (Ls ᾳ1/R)and
calculation and field implementation is very easy.

Length of transition curve
 Case-1:Rate of change of centrifugal acceleration
Where,
Ls= length of transition curve in ‘m’
C= allowable rate of change of centrifugal accleration, m/ sec²
R= Radius of the circular curve in ‘m’

 case-2:Rate of introduction of super-elevation
If the pavement is rotated about the center line.
If the pavement is rotated about the inner
edge
Where ,
W is the width of pavement
We is the extra widening
Rate of change of superelevation of 1 in N

 case-3:By empirical formula
 According to IRC standards:
For plane and rolling terrain:
For mountainous and steep
terrain:
NOTE: The design length of transition curve(Ls) will
be the highest value of case-1,2 and 3

Shift of the transition curve
 Shift of the transition curve ‘S’

Vertical Alignment
 The vertical alignment is the elevation or profile of the
centre line of the road.
 The vertical alignment consist of grade and vertical
curve and it influence the vehicle speed, acceleration,
sight distance and comfort in vehicle movements at
high speed.

Gradient
 It is the rate of rise or fall along the length of the road
with respect to the horizontal. It is expressed as a ratio
of 1 in x (1 vertical unit to x horizontal unit). Some
times the gradient is also expressed as a percentage i.e.
n% (n in 100).

Typical Gradients (IRC)
 Ruling Gradient
 Limiting Gradient
 Exceptional gradient
 Minimum Gradient
 Ruling gradient (design gradient):It is the maximum
gradient within which the designer attempts to design the
vertical profile of road, it depends on
 Type of terrain
 Length of grade
 Speed
 power of vehicles
 Presence of horizontal curves
 Mixed traffic

 Limiting Gradient: Steeper than ruling gradient. In hilly roads, it
may be frequently necessary to exceed ruling gradient and adopt
limiting gradient, it depends on
 Topography
 Cost in constructing the road
 Exceptional Gradient: Exceptional gradient are very
steeper gradients given at unavoidable situations. They
should be limited for short stretches not exceeding about
100 m at a stretch.
 critical length of the grade:The maximum length of the
ascending gradient which a loaded truck can operate
without undue reduction in speed is called critical length
of the grade. A speed of 25 kmph is a reasonable value. This
value depends on the size, power, load, initial speed.

 Minimum gradient: This is important only at
locations where surface drainage is important. Camber
will take care of the lateral drainage. But the
longitudinal drainage along the side drains require
some slope for smooth flow of water. Therefore
minimum gradient is provided for drainage purpose
and it depends on the rain fall, type of soil and other
site conditions.
 A minimum of 1 in 500 may be suﬃcient for concrete
drain and 1 in 200 for open soil drains.

SUMMIT CURVE
 Length of summit curve(L) for SSD
 Case-1(L > SSD)
• Case-2(L < SSD)

 Length of summit curve for OSD
 Case-1(L > OSD)
 Case-2(L < OSD)
Where,
S=sight distance i.e. SSD, OSD or ISD
N= deviation angle
i.e. algebraic difference between two grade
H=height of driver eye above the carriageway i.e. 1.2 m
h=height of driver eye above the carriageway i.e. 0.15 m

VALLEY CURVE
 Length of valley curve for comfort condition:
Where,
N= deviation angle i.e. algebraic difference between two grade
C= rate of change of centrifugal acceleration may be taken as 0.6
m/sec³
V= speed of vehicle in kmph

 Length of valley curve for head light sight distance
 Case-1(L > SSD)
 Case-2(L < SSD)
Where,
h1=height of head light above the carries way
α= inclination of focused portion of the beam of light w.r.t
horizontal or beam angle .
N= deviation angle i.e. algebraic difference between two grade.
S=head light distance is equal to SSD

Grade compensation
 At the horizontal curve, due to the turning angle α of the vehicle,
the curve resistance develop is equal toT(1-Cosα).When there is a
horizontal curve in addition to the gradient, there will be a
increase in resistance to fraction due to both gradient and curve.
It is necessary that in such cases the total resistance due to grade
and the curve should not exceeded the resistance due to
maximum value of the gradient specified.
 Maximum value generally taken as ruling gradient
 Thus grade compensation can be defined as the reduction in
gradient at the horizontal curve because of the additional
tractive force required due to curve resistance (T−Tcosα), which
is intended to offset the extra tractive force involved at the curve.
 IRC gave the following specification for the grade compensation.
 1.Grade compensation is not required for grades flatter than 4%
because the loss of tractive force is negligible.
 2.Grade compensation is (30+R)/R %, where ‘R’ is the radius of the
horizontal curve in meters.
 3.The maximum grade compensation is limited to 75/R%.

Unit 2

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