CHAPTER 2

ROAD GEOMETRIC
2 Road Geometric
▪ 2.1 Glossary of terms used in geometric and their importance,
right of way, formation width, road margin, road shoulder,
carriage way, side slopes, kerbs, formation level, camber and
gradient
▪ 2.2 Design and average running speed, stopping and passing
sight distance
▪ 2.3 Necessity of curves, horizontal and vertical curves including
transition curves and super elevation, Methods o f providing
super – elevation
2.1 The visible dimensions are technically known as road geometrics. Road geometrics can
be divided as follows :-
1. Right of way or permanent land width
2. Road margins
3. Formation width
4. Carriage way width
5. Shoulders or footpath
6. Side slopes
7. Kerbs
8. Formation level
9. Camber or cross fall or cross slope
10. Gradient
11. Super elevation
12. Curves
▪ 1. Right of way : It is the area of land acquired and reserved for construction and
development of the road along its alignment.
Permanent Land width as per Recommendations of I.R.C

▪ 2. Road margins : It is the portion of land width on either side of formation width of a road.
It includes footpaths, cycle track, guard raid, embankment slopes and parking lane etc.
3. Formation width : lt is the top width of road embankment or bottom width of road cutting
excluding the side drains. It is also known as crest.
Formation width as per Recommendation of I.R.C.
▪ 4. Carriage way : It is the portion of the roadways used by vehicular traffic. It is in
general the metalled portion of the road as per Indian Road Congress (I.R.C.) it is 3-8
metre for single lane traffic and 3-5 m. per lane in case of two or more than two lanes.
5. Shoulder for footpath : It is the portion of the roadway between the outer edge of the
pavement and top edge of the side slope. Its width generally varies between 1-2 to 1-8 m.
6. Side slopes : The slopes given to the sides of earthwork of road in embankment or
cutting for its stability are called side slopes.
7. Kerbs : The boundaries between the pavement and footpath is known as kerbs.
▪ 8. Formation level : The reduced level of the finished surface of the
earth work for a roadway o railway in embankment or cutting is
known as formation level.
9. Camber / Cross slope : The central highest point of a curved
road surface is known as crown of the road.
▪ Cross slope, cross fall or camber is a geometric feature of pavement
surfaces: the transverse slope with respect to the horizon. It is a
very important safety factor. Cross slope is provided to provide
a drainage gradient so that water will run off the surface to
a drainage system such as a street gutter or ditch. As per I.R.C.
Recommendations
10. Gradient : Gradient is the longitudinal slope of the road. The
slope of the road which is adopted in road design and calculations of
cuts and fills is called 'Ruling Gradient'. It is of three types :
1. Limiting gradient
2. Exceptional gradient
3. Minimum gradient
11. Super elevation : It is the inward tilt of the road surface provided
at the horizontal curves to compensate the effect of centrifugal force.
12. Curves : The geometrical arcs provided at the intersection of
straight alignments either in horizontal or in vertical plane to have
gradual change in direction is known as a curve.
▪ Ruling Gradient in Road
It is the maximum gradient within which the designer attempts to design the vertical
profile of a road. It is also known as design gradient. As per IRC, the recommended
value of ruling gradient for plain or rolling terrain is 1 in 30 or 3.3 %.
▪ Exceptional Gradient
Exceptional gradients are very steeper gradients given at unavoidable situations.
They should be limited for short stretches not exceeding about 100 metres at a
stretch. In mountainous and steep terrain, successive exceptional gradients must be
separated by a minimum 100 metre length gentler gradient.
▪ Limiting Gradient
The gradient steeper than the ruling gradient, which may be used for a limited
Road length, is called limiting gradient or maximum gradient. It is used where the
topography of place compels adopting a steeper gradient than the ruling gradient to
minimize the cost of road construction.
▪ Floating Gradient
The gradient on which a motor vehicle moving with a constant speed continues to
descend with the same speed without any application of power brakes is called
a floating gradient.
2.2 Design and average running speed, stopping and passing sight distance
SIGHT DISTANCE:-
▪ The safe and efficient operation of vehicles on the road depends very much on the
visibility of the road ahead of the driver. Thus the geometric design of the road should be
done such that any obstruction on the road length could be visible to the driver from some
distance ahead . This distance is said to be the sight distance.
▪ Three sight distance situations are considered for design:
• Stopping sight distance (SSD) or the absolute minimum sight distance
• Intermediate sight distance (ISD) is defined as twice SSD
• Overtaking sight distance (OSD) for safe overtaking operation
• Head light sight distance is the distance visible to a driver during night driving under the
illumination of head lights
• Safe sight distance to enter into an intersiection.
▪ Factors affecting sight distance:-
Factors affecting Sight distance:- (Road SE GF)
• Reaction time of the driver
Reaction time of a driver is the time taken from the instant the object is visible to the driver to the instant when the
brakes are applied. The total reaction time may be split up into four components based on PIEV theory. IRC
suggests a reaction time of 2.5 secs.
• Speed of the vehicle
Higher the speed, more time will be required to stop the vehicle. Hence it is evident that, as the speed increases,
sight distance also increases.
Efficiency of brakes
The efficiency of the brakes depends upon the age of the vehicle, vehicle characteristics etc. If the brake efficiency
is 100%, the vehicle will stop the moment the brakes are applied. But practically, it is not possible to achieve 100%
brake efficiency. Therefore the sight distance required will be more when the efficiency of brakes are less. Also for
safe geometric design, we assume that the vehicles have only 50% brake efficiency.
• Frictional resistance between the tyre and the road
The frictional resistance between the tyre and road plays an important role to bring the vehicle to stop. When the
frictional resistance is more, the vehicles stop immediately. Thus sight required will be less. IRC has specified the
value of longitudinal friction in between 0.35 to 0.4.
• Gradient of the road.
Gradient of the road also affects the sight distance. While climbing up a gradient, the vehicle can stop immediately.
Therefore sight distance required is less. While descending a gradient, gravity also comes into action and more time
will be required to stop the vehicle. Sight distance required will be more in this case.
▪ PIEV theory
1) Perception 2) Intellection 3) Emotion 4) Violation

▪ 1)Perception time: is time required for the sensations received by the eyes or ears of the driver to be transmitted to
the brain through the nervous system & spinal cord or it is the time required to perceive an object or situation.
▪ 2)Intellection time : is the time require for the driver to understand the situation it is also the time required for
comparing the different thoughts.
▪ 3) Emotion time: is the time elapsed during emotional sensational and other mental disturbance such as fear, anger
or any other emotional feeling superstition etc
▪ 4) Volitiontime: is the time taken by the driver for the final action such as brake application.
▪ PIEV is the amount of time it takes a driver to react to a hazard. piev mean PIEV time - perception, intellection,
emotion and volition. Before we can stop an automobile, four specific areas of activity need to happen
The total reaction time may be split up into four components based on PIEV theory. In practice, all these times are
usually combined into
Full form of PIVE theory perception intellection emotion and volition
▪ Stopping sight distance
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.
▪ Overtaking sight distance
▪ The overtaking sight distance is the minimum distance open to the
vision of the driver of a vehicle intending to overtake the slow
vehicle ahead safely against the traffic in the opposite direction.
The overtaking sight distance or passing sight distance is measured
along the center line of the road over which a driver with his eye
level 1.2 m above the road surface.
▪ The factors that affect the OSD are:
• Velocities of the overtaking vehicle, overtaken vehicle and of the
vehicle coming in the opposite direction.
• Spacing between vehicles, which in-turn depends on the speed
• Skill and reaction time of the driver
• Rate of acceleration of overtaking vehicle
• Gradient of the road
▪ Overtaking zones
Overtaking zones are provided when OSD cannot be provided throughout the length of the
highway. These are zones dedicated for overtaking operation, marked with wide roads. The
desirable length of overtaking zones is 5 time OSD and the minimum is three times OSD
2.3 Necessity of curves, horizontal and vertical curves including transition
curves and super elevation, Methods of providing super – elevation
CURVE:-
▪ A curve is nothing but an arc which connects two straight lines which are separated by some angle called
deflection angle. This situation occurs where the alignment of a road way or rail way changes its direction
because of unavoidable objects or conditions.
▪ The object may be a hill or a lake or a temple etc. so, for the ease of movement of vehicle at this point a curve
is provided.
Necessity of curves:-
1. To bring about gradual change in direction of motion.
2. To bring about gradual change in grade and for good visibility.
3. To alert the driver so that he may not fall asleep.
4. To layout Canal alignment.
5. To control erosion of canal banks by the thrust of flowing water in a canal.
 HORIZONTAL CURVES
▪ Curves provided in the horizontal plane to have the gradual change in direction are
known as horizontal curves.
VERTICAL CURVES
▪ Curves provided in the vertical plane to obtain the gradual change in grade are
called as vertical curves.

Horizontal curves VERTICAL CURVES

Horizontal curves are of different types as follows
▪ Simple circular curve
▪ Compound curve
▪ Reverse curve
▪ Transition curve
▪ Spiral
▪ Lemniscate
Simple Circular Curve
▪ Simple circular curve is normal horizontal curve which connect two straight lines with constant
radius
Compound Curve
▪ Compound curve is a combination of two or more simple circular curves with different radii. In
this case both or all the curves lie on the same side of the common tangent
Reverse curve
▪ Reverse curve is formed when two simple circular curves bending in opposite directions are meet
at a point. This points is called as point of reverse curvature. The center of both the curves lie on
the opposite sides of the common tangent. The radii of both the curves may be same or different.
Transition Curve
▪ A curve of variable radius is termed as transition curve. It is generally provided on the sides of
circular curve or between the tangent and circular curve and between two curves of compound
curve or reverse curve etc. Its radius varies from infinity to the radius of provided for the circular
curve.
▪ Transition curve helps gradual introduction of centrifugal force by gradual super elevation which
provides comfort for the passengers in the vehicle without sudden jerking.
Spiral Curve
▪ Spiral is a type of transition curve which is recommended by IRC as ideal transition curve because of its
smooth introduction of centrifugal acceleration. It is also known as clothoid.
Lemniscate
▪ Lemniscate is a type of transition curve which is used when the deflection angle is very large. In
lemniscate the radius of curve is more if the length of chord is less
Transition curve
▪ It is a curve in plan which is provided to change the horizontal alignment from straight to
circular curve gradually means the radius of transition curve varies between infinity to R or R to
infinity.
Objectives for providing transition curves
▪ For the gradual introduction Centrifugal force
▪ To introduce super elevation gradually
▪ To introduce extra widening gradually
▪ To provide comfort for the driver that is to enable smooth vehicle operation on road.
▪ To enhance aesthetics of highways.
IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons:
▪ It satisfies that rate of change of centrifugal acceleration is constant i.e., Ls.R = constant. Where
Ls = length of transition curve R = radius of curve.
▪ The calculation and field implementation of spiral curve is simple and easy.
▪ It enhances aesthetics also
Determining length of transition curve
The length of transition curve can be calculated by 3 conditions.
1. Based on rate of change of acceleration
2. Based on rate of change of super elevation and extra widening
3. Based in IRC empirical formula
1. Based on rate of change of acceleration
▪ Radius of curve is infinity at the tangent point and hence centrifugal acceleration is
zero. Similarly at the straight end radius of curve has minimum value means
centrifugal acceleration is maximum. So, the rate of change of centrifugal acceleration
should be adopted such that the design should not cause any discomfort to the drivers.
▪ Let Ls be the length of transition curve and a vehicle is moving with a speed of V m/s.
Let “C” be the coefficient of rate of change of centrifugal acceleration.
Ls = (V3/CR)

According to IRC, C = 80/(75+V) and C should be (0.5<C<0.8).

Based on rate of change of superelevation and extra
widening
▪ Let 1 in N is the allowable rate of introduction of super
elevation and E is the raise of the outer edge with respect
to inner edge. W is the normal width of pavement in
meters. We is the extra width of pavement in meters.
And e is the rate of superelevation. E = (W+We).e
▪ Therefore length of transition curve, Ls = (W+We).e.N

▪ If the pavement outer edge is raised and inner edge is

depressed with respect to center of pavement then,

Ls = [(W+We).e.N]/2

▪ Typical range of introduction of super elevation is as

follows according to IRC
Based on IRC empirical formula
▪ IRC given some direct formulae for finding the length of transition curve.
▪ For plain and ruling terrain:
▪ Ls = 2.7 (V2/R)
▪ For mountainous and steep terrains
▪ Ls = V2/R
▪ Hence these are the three criteria to determine the length of transition curve.
▪ The maximum of above three conditions will be considered as the length of transition
curve.
Q1. A national highway with designspeedof7% kmph, width of thepavement7 m,lengthofwheel base 7
m.superelevationprovidedi. 1/15 and coefficient of lateral friction is 0.15
▪ The ruling minimumradiusofthecurve,in m.is
▪ Total width of pavement on horizontal curve in

Q2. The extra widening required for a two-lane national highway at a horizontal curve of 300 m radius,
considering a wheelbaseof8m and a design speed of 100 kmph is
Q3.The design speed for a two lane road is 80 kmph, when a design vehicle with a wheel base of 6.6 m
is negotiating a horizontal curve on that road, the off tracking is measured as 0.096 m. The required
widening of carriageway of the two lane road on the curve is approximately
Q1 A two lane pavement in plane terrain with an extra widening of 0.2 m is provided on a horizontal
curve of radius 200 m. The allowable rate or change of centrifugal acceleration is 0.6 m/sec3, allowable
rate of change of super elevation is 1 in 100, design speed is 60 kmph. The pavement is rotated about
inner edge to achieve super elevation
1. The length of transition curve in meter is
2. The value of shift in meter is
Q.2 A highway is to be designed based on the following data:Design speed 80 kmph,
radius of circular curve 900 m; width of pavement on curve ( no extra widening is
provided use We= 0 ) 7 m: road is passing through plain terrain; rate of change of super
elevation is 1 in 150; the pavement is rotated about center line
1. The rate of change of centrifugalacceleration in m/sec³
2. The length of transition curve in meter is
Superelevation:-
▪ Superelevation is the transverse slope provided to counteract the effect of centrifugal
force and reduce the tendency of vehicle to overturn and to skid laterally outwards by
raising the pavement outer edge with respect to inner edge. superelevation is
represented by “ e ”.

Limits for maximum superelevation:

According to IRC the Maximum Superelevation in Areas
Which Are Bound by Snow fall – 7%
Which are not bounded by Snowfall – 10%
Limits for minimum superelevation
Minimum superelevation = camber or cross slope
Camber: Slope provide in the transverse direction to drain off rain water quickly is known
as Camber or Cross slope. This will also prevents slipping and skidding of vehicles.
▪ Analysis of superelevation
▪ Let us say Design speed = V m/s
▪ Radius = R m
Various forces acting on the vehicle:
Where e = rate of superelevation in %
f = lateral friction factor = 0.15
V = velocity of vehicle in m/s Derivation
g = acceleration due to gravity = 9.81 m/s 2
R = radius of circular curve in meters.
▪ Slip- slip occour when the wheel of vehicle revolves more than the corresponding longitudinal
movement along the road.
Slipping usually takes place in the driving wheel of a vehicle when the vehicle rapidly
accelerates from stationary position or From slow speed of vehicle on the road surface which is
either slippery and wet or when the road surface is loose with mud.
▪ Skid- skid occurs when the wheel of vehicle slide without revolving or when wheel partially
revolve I.e. when the path travelled along the road surface is more than the circumferential
movement of the wheel due to their rotation.
▪ When the breaks are applied, the wheel are locked partially or fully, and if vehicle moves
forward,
Method Of Providing Superelevation
▪ Introduction of superelevation on a horizontal curve of a road is
an important feature in road construction. Superelevation is
provided in the following two methods.
1. Elimination of the crown of the cambered section.
2. Rotation of pavement to attain full superelevation.
1. Elimination of The Crown of The Cambered Section
▪ In this method, the outer half of the camber is gradually
decreased. This may be done by two methods.
▪ In the first method, the outer half of the camber is rotated about
the crown at the desired rate such that the surface falls on the
same plane as the inner half.
▪ In the second method, the crown is progressively shifted
outwards. This method is not usually adopted.
2. Rotation of Pavement To Attain Full Superelevation
▪ In this stage, superelevation is gradually provided over the full
width of the carriageway so that the required superelevation is
available at the beginning of the circular curve.
The different method employed for attaining the superelevation is
as follows:
A. Revolving Pavement About The Center Line
▪ In this method the surface of the road is rotated about the center line of the
carriageway, gradually lowering the inner edge and rising the upper edge. The
level of the center line is kept constant. This method is widely used.
B. Revolving Pavement About The Inner Edge
▪ In this method, the surface of the road is rotated about the inner edge, raising the
center and outer edge.
C. Revolving Pavement About The Outer Edge
▪ In this method, the surface of the road is rotated about the outer edge depressing
the center and inner edge.