2. Highway Geometric Design
• Geometric design of highways deals with the
dimensions and layout of visible features of
the highway and vertical alignments, sight
distances and intersections.
• The geometrics of highway should be designed
to provide efficiency in traffic operations with
maximum safety at reasonable cost.
3. • Geometric design of highways deals with
following elements:
• Cross section elements
• Sight distance considerations
• Horizontal alignment details
• Vertical alignment details
• Intersection elements
4. Geometric design of highways depends on following
factors:
Design speed is the most important factor affecting geometric
design which is decided taking into account overall
requirements of the highway.
Rural
Roads
Design Speed in Kmph for various terrains
Urban
Roads
Design
Speed
Plain Rolling Mountainous Steep
Ruling Min. Ruling Min. Ruling Min. Ruling Min.
NE 120 100 100 80 80 60 80 60
NH &
SH
100 80 80 65 50 40 40 30 Arterial 80
MDR 80 65 65 50 40 30 30 20
Sub-
Arterial
60
ODR 65 50 50 40 30 25 25 20 Collector 50
VR 50 40 40 35 25 20 25 20 Local 30
5. Geometric design of highways depends on following
factors:
Topography or terrain are classified on the general slope of
the country across the alignment as plain, rolling, mountainous
& steep
Terrain Type % cross slope of the country
Plain 0-10
Rolling 10-25
Mountainous 25-60
Steep >60
6. • Geometric design of highways depends on following
factors:
• Traffic factors that affect geometric design of roads are
vehicular characteristics & road user characteristics
• Design hourly volume and capacity keeps on fluctuating
with time so it will be uneconomical to design the roadway
facilities for the peak traffic flow or the highest hourly traffic
volume
• Environmental & other factors such as aesthetics,
landscaping, air pollution, noise pollution & other local
conditions must be considered in geometric design
7. Pavement Surface Characteristics
• The pavement surface depends on the pavement
type. The important surface characteristics of the
pavement are
• Friction
• Unevenness
• Light reflecting characteristics
8. Highway Cross Section
Elements
FRICTION
• The Friction or Skid resistance between vehicle
tyre and pavement surface is one of the factors
determining the operating speed and the minimum
distance required for stopping the vehicles.
• Skid occurs when the wheels slide without revolving
or rotating or when the wheels partially revolve i.e.,
when the path travelled along the road surface is
more than the circumferential movements of the
wheels due to their rotation.
9. • Slip occurs when a wheel revolves more than
the corresponding longitudinal movement along
the roads.
• The value of longitudinal coefficient of friction
ranges from 0.35 to 0.40 and value of lateral
coefficient of friction is 0.15 as per Indian
Roads Congress
10. PAVEMENT UNEVENNESS
• The longitudinal profile of the road pavement
has to be even in order to provide good riding
comfort to fast moving vehicles and to minimise
the vehicle operation cost.
• Presence of undulations on the pavement
surface is called pavement unevenness which
results in:
• Increase in discomfort & fatigue to road users
• Increase in fuel consumption and tyre wear
• Increase in vehicle maintenance cost
• Reduction in vehicle operating speed
• Increase in accident rate
11. • The unevenness of pavement surface is
commonly measured by using a simple
equipment called Bump Integrator in terms of
unevenness index.
• Unevenness Index is the cumulative measure
of vertical undulations of the pavement surface
recorded per unit length of road.
12. LIGHT REFLECTING
CHARACTERISTICS
• Night visibility depends on the colour and light
reflecting characteristics of the pavement
surface.
• The glare caused by the reflection of head
lights is considerably high on wet pavements
than on dry pavements.
• Light coloured or white pavements give good
visibility at night but produces glare and eye
strain during bright sunlight.
• Black top surface give good visibility during
sunlight but yields poor visibility during night
time.
13. Cross Slope or Camber
• Cross slope or camber is the slope provided to the road surface in
the transverse direction to drain off the rain water from the road
surface.
• Cross slope is provided for following purpose:
• To prevent the entry of surface water into the pavement
layer and the subgrade soil through pavement
• To prevent the entry of water into bituminous pavement
layers
• To remove the rain water from the pavement surface as
quickly as possible and to allow the pavement to get dry
soon after the rain
• The camber is provided on the straight roads by raising the centre
of the carriageway with respect to the edges, forming a crown along
the centre line.
14. • At horizontal curves with super elevation, the
surface drainage is provided by raising the outer
edge of pavement with respect to the inner edge.
• The rate of camber is usually designated by 1 in
n which means 1 vertical to n horizontal.
• Camber may also be expressed as percentage. If
the camber is x %, the cross slope is x in 100
• The required camber of a pavement depends on:
• Type of pavement surface
• Amount of rainfall
15. • In the field, camber of the pavement can be
provided in any of the following shapes:
• Straight Line is generally provided for CC pavement
to facilitate construction
• Parabolic Shape is suitable on roads where vehicles
frequently cross the centre line and overtake at high
speed
16. Combined Shape in which a straight line slope
is provided at edges and the middle part is
curved
18. EXERCISE: In a district where the rainfall is heavy, two types of
road pavement are to be constructed:
• Two lane State Highway with bituminous concrete surface
• Major District Road of WBM pavement, 3.8 m wide
What should be the height of the crown with respect to the edges
in these two cases, assuming straight line camber?
SOLUTION:
1) For SH, width of two-lane pavement = 7.0 m
For BC surface in heavy rainfall area provide slope of 1 in 50, thus
rise of crown w.r.t. edges = (7.0/2.0) X (1/50) = 0.070 m
2) For WBM roads in heavy rainfall area provide slope of 1 in 33,
thus rise of crown w.r.t. edges = (3.8/2.0) X (1/33) = 0.058 m
19. Width of Pavement or
Carriageway
• Carriageway width depends on
• Width of traffic lane
• Number of lanes
• The portion of carriageway width that is intended
for one line of traffic movement is called traffic
lane.
• The width of traffic lane is decided on the basis of
standard vehicle, width of largest vehicle class,
lateral clearance on either side of moving vehicle.
• The number of traffic lanes required on a highway
depends on the predicted traffic or the design
traffic volumes and desired level of service.
22. Width of Pavement or Carriageway
The width of carriageway for various classes of
roads standardised by the Indian Roads Congress
(IRC) are as follows:
Class of Road
Width of
Carriageway,
m
Single lane road 3.75
Two lanes without
raised kerbs
7.0
Two lanes with raised
kerbs
7.5
Intermediate
carriageway
5.5
Multilane pavements 3.5 per lane
2.5 m is considered as standard width
of vehicle and clearance of 0.625 m is
added on both sides to achieve width
of 3.75 m
23. Highway Cross Section Elements
Medians or Traffic Separators
• In highways with divided carriageway, a median is
provided between two sets of traffic lanes intended to
divide the traffic moving in opposite directions.
• The main function of the median is to prevent head-on
collision between vehicles moving in opposite directions
on adjacent lanes
• The medians may also serve following functions:
• To channelize traffic into streams at intersections
• To protect the pedestrians
• To segregate slow traffic
25. Highway Cross Section Elements
Medians or Traffic Separators
• The IRC recommends a minimum desirable width of 5.0 m
for medians of rural highways and 3.0 m where land is
restricted.
• On long bridges the width of median may be reduced up to
1.2 to 1.5 m.
• The absolute minimum width of median in urban area is 1.2
m and desirable minimum is 5.0 m.
• The desirable width of median for expressways is 15 m and
minimum width is 10 m. If the median barriers are provided
the median width is reduced to 4.5 m.
26. Highway Cross Section Elements
Kerb
• Kerb indicates the boundary between the pavement and
median or foot path or shoulder.
• Kerbs may be mainly divided into three groups based on
their functions
• Low kerb or mountable type kerb
• Semi-barrier type kerb
• Barrier type kerb
27. Shoulders
• Shoulders are provided on both
sides of the pavement all along the
road in the case of undivided
carriageway and on the outer edge
of the carriageway in the case of
divided carriageway.
• The minimum shoulder width
recommended by IRC is 2.5 m.
• In India, the outward minimum
slope of shoulders for earthen
surfaces is 0.5 % steeper than the
pavement camber (which is
minimum 3%).
• Benefits of shoulder are
• Provides structural stability & support edges of the flexible
pavement
• Increases traffic capacity of carriageway
• Serves as an emergency lane for vehicle compelled to be taken out
of the main carriageway
• Act as service lanes for vehicles that are disabled
Shoul
der
28. Highway Cross Section Elements
Guard Rails
• They are provided at the edge of the shoulder usually when
the road is on an embankment. They serve to prevent the
vehicles from running off the embankment, especially when
the height of the fill exceeds 3 m.
29. Footpath or Side Walk
• Footpaths are exclusive right of way to pedestrians,
especially in urban areas. They are provided for the safety
of the pedestrians when both the pedestrian traffic and
vehicular traffic is high.
• The absolute minimum width of foot path is 1.5 m and the
desirable minimum width is 2.0 m.
Highway Cross Section Elements
30. Drive ways
• Drive ways connect the highway with commercial
establishment like fuel-stations, service stations etc.
Drive ways
Highway Cross Section Elements
31. Cycle tracks
• Cycle tracks are provided in urban areas where the volume
of cycle traffic on the road is very high. A minimum width of 2
m is provided for the cycle track and the width may be
increased by 1.0 m for each additional cycle lane.
Highway Cross Section Elements
32. Highway Cross Section Elements
Parking lanes
• Parking lanes 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 vehicles.
• For parallel parking, the minimum lane width should be 3.0 m.
33. Highway Cross Section Elements
Bus bays
• Bus bays may be provided by recessing the kerb to avoid
conflict with moving traffic. Bus bays should be located at least
75 m away from intersection.
34. Highway Cross Section Elements
Lay-byes
• Lay-byes are provided near public conveniences with guide
maps to enable drivers to stop clear off the carriageway.
• Lay-byes should normally be of 3.0 m width and at least 30 m
length with 15 m end tapers on both sides.
35. Frontage roads
• Frontage roads are provided to give access to properties
along an important highway with controlled access to
expressway or highway.
Highway Cross Section Elements
36. Highway Cross Section Elements
Embankment Slopes
• Embankment slopes should be as flat as possible for the
purpose of safe traffic movement and for aesthetic reasons.
• Though from the slope stability point, a steeper slope may be
possible, the slope may be kept as flat as permitted by financial
considerations.
• For safety considerations, the desirable slope for the
embankment as 1 in 3.
37. Highway Cross Section Elements
Width of Formation or
Roadway
• Width of formation or
roadway is the sum of
widths of pavement or
carriageway including
separators if any and the
shoulders.
• Formation or Roadway
width is the top width of
the highway embankment
or the bottom width of
highway cutting excluding
side drains
FORMA
TION
WIDTH
38. Highway Cross Section Elements
Road Classification
Roadway width, m
Plain & Rolling
Terrain
Mountainous &
Steep Terrain
National Highway
& State Highway
Single
lane
12.0 6.25
Two lanes 12.0 8.80
Major District Road
Single
lane
9.0 4.75
Two lanes 9.0 -
Other District Road
Single
lane
7.5 4.75
Two lanes 9.0 -
Village Road
Single 7.5 4.0
Width of roadway for various classes of roads as per IRC is
given in the table below:
39. Highway Cross Section Elements
Right of Way & Land Width
Right of way is the area of land acquired for the
road, along its alignment.
The width of the acquired land for the right of way is
known as land width.
40. Highway Cross Section Elements
Recommended land width in m for different roads in
rural & urban areas
Rural
Roads
Plain & Rolling Terrain
Mountainous &
Steep Terrain
Urban
Roads
Land
Width
Open Areas
Built-up
Areas
Open
Areas
Built-up
Areas
Norm
al
Ran
ge
Nor
mal
Ran
ge
Normal Normal
NE 90 -- -- -- 60/30 --
NH &
SH
45
30-
60
30
30-
60
24 20 Arterial 50-60
MDR 25
25-
30
20
15-
25
18 15
Sub-
arterial
30-40
ODR 15
15-
25
15
15-
20
15 12 Collector 20-30
VR 12
12-
18
10
10-
15
9 9 Local 10-20
41. Road Boundaries
Building Line, up to which no construction activity should take place.
Control Line, which comes after building line up to which construction activity is
permitted but under the control of government authority.
Road
Type
Plain and rolling terrain
Mountainous and
steep terrain
Open areas Built-up areas
Open
areas
Built-up
areas
Overall width
between
building lines,
m
Overall width
between control
lines, m
Distance between
building line and
road boundary (set-
back), m
Distance between
building line and road
boundary (set-back),
m
NE 110 130 5 5 5
NH & SH 80 150 3-6 3-5 3-5
MDR 50 100 3-5 3-5 3-5
ODR 25 35 3-5 3-5 3-5
VR 25 30 3-5 3-5 3-5
Highway Cross Section Elements
42. BUILDING LINE
BUILDING LINE
CONTROL LINE
CONTROL LINE
No building should be constructed
No building should be constructed
Construction permitted but under control of government authority
Construction permitted but under control of government authority
Set-back Distance
Set-back Distance
Highway Cross Section Elements
43. Sight Distance
• Sight distance is the length of road visible ahead to the driver
at any instance.
• Sight distance available at any location of the carriageway is
the actual distance a driver with his eye level at a specified
height above pavement surface has visibility of stationary or
moving object of specified height which is on the carriageway
ahead.
• Sight distance can be categorised into following:
• Stopping Sight Distance (SSD)
• Overtaking Sight Distance (OSD)
• Sight Distance at Intersection
• Intermediate Sight Distance (2 x SSD, ISD is provided when it is
not possible to provide OSD)
• Head Light Sight Distance (Distance visible to driver during
night and it is critical at vertical curves)
44. Sight Distance
Stopping Sight Distance (SSD)
• The minimum distance (length of roadway) visible to the
driver at any spot should be sufficiently long to stop a
vehicle travelling at or a near the design speed before
reaching a stationary object in its path to avoid accident.
• For the purpose of measuring SSD, IRC has suggested the
height of eye level of driver as 1.2 m and the height of the
object as 0.15 m above the road surface.
45. Sight Distance
• SSD depends on following factors:
• Total reaction time of driver is divided into four
parts
(i) Perception time is the time required for the
sensations received by the eyes or ears of the driver
to be transmitted to brain.
(ii)Intellection time is the time required for the driver to
understand the situation
(iii) Emotion time is the time elapsed during emotional
sensations and other mental disturbance such as fear,
anger or superstition feelings.
(iv) Volition time is the time taken by the driver for the
final action
Reflex Action
Intellection Emotion
46. Sight Distance
• SSD depends on following factors:
• Speed of vehicle increases and so stopping distance
increases
• Efficiency of Brakes is said to be 100% if the wheels
are fully locked resulting in skidding which is
undesirable. So to avoid skid, braking forces shall not
exceed the frictional force between road & tyre.
• Frictional resistance between road & tyres depends
on coefficient of friction ‘f’ between road & tyre. IRC has
suggested values of f in between 0.35 to 0.40
depending on design speed. As the value of ‘f’
decreases, the braking distance increases.
47. Sight Distance
Analysis of Stopping Sight Distance (SSD)
• SSD is the summation of following distances:
• The distance travelled by the vehicle at uniform speed during the total
reaction time ‘t’, which is known as lag distance.
• The distance travelled by the vehicle after the application of the
brakes, until the vehicle comes to a dead stop which is known as
braking distance.
• Lag distance in m = v x t, here v is in m/sec and t = 2.5 seconds & also
Lag distance in m = 0.278 V x t, here V is in km/Hr and t = 2.5 seconds
• Braking distance may be obtained by equating the work done in stopping
the vehicle and the kinetic energy of the vehicle moving at design speed.
49. Sight Distance
Analysis of Stopping Sight Distance (SSD)
• If the maximum frictional force developed is F (kg) and the
braking distance is ‘l’ m then the work done against the
friction force in stopping the vehicle of weight W is given by:
F x l = W x f x l
• The kinetic energy of vehicle is Wv2/2g
• Hence W x f x l = Wv2/2g, Braking Distance, l = V2/2gf
• SSD (m) = lag distance + braking distance = vt + v2/2gf
………v is in m/s
• SSD (m) = lag distance + braking distance = 0.278 Vt +
V2/254f ………V is in km/Hr
50. Analysis of Stopping Sight Distance (SSD)
• SSD (m) = lag distance + braking distance = vt +
v2/2g (f ± 0.01n) ………v is in m/s
• SSD (m) = lag distance + braking distance = 0.278
Vt + V2/254 (f ± 0.01n) ………V is in km/Hr
• Recommended longitudinal friction coefficient
values for providing SSD
Speed,
kmph
20-30 40 50 60 65 80
100 &
above
f 0.40 0.38 0.37 0.36 0.36 0.35 0.35
51.
52. SOLUTION:
1) SSD for two-way traffic on a two lane road = 61.4 m
2) SSD for two-way traffic on a single lane road = 61.4 x 2 = 122.8 m
53.
54. SOLUTION:
Total sight distance required to avoid head on collision of the two
approaching cars = 153.6 + 82.2 = 235.8 m say 236 m
236
m
57. Overtaking Sight Distance (OSD)
• If all the vehicles travel along a road at the
design speed, then theoretically there should be
no need for any overtaking.
• In fact all the vehicles do not move at the
design speed as each vehicle driver is free to
travel at lower speeds and this is particularly
true under ‘mixed traffic’ conditions.
• In such circumstances, it is necessary for fast
moving vehicles to overtake or pass the slow-
moving vehicles.
58. • Therefore efforts should be made to provide
adequate sight distance along the road alignment
to enable vehicles travelling at design speed to
safely overtake slow moving vehicles.
• 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)
• OSD is the distance measured along the centre of
the road which a driver with his eye level at 1.2 m
above the road surface can see the top of an
object 1.2 m above the road surface.
59. Analysis of Overtaking Sight Distance (OSD)
OSD is the summation of three distances d1 m, d2 m, d3 m
d1 d3d2
b ss
60. Analysis of Overtaking Sight Distance (OSD)
• Yellow car is travelling at speed of vb m/sec, Blue car and
cream car are travelling at higher speed of v m/sec
• d1 (distance travelled by blue car) = vbt………..Assume t = 2
secs
• Blue car must reduce its speed & travel behind yellow car at same speed as that of
yellow car waiting for an opportunity to overtake. The distance covered in reaction
time of t seconds at a speed of vb m/sec is d1
61.
62. Analysis of Overtaking Sight Distance (OSD)
• d3 (distance travelled by cream car) = vT
• d3 is the distance travelled by cream car moving at a design speed of v m/s during
the overtaking operation of blue car i.e., during overtaking time T seconds
• Thus OSD = d1 + d2 + d3 (For two-way traffic)
OSD = d1 + d2 (For one-way traffic)
63. • EXERCISE: The speeds of overtaking and overtaken vehicles are 70 and
40 kmph, respectively on a two-way traffic road. The average acceleration
during overtaking may be assumed as 0.99 m/sec2.
(a) Calculate safe overtaking sight distance
(b) What is the minimum and desirable length of overtaking zone?
(c) Draw a neat sketch of the overtaking zone and show the positions
of the signposts.
• SOLUTION:
Given: V = 70 kmph, v = 70/3.6 m/s = 19.4 m/s
Vb = 40 kmph, vb = 40/3.6 m/s = 11.1 m/s
Average acceleration = 0.99 m/sec2
Assume reaction time = 2.0 seconds
64.
65. SOLUTION:
(b) Minimum length of overtaking zone = 3 (OSD) = 3 x 278 = 834 m
Desirable length of overtaking zone = 5 (OSD) = 5 x 278 = 1390 m
(c) Sketch of overtaking zone
834 to 1390 m
OVERTAKIN
G ZONE
AHEAD
278 m
END OF
OVERTAKING ZONE
278 m
OVERTAKIN
G ZONE
AHEAD
278 m
END OF
OVERTAKING ZONE
278 m
66.
67. • SOLUTION:
• OSD for one-way traffic = d1 + d2 = 44.4 + 286.2 = 330.6 m
say 331 m
• OSD for two-way traffic = d1 + d2 + d3 = 44.4 + 286.2 + 291.8
= 622.4 m say 623 m
68. Design Of Horizontal
Alignment
• Various design element to be considered in the
horizontal alignment are horizontal curve,
super-elevation, radius of circular curve,
widening of pavement on curves, type & length
of transition curves, & required set-back
distance for fulfilling sight distance
requirements.
• Improper design of horizontal alignment of
roads would necessitate speed changes
resulting in higher accident rate and increase in
vehicle operation cost.
69. HORIZONTAL CURVE
• A horizontal curve is a curve in plan to provide
change in direction to the centre 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.
Centrifugal Force
70. HORIZONTAL CURVE
• The centrifugal force developed depends on the
radius of the horizontal curve and the speed of
the vehicle negotiating the curve.
• This centrifugal force is counter acted by the
transverse frictional resistance developed
between tyres & the pavement which enables
the vehicle to change the direction along the
curve & maintain stability of vehicle.
71. •Centrifugal force P is given by the equation
P = Wv2 / gR
W = Weight of the vehicle, kg
v = speed of the vehicle, m/s
g = gravitational acceleration, m/s2
R = Radius of circular curve, m
•The ratio of the centrifugal force to the weight of the
vehicle, P/W is known as the centrifugal ratio or the
impact factor. Centrifugal ratio, P/W = v2 / gR.
•The centrifugal force acting on a vehicle negotiating a
horizontal curve has the following two effects, if super
elevation is not provided
•Tendency to overturn the vehicle outwards about the
outer wheels
•Tendency to skid the vehicle laterally outwards
NOTE: Now we will discuss the analysis of these two
conditions if no superelevation is provided on
horizontal curve.
72. OVERTURNING EFFECT
• Let ‘h’ be the height of the centre of gravity of the vehicle
above the road surface and ‘b’ be the width of the wheel
base or the wheel track of the vehicle.
CENTRE OF GRAVITY
Inner Side of Curve Outer Side of Curve
h
W
b/2 b/2
P
b/2 b/2
73. OVERTURNING EFFECT
• The overturning moment due to ce-
ntrifugal force, P = P x h
• This is resisted by the restoring mo-
ment due to the weight of the vehicle
and is equal to Wb/2
• The equilibrium condition for over-
turning will occur when Ph = Wb/2
or when P/W = b/2h.
• This means that there is danger of overturning when the centrifugal
ratio P/W or V2/gR attains a value of b/2h.
74. TRANSVERSE SKIDDING EFFECT
• The centrifugal force developed has also tendency to push the vehicle
outwards in the transverse direction. The forces developed are shown in
figure below.
Inner Side of Curve Outer Side of Curve
W
P
RA RB
FA = f x RA FB = f x RB
CENTRE OF GRAVITY
75. TRANSVERSE SKIDDING EFFECT
• The equilibrium condition for the transverse skid resistance developed is
given by:
P = FA + FB = f (RA + RB) = f W,
‘f’ is the coefficient of friction
‘RA & RB’ are the normal reaction at both wheels
• Since P = f W, the centrifugal ratio P/W is equal to f.
• When the centrifugal ratio attains the value equal to f,
then there is a danger of lateral skidding.
• Thus to avoid both overturning & lateral skidding on a horizontal
curve, the centrifugal ratio should always be less than b / 2h and
also transverse friction coefficient f.
76. • The vehicle negotiating a horizontal curve with no superelevation has to
fully depend on coefficient of friction ‘f’ to resist lateral skidding.
• If either the speed of vehicle is high or the radius of the curve is less, the
centrifugal force may increase to an extent to cause overturning or lateral
skidding of the vehicle.
• If f < b/2h, then the vehicle would skid.
• If f > b/2h, then the vehicle would overturn on the outer side.
77. Superelevation
• 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 horizontal curve.
• This transverse inclination is called superelevation or cant or banking.
• The rate of superelevation, ‘e’ is expressed as the ratio of the height of
outer edge with respect to the horizontal width.
LEFT SIDE CURVE
RIGHT SIDE CURVE
79. • If e is the superelevation rate and E is the total superelevated height of
outer edge, the total rise in outer edge of the pavement with respect to the
inner edge = NL = E = Be.
• The forces acting on the vehicle moving on circular curve of Radius R
metres and at speed of v m/sec are shown in figure below:
W
P
E
M
L
NB
P cos Ɵ
W sin Ɵ
P sin Ɵ
W cos Ɵ
FA
FB
RB
RA
Ɵ
Ɵ
Ɵ
80. • The centrifugal force developed is opposed by:
• Friction between tyres & pavement.
• A component of force of weight of vehicle acting along the gravity.
• Considering the equilibrium of the components of forces acting parallel to
the plane, the component of centrifugal force (P cosƟ) is opposed by the
component of weight of vehicle (W sinƟ) and the frictional forces FA and FB.
• The forces acting are:
• Centrifugal force P acting horizontally outwards through CG.
• The weight W of the vehicle acting vertically downwards through CG.
• The frictional force developed between wheels & pavement
counteracting towards the centre of the curve.
81. • For equilibrium condition,
P cosƟ = W sinƟ + FA + FB
• The limiting equilibrium is reached when the full values of the
frictional forces are developed and the values FA & FB reach their
maximum value of f RA & f RB.
• Thus, P cosƟ = W sinƟ + f RA + f RB
P cosƟ = W sinƟ + f (RA + RB)
P cosƟ = W sinƟ + f (W cosƟ + P sinƟ)
P cosƟ = W sinƟ + f W cosƟ + f P sinƟ
P cosƟ – f P sinƟ = W sinƟ + f W cosƟ
P (cosƟ – f sinƟ) = W sinƟ + f W cosƟ
82.
83. Note:
• The maximum value of superelevation is
limited to 7% or 0.07 and the value of
coefficient of lateral friction is taken as 0.15
for design of superelevation.
• On hill roads not bound by snow max.
superelevation up to 10% is recommended.
• On urban roads stretches with frequent
intersections max. superelevation is taken as
4%.
