Often changes in the direction are necessitated in highway alignment due to various reasons such as topographic considerations, obligatory points.
The geometric design elements pertaining to horizontal alignment of highway should consider safe and comfortable movement of vehicles at the given design speed of the highway.
It is therefore necessary to avoid sudden changes in direction with sharp curves or reverse curves which could not be safely and conveniently negotiated by the vehicles at design speed.
Improper design of horizontal alignment of roads would necessitate speed changes resulting m higher accident rate and increase in vehicle operation cost.
Transition curve and Super-elevation
Transition Curve
Objectives of Transition Curve
Properties Of Transition Curve
Types Of Transition Curve
Length Of Transition Curve
Superelevation
Objective of providing superelevation
Advantages of providing superelevation
Superelevation Formula
Numerical
This document discusses railway turnouts. It begins by defining a turnout as the combination of points and crossings that allows a train to move from one track to another, either parallel or diverging. It then describes the key components of a turnout, including tongue rails, stock rails, lead rails, and a vee crossing. It also explains the classification of turnouts as left-hand or right-hand depending on the direction of diversion. Diagrams are included to illustrate the components and working principle of a turnout. The document concludes by stating that turnouts are essential for diverting traffic but can cause issues if not designed and maintained properly.
This document discusses various aspects of vertical alignment in transportation engineering. It describes how vertical alignment specifies the elevation of points along a roadway based on safety, comfort, drainage needs. Vertical curves are used to transition between different roadway grades and can be crest or sag curves. The coordination of vertical and horizontal alignment is also discussed to ensure driver safety and aesthetics. Maximum and minimum grades, as well as critical lengths of grades, are addressed based on truck performance.
This document discusses various aspects of railway track design including gradients, horizontal and vertical curves, super-elevation, and transition curves. It provides formulas for calculating ruling gradient, super-elevation, safe speeds on curves, and other key design elements. Track must be designed to suit the loads and speeds of trains based on safety and economic standards. Proper gradient, curvature, and super-elevation are necessary for smooth train operation.
This document discusses vertical alignment in road design. It defines vertical alignment as the vertical aspect of the road profile, including crest and sag curves. It describes the basic components of vertical alignment as grade and vertical curves. Grade is the slope of the road expressed as a percentage, while vertical curves are parabolic curves that provide gradual transitions between different grades to allow comfortable driving. The document discusses types of vertical curves such as sag curves at the bottom of hills and crest curves at the tops of hills, as well as symmetrical and unsymmetrical curves. It provides the equations used to design different types of vertical curves.
This document discusses the key concepts of geometric design of highways. It defines geometric design as dealing with the visible dimensions and layout of a highway. The goals of geometric design are to maximize comfort, safety and economy while providing efficient traffic operation. Some key factors that influence geometric design are design speed, topography, traffic, environment and cost. The document outlines various elements of highway cross-sections including the carriageway, shoulders, roadway width, right of way and median. It also discusses horizontal and vertical alignment, types of alignment, and considerations for factors like gradient, sight distance and curves.
In order to have smooth vehicle movements on the roads, the changes in the gradient should be smoothened out by the vertical curves.
The vertical alignment is the elevation or profile of the centre line of the road. The vertical alignment consists of grades and vertical curves.
Highway geometric design deals with dimensions and layout of visible features like horizontal and vertical alignments, sight distances, and intersections. Elements of geometric design include cross section, sight distance considerations, horizontal and vertical alignments, and intersections. Cross section elements comprise pavement characteristics, carriageway width, cross slope, median/separator, kerbs, road margins, and formation width. Horizontal alignment design considers factors like design speed, horizontal curves, super elevation, transition curves, pavement widening on curves, and setback distance. Super elevation is provided to counteract centrifugal forces on curves and is limited to a maximum of 7% as per Indian standards.
5.track or permanent way and track stressesMani Vel
The document discusses the components and stresses acting on railroad tracks. It describes the main parts of a track including the rails, sleepers, ballast, and formation. The rails are joined by fish plates and bolts and fastened to sleepers. Sleepers are embedded in ballast which provides drainage and load distribution. A good track requires proper gauge, cross-leveling, alignment, gradient, and resilience to provide a comfortable ride while withstanding forces from train movement and varying temperatures. Wheels are coned rather than flat to reduce wear on flanges and rails and allow for lateral movement.
The geometric design of roads is the branch of highway engineering concerned with the positioning of the physical elements of the roadway according to standards and constraints. The basic objectives in geometric design are to optimize efficiency and safety while minimizing cost and environmental damage. Geometric design also affects an emerging fifth objective called "livability," which is defined as designing roads to foster broader community goals, including providing access to employment, schools, businesses and residences, accommodate a range of travel modes such as walking, bicycling, transit, and automobiles, and minimizing fuel use, emissions and environmental damage.
Geometric roadway design can be broken into three main parts: alignment, profile, and cross-section. Combined, they provide a three-dimensional layout for a roadway.
The alignment is the route of the road, defined as a series of horizontal tangents and curves.
The profile is the vertical aspect of the road, including crest and sag curves, and the straight grade lines connecting them.
The cross section shows the position and number of vehicle and bicycle lanes and sidewalks, along with their cross slope or banking. Cross sections also show drainage features, pavement structure and other items outside the category of geometric design.
#source:
1. Highway Engineering by: Khanna & Justo
2. Wikipedia
The Bombay road development plan from 1961-1981 outlined targets for expanding the road network, including constructing over 10,000 km of new roads, 1,600 km of expressways, and increasing the road density to 32 km per 100 sq km. The plan aimed to ensure all areas were within a set distance of different road categories, with more developed areas closer to metalled roads than less developed or undeveloped areas.
This document provides an overview of the IRC method for designing flexible pavements according to IRC: 37-2012. It discusses the key considerations and calculations involved, including design traffic, subgrade properties like CBR and resilient modulus, material properties, and traffic data collection. The goal is to design a flexible pavement for a new four-lane divided national highway using the IRC guidelines and given traffic and material property data.
The document discusses airport obstructions and imaginary surfaces. It defines obstructions as objects that interfere with aircraft movement and lists different types of imaginary surfaces like approach, takeoff, horizontal, and conical surfaces established around airports and runways. These surfaces define the heights and areas where no obstructions are allowed based on factors like runway length and type of landings. The document also discusses zoning laws that govern land use and height of developments near airports to ensure safety of aircraft operations.
This document provides information on the geometric design of highways. It discusses the key elements of highway design including the width of the carriageway and roadway, right of way, shoulders, side slopes, medians, and design speed. The objectives of geometric design are to optimize efficiency, safety, and cost while minimizing environmental impacts. Standard widths and specifications for elements like carriageways, medians, and shoulders are provided based on highway class and roadway conditions.
This document discusses the design principles, components, and methods for designing both flexible and rigid pavements according to IRC standards, describing the roles of subgrade soil, pavement layers, traffic characteristics, and materials used for flexible pavements consisting of granular bases and bituminous surfaces, as well as jointed concrete slabs for rigid pavements. It also provides an example of designing a two-lane bypass pavement based on initial traffic volume, design life, growth rate, and subgrade CBR value.
Geometric Design - Horizontal and vertical curvessachin dass
The document discusses key aspects of highway geometric design including horizontal and vertical alignment. It covers topics such as superelevation design, centrifugal force effects, transition curves, extra widening for curves, and vertical curve types. The key points are:
- Superelevation is used to counteract centrifugal force when negotiating curves, and its design considers factors like design speed, radius of curve, and coefficient of friction.
- Transition curves are used between tangents and circular curves to gradually change curvature and introduce superelevation for driver comfort.
- Extra widening is required for curves to accommodate off-tracking of vehicles and driver tendencies, calculated based on number of lanes, wheel base, design
This document discusses the geometric design of highways, specifically horizontal alignment. It covers key elements of horizontal alignment including horizontal curves, spiral transitions, sight distance, and super elevation. The purpose of horizontal curves is to provide a change in direction while spirals provide a gradual transition. Design is based on relationships between speed, curvature, side friction, and super elevation to prevent skidding and overturning. Methods for calculating minimum radius and attaining proper super elevation are presented.
Superelevation, or banking, refers to the transverse slope provided in highway curves to counteract the centrifugal force on vehicles traveling through the curve. It involves raising the outer edge of the pavement above the inner edge. This helps prevent vehicles from overturning or skidding laterally due to centrifugal force. The document discusses the objectives of providing superelevation, how to analyze superelevation requirements based on design speed and curve radius, and the four-step process for designing superelevation values.
The document discusses various aspects of highway engineering related to horizontal and vertical alignment of roads. It describes extra widening needed on curved sections of roads to accommodate vehicles. It discusses the analysis and formulas to calculate mechanical and psychological widening. It also covers horizontal transition curves, their objectives and methods to determine length. The document discusses setback distance for obstructions on curved sections and the formulas to calculate setback based on sight distance and curve length. It concludes with definitions of gradient, ruling gradient and other types for vertical alignment considerations.
Horizontal curves provide a transition between two straight sections of roadway. They are necessary for gradual changes in direction when a direct turn is not feasible. Design considerations for horizontal curves include radius, design speed, side friction, and superelevation. Superelevation transitions consist of runoff sections at the beginning and end of curves to transition the pavement cross-slope from normal to fully banked, or vice versa, over a specified length to maintain safety and comfort.
The document discusses transition curves in highways. Transition curves are curves that gradually change the horizontal alignment from straight to circular. This is done to introduce centrifugal force, super elevation, extra widening, and aesthetics gradually for driver comfort and safety. There are three main types of transition curves: spiral, cubic parabola, and lemniscate. The length of the transition curve can be calculated based on the rate of change of centrifugal acceleration, rate of introduction of designed super elevation, or empirical formulas based on vehicle speed and radius of the circular curve. The maximum length from these three criteria is used as the final length of the transition curve.
Alighnment & horizontal alignment of highway (transportation engineering)Civil Zone
This document discusses the alignment of highways, including horizontal and vertical elements. It covers topics such as grade line, horizontal and vertical curves, sight distance requirements, and super elevation. The key points are:
- Highway alignment consists of horizontal and vertical elements, including tangents and curves. Curves can be simple, compound, spiral, or reverse.
- Grade line refers to the longitudinal slope/rise of the highway. Factors in selecting a grade line include earthwork, terrain, sight distance, flood levels, and groundwater.
- Horizontal alignment deals with tangents and circular curves that connect changes in direction. Vertical alignment includes highway grades and parabolic curves.
- Proper design of curves
This document discusses various factors that influence the geometric design of highways, including topography, land use, functional road classification, design speed, design vehicle, traffic volume, environmental and safety considerations, and economics. It describes key elements of horizontal alignment like straights, circular curves, transition curves, superelevation, and curve widening. Minimum radii for circular curves are provided for different design speeds. The objectives and methods for implementing transition curves and superelevation are also summarized.
Geometric design of tracks aims to provide smooth and safe running of trains at maximum speed while carrying heavy loads. This involves proper design of gradients, curvature, and super elevation (cant).
There are different types of gradients - ruling gradient which is the maximum gradient permitted, momentum gradient which is steeper and uses train momentum, and pusher gradient requiring extra locomotives. Gradients are designed considering train performance and load. Curvature introduces greater resistance requiring grade compensation of ruling gradients.
Super elevation (cant) involves raising the outer rail on curves to counteract centrifugal forces. Equilibrium cant provides equal wheel load distribution. Higher speeds result in cant deficiency which must be limited for passenger safety. Contrary flexures like
This document discusses transition curves, which are curves used to gradually change a roadway from a straight alignment to a circular curve. This allows vehicles to smoothly negotiate the curve without sudden shifts in centrifugal force. Transition curves decrease the radius gradually from infinity to the curve radius. They also provide a gradual increase in superelevation or banking from 0 to the level needed for the circular curve. Common transition curve types include spiral curves and parabolic curves. The length of a transition curve depends on factors like design speed, curve radius, and the rate of superelevation introduction. Formulas are provided to calculate superelevation and transition curve length for road design. Examples are included to demonstrate using the formulas.
Overview:
The vertical alignment of a road consists of gradients(straight lines in a vertical plane) and vertical curves. The vertical alignment is usually drawn as a profile, which is a graph with elevation as vertical axis and the horizontal distance along the centre line of the road as the the horizontal axis.
1) The document discusses different types of follower motion in cams including uniform velocity, simple harmonic motion, and uniform acceleration and deceleration. It provides equations to describe the displacement, velocity, and acceleration of the follower based on the cam properties.
2) Graphical methods are presented for drawing displacement diagrams based on different follower motions. Parabolic curves are used for uniform acceleration motion to allow gradual acceleration and deceleration of the follower.
3) Maximum velocities and accelerations of the follower are defined based on the stroke, angular displacement of the cam, and angular velocity of the cam. Equations are given relating these values for different types of follower motion.
This presentation constitutes an integral component of a designated course curriculum and is crafted and disseminated for its intended audience. None of the contents within this presentation should be construed as a formal publication on the subject matter. The author has extensively referenced published resources in the preparation of this presentation, and proper citations will be provided in the bibliography upon completion of its development.
This document discusses sight distance and horizontal curves, superelevation, and transition curves. It provides the following key points:
1. Sight distance must be provided on horizontal curves to avoid obstructions. The middle ordinate equation calculates the maximum distance an obstruction can be from the centerline while maintaining sight distance.
2. Superelevation is used on curves to counteract centrifugal force. It is expressed as a ratio of outer edge height to width. Maximum rates vary from 4-12% depending on conditions.
3. Transition curves like spirals are used between tangents and curves to gradually change the radius. Their minimum length is calculated using equations involving design speed, radius, and rate
This document discusses the key considerations for geometric design of highways. It covers standards for rural and urban roads, including lane widths, shoulders, sidewalks and bike lanes. It also discusses elements of horizontal and vertical alignment like curvature, sight distances, super elevation, transitions curves and gradients. Special considerations for designing highways through hilly terrain include ensuring stable slopes, adequate drainage, meeting geometric standards and minimizing unnecessary rises and falls in the road.
1. Cams are machine elements that impart motion to followers through cam-follower contact. They provide a simple way to achieve various follower motions.
2. There are different types of cams and cam followers based on their shape. Common cams include disk cams, translation cams, and cylindrical cams. Common followers include knife-edge, roller, and flat-faced followers.
3. The cam profile is the surface that contacts the follower. Important aspects of cam design include the base circle, trace point, cam angle, pitch curve, and pressure angle. The selection of cam motion such as simple harmonic motion or cycloid motion depends on factors like speed and load.
This document discusses key concepts in the design of roadway and highway vertical curves. It covers topics such as vertical point of curvature (VPC), vertical point of intersection (VPI), vertical point of tangency (VPT), types of vertical curves, factors considered in determining vertical curve length, equations for calculating length, sight distance criteria, and design procedures. Minimum vertical curve lengths are based on design speed, sight distance, and the algebraic difference in grades as defined in design standards.
This document discusses various concepts related to transportation engineering and highway geometric design. It defines key terms like transition curves, horizontal curves, vertical curves, gradient, sight distance, super elevation and camber. It discusses factors that influence highway alignment and geometric design such as terrain, design speed, sight distance requirements. It also provides recommended values of super elevation and camber for different pavement types.
1. 1 Stabilization of Laterite Soil Using Waste Paper Sludge.pdfAkshathaBhandary
This research article investigates the use of waste paper sludge (WPS) to stabilize lateritic soil for rural road construction. Laboratory tests were conducted on mixtures of lateritic soil replaced with 2%, 4%, 6%, 8%, and 10% WPS. The results showed that replacing 6% of lateritic soil with WPS decreased the liquid limit, plastic limit, and plasticity index, increased the optimum moisture content, and decreased the maximum dry density. Strength tests found increases in unconfined compression strength and California bearing ratio with 6% WPS replacement. Durability testing also indicated that mixtures with 8-10% WPS replacement survived more wet-dry cycles than mixtures with lower WPS content. The study demonstrates that
Disaster management is more than just response and relief.
It is a systematic process i.e., is based on the key management principles of planning, organizing and leading which includes coordinating and controlling.
This aims to reduce the negative impact or consequences of adverse events i.e., disasters cannot always be prevented, but the adverse effect can be minimized
Friction Considerations : The friction of skid resistance between vehicle tyre and pavement surface is one of the factors determining the operating speed and the minimum distance requires for stopping of vehicles.
Unevenness : The longitudinal profile of the road pavement has to be even' in order to provide a good riding comfort to fast moving vehicles
Light Reflecting Characteristics : Night visibility depends upon the colour and light reflecting characteristics of the pavement surface. The glare caused by the reflection of head lights is considerably high on wet pavement surface than on the dry pavement.
Drainage of Surface Water
Sight distance is the length of road visible ahead of the driver at any instance.
Sight distance available at any location of the carriageway is the actual distance a driver with his eye level at a specified height above the pavements surface has visibility of any stationary or moving object of specified height which is on the carriageway ahead.
The sight distance between the driver and the object is measured along the road surface.
Valuation is the technique of estimation or determining the fair price or value of property such as building, a factory, other engineering structures of various types, land etc.
By valuation the present value of a property is defined. The present value of property may be decided by its selling price, or income or rent it may fetch.
The value of property depends on its structure, life, maintenance, location, bank interest, etc.
Cost means original cost of construction of purchase.
.
The document discusses the tender process, beginning with defining a tender as an invitation from an owner to contractors to execute work at a specified cost and time. It then outlines the different types of tenders such as single, limited, open, and global tenders. The purpose and issuing of tenders is also explained along with the typical elements included in tender request documents. Finally, the seven main steps in the tender process are provided, from determining the tender type to establishing and managing the resulting contracts.
A PRAPOSAL WHEN ACCEPTED BECOMES A PROMISE
A PROMISE ( OR A SET OF PROMISES) WITH CONSIDERATION IS AN AGREEMENT
AN AGREEMENT ENFORCEABLE BY A LAW IS A CONTRACT
“Bid” is increasingly being used by the bidder (the supply side) and the term “tender” used on the procurement side (the buyer).
Bid – an approach to a client in order to gain significant new or repeat business.
Internship Report Construction Site and Office WorkAkshathaBhandary
Sai Radha Developers is a real estate developer based in Udupi, India that has completed several residential projects and has ongoing projects. It aims to provide high-quality housing to middle-income families at affordable prices. Their ongoing projects include Sai Radha Pride J Wing, a residential tower with 56 units, and Sai Radha Nest 1 & 2, two residential complexes with a total of 115 and 68 units respectively. The company focuses on timely delivery, quality construction, and customer satisfaction.
Trenchless Technology is the the science science of installing, repairing and renewing underground pipes, ducts and cables using techniques which minimize or eliminate the need for excavation.
It is basically basically making a tunnel below the surface and installing service lines like water or gas pipes, pipes, electric or tele communication cables etc.,with out any disruption to the public .
This document provides an overview of trenchless technology for installing underground pipes and cables. It discusses the disadvantages of open trench methods, classifications of trenchless techniques for new installations and rehabilitations, and methods like microtunneling, horizontal directional drilling, impact moling, pipe bursting and pipe eating. The advantages of trenchless technology are also summarized, and a case study of installing fiber optic cables using horizontal directional drilling in New Delhi is presented. In conclusion, trenchless methods provide an attractive solution to installing underground infrastructure in congested urban areas with minimal surface disruption.
This document provides an overview of Coastal Projects Limited (CPL), an infrastructure construction company, and CPL's role in the Bangalore Metro Rail Project. It discusses CPL's vision, mission, values and quality assurance policies. It then describes the Majestic Metro Station project, including station layout details. CPL is constructing the underground Majestic Metro Station, which will be an interchange station for the Purple and Green metro lines. Construction is proceeding according to a grid-wise plan from the center of Zone E outwards in all directions.
How to Use Pre Init hook in Odoo 17 -Odoo 17 SlidesCeline George
In Odoo, Hooks are Python methods or functions that are invoked at specific points during the execution of Odoo's processing cycle. The pre-init hook is a method provided by the Odoo framework to execute custom code before the initialization of the module's data. ie, it works before the module installation.
How to Make a Field Storable in Odoo 17 - Odoo SlidesCeline George
Let’s discuss about how to make a field in Odoo model as a storable. For that, a module for College management has been created in which there is a model to store the the Student details.
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...Codeavour International
Unlocking potential across borders! 🌍✨ Discover the transformative journey of Codeavour 5.0 International, where young innovators from over 60 countries converged to pioneer solutions in AI, Coding, Robotics, and AR-VR. Through hands-on learning and mentorship, 57 teams emerged victorious, showcasing projects aligned with UN SDGs. 🚀
Codeavour 5.0 International empowered students from 800 schools worldwide to tackle pressing global challenges, from bustling cities to remote villages. With participation exceeding 5,000 students, this year's competition fostered creativity and critical thinking among the next generation of changemakers. Projects ranged from AI-driven healthcare innovations to sustainable agriculture solutions, each addressing local and global issues with technological prowess.
The journey began with a collective vision to harness technology for social good, as students collaborated across continents, guided by mentors and educators dedicated to nurturing their potential. Witnessing the impact firsthand, teams hailing from diverse backgrounds united to code for a better future, demonstrating the power of innovation in driving positive change.
As Codeavour continues to expand its global footprint, it not only celebrates technological innovation but also cultivates a spirit of collaboration and compassion. These young minds are not just coding; they are reshaping our world with creativity and resilience, laying the groundwork for a sustainable and inclusive future. Together, they inspire us to believe in the limitless possibilities of innovation and the profound impact of young voices united by a common goal.
Read the full impact report to learn more about the Codeavour 5.0 International.
Open Source and AI - ByWater Closing Keynote Presentation.pdfJessica Zairo
ByWater Solutions, a leader in open-source library software, will discuss the future of open-source AI Models and Retrieval-Augmented Generation (RAGs). Discover how these cutting-edge technologies can transform information access and management in special libraries. Dive into the open-source world, where transparency and collaboration drive innovation, and learn how these can enhance the precision and efficiency of information retrieval.
This session will highlight practical applications and showcase how open-source solutions can empower your library's growth.
Plato and Aristotle's Views on Poetry by V.Jesinthal Maryjessintv
PPT on Plato and Aristotle's Views on Poetry prepared by Mrs.V.Jesinthal Mary, Dept of English and Foreign Languages(EFL),SRMIST Science and Humanities ,Ramapuram,Chennai-600089
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdfnservice241
The University of Ghana has launched a new vision and strategic plan, which will focus on transforming lives and societies through unparalleled scholarship, innovation, and result-oriented discoveries.
2. DESIGN OF HORIZONTAL
ALIGNMENT Often changes in the direction are necessitated in highway alignment
due to various reasons such as topographic considerations, obligatory
points.
The geometric design elements pertaining to horizontal alignment of
highway should consider safe and comfortable movement of vehicles at
the given design speed of the highway.
It is therefore necessary to avoid sudden changes in direction with sharp
curves or reverse curves which could not be safely and conveniently
negotiated by the vehicles at design speed.
Improper design of horizontal alignment of roads would necessitate
speed changes resulting m higher accident rate and increase in vehicle
operation cost.
2
3. Various design elements to be considered in the horizontal alignment are
1. Design speed
2. Radius of circular curve,
3. Type and length of transition curves,
4. Super elevation,
5. Widening of pavement on curves
6. And required set-back distance for fulfilling sight
7. Distance requirements.
DESIGN ELEMENTS OF THE
HORIZONTAL ALIGNMENT
3
4. All the important geometric elements such as sight distances, radius of
horizontal curve, length of horizontal transition curve, rate of super
elevation, extra widening of pavement at horizontal curve, length of summit
and valley curves are dependent on the design speed.
The design speed of roads depends upon
1) Class of the Road
2) Terrain
Two values of design speeds are considered at the design stage of highway
geometries namely,
1) Ruling design speed
2) Minimum design speed
Design Speed
4
5. The recommended design speeds for different classes of urban roads
1) Arterial Roads: 80 Kmph
2) Sub-Arterial Roads: 60 Kmph
3) Collector Streets: 50 Kmph
4) Local Streets: 30 Kmph
5
6. Horizontal Curves
A horizontal highway curve is a curve in plan to provide change in direction
to the centre line of a road.
A simple circular curve may be designated by either the radius, R of the
curve in meters or the degree, D of the curve.
The degree of the curve (D°) is the central angle subtended by an arc of
length 30 m and is given by the relation,
RD𝜋/180 = 30.
Therefore, the relation between the radius and degree of the circular curve is
given by,
R = 1720 / D
6
7. When a vehicle traverses a horizontal curve, the centrifugal force acts
horizontally outwards through the centre of gravity of the vehicle.
The centrifugal force developed depends on the radius of the horizontal
curve and the speed of the vehicle negotiating the curve.
This centrifugal force is counteracted by the transverse frictional
resistance developed between the tyres and the pavement which enables
the vehicle to change the direction along the curve and to maintain the
stability of the vehicle.
Centrifugal force P is given by the equation:
Cont.,
𝐏 =
𝐖𝐯 𝟐
𝐠𝐑Where,
P = centrifugal force, kg
W = weight of the vehicle, kg
R = radius of the circular curve, m
v = speed of vehicle, m/sec
g = acceleration due to gravity = 9.8 m/sec
7
8. The centrifugal force acting on a vehicle negotiating a horizontal curve has
the following two effects:
1) Tendency to overturn the vehicle outwards about the outer wheels
2) Tendency to skid the vehicle laterally, outwards
Overturning Effect
The overturning moment due to centrifugal force,
P = P x h
This is resisted by the restoring moment due to weight of the vehicle W and
is equal to (Wb/2)
The equilibrium condition for overturning will occur when
𝐏𝐡 =
𝐖𝐛
𝟐
Or
𝐏
𝐖
=
𝐛
𝟐𝐡
And for safety
𝐛
𝟐𝐡
>
𝐯 𝟐
𝐠𝐑
8
9. Transverse Skidding Effect
The centrifugal force developed has the tendency to push the vehicle
outwards in the transverse direction.
The equilibrium condition for the transverse skid resistance developed is
given by F
= FA + FB
= f (RA + RB)
= f W
Where f = coefficient of friction between the tyre and the pavement surface in
the transverse direction
RA, RB = Normal Reactions at the wheels A and B
W = weight of the vehicle
When the centrifugal ratio
𝐏
𝐖
= 𝐟 =
𝐯 𝟐
𝐠𝐑
skidding takes place
For safety
𝒇>
𝐯 𝟐
𝐠𝐑
Thus, to avoid both overturning and lateral skidding on a horizontal curve,
the
𝐏
𝐖
<
𝐛
𝟐𝒉 9
10. In order to counteract the effect of centrifugal force and to reduce the
tendency of the vehicle to overturn or skid, the outer edge of the pavement is
raised with respect to the inner edge, thus providing a transverse slope
throughout the length of the horizontal curve. This transverse inclination to
the pavement surface is known as SUPER ELEVATION or CANT or
BANKING.
𝒆 + 𝒇 =
𝒗 𝟐
𝒈𝑹
e = rate of super elevation = tan θ
f = design value of lateral friction coefficient = 0.15
v = speed of the vehicle, m/sec
R = radius of the horizontal curve, m
g = acceleration due to gravity = 9.8 m/sec2
Super elevation
10
11. Horizontal curves of highways are generally designed for the specified ruling
design speed of the highway.
To keep the centrifugal ratio P/W or v2 /g R within a low limit, the radius of
the horizontal curve should be kept correspondingly high.
The centrifugal force, P developed due to a vehicle negotiating a horizontal
curve of radius, R at a speed, v m/sec or V kmph is counteracted by the
superelevation, e and lateral friction coefficient, f.
R 𝑟𝑢𝑙𝑖𝑛𝑔 =
𝑣2
𝑒 + 𝑓 𝑔
Also
R 𝑟𝑢𝑙𝑖𝑛𝑔 =
𝑣2
127 𝑒 + 𝑓
Radius Of Horizontal Curve
11
12. The minimum design speed is V’ Kmph, the absolute minimum radius of
horizontal curve
R 𝑚𝑖𝑛 =
𝑉′2
127 𝑒 + 𝑓
v and V – ruling speeds in m/sec and Kmph
V’ – minimum design speed in kmph
e - rate of superelevation, (0.07)
f – co efficient of friction 0.15
g - acceleration due to gravity 9.8 m/sec2
Cont.,
12
13. WIDENING OF PAVEMENT ON HORIZONTAL
CURVESThe extra widening of pavement on horizontal curves is divided into two
parts.1. Mechanical Widening
The widening required to account for the off-tracking due to rigidity of
wheel base is called as ‘Mechanical Widening’ (Wm) and is given by
2. Psychological Widening
Widening of pavements has to be done for some psychological reasons also.
13
14. Note: For multi lane roads, the pavement widening is calculated by adding
half extra width of two lane roads to each lane of the multi lane road.
14
15. Horizontal Transition Curves
Transition curve is provided to change the horizontal alignment from
straight to circular curve gradually and has a radius which decreases from
infinity at the straight end (tangent point) to the desired radius of the circular
curve at the other end (curve point)
Thus, the functions of transition curve in the horizontal alignment are given
below:
To introduce gradually the centrifugal force between the tangent point
and the beginning of the circular curve, avoiding sudden jerk on the
vehicle. This increases the comfort of passengers.
To enable the driver, turn the steering gradually for his own comfort and
safety
To enable gradual introduction of the designed super elevation and extra
widening of pavement at the start of the circular curve. 15
16. Type of transition curve
Different types of transition curves are
a) Spiral or Clothoid
b) Cubic Parabola
c) Lemniscates
IRC recommends spiral as the transition curve because:
1) It full fills the requirement of an ideal transition, as the rate of change of
centrifugal acceleration is uniform throughout the length.
2) The geometric property of spiral is such that the calculation and setting
out the curve in the field is simple and easy.
16
17. Length of transition curve
The length of the transition curve should be determined as the maximum
of the following three criteria
1) Rate of Change of Centrifugal Acceleration
2) Rate of Change of Super Elevation
3) An Empirical Formula Given by IRC
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18. At the tangent point, radius is infinity and hence centrifugal acceleration
(v2 /R) is zero, as the radius is infinity. At the end of the transition, the
radius R has minimum value Rm. Hence the rate of change of centrifugal
acceleration is distributed over a length Ls
Rate of Change of Centrifugal Acceleration
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