Highway-Chapter-2 highway class note unacademy

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CHAPTER-2 GEOMETRIC DESIGN
Geometric design of a highway deals with all the dimensions and layout of visible
features of highway, such that it provides maximum efficiency at minimum cost and
reasonable safety.
Geometric design of highway deals with:
1.Cross-sectional elements
2.Sight distance considerations
3.Horizontal alignment details
4.Vertical alignment details
5.Intersection detailsJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

For designing of highway elements, following factors are considered:
I.DESIGN SPEED
•Design speed of vehicle depends upon type of road over which it ply (moves), for
eg–NH, SH, etc.
•Design speed of vehicle decides the cross-sectional elements like-width,
clearance, sight distance, radius of curve, superelevation, transition, gradient,
length of summit, valley, etc.
II.TOPOGRAPHY
•Topography or terrain condition influences the design speed, that in turn governs
the designing of the highway element as above.
•For eg–in plain terrain, on SH, V
per= 100 kmph whereas the same speed on
rolling terrain is, V
per= 80 kmph and on mountaneousterrain, V
per= 50 kmph.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

III.TRAFFIC FACTORS
•Traffic factors includes vehicle characteristics and human characteristics.
•In order to design highway, standard size of vehicle is considered (car) in case of
mixed traffic operation.
•Human traffic includes physical, mental and psychological characteristics of
driver and pedestrians.
IV.DESIGN HOURLY VOLUME AND CAPACITY
•The traffic volume fluctuates over the period of time, hence, the designing must be
done for peak hours, but it will be highly uneconomical to do so, hence designing
is being done for reasonable value of traffic volume, termed as “Design Hourly
Volume”.
V.ENVIRONMENTAL FACTORS
Factors like aesthetics, air pollution, noise pollution, landscaping also governs the
designing of highway elements.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

HIGHWAYELEMENTS
I.HIGHWAY CROSS -SECTION ELEMENTS
1.PAVEMENT SURFACE CHARACTERISTICS
•It depends upon pavement type, which in turn depends on availability of material,
cost, composition of traffic, climatic conditions, method of construction, etc.
•Pavement surface characteristics include:
(i)Friction
(ii)Unevenness
(iii)Reflection properties
(iv)Drainage of surface waterJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

FRICTION/SKID RESISTANCE
•It decides the operating speed and minimum distance required for stopping the
vehicle.
•It is further classifies into two:
1.Longitudinal friction
2.Lateral or transverse friction
•Maximum friction is developed when brakes are applied uptocomplete extent.
•Friction also governs rotational and translational movement of the vehicle.
•For uniform condition, Rotation = TranslationJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: (i) When the path travelled along the road surface is more than the
circumferential movement of wheels due to their rotation, it is termed as “Skid”.
Translational motion > Rotational motion
For pure skid, Rotational motion = 0
For eg-When brakes are applied, rotation stops but skidding occurs
(ii) When the circumferential movement of wheels is more than the path travelled
along the road surface, it is termed as “Slip”.
Rotational motion > Translational motion
For pure slip, translational motion = 0
For eg-When wheels of vehicle are in mud, it rotates but do not move ahead.
Condition Rotation Translation Impact
If longitudinal friction is
more
No Yes Tyreburn
If longitudinal friction is lessYes No No movement of vehicle (fuel burn)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Friction depend upon following factors:
1.Type of pavement surface (bitumen, concrete, earthwork)
2.Roughness of pavement (texture)
3.Condition of surface (dry or wet, rough or smooth)
4.Condition of tyre(new or old)
5.Speed of vehicle (high speed: less friction, low speed: more friction)
6.Extent of brake application (full or partial)
7.Temperature of tyreand pavement
NOTE: New tyreis more dependable in adverse conditionsJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•For the calculation of stopping sight distance, the longitudinal friction co-
efficient is taken to be (0.35-0.40).
•At f = 0.40, the retardation available is approximately 4m/s
2
.
•Lateral friction is taken as 0.15.
UNEVENESS
•Presence of undulations on the pavement surface is called unevenness.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•This unevenness results in:
1.Increased fatigue
2.Reduces speed
3.Increases fuel consumption
4.Increases wear and tear of vehicles
5.Increases chances of accidents
•The unevenness of pavement is measured with the help of equipment called
“Bump Indicator” (BI) in terms of unevenness index, which is the vertical
undulations of pavement surface recorded per unit length of road (in India,
mm/km is used).
•The different values of unevenness index and the corresponding serviceability of
road is as follows:
Unevenness index (mm/ km) Type of road
< 1500 Good
1500 -2500 Satisfactory
2500 -3500 Bad
> 3500 Uncomfortable Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

BUMP INDICATORJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 1. Internationally, the riding quality of pavement surface is quantified in
terms of roughness and is expressed as “International Roughness Index”.
2. It can also be related with unevenness index as follows:
BI (mm/km) = (IRI)
1.12
(m/km)
Unevenness of the pavement depends on following factors
1.Improper compaction
2.Use of improper compaction methods
3.Use of inferior quality materials
4.Improper surface and sub-surface drainage
5.Poor maintenance of pavement surfaceJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. ASSERTION (A): IRC has recommended a minimum coefficient of friction in
the longitudinal direction on wet pavements after allowing a suitable factor of safety
in the range 0.15 –0.30.
REASON (R): When the longitudinal coefficient of friction of 0.40 is allowed for
stopping the vehicle, the resultant retardation is 3.93 m/s
2
, which is not too
uncomfortable to the passengers.
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true and R is not a correct explanation of A
c) A is true but R is false
d) A is false but R is true.
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Q. ASSERTION (A): Worn out (smooth) tyresoffer higher friction factors on dry
pavements than new tyreswith treads well intact.
REASON (R): Reduced pneumatic pressure is held in tubes which carry smooth
tyresover them
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true and R is not a correct explanation of A.
c) A is true but R is false
d) A is false but R is true
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Q. The value of lateral friction or side friction used in the design of horizontal curve
as per Indian Roads Congress guidelines is
a)0.40
b)0.35
c)0.24
d)0.15.
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Q. The longitudinal co-efficient of friction on highway for calculation of stopping
distance in geometrical design is:
a)0.3 to 0.34
b)0.5
c)0.25 to 0.29
d)0.35 to 0.4.
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Q. Which instrument is used for the measurement of the longitudinal co-efficient of
friction?
a)Bump integrator
b)Both bump integrator and roughometer.
c)Roughometer
d)Speedometer
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REFLECTIVE PROPERTIES
•Visibility over the pavement surface depends upon its color and light
characteristics, the glare caused by the reflection of head light is high on wet
pavement surface than dry pavement surface.
•Light colored pavement gives good visibility at night but produces more glare
during sunlight. On the other hand, dark color pavement offers good visibility at
day and poor at night.
2.CROSS-SLOPE/ CAMBER
•It is the slope provided to the road surface in the transverse direction to drain the
rain water from the road surface to avoid the following:
1.Stripping of bitumen from the aggregates in the presence of water.
2.Swelling and heaving of subgrade, in case water seeps into it.
3.To avoid the slipping of vehicle over the wet pavement.
4.To avoid the glare in wet pavement.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•On straight roads, it is provided by raising the centreof the carriageway w.r.t.the
edges forming the crown on the highest point along the centreline.
•On horizontal curve, with super-elevation, the drainage is provided by lifting the
outer edge.
STRAIGHT ROADS HORIZONTAL CURVE
•It is represented by any of the following ways:
1. As % : for eg-cross-slope = 5%; tan??????= 5/100
2. As fraction: for eg-cross-slope = 1 in 20 or 1/20 or 0.05; tan??????= 1/20
1 in 20 means, 1V: 20HJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•The value of cross-slope depends upon following factors:
1.Type of pavement surface
2.Amount of rainfall
•Cross-slope provided would be comparatively increased if amount of rainfall is
more and pavement surface is permeable.
•The cross-slope of shoulder should be more than that of pavement, so as to avoid
accumulation of water at junction of the two.
Type of road surface Range of cross-slope
Heavy rainfallLight rainfall
Cement concrete and high type bituminous surface2% 1.7%
Thin bituminous surface 2.5% 2%
WBM and gravel pavement 3% 2.5%
Earthernroad 4% 3%Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Cross-slope of shoulder should be 0.5% more than cross-slope of adjoining
pavement, having minimum value of 3% and maximum value of 5%.
5% ≮CS
shoulder= (0.5% + CS
pavement) ≮3%
•The cross-slope on expressways for carriageway and paved shoulder and edge
strip with bituminous surface is 2.5% with rainfall exceeding 1000mm and 2% for
places having rainfall less than 1000mm.
•If too steep cross-slope is provided, then:
1.Toppling of slow moving and over-loaded vehicles.
2.Tendency of most vehicles to travel along the centreline.
3.Uncomfortable side thrust and drag on the vehicle.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

TYPES OF CROSS-SLOPE
Cross-slopes are of following types:
1.Straight line Camber:
1
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=
H
Τ
w
2
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2.Parabolic Camber:
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3.Composite Camber:
Parabolic at top and straight at sides.
NOTE: For CC pavement, straight line camber is preferred as it is easier to lay.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

3.WIDTH OF PAVEMENT/ CARRIAGEWAY
•Width of pavement depends upon width of traffic lane and number of lanes.
•The portion of carriageway width that is intended for one line of traffic movement
is termed as “traffic lane”.
•Width of traffic lane is decided on the basis of type of vehicle moving it along
with some clearance in both the sides.
•Passenger car is considered as standard vehicle to decide the width of
carriageway.
NOTE: Width of passenger car = 2.44 ≈2.5m
•For rural highway, if pavement has two or more lanes (multi-lanes), width of
single lane = 3.5m.
•The number of lanes to be provided depends upon traffic volume.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

The width of the carriageway for different conditions are as follows:
Type of road Width of carriageway
1. Single lane road 3.75 m
2. Two lane road without raised kerbs 7 m
3. Two lane road with raised kerbs 7.5 m
4. Intermediate carriageway 5.5 m
5. multi-lane pavement 3.5 m per laneJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

4.MEDIANS/ TRAFFIC SEPARATOR
•In highway with divided carriageway or pavement, a median is provided between
two sets of traffic lanes intended to divide the traffic moving in opposite
directions.
•The main function of median is to prevent head-on collision between vehicles
moving in opposite direction.
•It also serves following other functions:
1.To channelize traffic into streams.
2.To protect the pedestrians.
3.It can be used to reduce the glare of the head light of opposite moving vehicle by
providing green cover on it.
4.To segregate the slow traffic.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

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•Medians can be provided in following forms:
1.As pavement marking
2.As physical divider (mechanical separator)
•Desirable width of median is (8-14)m.
•It includes the provision for future expansion of roads.
•In order to reduce the glare of headlight of opposite vehicle, a minimum of 6m
width is required.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•IRC recommends minimum width of 5m for median, that can be reduced to 3m
where land is restricted.
•On bridges, width required for median is in the range of (1.2-1.5)m.
•The median should be normally of uniform width throughout the length of the
pavement or carriageway, but where its width is changed atransition of 1 in 15 to
1 in 20 must be provided.
•In urban areas, minimum width of median to be provided is 1.2m and desirable
width is 1.5m
•For expressways, minimum width to be provided is 12m and desirable width is
15.5m.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

5.KERB
•Kerbindicates the boundary between the pavement and median or foot path or
island or shoulder.
•Kerbsare mainly divided in following three categories:
A. Low kerb: It is of height 100mm (10cm) above the pavement surface (edge)
with a slope to enable the vehicle to climb the kerbat slow speed.
•It is also termed as “Mountable Kerb” which encourages the traffic to remain in
the through traffic lanes yet allows the driver to enter the shoulder area at slow
speed.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

B. Semi-barrier type kerb: It is provided on the periphery of the roadway where
the pedestrian traffic is high. This type of kerbis of height of about 150mm above
the pavement edge with slope of 1:1 on top 75mm.
•This kerbprevents encroachment by parking vehicles, but in case of emergency, it
is possible to drive over this kerbwith difficulty.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

C. Barrier type kerb: It is provided in built-up areas adjacent to footpaths with
considerable pedestrian traffic. Height is 20cm (200mm) above the pavement edge
of step slope of 1V: 0.25H.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

6.SHOULDER
•Shoulders are provided on both sides of the pavement, all along the road in the
case of undivided carriageway and on outer edge of divided carriageways.
•The earthernshoulder should have sufficient strength to carry the vehicular load in
case of emergency.
•The minimum shoulder width as per IRC is 2.5m.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

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FUNCTIONS OF SHOULDER
Shoulder serves the following functions:
1.It imparts structural stability to the pavement.
2.It increases the capacity and operating speed of pavement.
3.In emergency, it can be sued as mode of movement.
4.It can also act as a service lane for the vehicles that are disabled.
5.The surface of the shoulder may be rougher than the traffic lanes, so as to
discourage the vehicle to fly over it.
6.The color of the shoulder should be different from that of pavement, so as to
differentiate between the two.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

7.ROAD MARGINS
The various elements included in the road margins are guard rails, foot path, drive
way, cycle track, parking lane, lay-bays, front edge, road and embankment slope.
(i)Guard rail: These are provided at the edge of the shoulder when the road is
constructed running of the embankment, especially when the height of fill is
more than 3m.
(ii)Foot path/ Side walk: In order to provide safe facility to the pedestrian to walk
along the roadway, footpath/ side walk is provided in urban areas, where the
pedestrian traffic is comparatively more.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Its minimum width required is 1.5m and desirable width is 2m.
•It is provided with cross-slope of 2.5 –3% and has comparatively smoother
surface than pavement.
(iii) Drive ways: It connects the highway with local commercial establishment like
service station, fuel station, restaurant, etc.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(iv) Cycle track: These are provided in urban areas for the safe movement of cycle
traffic.
•The minimum width required is 2m for cycle track and it can be increased by 1m
for each additional cycle way.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(v) Parking lanes: These are provided on urban roads to allow kerbparking.
•As far as possible, only parallel parking should be allowed as it is safer for moving
vehicles and space required would also be less.
•For parallel parking, the minimum width is 3m.
(vi) Bus bays: It may be provided by pushing back the kerbto avoid the conflict
with the moving traffic and must be located atleast75m away from intersection.
•It is used for safe loading and unloading of passengers.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(vii) Lay byes: These are provided near public convenience to avoid the conflict with
running traffic. Minimum width is 3m.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(viii) Frontage roads: These are provided to give access to the property along the
highway to control the access to the expressway.
(ix) Embankment slope: If pavement is constructed over embankment, slopes are
also provided along it, of magnitude 1:3.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 1. ROADWAY/ WIDTH OF FORMATION
It is the sum of width of pavement or carriageway including separator and the
shoulder. Roadway width is the top width of highway embankment or bottom width
of highway cutting excluding the side ways.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Width of roadway of various class of roads are as follows:
Type of roads Roadway width (m)
Plain and rolling terrainMountaineousand steep terrain
NH and SH
(a)Single lane
(b)Two lane
12
12
6.25
8.8
MDR
(a)Single lane
(b)Two lane
9
9
4.75
-
ODR
(a)Single lane
(b)Two lane
7.5
9
4.75
-
Village roads 7.5 4Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 2. ROADLAND/ LAND WIDTH/ RIGHT OF WAY
•It is the area of the road, along its alignment keeping in view its future expansion
also.
•Construction of a particular type of building is only permitted with sufficient
setback from the road boundary uptocontrol line.
•Width of land for different roads in rural areas are as follows:
Road ClassificationPlain and Rolling Mountaneous
Open Built areaOpen Built area
Expressway 90m - 60m -
NH and SH 45m 30m 24m 20m
MDR 25m 20m 18m 15m
ODR 15m 15m 15m 12m
VR 12m 10m 9m 9mJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. ASSERTION (A): Road camber helps in surface drainage.
REASON (R): In a curved road alignment, superelevation serves the purpose of
camber.
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true and R is not a correct explanation of A.
c) A is true but R is false
d) A is false but R is true
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Q. Width of carriageway for a single lane is recommended to be
a)7.5m
b)7.0m
c)3.75m.
d)5.5m
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Q. Cross-slope given to the pavement for safe drainage of water is:
a)Cant
b)Kerb
c)Shoulder
d)Camber.
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Q. The camber for hill roads in case of bituminous surface is adopted as:
a)2.0%
b)2.5%.
c)3.0%
d)3.5%
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Q. A portion of the roadway contiguous with the travelled way and is intended for
accommodation of stopped vehicle is called as:
a)Carriageway width
b)Curbs
c)Shoulder.
d)Median
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Q. Right of way is the summation of the width of
a)Carriageway and shoulder
b)Carriage way, shoulder and road margins.
c)Carriage way and road margins
d)Road margins and shoulder
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Q. Which of the following is correct statement for the cross-slope of the shoulder?
a)It is 1% flatter than the cross-slope of pavement
b)Its minimum value is 2%
c)It is 0.5% steeper than the cross-slope of the pavement.
d)Its value is equal to the cross-slope of pavement
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Q. The cross section for a highway is taken at
a)Right angle to the centreline
b)30m apart
c)Intermediate points having abrupt change in gradient
d)All options are correct.
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Q. Pick up the incorrect statement from the following:
The width of the right of way is decided to accommodate
a)Formation width
b)Side slopes
c)Horizontal curve
d)Vertical curve.
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SIGHT DISTANCE
•Sight distance is the length of the road visible ahead to the driver at any instance.
It is considered by taking the height of the eye of driver to be 1.2m and height of
object as 0.15m.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Restriction to the visibility or sight distance will be caused in following cases:
1.At horizontal curve: When line of sight is obstructed by object at the inner side
of the curve.
2.At vertical curve: The LOS is obstructed by the road surface of the curve.
3.At an uncontrolled intersection: When a driver from one of the approach road is
able to sight a vehicle from another approach road towards it.
NOTE: When obstruction is not there, more sight distance is available.
•The sight distance available to the driver is dependent upon following factors:
1.Features of road, for eg-horizontal curve, traffic conditions, position of
obstruction, etc.
2.Height of driver’s eye above road surface
3.Height of object above road surfaceJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

TYPES OF SIGHT DISTANCE
STOPPING SIGHT DISTANCE
SAFE OVERTAKING DISTANCE
SAFE SIGHT DISTANCE (for entering into uncontrolled intersection)
INTERMEDIATE SIGHT DISTANCE
HEADLIGHT SIGHT DISTANCEJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

STOPPING SIGHT DISTANCE
•The minimum distance visible to a driver ahead to safely stop a vehicle travelling
at design speed without collision is termed as “Stopping Sight Distance” (SSD).
•It is also termed as “Absolute Minimum Sight Distance” or “Non-Passing
Sight Distance”.
•Factors governing stopping sight distance are:
A.TOTAL REACTION TIME OF DRIVER:
•It is the time taken from the instant the object is visible to the driver to the instant
brakes are applied effectively.
•This total reaction time is further divided into different components and can be
explained as follows:Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

A. PERCEPTION TIME (P)
•It is the time required for the sensation received by the eyes or ears of the driver to
be transmitted by the brain through the nervous system and spinal cord.
B. INTELLECTION TIME (I)
•It is the time required by the driver to understand the situation. It is also the time
required for comparing different thoughts, re-grouping and registering new
sensations.
C. EMOTION TIME (E)
•It is the time elapsed during emotional sensations and other mental disturbances,
fear, anger, superstition, etc, with reference to the situation to come into play. This
time varies from person to person and even for same person in different situations.
D. VOLITION TIME (V)
•It is the time taken by the driver for final action, like application of brakes.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•The above can be termed as “PIEV” analysis for total reaction time.
t
R= (P+I+E+V) time
t
R, min= Reflex action time
NOTE: 1. It is also possible that the driver may apply the brake or take any other
avoiding action, like turning by the reflex action, without normal thinking process,
that is observed to be minimum time for avoiding the collision.
2. This reaction time depends upon several factors, like driver’s skill, type of
obstruction involved, environmental conditions, age, mental health, etc.
B.DESIGN SPEED:
•During the total reaction time of the driver, the distance moved by the vehicle
depends upon design speed.
•Braking distance, i.e. distance travelled by vehicle before coming to stop/ halt alos
depends on design speed.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

C.BRAKING EFFICIENCY:
•It is defined as the % of force developed by application of brakes in relation to
maximum friction available between tyreand road.
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If η
B=100%, skid will occur on application of brakes; which is difficult to control.
Hence, braking force should not exceed the friction force between wheels and tyres.
D.FRICTIONAL RESISTANCE BETWEEN ROAD AND TYRE:
•The frictional resistance developed between the road and tyredepends upon co-
efficient of friction. Higher is co-efficient of friction, higher is the frictional
resistance and lower is SSD.
•Co-efficient of friction further depends upon condition of tyreand roads.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•It is often linked with the design speed of vehicle as follows:
E.GRADIENT:
•Gradient of the road, either in assistance or resistance of the vehicle, depends upon
type of gradient (up or down), thereby either increases or decreases SSD.
Speed (kmph) 20 –30 40 50 60 70 80 ≥100
Longitudinal friction0.4 0.38 0.37 0.36 0.36 0.350.35Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Total reaction time of a driver does not depend upon
a)Perception time
b)Brake reaction time
c)Condition of mind of the driver
d)Speed of vehicle.
[IES: 2000]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

ANALYSIS OF STOPPING SIGHT DISTANCE
SSD = L
L+ L
B
The stopping sight distance of vehicle includes:
•The distance travelled by the vehicle at uniform design speed during the total
reaction time, termed as “Lag distance” (L
L).
•Distance travelled by the vehicle after the application of brake, until it stops,
termed as “Braking distance” (L
B).Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

1. LAG DISTANCE &#3627408395;
&#3627408395;=&#3627408431;
&#3627408387;×&#3627408429;
&#3627408401;
Where L
L= Lag distance (m)
v
D= Design speed (m/s)
t
R= Reaction time (s)
&#3627408395;
&#3627408395;=&#3627409358;.&#3627409360;&#3627409365;&#3627409366;×&#3627408405;
&#3627408387;×&#3627408429;
&#3627408401;
Where, V
D= Design speed (kmph)
NOTE: Reaction time, t
R= 2-4 sec, but as per IRC, t
R–2.5 sec for SSD.
2. BRAKING DISTANCE
(i) For flat road:Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

∆KE=Workdonebyfriction
1
2
mv
f
2
−
1
2
mv
i
2
=−FL
B
&#3627408395;
&#3627408385;=
&#3627408431;
&#3627409360;
&#3627409360;&#3627408416;&#3627408415;
(&#3627408422;)where v (m/s); g(m/s
2
)
&#3627408395;
&#3627408385;=
&#3627408405;
&#3627409360;
&#3627409360;&#3627409363;&#3627409362;&#3627408415;
(m) where V (kmph)
(ii) For gradient (ascending and descending):Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

∆KE=Workdonebyfriction
0−
1
2
mv
2
=−FL
B∓WsinθL
B
−
1
2
mv
2
=−fmgcosθL
B∓mgsinθL
B
When θis small, θ≈sinθ≈tanθ=s;cosθ=1
&#3627408395;
&#3627408385;=
&#3627408431;
&#3627409360;
&#3627409360;&#3627408416;(&#3627408415;±&#3627408428;)
where v (m/s)
&#3627408395;
&#3627408385;=
&#3627408405;
&#3627409360;
&#3627409360;&#3627409363;&#3627409362;(&#3627408415;±&#3627408428;)
where V (kmph)
+ is used for ascending gradient
-is used for descending gradient
SSD = L
L+ L
B
SSD = &#3627409358;.&#3627409360;&#3627409365;&#3627409366;×&#3627408405;
&#3627408387;×&#3627408429;
&#3627408401;+
&#3627408405;
&#3627408387;
&#3627409360;
&#3627409360;&#3627409363;&#3627409362;(&#3627408415;±&#3627408428;)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 1. SSD must be available at each and every section of the road.
2. As the SSD required on descending gradient is higher, it is necessary to determine
the critical value of SSD for the descending gradient on the road with gradient and
for two way traffic flow.
3. On the restricted width or on single lane road, when two-way movement of
traffic is permitted, the minimum stopping distance is equal to twice the SSD to
enable both the vehicles coming from opposite sides to stop.
4. If SSD cannot be provided on any stretch of road due to unavoidable reasons, for
the design speed available, the speed should be restricted either by installing speed
limit regulation signs or by forced reduction of speed (by speed breaker).Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•This is however temporary and efforts must be made to provide SSD over the
period of time by changing the alignment or by moving the obstruction.
•IRC recommends the SSD values as follows:
Design speed (kmph) SSD (2m)
20 20
25 25
30 30
40 45
50 60
60 80
65 90
80 120
10020 180Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Consider the following factors:
1.Reaction time
2.Speed
3.Coefficient of longitudinal friction
4.Gradient
Which of these factors are taken into account for computing braking distance?
a)1 and 3
b)1, 2 and 4
c)2, 3 and 4.
d)2 and 3
[IES: 2002]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Stopping sight distance depends upon
a)Total reaction time of the driver
b)Speed of the vehicle
c)Efficiency of brakes
d)All of the given options.
[SSC: 2016]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. SSD and friction co-efficientsare
a)Directly proportional to each other
b)Unrelated
c)Inversely proportional to each other.
d)Either directly of inversely proportional; they depends upon nature
[GATE: 2002]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Stopping sight distance is the minimum distance available on a highway which is
the
a)Distance of sufficient length to stop the vehicle without collision.
b)Distance visible to a driver driving night driving
c)Height of the object above the road surface
d)Distance equal to the height of the driver’s eye above the road surface
[GATE: 2000]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The reaction time for calculating stopping sight distance may be assumed as
a)5 sec
b)2.5 sec.
c)0.5 sec
d)10 sec
[GATE: 1999]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The distance travelled by a moving vehicle during perception time and brake
reaction time is known as
a)Sight distance
b)Stopping distance
c)Lag distance.
d)Braking distance
[GATE: 1987]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

OVERTAKING SIGHT DISTANCE
•If all the vehicles ply on a road at the design speed, then there would be no need
for overtaking, but practically this never happens.
•Hence, vehicle moving at design speed needs to overtake slow moving vehicle.
•The minimum distance open to the vision of the driver of a vehicle intending to
overtake slow vehicle with safety against traffic in opposite direction is termed as
“OSD” or “Safe Passing Sight Distance” or “Safe Passing Sight Distance”.
•OSD is measured along centreline of the road, considering eye level of the driver
at 1.2m above the surface, observing the object at height of 1.2m.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

FACTORSAFFECTING OSD
1.Speed of vehicle
a)Overtaking vehicle
b)Overtaken vehicle
c)Vehicle coming from opposite direction
2.Reaction time and skill of the driver
3.Gradient of road
4.Condition of overtaking vehicle, which governs the rate of acceleration
5.Distance between two vehicles (overtaking and overtaken)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

ANALYSISOF OSD
A = Overtaking vehicle
B = Overtaken vehicle
V = Design speedJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

a)d
1= It is the distance travelled by overtaking vehicle “A” during the reaction
time “t
r” of the driver, before starting to overtake vehicle “B” at speed of V
B.
b)d
2= It is the distance travelled by vehicle “A” during the actual overtaking
operation of time “T”.
c)d
3= It is the distance travelled by on coming vehicle “C” during the actual
overtaking operation of “A” for time “T”.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

ASSUMPTIONS IN ANALYSIS OF OSD
1.Overtaking vehicle is forced to reduce its speed uptothe speed of overtaken
vehicle for reaction time.
2.When the driver of vehicle finds sufficient clear gap, decides within the reaction
time to overtake.
3.The vehicle ‘A’ accelerates and overtakes the vehicle ‘B’ within a distance ‘d
2’
during the time ‘T’.
4.The distance ‘d
2’ can be splittedinto three components.
5.During this overtaking time, the vehicle ‘C’ coming from opposite direction
travels through distance ‘d
3’.
d
1= v
b×t
r
d
1= 0.278 V
b×t
r(where V
bis in kmph)
NOTE: t
r= 2 secJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

d
2= 2s + b
Where s = space headway = minimum spacing between two vehicles which depends
upon the speed of the vehicle
s = (0.7 v
b+ 6) (where v
bis in m/s)
s = (0.2 V
b+ 6) (where V
bis in kmph)
B = v
b×T = 0.278 V
b×T
d
2= v
b×T +
1
2
a T
2
d
2= 0.278 V
b×T +
&#3627409359;
&#3627409360;
a T
2
2s + b = 0.278 V
b×T +
1
2
a T
2
&#3627408403;=
&#3627409362;&#3627408428;
&#3627408410;
Where, a = acceleration of overtaking vehicle (m/s
2
)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: Overtaking time ‘T’ depends upon its average acceleration and speed of
overtaken vehicle
d
3= v
d×T = 0.278 V
d×T
Where, V
d= design speed (kmph)
OSD = d
1+ d
2+ d
3
OSD = (0.278 V
b×t
r) + (0.278 V
b×T +
&#3627409359;
&#3627409360;
a T
2
) + (0.278 V
d×T)
NOTE: In case the speed of overtaken vehicle is not given, it may be taken as 4.5
m/s or 16 kmph less than design speed.
v
b(m/s) = v
d(m/s) –4.5 m/s
V
b(kmph) = V
d(kmph) –16 kmph Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

The acceleration of the overtaking vehicle varies depending upon the several
factors:
1.Type of vehicle
2.Condition of vehicle
3.Load on the vehicle
4.Speed of vehicle
5.Characteristics of driver
Maximum overtaking acceleration at different speeds are as follows:
Speed (kmph) Acceleration (m/s
2
)
25 1.41
30 1.30
40 1.24
50 1.11
65 0.92
80 0.72
100 0.53Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

EFFECT OF GRADIENT ON OSD
•The overtaking sight distance requirement may increase on ascending as well as
descending gradient.
•In descending gradient, acceleration of overtaking vehicle increases, but overtaken
vehicle may also accelerate to a greater distance ‘b’ during the overtaking time.
Thus, we cannot comment as there are two variables.
•In ascending gradient, the acceleration of overtaking vehicle will be less but
overtaken vehicle would also move with lower velocity, hence we cannot
comment on OSD.
•Hence, on mild gradient (as that in plain and rolling terrain), OSD at both
ascending and descending gradient are generally equal to that of level stretch.
•However, for steeper grades, OSD should be greater than minimum OSD at plain
level road.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

OSD on two-lane highway for different speeds are as follows:
Speed (kmph) OSD (m)
40 165
50 275
60 300
65 340
80 470
100 640Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: . It is desirable that OSD should be available on most of the road stretches.
•On road stretches with two-way traffic:
OSD = d
1+ d
2+ d
3
•On road stretches with one-way traffic
OSD = d
1+ d
2Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

OVERTAKING ZONE
•If OSD cannot be provided over a particular stretch of a road section, in such
cases, for same overtaking of the vehicle at design speed, opportunity must be
given to the vehicle. Such zones are termed as “Overtaking Zones”.
SP
1= Sign post “Overtaking zone ahead”
SP
2= Sign post “End of Overtaking zone”Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 1. If at stretches of road, OSD cannot be provided as suggested by IRC, in
such case, sight distance is desirable to be kept as twice of SSD and it is termed as
“Intermediate Sight Distance” (ISD).
ISD = 2×SSD
2. The measurement of ISD can be made assuming both the height of eye of driver
and that of object to be 1.2m.
OSD > ISD > SSD
Distance (m) Reaction time (s) Height (m)
Driver’s eye Object
SSD 2.5 1.2 0.15
OSD 2 1.2 1.2
ISD 2.5 1.2 1.2
Space headway 0.7 - -Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. At highway stretches where the required overtaking sight distance cannot be
provided, it is necessary to incorporate in such sections the following:
a)At least twice the stopping sight distance.
b)Half of the required overtaking sight distance
c)One-third of the required overtaking sight distance
d)Three times the stopping sight distance
[GATE: 1998]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

SIGHT DISTANCE AT INTERSECTION
A.UNCONTROLLED INTERSECTION
•On all approaches of intersecting roads, there should be clear view across the
corner from the sufficient distance so as to avoid the collision.
•The design sight distance at intersection may be based on three possible
conditions:
1.Enabling the approaching vehicle to change the speed (slow down).
2.Enabling the approaching vehicle to stop.
3.Enabling stopped vehicle to cross the road.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

1.The sight distance should be sufficient to enable either one or both approaching
vehicle to change the speed to avoid collision.
•The vehicle approaching from the minor must slow down.
•Total reaction time required for the driver to decide to change speed is 2s and
at-least one more second is required for making the change in speed.
Total time = 2 + 1 = 3 sec
Hence, SD = 0.278 V
d×t
r= (0.278 V
d×3 ) mJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

2.The distance for the approaching vehicle should be sufficient to bring either both
or one of the vehicle before reaching the conflict. Hence, it will be equal to SSD.
3.In this case, vehicle entering the intersection from the minor roads are controlled
by ‘STOP’ or ‘GIVE WAY’ sign. So, the vehicles have to stop and then proceed
to cross the main road.
•In this case, the total time required by the stopped vehicle would include to start,
accelerate and cross the main road before another vehicle travelling at design
speed approaches it from main road.
NOTE: For safety consideration, the sight distance at uncontrolled intersection is
maximum of above three cases.
B.CONTROLLED INTERSECTION
•At signalized intersection, the above three requirements are not applicable.
•At rotary intersection, the sight distance should be atleastequal to SSD, for design
speed of rotary.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The sight distance available on a road to a driver at any instance depends on
1.Features of the road ahead
2.Height of the driver’s eye above the road surface
3.Height of the object above the road surface
a)1 and 2 only
b)1 and 3 only
c)2 and 3 only
d)1, 2 and 3.
[IES: 2020]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

HORIZONTAL ALIGNMENT OF HIGHWAY
•Change in direction is required in highway alignment due to the various reasons:
1.Topographic conditions
2.Obligatory points
•Various design elements to be considered in the horizontal alignment are:
1.Design speed
2.Radius of curve
3.Type and length of transition curve
4.Width of pavement
5.Superelevation
6.Set-back distanceJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

DESIGNSPEED
•The design speed is the main factor on which most of the geometric design
elements depends including horizontal alignment.
•The design speed of road depends upon class of road and terrain.
•Classification of terrain and design speed for different class of road are as follows:
Terrain Classification Cross slope (%)
Plain 0 –10
Rolling 10 –25
Mountaneous 25 –60
Steep Above 60Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Design speeds are also being defined for urban roads.
•Two values of the speed i.e. ruling and minimum are being specified for each type of road.
•As far as possible, an attempt should be made to design all the geometric elements for
ruling speed. However, if site conditions and economic considerations doesn’t permits so,
designing must be done for minimum design speed.
Type of road Design speed (kmph)
Plain Rolling Mountaneous Steep
Ruling Minimum Ruling Minimum Ruling Minimum Ruling Minimum
Expressway 120 100 100 80 80 60 40 60
NH and SH 100 80 80 65 50 40 40 30
MDR 80 65 65 50 40 30 30 20
ODR 65 50 50 40 30 25 35 20
VR 50 40 40 35 25 20 25 20Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

HORIZONTAL CURVE
•It is a curve, in plan to provide change in direction to centreline of the road.
•It may be different in terms of:
a)Radius of the curve (m)
b)Degree of the curve: It is the central angle subtended by an arc of length 30m.
2πR
360
o
=
30
D°
D°=
180°
πR
×30=
1720
??????
??????=
&#3627409359;&#3627409365;&#3627409360;&#3627409358;
??????°Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•When a vehicle travels on horizontal curve, the centrifugal force acts horizontally
outwards through the CG of the vehicle.
•This centrifugal force depends upon speed of vehicle on a radius of horizontal
curve.
•It will be counteracted by lateral/ transverse
friction developed between the tyreand
pavement which helps the vehicle to change
direction along the curve.
P
c=
mv
2
R
=
Wv
2
gR
Here,
??????&#3627408412;
&#3627408406;
=
&#3627408431;
&#3627409360;
&#3627408416;&#3627408401;
istermedas“Impact factor”
or “Centrifugal Ratio”.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•The force acting on vehicle has the tendency to either overturn the vehicle
outwards about wheels and to skid the vehicle laterally outwards.
For stability of vehicles, both the conditions are to be checked as follows:
A.OVERTURNING EFFECT
For no overturning, M
R≥M
o
M
R= W×
b
2
≥P
c×h
Where, b = c/c distance of tyreJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

??????&#3627408412;
&#3627408406;
=&#3627408392;.&#3627408389;.≤
&#3627408411;
&#3627409360;&#3627408417;
(Condition to prevent overturning)
If I.F. =
b
2h
: Vehicle is on verge of overturning
If I.F. >
b
2h
: Vehicle will overturn
B.TRANSVERSE SKIDDING EFFECT
For no skidding, F
A+ F
B≥P
C
μ(R
A+R
B)≥P
c
μW≥P
c
P
c
W
≤μorf
I.F. ≤??????&#3627408424;&#3627408427;&#3627408415;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 1. If pavement is kept horizontal across the alignment, the pressure on the
outer wheel will be higher due to P
cacting outwards.
2. When the limiting condition for overturning occurs, the pressure on the inner
wheels becomes zero.
3. Since pressure on outer wheel is comparatively more, it damages the pavement by
the development of ruts over it.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Hence, to avoid both overturning and sliding,
??????&#3627408412;
&#3627408406;
≤min (i)
&#3627408411;
&#3627409360;&#3627408417;
(ii) f
The relative danger of lateral skidding and overturning depends upon whether ‘f’ is
lower or higher than
b
2h
.
If f <
b
2h
: Transverse skidding before overturning
If f >
b
2h
: Overturning before transverse skiddingJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

SUPERELEVATION
•In order to counteract the effect of centrifugal force, and to reduce the tendency of
the vehicle to overturn and skid, outer edge of pavement is raised w.r.t.inner
edges, thus providing a transverse slope throughout the length of the horizontal
curve.
•This transverse inclination to the pavement surface is known as “Superelevation/
Cant/ Banking”.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

E = Total superelevation height of outer edge
E = eB
ANALYSIS OF SUPERELEVATION
Forces acting on vehicles are:
1.Self-weight (W) (vertically downward)
2.Centrifugal force (P
c) (acting horizontally in outward direction)
3.Frictional force (F) (Laterally inward along the pavement surface)
For equilibrium condition, σF
x=0
Wsinθ+F
1+F
2=P
ccosθ……(i)
෍F
y=0
R
1+R
2=Wcosθ+P
csinθ…..(ii)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

From (i) and (ii), P
ccosθ−fsinθ=Wsinθ+fcosθ
P
c
W
=
sinθ+fcosθ
cosθ−fsinθ
When θis small, sinθ≈tanθ,cosθ≈1
&#3627408392;&#3627408422;&#3627408425;&#3627408410;&#3627408412;&#3627408429;&#3627408415;&#3627408410;&#3627408412;&#3627408429;&#3627408424;&#3627408427;=&#3627408386;&#3627408414;&#3627408423;&#3627408429;&#3627408427;&#3627408418;&#3627408415;&#3627408430;&#3627408416;&#3627408410;&#3627408421;&#3627408427;&#3627408410;&#3627408429;&#3627408418;&#3627408424;=
??????
&#3627408412;
&#3627408406;
=
&#3627408429;&#3627408410;&#3627408423;&#3627409097;+&#3627408415;
&#3627409359;−&#3627408415;&#3627408429;&#3627408410;&#3627408423;&#3627409097;
=
&#3627408414;+&#3627408415;
&#3627409359;−&#3627408414;&#3627408415;
1-ef ≈1
??????
&#3627408412;
&#3627408406;
=&#3627408414;+&#3627408415;=
&#3627408431;
&#3627409360;
&#3627408416;&#3627408401;
&#3627408432;&#3627408417;&#3627408414;&#3627408427;&#3627408414;&#3627408431;&#3627408418;&#3627408423;
&#3627408422;
&#3627408428;
&#3627408414;+&#3627408415;=
&#3627408405;
&#3627409360;
&#3627409359;&#3627409360;&#3627409365;&#3627408401;
&#3627408432;&#3627408417;&#3627408414;&#3627408427;&#3627408414;&#3627408405;&#3627408418;&#3627408423;
&#3627408420;&#3627408422;
&#3627408417;&#3627408427;
R = Radius of curve (m)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 1. It may be seen that the contribution of superelevation ‘e’ (0.07) is much
less than that of lateral friction ‘f’ (0.15) in counteracting centrifugal force.
2. In some situations, eg-at intersection or some obstruction, it is not possible to
provide superelevation, in such cases, friction counteracts the centrifugal force and
if friction is also not sufficient, then radius of curve is increased which if not
possible, speed of vehicle negotiating a turn must be reduced to following: Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

e + f =
??????
2
127&#3627408453;
When e = 0, ??????
??????=127????????????
Where, V
a= allowable speed
3. In some cases, superelevation may be negative, in such cases,
f –e =
??????
2
127&#3627408453;
4. e = f (V, R, f)
Hence, the value of e needed increases with increase in speed and with decrease in
radius of curve.
Hence, ‘e’ cannot be increased beyond a particular limit, as it would lead to the
toppling/ instability of slow moving vehicles with high CG, eg-bullock carts, truck,
lorry, etc.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Value of e
maxfor different terrain are as follows:
•From drainage consideration, it is necessary to have minimum cross-slope to
drain out surface water.
•If e
calculated< cross-slope of road, then cross-slope may be provided as
superelevation only, by eliminating the crown and negative superelevation on
outer edge.
•In very flat curve with large value of P
c, and negative superelevation may be
permitted on outer edge.
Terrain type e
max(%)
1. Plain and rolling 7
2. Mountaneousand steep: not bounded by snow10
3. urban/ built-up area 4Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•As per IRC, radius of the curve beyond which ‘e’ is not required is as follows:
Design speed
(kmph)
Radius of horizontal curve (m)
4% 3% 2.5% 2% 1.7% (Camber)
20 50 60 70 90 100
25 70 90 110 140 150
30 100 130 160 200 240
35 140 180 220 270 320
40 180 240 280 350 420
50 280 370 450 550 650
60 470 620 750 950 1100Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

DESIGN OF SUPERELEVATION
•Since, mixed traffic operates on our road, the superelevation design is very
complex.
•Providing a lower value of superelevation and relying on lateral friction would be
unsafe for fast moving vehicles and providing higher value of superelevation
creates problem for slow moving vehicles.
•Hence, a compromised value for ‘e’ is designed as follows:
Step-1: The superelevation is calculated for 75% of design speed, neglecting the
lateral friction
f = 0; V
design= 0.75V
e=
(0.75V)
2
127R
=
V
2
225RJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Step-2: If the calculated value of e is less than 7%, so obtained ‘e’ is provided.
If value of ‘e’ obtained is more than 7%, then provide e = 7% and check for lateral
friction only (plain and rolling).
Step-3: Check for friction developed for maximum value of e = 7% at full value of
design speed.
f=
V
2
127R
−0.07
If the value of ‘f’ calculated is less than 0.15, the superelevation of 7% is safe for
design but if it comes out to be more than 0.15, then the speed of vehicle has to be
restricted to safe value, which is less than design speed.
Step-4: The allowable speed at the corner is computed as follows:
e + f =
V
2
127R
0.07 + 0.15 =
V
a
2
127RJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

&#3627408405;
&#3627408410;=&#3627409363;.&#3627409360;&#3627409366;&#3627408401;
Where, V
ais in kmph and R is in m.
•If the allowable speed is higher than the design speed, then the design is adequate
but if it is less than design speed, the speed is limited to the allowable speed.
•Speed can be reduced by warning sign or by speed limit regulation signs.
•On important highways, speed is not reduced, hence, the curve should be re-
aligned with larger radius of curvature.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

ATTAINMENT OF SUPERELEVATION IN THE FIELD
•Introduction of superelevation on horizontal curve in the field is very typical as on
straight portion of road cross-section, normal camber is provided with crown at
the centre, sloping downwards on both the sides.
•But the portion of cross-section on circular curve is superelevated uniformly
sloping down from outer edge uptothe inner edge of the pavement.
•The attainment of superelevation is done in two stages:
1.Elimination of the crown of camber section
2.Rotation of pavement to attain full superelevationJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

STAGE-1: ELIMINATION OF CROWN OF CAMBERED SECTION:
It can also be achieved by two methods:
a)In first method, outer half of the cross-slope is rotated about the crown at
desired rate, to attain the superelevation of inner half and centreline is not
altered.
b)In second method, (DIAGONAL CROWN METHOD), crown is shifted
progressively outwards, thus increasing the width of the inner half of cross-
section. (Negative superelevation is increased which is not safe for slow moving
vehicle).Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

STAGE-2: ROTATION OF PAVEMENT TO ATTAIN FULL
SUPERELEVATION:
•When the crown of the camber is eliminated, it does not signify the superelevation
desired at that section is attained.
•If desired superelevation is more than camber/ cross-slope, the pavement section
is rotated further till the desired elevation is attained.
•Desired superelevation can be attained by two methods:
1.By rotating the pavement cross-section about the centreline, depressing the
inner edge and raising the outer edge, each by half the total amount of
superelevation required.
2.By rotating the pavement cross-section about inner edge of the pavement
raising both centreas well as the outer edge of the pavement, such that the outer
edge is raised by full amount of superelevation desired.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

From 1 to 3, drainage problem will occur.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•In cases where T-curve cannot be provided for some reason, two-third of
superelevation may be attained at straight portion before the start of the circular
curve and the balance one-third is provided at the beginning of the curve.
•The superelevation is introduced by the raising of outer edge of pavement at a rate
not exceeding 1 in 150 in plain and rolling, and 1 in 60 in mountaneousand
steep terrain.
Rotation about centreline Rotation about inner edge
1. It may interfere with drainage system1. No interference with drainage system
2. Centre line remains unchanged 2. Centre line is elevated
3. earthwork is balanced in filling and cutting3. Filling is requiredJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. If a road surface is adequately super-elevated on horizontal curve, which one of
the following is the proper distribution of pressure on the vehicle wheels?
a)Pressure on both outer and inner wheels is equal.
b)Pressure on inner wheels is more than the outer wheels
c)Pressure on inner wheels is less than the outer wheels
d)Pressure on front wheels is thrice the pressure on rear wheels
[IES: 2007]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. What is the maximum superelevation that is fixed by Indian Road Congress
(IRC) for roads in plain and rolling terrain and in snowbound areas, taking mixed
traffic into consideration?
a)10.0%
b)5.5%
c)4.0%
d)7.0%.
[SSC: 2018]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. A superelevation ‘e’ is provided on a circular horizontal curve such that a vehicle
can be stopped on the curve without sliding. Assuming a design speed ‘v’ and
maximum co-efficient of side friction ‘f
max’, which one of the following criteria
should be satisfied?
a) e≤f
max.
b) e > f
max
c) No limit of ‘e’ can be set
d) e=
1−(f
max)
2
f
max
[GATE: 2017]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The rate of equilibrium superelevation on a road is:
1.Directly proportional to the square of vehicle velocity
2.Inversely proportional to the radius of the horizontal curve
3.Directly proportional to the square of the radius of the horizontal curve
Which of the above statements are correct?
a)1 and 2 only.
b)1 and 3 only
c)2 and 3 only
d)1, 2 and 3
[IES: 2018]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. If superelevation is not provided on a horizontal curve of a highway, then on
which portion of the road, are pot holes likely to develop?
a)Outer edge of road.
b)Inner edge of road
c)Centre of road
d)Shoulder of road
[IES: 2010]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. With all other relevant conditions remaining the same, the speed of a vehicle
negotiating a curve is proportional to
a)Weightofthevehicle
b)Weight of the vehicle
c)
1
Weightofthevehicle
d)
1
Weightofthevehicle
.
[IES: 2011]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

RADIUS OF HORIZONTAL CURVE
•Horizontal curve of highways are designed for specified design speed (ruling and
minimum).
•However, if this is not possible due to site conditions, then horizontal curve may
be re-designed.
•On the basis of speed, it is classified into following:
A.RULING MINIMUM RADIUS (RMR)
e+f=
V
2
127RMR
&#3627408401;&#3627408396;&#3627408401;=
&#3627408405;
&#3627409360;
&#3627408414;
&#3627408422;&#3627408410;&#3627408433;+&#3627408415;&#3627409359;&#3627409360;&#3627409365;
Where, V = Ruling design speed (kmph)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

B.ABSOLUTE MINIMUM RADIUS (AMR)
e+f=
V
2
127AMR
&#3627408384;&#3627408396;&#3627408401;=
&#3627408405;
&#3627409360;
&#3627408414;
&#3627408422;&#3627408410;&#3627408433;+&#3627408415;&#3627409359;&#3627409360;&#3627409365;
Where, V = Minimum design speed (kmph)
C.RADIUS BEYOND WHICH NO SUPERELEVATION IS REQUIRED
It is the radius corresponding to which camber serves the purpose of superelevation.
e = camber; f = 0; V = 75% V
d
&#3627408401;
&#3627408401;&#3627408385;&#3627408397;&#3627408402;=
&#3627408405;
&#3627409360;
&#3627409360;&#3627409360;&#3627409363;×&#3627408386;&#3627408410;&#3627408422;&#3627408411;&#3627408414;&#3627408427;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

WIDENING OF PAVEMENT ON HORIZONTAL
CURVE
•On horizontal curve, which are not of very large radius, common practice is to
widen the pavement slightly more, than the normal width.
•The object of providing this extra widening on horizontal curve is as follows:
a)To avoid the off-tracking of vehicle:
•An automobile has a rigid axle and only the front wheels can be turned, hence
when the vehicle takes a turn to negotiate horizontal curve, the rear wheel do not
follow the same path as that of front wheel.
•If no lateral skidding of rear wheels takes place, the rear wheels follows the inner
path on the curve as compared to front wheels.
•This implies if inner front wheels takes a path on the inner edge of pavement on
horizontal curve, the inner rear wheels will be off the pavement of inner shoulder
and vice-versa.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

b)To encounter psychology of the driver:
To maintain clearance between the opposite moving vehicles or overtaking vehicle.
c)To avoid lateral skidding
d)To increase the visibility at the curve
NOTE: Extra widening is the function of length of wheel base (l), radius of curve
(R), and psychological factor.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•The extra widening of the pavement on horizontal curve is divided into two parts:
a.Mechanical widening
b.Psychological widening
OFF-TRACKING OF THE VEHICLE:
R
2
2
= R
1
2
+ L
2
Also, R
2–R
1=W
m
W
m=
L
2
2R
2−W
m
2R
2>> W
m, 2R
2–W
m≈2R
Where, R = Radius of curve
&#3627408406;
&#3627408422;=
&#3627408395;
&#3627409360;
&#3627409360;&#3627408401;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

For ‘n’ lane roads,
&#3627408406;
&#3627408422;=
??????&#3627408395;
&#3627409360;
&#3627409360;&#3627408401;
NOTE: Hence, in a road having ‘n’ traffic lanes as ‘n’ vehicles can travel
simultaneously, W
mrequired will be more.
Length of wheel base = l = 6.1m
PSYCHOLOGICAL WIDENING
At horizontal curve, drivers have the tendency to maintain a greater clearance
between the vehicles, than a straight stretch of road. Therefore, an extra width is
required for this, which is given empirically by following relation:
&#3627408406;
&#3627408425;=
&#3627408405;
&#3627409367;.&#3627409363;&#3627408401;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Where, V = design speed (kmph)
R = Radius (m)
Hence, total widening = W
e= W
m+ W
p
&#3627408406;
&#3627408414;=
??????&#3627408395;
&#3627409360;
&#3627409360;&#3627408401;
+
&#3627408405;
&#3627409367;.&#3627409363;&#3627408401;
NOTE: 1. For single lane road and two-lane road, if radius is greater than 300m,
then extra widening is not required.
2. For single lane road, psychological widening is not considered (W
p= 0).
3. Extra widening is provided gradually through transition curve.
4. Generally, extra widening is provided equally on both the sides of curve. But, on
hilly roads, extra widening is provided only on inner side.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Extra width of the pavement at horizontal curve are as follows:
Radius of curve (m)≤20m20 –40m41 –60m61 –100m101 –300m> 300m
Extra width on two-
lane road
1.5 1.5 1.2 0.9 0.6 -
Extra width on single
lane road
0.9 0.6 0.6 - - -Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

The widening is introduced gradually starting from the tangent point, i.e. beginning
of T-curve at uniform rate equally on both sides in plain terrain and on inner side on
hilly terrain such that designed widening is attained at end of the transition curve.
On horizontal circular curve, without T-curve, two-third of the widening is
provided at the end of the straight portion and remaining one-third widening is
provided on circular curve.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Extra-widening of pavements provided because of off-tracking is known as:
a)Psychological widening
b)Mechanical widening.
c)Physical widening
d)Frictional widening
[SSC: 2018]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

HORIZONTAL TRANSITION CURVE
•T-curve is provided to change the alignment of pavement from straight to circular
gradually.
•The T-curve has a radius which decreases from infinity at the tangent point to the
designed radius of circular curve.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

OBJECTIVES OF PROVIDING THE TRANSITION CURVE
1.To introduce centrifugal force gradually over the vehicle.
2.To reduce the sudden jerk.
3.To introduce superelevation and extra widening gradually.
4.To improve the aesthetic appearance of road.
NOTE: 1. For an ideal T-curve, the length of the curve should be inversely
proportional to the radius.
&#3627408395;∝
&#3627409359;
&#3627408401;
LR = constant
At TP, R = ∞, L = 0
At CC, R = R
c, L = L
sJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

For transition curve to be provided, following options are available:
1.Spiral
2.Lemniscate
3.Cubical parabola
•All the three curves follow same path uptodeflection angle of 4
o
and are almost
same upto9
o
.
•In all these curves, radius decreases as length increases.
•But, the rate of change of radius or rate of change of centrifugal force is not
constant in case of lemniscate and cubical parabola.
•Hence, “Spiral curve” is used as transition curve as it fulfils the basic requirement
of ideal transition curve. Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

LENGTH OF TRANSITION CURVE
Length of the transition curve is designed to fulfil three requirements:
A.RATE OF CHANGE OF CENTRIFUGAL FORCE
•Length of the transition curve is designed such that the rate of change of
centrifugal force is low.
•Rate of change of acceleration, c=
∆a
T
=
a
f−a
i
T
=
(0.278V)
3
LsRs
&#3627408395;
&#3627408428;=
&#3627409358;.&#3627409358;&#3627409360;&#3627409359;&#3627409363;&#3627408405;
&#3627409361;
&#3627408386;&#3627408401;
Where V = Design speed (kmph)
•The maximum allowable value of rate of change of acceleration ‘c’ without
producing discomfort to the vehicle/ passenger is given by:
&#3627408412;=
&#3627409366;&#3627409358;
&#3627409365;&#3627409363;+&#3627408405;
&#3627409358;.&#3627409363;−&#3627409358;.&#3627409366;&#3627408422;/&#3627408428;&#3627408414;&#3627408412;
&#3627409361;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

B.RATE OF INTRODUCTION OF SUPERELEVATION (N)
Let rate of introduction of superelevation is 1V: NH
As per IRC:
1.1:150 for Plain/ rolling terrain
2.1:100 for built-up areas
3.1:60 for mountaneous/ steep terrain
Hence, length of TC = Nx
Where, x = elevation of outer edge
CASE-I: If rotation is done about centre-line
tanθ=
x
w+w
e
2Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

&#3627408433;=
&#3627409359;
&#3627409360;
&#3627408414;(&#3627408432;+&#3627408432;
&#3627408414;)
&#3627408395;
&#3627408428;=
&#3627409359;
&#3627409360;
&#3627408414;&#3627408432;+&#3627408432;
&#3627408414;&#3627408397;=
&#3627408397;&#3627408388;
&#3627409360;
CASE-II: If rotation is done about inner edge
tanθ=
x
w+w
e
X = e (w + w
e)
&#3627408395;
&#3627408428;=????????????=&#3627408414;&#3627408432;+&#3627408432;
&#3627408414;&#3627408397;=&#3627408397;&#3627408388;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

C.AS PER IRC
As per IRC, length of horizontal T-curve is given by following empirical
relationship:
a)For plain and rolling terrain:
&#3627408395;
&#3627408428;=
&#3627409360;.&#3627409365;&#3627408405;
&#3627409360;
&#3627408401;
b)For mountaneousand steep terrain:
&#3627408395;
&#3627408428;=
&#3627408405;
&#3627409360;
&#3627408401;
Where, V= design speed (kmph)
Length of T-curve to be provided is maximumof three calculated from previous
criteria.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Which one of the following conditions is not correct with respect to transition
curve?
a)It should be tangential to the straight approaches at the two ends
b)It should meet the circular curve tangentially
c)Its curvature will necessarily be non-zero at the point of take-off from the
straight approaches.
d)The rate of increase of curvature along the transition reach should match with
the increase of cant
[IES: 2019]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Full amount of superelevation on a horizontal curve is provided at the
a) Beginning of the transition curve
b) Centre of the circular curve
c) End of the transition curve.
d) Centre of the transition curve
[IES: 2010]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The following purposes served by a transition curve in a highway alignment
include:
1.Gradual introduction of the centrifugal force on moving vehicles from zero on
the straight alignment to a constant final value on the circular curve
2.Enabling the gradual introduction of superelevation on the roadway
Select the correct answer using the codes given below:
a)1 only
b)2 only
c)Both 1 and 2.
d)Neither 1 nor 2
[IES: 2017]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. An ideal horizontal transition curve is a:
a)Parabola
b)Circle
c)Spiral.
d)Hyperbola
[IES: 2012]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Which of the following are requirements for the design of a transition curve for a
highway system?
1.Rate of change of grade
2.Rate of change of radial acceleration
3.Rate of change of superelevation
4.Rate of change of curvature
Select the correct answer using the code given below:
a)1, 2 and 3
b)2, 1 and 4
c)1, 3 and 4
d)2, 3 and 4.
[IES: 2005]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Consider the following statements:
A transition curve is provided on a circular curve on a highway to provide:
1.Gradual introduction of centrifugal force
2.Minimum stopping sight distance
3.Gradual introduction of superelevation
4.Comfort and security to passengers
Which of the statements given above are correct?
a)1, 2 and 3
b)1, 3 and 4.
c)2, 3 and 4
d)1, 2 and 4
[IES: 2004]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The relationship between the length (l) and radius (r) of an ideal transition curve
is given by:
a)l∝r
b)l∝r
2
c)l∝
1
r
.
d)l∝
1
r
2
[GATE: 1999]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

SETBACKDISTANCE
•It is the clearance distance required from the centreline of pavement/ road to the
obstruction in order to maintain the adequate sight distance to the curve.
•The setback distance or clearance which is required from the centreline of
horizontal curve depends upon:
1.Required sight distance
2.Radius of horizontal curve
3.Length of the curve (L
cc)
CASE-I: When L
cc> SD
(a)For narrow roads such as single lane road:
O = Obstruction
AB = Sight lineJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

OD = m = setback distance
m = CD –CO = R –CO
Arc length AD = R×
α
2
α=
SD
R
×
180°
π
degrees
In ∆ACO,
cos
α
2
=
OC
R
CO=Rcos
α
2
m=R−Rcos
α
2
&#3627408422;=&#3627408401;&#3627409359;−&#3627408412;&#3627408424;&#3627408428;
&#3627409090;
&#3627409360;
NOTE: SD is calculated along the centreline of road in single lane road
m = set-back distance measured from centrelineJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(b) Wide roads/ two or more lane roads:
•Here, the stopping distance is measured along the centreline of the inner lane and
the setback distance is measured from the centreof the road.
•Let ‘d’ be the distance between the centreline of the road and centrelineof the
inside lane.
CA = R –d
CB = R –d
DO = m = setback distance
d=
w+w
e
4
α=
SD
(R−d)
×
180°
π
degreesJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

m = CD –OC = R –(R –d) cos
α
2
&#3627408422;=&#3627408401;&#3627409359;−&#3627408412;&#3627408424;&#3627408428;
&#3627409090;
&#3627409360;
+&#3627408413;&#3627408412;&#3627408424;&#3627408428;
&#3627409090;
&#3627409360;
Set back distance from:
1.Outer edge of outer lane = m + 2d
2.Centre of outer lane = m + d
3.Centre of inner lane = m –d
4.Inner edge of inner lane = m –2d
CASE-II: When L
cc< SD
(a)For narrow roads such as single lane road:
OF = m = Set-back distance
m = FO = FG + GOJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

α=
L
cc
R
×
180°
π
degrees
FG = R (1 -cos
α
2
)
GO =
SD−Lcc
2
sinΤ
α
2
&#3627408422;=R(1−&#3627408412;&#3627408424;&#3627408428;
&#3627409090;
&#3627409360;
)+
&#3627408402;&#3627408387;−&#3627408395;
&#3627408412;&#3627408412;
&#3627409360;
&#3627408428;&#3627408418;&#3627408423;ൗ
&#3627409090;
&#3627409360;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(b) Wide roads/ two or more lane roads:
α=
L
cc
(R−d)
×
180°
π
degrees
&#3627408422;=R(1−&#3627408412;&#3627408424;&#3627408428;
&#3627409090;
&#3627409360;
)+
&#3627408402;&#3627408387;−&#3627408395;
&#3627408412;&#3627408412;
&#3627409360;
&#3627408428;&#3627408418;&#3627408423;ൗ
&#3627409090;
&#3627409360;
+&#3627408413;&#3627408412;&#3627408424;&#3627408428;ൗ
&#3627409090;
&#3627409360;
NOTE: Set-back distance from centreline of inner lane = m –d
Set-back distance from centreline of outer lane = m + dJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

CURVERESISTANCE
•The automobiles are steered by turning the front wheels but the rear wheels do not
turn.
•When a vehicle is driven by rear wheel on a horizontal curve, the direction of
rotation of rear and front wheel are different.
•If tractive force ‘T’ is provided to the rear wheel in direction normal to its axis,
then the tractive force available for the front wheel is Tcosα, where αis angle of
turn.
•Hence, loss of tractive force due to turning
of vehicle on horizontal curve is
T -T&#3627408412;&#3627408424;&#3627408428;&#3627409090;, termed as “Curve Resistance”.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

VERTICALALIGNMENT
•The natural ground may be level at some places and may have slope of different
magnitude at other locations.
•Generally, highway is aligned to follow the natural topography keeping in view
the drainage and other design considerations.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•The vertical alignment of the highway affects:
1.Acceleration and deacceleration
2.Operational cost of vehicle
3.Speed
4.Sight distance
5.Comfort while driving
The vehicle alignment consists of two elements:
1.Gradient
2.Vertical curveJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

GRADIENT
•It is defined as change in elevation/ height of road along the road or may be
defined as rise or fall along the length of road w.r.t.horizontal.
•It can be represented as follows:
1.1 in x
2.
1
x
×100%
3.Tanα
NOTE: The angle which measures change in direction at the intersection of two
grades is called as “deviation angle”.
N=α
1+α
2
Or,
N=α
1−α
2Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

TYPES OF GRADIENT
Gradient are of following types:
1.RULING GRADIENT/ DESIGN GRADIENT:
•It is the maximum gradient with which the designer attempts to design the vertical
profile of the road.
•Gradients uptoruling gradient are adopted as a normal course in design.
•However, flatter gradients may be preferred wherever it can be provided.
2.LIMITING GRADIENT:
•Wherever topography of a place forces to adopt steeper gradient than ruling
gradient, it can be extended uptolimiting gradient, or else enormous cost of
construction would be observed.
•However, the length of road on which this gradient is provided is limited.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

3.EXCEPTIONAL GRADIENT:
•In some extreme situations, it may be unavoidable to provide still steeper gradient than
limiting gradient for short stretches of road, in such cases, exceptional gradient can be
provided but upto100mat a stretch.
•As per IRC, values of different gradients are as follows:
Type of terrain Ruling gradientLimiting gradientExceptional gradient
Plain or rolling 1 in 30 1 in 20 1 in 15
Mountaneousand steep terrain
having RL more than 300m above
MSL
1 in 20 1 in 16.7 1 in 14.3
Steep terrain uptoRL 300m above
MSL
1 in 16.7 1 in 14.3 1 in 12.5Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: Above 300m, oxygen is less, so it is difficult in combustion of engine,
hence, optimum power is not generated.
4.MINIMUM GRADIENT
•The minimum gradient to be provided from drainage point of view in order to
allow gravity flow of water (rain) inside the drainage system is termed as
“minimum gradient”.
•As per IRC, minimum gradient are as follows:
1.Concrete drain: 1/500 (0.2%)
2.Kutcha/ soil drain: 1/200 (0.5%)
•Depending upon type of soil, it can be taken up to 1/100 (1%) (highly permeable
soil).
NOTE: EG > LG > RG/DG > MGJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

GRADE COMPENSATION ON HORIZONTAL
CURVE
•At horizontal curve, due to the turning angle of vehicles with rear wheel drive,
curve resistance of (T –T cosα) is developed.
•When there is horizontal curve in addition to the gradient, there will be increased
resistance due to both horizontal curve (curve resistance) and gradient (grade
resistance).
•Total resistance = Grade + Curve
•Hence, when sharp horizontal curve is introduced on a road which has already the
maximum permissible gradient (ruling), the reduction in the gradient is to be
carried out.
•This restriction in gradient at horizontal curve is termed as “Grade
Compensation”.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

????????????%=
30+??????
??????
Where, R = Radius of horizontal curve (m)
•The maximum value of GC is limited to (75/R) as per IRC. Thus,
GC = min (i)
&#3627409361;&#3627409358;+??????
??????
(ii) 75/R
•GC is not necessary for gradient flatter than 4%. Hence, it is not being provided
beyond (less than) 4%.
NOTE: When camber and gradient is provided together to the road, water flows in
direction resultant to the camber known as “Hydraulic Gradient”.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. ASSERTION (A): When a sharp horizontal curve is to be introduced on a road
which already has the maximum permissible gradient, the gradient should be
decreased
REASON (R): The gradient should be decreased to compensate for the loss of
tractive effort due to the introduction of sharp horizontal curve on the road
a) Both A and R are true and R is correct explanation of A.
b) Both A and R are true and R is not a correct explanation of A
c) A is true but R is false
d) A is false but R is true
[IES: 2001]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

VERTICAL CURVE
•Due to change in vertical alignment of road, it is necessary to introduce vertical
curve at the intersection of different grades to smoothen out the ride.
•These curves are broadly classified into two:
•Convexity upward
SUMMIT/ CREST
CURVE
•Concavity upward
VALLEY/ SAG
CURVEJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

SUMMITCURVE
These are vertical curves with convexity upward and concavity downward.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

•Summit curve is formed by two gradients, starting and end gradient as follows:Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Significant points regarding summit curves are:
1.Vertical point of Intersection (VPI) always lies above the curve.
2.Summit curves are designed only for “sight distance” criteria. Minimum SSD
must be provided but it is desirable to provide OSD. If OSD is not possible, then
go for ISD.
3.When a fast moving vehicle travels along a summit curve, centrifugal force acts
upwards against gravity, hence, effective weight of vehicle is reduced. Thereby,
pressure on tyreand suspension are relieved. Hence, there is no problem of
discomfort.
4.Since design of summit curve is governed by stopping distance or sight distance
criteria, “circular curve” is ideal for this, as the sight distance in this case
remains constant. Hence, it is available throughout the curve.
5.The deviation angles in vertical curve are very small, hence a simple
“parabola” or “square parabola ” is nearly analogous to circular arc, also a
parabola is easy to manipulate mathematically for computation. Moreover, it
offers good riding comfort. Hence, being provided practically.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

ANALYSIS OF SUMMIT CURVE
•This curve is non-symmetrical as n
1≠n
2.
(1)GENERAL EQUATION
y’ = ax
2
+ bx + c
At point A: x = 0; y’ = 0
Hence, c = 0
dy′
dx
=2ax+b(gradientorslope)
At point A: x = 0;
dy′
dx
=n
1
Hence, n
1= b
At point B: x = L
s;
dy′
dx
=-n
2
hence, a=
−N
2L
sJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

y’ = ax
2
+ bx + c
&#3627408434;
′
=
−&#3627408397;
&#3627409360;&#3627408395;
&#3627408428;
&#3627408433;
&#3627409360;
+&#3627408423;
&#3627409359;&#3627408433;
This is the “General Equation” in parameters x and y’.
(2)POSITION OF SUMMIT/ CREST/ HIGHEST POINT OF CURVE FROM
VPC
For maximum y’,
dy′
dx
=0
&#3627408433;=
&#3627408423;
&#3627409359;&#3627408395;
&#3627408428;
&#3627408397;
(3)APEX EQUATION
Here, apex means parameters above the road or ground, i.e. (x and y)
At A, tanθ= n
1Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

&#3627408486;+&#3627408486;′
&#3627408485;
=??????
1
y = n
1x –y’
y = n
1x +
N
2Ls
x
2
-n
1x
y =
&#3627408397;
&#3627409360;&#3627408395;
&#3627408428;
&#3627408433;
&#3627409360;
(4)POSITION OF VPI FROM VPC
In ∆AVE,tanθ
1=n
1=
VE
x
VE = n
1x…….(i)
In ∆VBD,tanθ
2=n
2=
VD
(Ls−x)
VD = n
2(L
s–x)…..(ii)Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

y′
B=
−N
2L
s
L
s
2
+n
1L
s=
−N
2
L
s+n
1L
s
y′
B=VE−VD
&#3627408433;=
&#3627408395;
&#3627408428;
&#3627409360;
The above equation is valid for both symmetrical and unsymmetrical curves.
NOTE: 1. WHEN CURVE IS SYMMETRICAL:
•Vertical line passing through VPI will bisect the length of curve (L
s) in two equal
halves.
•This line will always pass through summit point of the curve.
•In this case, RL of starting point and end point will be same.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

NOTE: 2. WHEN CURVE IS UNSYMMETRICAL:
•Vertical line passing through VPI will bisect the length of curve in two equal
halves.
•This line will never pass through summit point of the curve.
•In this case, RL of starting and end points are different and the curve will be lifted.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

LENGTH OF SUMMIT CURVE
•While designing the length of parabolic summit curve, it is necessary to consider
SSD or OSD respectively
CASE-I: Length of Summit curve for SSD:
(a)L
s> SSD
&#3627408395;=
&#3627408397;&#3627408402;
&#3627409360;
(&#3627409360;&#3627408391;+&#3627409360;&#3627408417;)
&#3627409360;
(From apex equation)
Where S = sight distance
L = L
s= Length of summit curve
As per IRC, H = 1.2m, h = 0.15m
&#3627408395;=
&#3627408397;&#3627408402;
&#3627409360;
&#3627409362;.&#3627409362;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(b)L
s< SSD
&#3627408395;=&#3627409360;&#3627408402;−
(&#3627409360;&#3627408391;+&#3627409360;&#3627408417;)
&#3627409360;
&#3627408397;
As per IRC,
&#3627408395;=&#3627409360;&#3627408402;−
&#3627409362;.&#3627409362;
&#3627408397;
CASE-II: Length of Summit curve for OSD:
(a)L
s> OSD
&#3627408395;=
&#3627408397;&#3627408402;
&#3627409360;
(&#3627409360;&#3627408391;+&#3627409360;&#3627408417;)
&#3627409360;
(From apex equation)
Where S = sight distance
L = L
s= Length of summit curve
As per IRC, H = 1.2m, h = 1.2m
&#3627408395;=
&#3627408397;&#3627408402;
&#3627409360;
&#3627409367;.&#3627409364;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

(b)L
s< OSD
&#3627408395;=&#3627409360;&#3627408402;−
(&#3627409360;&#3627408391;+&#3627409360;&#3627408417;)
&#3627409360;
&#3627408397;
As per IRC,
&#3627408395;=&#3627409360;&#3627408402;−
&#3627409367;.&#3627409364;
&#3627408397;
NOTE: 1. While calculating the length of summit curve, first assume case –(a) L
s>
SD, if it fails, then go for case –(b).
2. When deviation angle are strong, the length of summit curve generally works out
to be less than sight distance.
3. In very small deviation angle (N), the length of summit curve works out to be
negative, indicating that there is no problem of sight restriction at the summit curve.
4. For calculating SD (SSD and OSD), the effect of gradient is not to be considered.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

5. The minimum radius of the curve ‘R’ is given by:
&#3627408401;=
&#3627408395;
&#3627408397;
6. The minimum length of vertical curve for different speeds and for maximum
grade change which do not require vertical curve as per IRC are given as follows:
Design speed (kmph) Maximum grade change (%) not
requiring a vertical curve
Minimum length of
vertical curve
35 1.5 15
40 1.2 20
50 1.0 30
65 0.8 40
80 0.6 50
100 0.5 60Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The length of summit curve on a two-lane two-way highway depends upon
a)Allowable rate of change of centrifugal acceleration
b)Coefficient of lateral friction
c)Required stopping sight distance
d)Required overtaking sight distance.
[GATE: 2005]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The ideal form of the curve for the summit curve is:
a)Spiral
b)Parabola
c)Circle.
d)Lemniscate
[SSC: 2011]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

VALLEYCURVE
•These are the vertical curve with concavity upward and convexity downward.
•It is also formed by two gradients in following ways:Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Some important points of reference for valley curve are:
1.VPI always lie below the curve.
2.As fast moving vehicle negotiate valley curve, the centrifugal force developed
acts downward in addition to the self-weight, thus additional pressure on the
suspension system is created. Hence, discomfort to the passengersdue to
impact is created.
3.In order to avoid discomfort due to impact caused by centrifugal force acting
downward, the rate of change of centrifugal acceleration should be induced
gradually along the valley curve.
4.For this, transition curve is to be provided. Infact, valley curve is formed by
joining two T-curves.
NOTE: “Cubic parabola” is generally preferred in valley curve.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

5.During night driving, the visibility ahead is dependent on head light of vehicles,
when the road lightening is not adequate.
6.There is restriction of SD at valley curve as the head light gets intercepted by the
ascending portion of the curve.
7.Hence, in this case, SSD must be equal to HSD (Headlight Sight Distance).
8.However, there is no problem of OSD during night time as other vehicles with
head light can be seen from considerable distance.
9.In India, minimum height of head light is considered to be 0.75m.
h = 0.75m
β= Beam angle = 1
oJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Valleys curves are designed taking following considerations into account:
1.Comfort to passengers
2.SSD at night (HSD)
3.Drainage in the valley curve at lower most point
4.Aesthetic considerations
A.POSITION OF LOWEST POINT OF VALLEY CURVE FROM
STARTING OF THE CURVE (VPC)
&#3627408433;=
&#3627408423;
&#3627409359;
&#3627409360;&#3627408397;
ൗ
&#3627409359;
&#3627409360;
&#3627408395;
&#3627408431;
Where, L
v= length of valley curveJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

B.LENGTH OF VALLEY CURVE
The valley curve and its length are designed as transition curve to fulfill two criteria:
a)Allowable rate of change of acceleration
b)Required HSD at night
•The maximumof two values is adopted
•Generally, second criteria i.e. HSD is higher, hence, it governs the design of the
valley curve.
I.Length of valley curve from comfort condition:
L
s= length of T-curve =
v
3
CR
R=
L
s
N
=
L
v
2N
&#3627408395;
&#3627408431;=&#3627409360;
&#3627408397;&#3627408431;
&#3627409361;
&#3627408386;
ൗ
&#3627409359;
&#3627409360;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

C is taken to be 0.6 m/s
3
and when design speed (V) is taken in kmph:
&#3627408395;
&#3627408431;=&#3627408397;&#3627408405;
&#3627409361;
(&#3627408422;)
II.Length of valley curve from HSD Criteria:
Case (i): L > HSD
For case of simplicity, we assume the valley curve to be simple parabola.Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

y=
N
2L
v
x
2
When x = S, y = h + S tanβ
h + S tanβ=
N
2L
v
S
2
&#3627408395;
&#3627408431;=
&#3627408397;&#3627408402;
&#3627409360;
&#3627409360;(h+S&#3627408429;&#3627408410;&#3627408423;&#3627409091;)
As per IRC, h = 0.75m, β= 1
o
&#3627408395;
&#3627408431;=
&#3627408397;&#3627408402;
&#3627409360;
&#3627409359;.&#3627409363;+0.035S)
Case (i): L < HSD
h + S tanβ= S−
L
v
2
NJaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

&#3627408395;
&#3627408431;=&#3627409360;&#3627408402;−
&#3627409360;(&#3627408417;+&#3627408402;&#3627408429;&#3627408410;&#3627408423;&#3627409091;)
&#3627408397;
As per IRC, h = 0.75m, β= 1
o
&#3627408395;
&#3627408431;=&#3627409360;&#3627408402;−
&#3627409359;.&#3627409363;+&#3627409358;.&#3627409358;&#3627409361;&#3627409363;&#3627408402;
&#3627408397;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Which of the following are the criteria associated with the design of sag vertical
curve?
1.Provision of minimum stopping distance during day time
2.Adequate drainage
3.Comfortable operation
4.Pleasant appearance
Select the correct answer using the codes given below:
a)1, 2 and 4
b)2 and 3
c)2, 3 and 4.
d)1 and 3
[IES: 1996]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Which one of the following statement is correct?
a)The radius of transition raises from infinity to a selected minimum in order to
attain full superelevation and curvature gradually.
b)The compound curve is an arc of a circle
c)The radius of transition curve is constant for entire length
d)The horizontal curves are provided whenever there is a change in gradient
[IES: 2020]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Light reflecting devices used to guide the driver along the proper alignment are
called:
a)Rumble strips
b)Delineators.
c)Attenuators
d)Litter bin
[IES: 2010]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Match List-I with List-II and select the correct answer using the codes given below the lists:
(adopting standard notations)
Codes: A B C D
a) 1 2 3 4
b) 3 4 1 2
c) 1 5 2 4
d) 4 2 3 1.
[IES: 1996]
List-I List-II
A. Cubic parabola equation
1.
??????&#3627408454;
2
4.4
B. Shift in transition curve
2.
??????
2
24&#3627408453;
C. Valley curve
3.
??????&#3627408454;
2
1.5+0.035&#3627408454;
D. Summit curve
4.
??????
3
6&#3627408453;??????
5.
??????
2
??????&#3627408453;Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Which one of the following expressions gives Intermediate Sight Distance as per
IRC standards? [SSD = Stopping sight distance; OSD = Overtaking sight distance]
a)2 SSD.
b)
(SSD+OSD)
2
c)
(OSD−SSD)
2
d)2 OSD
[IES: 1999]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. The curve provided at the change of gradient is called:
a)Horizontal curve
b)Transition curve
c)Reverse curve
d)Vertical curve.
[SSC: 2011]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Superior the road,
a)Steeper is the cross-slope or camber
b)Gentler is the camber.
c)Steeper is the superelevation
d)Lesser is the cost
[GATE: 1987]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Q. Consider the following statements in the context of geometric design of roads:
1.A simple parabolic curve is an acceptable shape for summit curves
2.Comfort to passengers is an important consideration in the design of summit
curves
The correct option evaluating the above statements and their relationship is:
a)1 is true, 2 is false.
b)1 is true, 2 is true and 2 is the correct reason for 1
c)1 is true, 2 is true and 2 is not the correct reason for 1
d)1 is false and 2 is true
[GATE: 2010]Jaspal Sir Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.

Highway-Chapter-2 highway class note unacademy

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