Friday, August 30, 2013

Sight Distance - Stopping Sight Distance and Overtaking Sight Distance


Sight Distance:
It is the length of the road ahead visible to a driver at any instance. IRC (Indian Roads congress) has standardized the definition by assuming the eye level of driver as 1.2 m above the road surface and height of obstruction 0.15 m from the road surface.

These are the three main types of sight distances, that are considered while the design of the roads:
(a) Stopping Sight Distance
(b) Overtaking Sight Distance
(c) Sight Distance at the Intersections

(a) Stopping Sight Distance: Stopping Sight Distance is the sight distance required for a driver to effectively apply the brakes and stop the vehicle without collision with the obstruction on the road.
  Stopping Sight Distance = Lag Distance + Braking Distance = v.t + v^2/2gf   where, v is in m/sec

(b) Overtaking Sight Distance: Overtaking Sight Distance is the sight distance which is required by the vehicle running at the design speed to overtake a vehicle running in the same lane at relatively smaller speed.

OSD = d1+ d2+ d3 = vb.t + vb.T + 2S + v.T      

(c) Sight Distance at the Intersection: Sight distance on the uncontrolled intersections should be sufficient enough  for the safety of the traffic, it should be at least equal to the stopping sight distance. 

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Sunday, August 25, 2013

Length of Transition Curves

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Length of Transition Curves:
Transition curves are provided in between a straight road and the Curve of a design radius. 

The radius of a transition curve varies from infinity to the design radius or vice verse.  The length of the transition curve must fulfill some requirements. It is designed to fulfill the following three conditions:
(a) Rate of change of centri-fugal Acceleration(C):
 C = (v^2/R)/t =  (v^2/R)/ (Ls/v) = v^3/( LsR)  m/sec^3

As per IRC recommendations, C= 80/(75+v)   m/sec^3

Here, C= allowable rate of change of centrifugal acceleration ( m/sec^3)
Ls= Length of the transition curve.

(b) Rate of introduction of Designed super-elevation:
If pavement is rotated about centre line,  then
1/N = (E/2)/Ls
=> Ls= EN/2 = e.B.N/2 = e.(W+We).N/2

If pavement is rotated about inner edge, then
I/N = E/Ls
=> Ls= EN = e.B.N= e.(W+We).N
 where, Ls= Length of transition curve
              B= width of the pavement
(c) By Empirical Formula given by IRC(Indian Roads congress):
It should not be less than
(i) For plain and ruling terrain:   Ls = 2.7 V^2/R
(ii) For mountainous and steep terrain: Ls = V^2/R

Find out the greatest length of the transition curve by the above three criteria and use to construct the transition curve.

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Saturday, August 24, 2013

Super-elevation at horizontal curves


Super-elevation: It is the inward transverse slope provided throughout the length of the horizontal curves to counteract the centrifugal force and therefore to check the tendency of the vehicle to over turn or skid.
Outer edge of the pavement is raised with respect to the inner edge of the pavement, the ratio of the height raised to the width of the pavement is called super-elevation.

Superelevation on the horizontal curves
e = E/B = tan(angle w.r.t. horizontal)

Or E = e.B

e+f = v^2/ g.R
Here, e = rate of super-elevation
          f= design value of the lateral friction co-efficient = 0.15
        v = speed of vehicle in m/sec.
        R= Radius of the horizontal curve, m
  If velocity is in Kmph, then
  e+f = V^2/(127.R)

Methods of Providing Super-elevation:
Superelevation is provided at a gradual rate along the length of the transition curve. It  is done by changing crowned camber  a single cross slope before the start of the circular curve.  Full superelevation is attained at the end of transition curve or at the start of the circular curve.

Attainment of the Superelevation may be completed in following steps:
(i) Elimination of the crown of the cambered section.
(ii) Rotation of the pavement to attain a full super-elevation.

Second step can be completed in three ways,  (a) by rotating the pavement with respect to inner edge,  (b) by rotating the pavement with respect to the center of the pavement or  (c) by rotating the pavement with respect to the outer edge of the pavement.

Superelevation is introduced by rise in the outer edge of the pavement at a rate not exceeding 1 in 150 in plain and rolling terrain and 1 in 60 on mountainous and steep terrain as per the recommendations of the IRC(Indian Roads Congress).

Designing Superelevation:
The design procedure for providing the superelevation follows the following Four steps:

(1) Friction is neglected and super-elevation is designed for 75% of the design speed value,
     e = (0.75. v)^2/ (gR)   where v is in m/sec
 or e = (0.75. V)^2/ (127R)   where v is in Kmph/sec

(2) If e < 0.07 then value so obtained is provided
If e>0.07, then provide the maximum super-elevation equal to 0.07 and proceed with steps 3 and 4.

(3) Check the co-efficient of friction developed for the maximum value of e equal to 0.07 for the full design speed v.

   f= v^2/(g.R) - 0.07
if  f< 0.15, then e = 0.07 is safe for the design speed. If not, calculate the restricted speed as follows

(4) 0.07 + 0.15 = Va^2/ (g.R)
         Where, Va = allowable safe speed.

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Friday, August 23, 2013

Widening of Pavement on Horizontal Curve


If you have observed the pavement width on the horizontal curves, you will find that to be somewhat larger than the width on the straight roads. The pavement is extra widened on the horizontal curves due to the following reasons:

  1. The wheel base of the vehicles is rigid and therefore while taking the turn, only front wheel are able to change direction. Path traveled by the front will be different and will be at certain distance outwards from the path traced by the inner wheel. This can be understood with the help of the diagram and image shown below.
    Extra widening on horizontal curves
  2. There is a tendency of the driver to take the outer path at the curves to have more sight distance visible ahead.
  3. While overtaking operations on horizontal curves driver will need more spacing from the other vehicles to feel safer.

Widening of the Pavement on the Horizontal Curves:
Horizontal curve on a hilly road (Gocind Sagar view point-Himachal Pradesh)

Widening of the pavement on the horizontal curves is governed by the following factors:
(a) Length of the wheel base
(b) Radius of the curve negotiated, R
(c) Psychological factor which depends upon the velocity of the vehicle and the Radius of the curve.
 In general extra width is provided on the horizontal curves when the radius is less than 300 m.
Extra widening = mechanical Widening + Psychological Widening
IRC recmmended values for the Extra widening of pavement on Horizontal curves
           We = Wm + Wps
           We =  nl^2/ 2R + V/ [9.5R^(1/2)]
Here, n = number of traffic lanes
           l = Length of the wheel base
           V= Design speed in kmph
            R = Radius of the horizontal curve in m
The figure given above shows the IRC recommended values of the extra width for the curves of different radius.

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Thursday, August 22, 2013

Highway Curves

Here are the images which explains the Highway curves, be it horizontal or vertical curves. Horizontal curves are simple circular curves, compound curves, reverse curves etc.
There are transition curves, and at end vertical curves are explained.

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Wednesday, August 21, 2013

Highway Geometrics- (Camber, Land Width, Carriage way, Sight Distance, Super Elevation, Gradient)


  • Highway Geometric: This is the branch of the highway engineering which deals with the geometrical elements of the roads like, land of width, formation width, carriage way, side slopes, shoulders, kerbs, sight distance, superelevation and highway curves.
  • Land Width: It is total width of the land acquired by the Govt. along the road for the construction and maintenance of the roads. No other buildings by public can be constructed on the land width. Land width depends upon the following factors:

(a) It depends on the type of the road to be constructed, like NH require more width as compared to the lower level highways.
(b) It depends on the anticipated future increase in the traffic on the route or the economic or industrial development of the areas which it aligns along its route.
  • Carriage Way: 
    Carriage way and formation width
 It is the width of the road which is used by the traffic for moving on it. It is generally central portion of the total land width and is paved and surfaced with the bituminous concrete for service to the road users. Width of the carriage way depends on the number of the lanes in the road which again depends on the class of the highway. If it is higher level road like NH then it will need more numbers of lanes and therefore the carriageway width will be more.
  • Camber: 
Camber is the transverse slope provided to the road surface for the drainage of the rainwater for the better performance of the road. Camber can be written as 1 in n or x%.

Drainage of the rainwater is necessary
(1) To maintain the safe value of the friction between the road surface and the tyres
(2) To maintain the strength and durability of the surface concrete
(3) To maintain the durability and strength of the sub-grade soil which can be harmed if the infiltration of the water takes place to it.
There are generally three types of the cambers: (a) Straight Camber  (b) Parabolic Camber  (c) Mixed Camber.
Types of Camber

(a) Straight Camber: This type of camber is provided by meeting two straight surfaces at the crown. Crown is the central and top most point on the surface of the road. The edge shape produces inconvenience to the traffic so it is not used in general.

(b) Parabolic Camber: Parabolic camber is provided by providing a parabolic shape to the surface of the road. It is also not used in general because it has steep slopes towards the edges, which can create the outward thrust to the vehicles.

(c) Mixed Camber: Mixed camber is formed by use of the straight surfaces at the edges but parabolic surface at the centre. It is mostly used for the road construction because both the problem of the earlier two are solved if we use this camber.

  • Gradient: It is the slope provided to the surface of the road in the longitudinal direction for the vertical alignment of the road. There are three kinds of gradients:
    A vehicle on ascending gradient

(a) Ruling Gradient  (b) Limiting Gradient (c) Exceptional Gradient  (d) Minimum Gradient.

  • Ruling gradient is the design gradient, so it is used to design the road in the vertical alignment.
  •   Limiting and exceptional gradients are provided in the limited stretch of the roads where necessary and in case of the emergencies or exceptional cases when such need arises respectively.
  • Minimum gradient is the gradient which is required as the minimum from the drainage point of view in case of  the plane areas.
  • Sight Distance: Sight distance at any instance is the distance along the centerline of the road which is visible to the eye of a driver at an height of 1.2 m from the road surface such that an obstruction of height 0.15 m is visible to him. The heights of the eye of the driver and the obstruction is standardized by the Indian Roads Congress.
    Sight Distance
Most important sight distance which are necessary to be studied here in the design point of view are:
(a) Stopping Sight distance
(b) Overtaking sight Distance
  • Stopping sight distance(SSD): SSD is the sight distance which is necessary for a driver to stop a vehicle from the design speed to the 0 speed without any collision with the obstruction on the road. It is also known as the absolute minimum sight distance so this much sight distance is provided at all the cross section of the road.
  • Overtaking Sight Distance(OSD): OSD is the sight distance which is necessary for a vehicle running at the design speed to overtake a slower moving vehicle without collision with the vehicles coming from the opposite direction. Generally It is not possible to provide the OSD at every cross section of the road so, it is provided after a stretch of the road.
  • Super- Elevation: The outer edge of the road with respect to the inner edge of the road is raised in case of the horizontal curves, this is called super-elevation. Super-elevation is necessary to counter-act the centrifugal force due to the radius of the curve and speed of the vehicle.
 e+f = v^2/ gR
where e= superelevation
           f = value of the friction
           v = Design speed in m/sec
            R = Radius of the horizontal curve in meters.

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Sunday, August 18, 2013

IRC classification of the Roads/highways in India

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IRC(Indian Roads Congress) has classified the roads in the India in the following 5 categories:
(a) National Highways
(b) State Highways
(c) Major District Roads
(d) Other District Roads
(e) Village Roads
  • National Highways(NH):  National highways are the major arterial roads spanning in the length and breadth of the country and connects the Capital to the various state capitals of the country or with the neighboring countries. 
They also connect the famous tourism places of the country. National highways are numbered and written as NH-1, NH-2 etc. They have the highest design specifications.
 Example : NH -1 Delhi-Ambala-Amritsar, NH-21 Chandigarh- Mandi- Manali.
  • State Highways(SH): State highways are the roads which connect the state capital to other states and to the district headquarters in the state.  They have design specifications similar to those of the National Highways because they carry enough traffic.
  • Major District Roads(MDR): These roads connect the district headquarters to the main town centers in the district, and to the headquarters of the other districts also. They also connect these major town centers to the other state highways of importance. They have lower design specifications as compared to the NH and SH.
  • Other district roads(ODR): These roads connect the rural areas town centers to the major district roads of higher importance.They provide the facilities for the transportation of the raw materials or the goods mainly of agricultural products from the rural towns to the higher markets and vice-versa.
  • Village Roads(VR): These roads connect the rural villages with one another and to the nearest higher level road or to the nearest town center. They have lower design specifications and many of them are not even metaled.
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Derivation of Mass moment of Inertia for a Solid Cone

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