Geometric design of highway

Geometric Design of Highway
(IS-73: 1980)
By
Prof. Hole G.R.
Civil Engineering Department

Content
• Introduction
• Factors affecting Geometric Design
• Elements of Geometric Design
a. Cross Sectional Element
b. Sight Distance
c. Horizontal Alignment
d. Vertical Alignment

Introduction
• Geometric Design is deals with Dimensions and layout of visible
features of 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.
 Objective:
• Maximize the comfort, safety and economy of facilities.
• Provide efficiency in traffic operation.
• Provide maximum safety at reasonable cost.
• Minimize the environmental impacts.

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).

Introduction
• Geometric design of highways deals with following
elements:
a. Cross section elements
b. Sight distance consideration
c. Horizontal alignment details
d. Vertical alignment details

Cross section of NH in Embankment
i

Cross section of NH in Cutting

Cross section of SH in Embankment

Cross section of SH in Cutting

Cross section elements
i. Pavement surface characteristics
ii. Width of Pavement or Carriageway
iii. Cross Slope or Camber
iv. Median or Traffic Separator
v. Kerbs
vi. Road Margins
vii. Width of Formation

1.Pavement surface characteristics
A. Friction:
Definition:-
It is resistance developed on the road surface due to
movement of vehicles on road surface.
• In road friction there are mainly two types of friction.
• 1. Longitudinal / Rolling Friction
• 2. Lateral Friction
Vehicle
Lateral
Friction
Longitudinal
Friction

A. Friction: (f)
Longitudinal Friction
• It is the friction which acts along
the direction of length of road .
• It helps for movement of vehicle.
• It is depends on:
1. Roughness of surface
2. Contact area b/w two surface
3. Directly proportional to speed .
Note:
- Smooth tires offers more friction
than New tires in dry Pavement bcoz
of large point of contact and vice-
versa in Wet Condition
Lateral Friction
• It is type of friction which comes
in picture only when there is force
in lateral Direction.
• E.g.: When vehicle moving on
Horizontal Curve, Centrifugal
force generated which is acting in
outward direction and that
centrifugal force is resisted by
Lateral Friction.
As per IRC
f (longitudinal) = 0.35 to 0.40
As per IRC
f ( Lateral) = 0.15

B. Skid and Slip
• In Safe Case :
• During Slip:- (Acceleration)
• During Skid:- (Breaking)
( Rotational Moment) = ( Translational Moment)
( Rotational Moment) > ( Translational Moment)
( Rotational Moment) < ( Translational Moment)

C. Light Reflection Characteristics
 Rigid Pavement (White Color) :
Having good visibility during Night and Glare Effect During Day.
 Flexible Pavement (Black Color) :
Having poor visibility during Night and No Glare Effect During Day.
 Rigid Pavement (Gray Color):
Having good visibility during Night and No Glare Effect During Day.

D. Unevenness Index
 It is an Cumulative vertical Undulations (Sudden Rise & Fall) per
unit horizontal length.
 Bump Integrator is Used to
measure UI developed by CRRI.
• In case of Bad and Uncomfortable
Reconstruction of Pavement is Needed.
Unevenness Index Type of Pavement
0-1500 mm/ km Good
1500-2500 mm/km Satisfactory
2500- 3200 mm/km Bad
> 3200 mm/km Uncomfortable

2. Width of Pavement/ Carriageway
• It is total width of road on which vehicles are allowed to move.
• The width of pavement depends on width of traffic lane and
number of lanes.
• Width of lane is decided based on maximum width of heavy
commercial vehicle (HCV) which is legally permitted to use the
roadway.

2. Width of Pavement/ Carriageway
• The width of carriageway for various classes of roads standardized
by Indian Roads Congress (IRC) are given below:
Class of Road Width of
Carriageway(m)
Single lane road 3.75m
Two lanes, without raised kerbs 7m
Two lanes, with raised Krebs 7.5m
Intermediate Carriageway 5.5m
Multi-lane pavements 3.5m per lane

3. Cross Slope / 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.
 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 prevent entry of surface water into subgrade soil through
pavement.
• To make pavement surface attractive.

3. Camber
 Types of Camber :
1. Parabolic Camber
2. Straight Camber
3. Combined Camber
1. Parabolic Camber:
• The camber is given a continuous curve
of parabolic or elliptical shape from the
edge to crown
• Used for High speed vehicle
2. Straight Camber:
• Joining the crown of the road to its
edges by straight lines forms
• This shape is easy to construct.
• Used in High Rainfall Area
• It is Highest Camber than other types.

3. Camber
C
 Minimum Camber Required as per IRC:
3. Combined Camber:
• It is a combination of parabolic and
straight camber.
• In this camber the central crown portion
is made parabolic and outer edges are
connected by straight lines.
• It is used for Expressway
Types of Road Camber in %
Heavy Rainfall Area
Camber in %
Light Rainfall Area
Cement Concrete/High Bit 2 1.7
Thin Bitumen 2.5% 2%
WBM/ Gravel Road 3% 2.5%
Earth Road 4% 3%

4. Shoulder
• Shoulders are the extra width provided adjacent to outer edge of road for
Emergency purpose.
 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.
 As per IRC:
 Minimum width of shoulder for Two lane Road = 2.5m
 Camber of shoulder is 0.5% more than Camber of Road but it should not less
than 3% in any case.
 On Super elevation Section, (Camber of Shoulder )= (Camber of Road)

4. Kerb
 The boundaries between pavement and shoulders or footpath are
known as Krebs.
• Types of Kerb:
1. Low Kerb
2. Semi-Barrier Kerb
3. Barrier Kerb
4. Submerged Kerb

4. Kerb
1.Mountable kerbs :
• These Krebs 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 Krebs and use the shoulder
incase of emergency.
• Its height is kept on 10cm above the
pavement edge.
2. 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

4. Kerb
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.
Submerged Kerbs:
• They are provided in village Roads.
• They are provided such that top is at
ground level.
• It provides lateral support to pavement

5. 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)

6. Land Width/ Right of way
• It is the total width of road acquired along the alignment of road up to Road
Boundary is called Right of Way.
• (Right of Way) = (Formation Width) + (Road Margin)

7. Borrow Pits
 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 at least 5m from toe of embankment.
• The small portion left undug in a borrow pit to measure the depth of
• excavation is called deadman.

8. Spoil Bank
 When earthwork in excavation of side gutter or borrow pit exceeds earthwork in
filling then it is stored on banks of Excavated pit is called spoil Bank.

9. Lead and Lift
 Lead:
It is the horizontal distance up to which excavated material is transported for
dumping, for which extra payment is not required to pay to the contractor, such
min. Distance is known as Lead.
 Lift:-
It is the vertical distance through which materials are raised after excavation, for which
contractor need not to pay extra payment

B.
Sight Distances
Consideration

Sight Distance
 Definition:
• It is the total Safe Horizontal distance at which Driver can see the Obstacle of
height 0.15m when the driver Height is at 1.2m above Ground Level so that
vehicle can stop without collision is called Sight Distance.

Sight Distance
 Types of Sight Distances:-
1. Stopping Sight Distance (SSD)
2. Overtaking Sight Distance (OSD)
3. Intermediate Sight Distance (ISD)
4. Headlight Sight Distance (HSD)

Stopping Sight Distance (SSD)
 Definition:-
“ SSD is the sufficient length of road available so that driver can
observe the object and stop the vehicle before colliding with object”
SSD = ( Lag Distance) +( Break Distance)

Where,
 Lag distance = Distance travelled by vehicle during reaction time.
(Lag Distance) = (Velocity of Vehicle) x (Reaction Time)
LD = Vkmph* t m/s
--------------(1)
 Breaking Distance = Distance travelled by vehicle after application of Break
 𝐵𝑟𝑒𝑎𝑘𝑖𝑛𝑔 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑓𝑓𝑜𝑟 𝑎𝑠𝑠𝑒𝑛𝑑𝑖𝑛𝑔 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑉2
254(𝑓+𝑛%)
 𝐵𝑟𝑒𝑎𝑘𝑖𝑛𝑔 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑓𝑓𝑜𝑟 𝐷𝑒𝑠𝑒𝑛𝑑𝑖𝑛𝑔 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑉2
254(𝑓−𝑛%)
• n% = +ve for Rising Grade , f = Longitudinal Friction
• n% = -ve for Falling Grade t = Reaction Time
• n% = 0 for Plain Road
LD = 0.278* Vkmph* t m/s
SSD = ( Lag Distance) +( Break Distance)
SSD = 0.278* Vkmph* t m/s +
𝑽 𝟐
𝟐𝟓𝟒(𝒇+𝒏%)

 Reaction Time as per IRC:- ( Depends on PIEV Theory)
Note:-
One Lane, One Way Traffic
Single Lane, Two Way
Two Lane, Two Way
Two Lane, Two Way when one lane is under maintenance
Conditions Reaction Time(Sec)
SSD 2.5
OSD 2
Min Space Headway 0.7
SSD =SSD
SSD = 2*SSD
SSD = SSD
SSD = 2*SSD

Overtaking Sight Distance (OSD)
 Definition:-
“To provide the sufficient distance to the driver to overtake the slow
moving vehicle ahead safely against the traffic in opposite direction.”
• D1 = Distance travelled by fast moving vehicle before overtaking started.
• D2 =Distance travelled by fast moving vehicle during Overtaking Action
• D3 =Distance travelled by opposite moving vehicle during operation of overtaking

 D1 = Distance travelled by fast moving vehicle before overtaking started.
D1 = (Velocity of fast moving vehicle(Vb) x ( Reaction Time)
 D2 = Distance travelled by fast moving vehicle during Overtaking Action.
D2 = 2S + b
Where S = (0.7* Vb+6) m……………..(Min Space Headway)
b = Vb * T m ………………….(T = Overtaking Operation Time)
a = Acceleration of vehicle ( m/s2)
 D3 =Distance travelled by opposite moving vehicle during operation of overtaking
D3 = (Velocity of opposite moving vehicle (Vb) x ( Overtaking Operation Time)
D1 = 0.278* Vb * t
D2 = 2S+0.278* Vb * T
D3 = 0.278* Vb * T
OSD = D1+D2+D3

 Important:-
Minimum Length of Overtaking Zone = 3*OSD
Maximum Length of Overtaking Zone = 5*OSD

Intermediate Sight Distance (ISD)
 Definition:
It is the provided only when other type of sight distances are not able
to provided.
E.g.: Sight Distance at Intersection
• Generally
Note:
ISD = 2 * SSD
ISD = SSD for leg B + SSD for leg A
Sight
Distance
Ht of Driver
Eye(m)
Ht. of
Obstruction(m)
SSD 1.2 0.15
OSD/ISD 1.2 1.2
SSD< ISD< OSD

Alignment of Highway
 Definition:
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.
 Classification of Alignment:-
1) Horizontal Alignment
2) Vertical Alignment

Design Speed and Factors affecting D.S:-
Design Speed.
The maximum safe speed of vehicle assumed for geometrical design of a highway is
known as Design Speed.
Factors affecting design speed:-
1) Class and condition of the road surface
2) Nature, intensity and type of traffic
3) Type of curve along the road
4) Sight distance required
5) Topography of the area

Elements of Horizontal Alignment:-
1. Horizontal Curve
2. Extra Widening
3. Transition Curve
4. Set Back Distance

1. Horizontal Curve:-
 The presence of Horizontal curve in Horizontal alignment
introduce Centrifugal Force in outward direction of curve.
 Effect of Centrifugal Force on Vehicle:-
Effect of Centrifugal Force on
Vehicle
Overturning of
Vehicle
Lateral Skidding
Combined Effect of
both

Super Elevation:-
• Definition:-
“ It is the Raising of outer edge w.r.to inner
edge to Balance the effect of Centrifugal
Force and Reduce the tendency of overturning
of vehicle is called S.E.”
 Purpose/ Objectivies of Providing S.E.:-
• To avoid skidding off vehicles at sharp horizontal turns.
• To turn vehicles smoothly even at high speed at curves.
• To minimize wear and tear of wheels and road surface in contact.
• To avoid overturning of vehicles at corners by counteracting centrifugal
force

Super Elevation:-
• The centrifugal force is given by the equation:
P = Wv²∕gR
where,
P=centrifugal force in kg
W=Weight of the vehicle in kg
R=radius of the circular curve in m
v=speed of the vehicle in m/s
g=acceleration due to gravity=9.8 m/s2

Super Elevation:-
• For equilibrium condition,
P cosө=W sinө+FA+FB
P cosө=W sinө+ f.RA + f.RB
P cosө=W sinө+f(RA+RB)
P cosө=W sinө+f(W cos ө+P sin ө)
P(cosө – f sinө)=W sinө+f Wcosө
Dividing by cosө,
P (1- f tanө) = W tanө+ Wf
P(1- f tanө)= W(tanө+f)
Centrifugal ratio =P/W= tanө+f /(1-f tanө)
But tanө = e ( SE)
P(1-ef) = W(e+f)

Super Elevation:-
P(1-ef) = W(e+f)
P/W = (e+f)/ (1-ef)
but P/W = v²∕gR
v²∕gR = e+f …………….(1-ef)=1…..ef=0
• If „V‟ speed of the vehicle is in kmph,
• where,
e = rate of Super elevation per unit width of road=tanӨ
f = design value of lateral friction coefficient = 0.15
v = speed of the vehicle, kmph
R = radius of the horizontal curve, m
g = acceleration due to gravity = 9.81 m/sec²
e + f = V²∕ 127R

Equilibrium Super Elevation:-
• It is a special case in which Centrifugal force is fully balanced
by S.E. alone i.e. Coefficient of lateral friction is assumed to be
zero
Basic Equation of S.E. is,
e + f = V²∕ 127R
But in Equilibrium S.E. f = 0
e equil = V²∕ 127R

Super Elevation As per IRC:-
Terrain Maximum S.E.(%)
Urban area 4% (0.04)
Urban and Rolling 7 % (0.07)
Mountainous & steep 10 % (0.10)
Maximum S.E.
Minimum Super Elevation = Camber of Road
Min. S.E < Cal. S.E. < Max. S.E.

Design of Super Elevation
• Design of S.E. is for mixed traffic condition is complex problem as
vehicles are moving with different speed.
• For fast moving vehicle, provides higher S.E. without considering
coefficient of friction is safe. i.e. centrifugal force is fully counteracted
by S.E. only.
• For slow moving vehicle, S.E. is provided by considering Coefficient
of Friction is Safe. i.e. Centrifugal Force is fully balanced by S.E. and
Coeff. of Friction both.
• By considering both slow and fast moving vehicle, IRC suggested
that use 75% Design Speed for Design of S.E. and Consider
coefficient of friction(f) is as Zero.
For Design of S.E.:-
• f=0 always for mixed traffic condition and Design of S.E. Numerical.
• V = 0.75 * VD
• If value of friction(f) given in problem, then also consider it as Zero.

Design Steps of Super Elevation
1. Step-1:- Calculate S.E. for 75% Design Speed with f = 0
e + (f=0) = (0.75*V²) ∕ 127R
e cal > emax
• If ecal ≤ e max, Provide S.E. = e cal
• If ecal > e max, Go to step- II
2. Step – 2 If e cal greater than to e max :-
Provide, e cal = e max and apply check for “ f ” with 100% Design speed.
(f cal) = (V² ∕ 127R ) – e max ……………. ( > f max = 0.15)
• f cal ≤ 0.15 then it is ok
• f cal > 0.15, then Go to Step- III
e cal = V²∕ 225*R

Design Steps of Super Elevation
1. Step-3 as fcal > 0.15 , then Restrict Speed
• This Vmax is the Speed Limit ( Sign Board Value)
• Ruling Minimum Radios:-
Vmax = √ (127*R * ( emax + 0.15))
R ruling = V² / 127* (emax + 0.15)

Methods to Attainment of Super Elevation

1) Outer edge rotated @ Crown:-
• In this method the outer edge of pavement
is rotated about Crown.
• Gradually the OUTER edge is rotated in
transition Zone and Design S.E. is
achieved at the start of Horizontal Curve
2) Diagonal Crown Method:-
• In this Method the crown is gradually
shifted towards outer edge and Design
S.E. is aachieved.
Method –I Elimination of Crown of Camber

1) Outer edge rotated @ Inner Edge:-
• In this method the outer edge of pavement
is rotated @ inner edge.
• No Drainage problem.
• Center line changed
• Earthwork is not balanced
• Used for High speed
• Used in High Rainfall area.
2) Rotation of Pavement @ Centerline:
• Whole pavement is rotated @ Centerline.
• There may be Draianage Problem.
• Centerline remains Unchanged.
• Earthwork is Balanced.
• Used in Hilly or Ghat Region
Method –II Rotation of Pavement

Extra Widening
• Extra widening = Mechanical widening+ Psychological widening
n = no of Lanes
L = Length of Wheel Base
R = Radius of Curve
V = Speed of Vehicle (kmph)

Extra Widening
• Special Case:-
as per IRC Psychological Widening should not be considered for single lane road
Wp = 0
We = Wm + Wp
We = Wm
We =
𝑛𝑙2
2𝑅
We =
1∗62
2𝑅
…..(only for single lane road n = 1)
We =
𝟏𝟖
𝑹
If Radius = R
Then Curvature =
𝟏
𝑹

Extra Widening
If Radius > 300m Not to provide any extra Widening
If 50 ≤ R ≤ 300 m
Provide Extra Widening on both side of
Curve
If R < 50m
Provide Extra Widening only on Inner Side

Curve
 Definition:
“ It is an Geometrical Arc provided at change in alignment or change
in Gradient is called Curve”

Necessity of Curves:
1. Straight routes are become monotones so to keep driver
alert curves are provided.
2. To balance the Earth work the alignment of road is
changed in vertical plane which introduces Vertical
curves.
3. To avoid the alignment passing through valuable land.
4. To make alignment of road in safe and stable condition
in Hilly area.

Types of Curves:
Types of Curves
Horizontal Curves Vertical Curves
1. Simple Curve
2. Compound Curve
4. Transition Curve
3. Reverse Curve
a. Spiral
c. Cubic Parabola
b. Lemniscate
2. Valley Curve
1. Summit Curve

A. Horizontal Curves:
“ It is an arc provided in Horizontal plane when there is change in
alignment is called Horizontal Curve”
• When vehicle is moving on Horizontal curve, the centrifugal
force which acts in outward direction at C.G. of vehicle.
• Centrifugal force acting outward has following effect:
1. Overturn of vehicle
2. Lateral skidding
• Types of Horizontal Curve:
a. Simple Curve
b. Compound Curve
c. Reverse Curve
d. Transition Curve

1. Simple Curve:
• It is the type of horizontal curve in
which whole curve is consist of
Single Radius then it is called as
Simple Curve.
• It is provided in Hilly Area
2. Compound Curve:-
• It is the type of Horizontal curve
having two or more simple curve or
Radius is called Compound Curve.
• Provided where land available to set
out the curve is less.
• Used at to connect Runway to taxiway
at Airport.

3. Reverse Curve:
• It is the curve which having two
simple curves of same radius or
different radius but laying in
opposite direction.
• Used in Pipeline, Flumes, Levees,
Canal etc.
4. Transition Curve:
• It is the curve of varying radius.
The radius of such curve changes
from infinity to certain fixed value.
• It is Provided in Flyovers and Railway
track.
• Used to introduce S.E in Horizontal
Curve

Purpose of Transition Curves:
1. To introduce gradual centrifugal force to avoid sudden jerk in
horizontal curve.
2. To provide comfort and security.
3. To introduce Super Elevation and Extra widening on curve
gradually.
4. To improve the aesthetic appearance of Road
 Types of Transition Curve:
a. Spiral
b. Lemniscate
c. Cubic Parabola

Types of Transition Curves:
a. Spiral T.C:-
• Radius of curvature inversely proportional to the distance of point from starting
point
• Ratio of Rate of change of acceleration is Uniform.
• As per IRC Spiral curve is Ideal Transition Curve.
b. Lemniscate Curve:
• Radius of curve decreases more rapidly with increase in length.
• Mostly used in Modern roads.
• Used where deflection angle of curve is large.
• Set by Using Polar Coordinates
C. Cubic Parabola:
• used in valley curve
• Set by using simple Cartesian coordinates.

Length of Transition Curves:
a. Based on Rate of change of acceleration:-
C =
80
75+𝑉
Where,
C = Rate of change of acceleration
V = Velocity in (m/s)
R = Radius of T.C. (m)
b. Based on Rate of Change of Super Elevation:
1. Pavement rotation abut Inner Edge :-
2. Pavement Rotation @ centerline:-
Ls =
𝑉3
𝐶∗𝑅
L = e N (W+We)
L = e
𝑁
2
(W+We)

Length of Transition Curves:
Where,
e = Super elevation
W = Normal width of pavement
We = Extra Widening
N = rate of change of S.E.
C. Based on Comfort Condition:-
Value of “N” as Per IRC
150 Plain & Rolling Area
60 Mountainous & Steep Terrain
Ls = 𝟐. 𝟕 ∗
𝑉 𝟐
𝑅
Plain & Rolling Area
Ls =
𝑉 𝟐
𝑅
Mountainous & Steep Terrain
Shift of the Curve: Shift =
𝐿𝑠 𝟐
24∗𝑅

Gradient
 Definition:
“ It is the rise or fall along the length of road is called Gradient”
Rising/ Positive/ Ascending Gradient
Gradient = (+n%) or =
𝑛
100
=
1
(
100
𝑛
)
=
1
𝑁
Falling / Negative / Descending Gradient
Gradient = (-n%) or =
𝑛
100
=
1
(
100
𝑛
)
=
1
𝑁

Types of Gradient
1. Ruling Gradients: (RG)
• The gradient which is commonly provided under normal condition is known as ruling
gradient
• Also called Design Gradient
• Depend on Topography, Design Speed and Cost of Construction
2. Limiting Gradient: (LG)
• The maximum gradient provided more than ruling gradient due to topography, is known
as limiting gradient.
• Provide only when cost of R.G. is more than L.G
3. Exceptional gradient – (EG)
• The gradient provided in extraordinary situation (very short length road) is known as
exceptional gradient.
4. Minimum gradient –
The minimum value of gradient provided for removal of water, is known as minimum
gradient.
M.G < R.G < L.G < E.G

Gradient As per IRC
Sr.
No.
Terrain RG LG EG
1 Plain and Ruling 3.3% 5% 6.7%
2 Mountainous and Steep
Elevation > 3000m
above MSL
5% 6% 7%
3 Steep Terrain
Elevation up to 3000m
above MSL
6% 7% 8%
At Higher Elevation lesser Gradient is provided because available oxygen is less due to
which less fuel burned and hence it reduces pulling power of vehicle

B. Vertical Curves
 Definition:
“ It is an arc provided in a vertical plane when there is change in
gradient of road”

Types of Vertical Curves
Summit Curve
• The in which convexity in upward
direction is called summit curve
Valley Curve
• It is type vertical curve in which
convexity downward is called valley
curve

Types of Summit Curves
1. Rising gradient meets another Rising Gradient 3. Rising gradient meets another Falling Gradient
2. Rising gradient meets Horizontal Gradient 4. Falling gradient meets another Falling Gradient

Types of Valley Curves
1. Falling gradient meets Rising Gradient 3. Falling gradient meets another Falling Gradient
2. Falling gradient meets Horizontal Gradient 4. Rising gradient meets another Rising Gradient

Geometric design of highway

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