Civil Engineer's Hub Solan

Highway Geometrical Desgin

Sight Distances

Stopping Sight Distance (SSD)

The minimum sight distance available in a highway at any spot should be of sufficient length to stop a vehicle traveling as design speed, safely without collision with any other obstruction. The absolute minimum sight distance is therefore equal to the stopping sight distance, which is also some times called non-passing sight distance.

The stopping distance of a vehicle is the sum of:

1. The distance travelled by the vehicle during the total reaction time known as lag distance and

2. The distance travelled by the vehicle after the application of the brakes, to a dead stop position which is known as the braking distance.

(i) lag distance = 0.278 Vt

Where, V = Speed in km/hr.

t = Reaction time in sec

(ii) Breaking distance

f = Coefficient of friction

= 0.40 for v = 20 to 30 km/hr

= 0.35 for v = 100 km/hr

(iii) SSD = lag distance + breaking distance

Where, S% is gradient + ve sign for ascending gradient & -ve sign for descending gradient

SSD = Stopping sight distance in ‘m’.

Overtaking Sight Distance (OSD)

The minimum distance open to the vision of the driver of a vehicle intending to overtake slow vehicle ahead with safety against the traffic of opposite direction is known as the minimum overtaking sight distance (OSD) or the safe passing sight distance available

OSD = d₁+d₂+d₃

Where, O.S.D = Overtaking sight distance in ‘m’

d = Distance travelled by overtaking vehicle A during the reaction time t sec of the driver from position A₁ to A₂.

d₁ = 0.278 V_bt

d₂ = Distance travelled by the vehicle A from A₂ to A₃ during the actual overtaking operation in time T sec.

where S = Minimum spacing between two vehicle.

s=0.2V_b+6 here V_b is in km/hr.

where, a = acceleration in m/s².

where a is in km/hr/sec.

d₃=0.278V_CT

Where, d₃ = Distance travelled by on coming vehicle C from C₁ to C₂ during the overtaking operation of A i.e., T sec.

V_C = V = Speed of overtaking vehicle or design speed (km/hr)

If V_b is not given then

V_b = (V-16)km/hr

V_b = (V-4.5)m/s

v = design speed in m/s.

Overtaking Zone

It is desirable to construct highways in such a way that the length of road visible ahead at every point is sufficient for safe overtaking. This is seldom practicable and there may be stretches where the safe overtaking distance cannot be provided. In such zones where overtaking or passing is not safe or is not possible, sign posts should be installed indicating “No passing” or “Overtaking Prohibited” before such restricted zones starts. But the overtaking opportunity for vehicles moving at design speed should be given at frequency intervals. These zones which are meant for overtaking are called overtaking zones.

O.S.D. = d₁+d₂

For one way traffic

O.S.D. = d₁+d₂+d₃

For two way traffic

Minimum length of overtaking zone = 3. (OSD)

Desirable overtaking zone = 5 (OSD)

Super Elevation (e)

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.

The superelevation ‘e’ is expressed as the ratio of the height of outer edge with respect to the horizontal width.

Where V = Speed in km/hr

R = Radius in ‘m’

F = Design value of lateral friction = 0.15

e = Rate of super elevation ∼tanθ

Maximum Super Elevation (e_max)

Ruling Minimum Radius of the Curve (R_ruling)

Where, V = Ruling design speed in km/hr

e = Rate of super elevation

f = Coefficient of friction ∼0.15

Extra Widening (E_W)

The extra widening of pavement on horizontal curves is divided into two parts (i) Mechanical and (ii) Psychological widening.

Mechanical Widening (W_m): The widening required to account for the off-tracking due to the rigidity of wheel base is called mechanical widening. (W_m).

Psychological widening (W_p): Extra width of pavement is also provided for psychological reasons such as, to provide for greater maneuverability or steering at higher speeds, to allow for the extra space requirements for the overhangs of vehicles and to provide greater clearance for crossing and overtaking vehicles on the curves. Psychological widening is therefore important in pavements with more than one lane.

Where, n = number of traffic lanes

l = length of wheel base (m)

R = radius of the curve (m)

V = velocity (kmph)

Transition Curve

The Indian Roads Congress recommends the use of the spiral as transition curve in the horizontal alignment of highways due to the following reasons:

The spiral curve satisfies the requirements of an ideal transition.

The geometric property of spiral is such that the calculations and setting out the curve in the field is simple and easy.

Length of Transition Curve (L)

(i) According to rate of change of centrifugal acceleration

Where, V = Speed of vehicle in (km/hr)

C = Allowable rate of change of centrifugal acceleration in m/sec³

R = Radius of curve in ‘m’.

L = Length of transition curve in ‘m’.

(ii) According to rate of change of super elevation

Where, x = Raise of outer line of road.

X = (w + E_w)e it pavement is rotated about inner side.

it pavement is rotated about centre line.

(iii) According to empirical formula

Set Back Distance (m)

The clearance distance or set back distance required from the centre line of a horizontal curve to an obstruction on the inner side of the curve to provide adequate sight distance depends upon the following factors:

(i) Required sight distance (SSD)

(ii) Radius of horizontal curve, (R)

(iii) Length of the curve (L_c)

1. For single lane road

(a) when L_C > SSD

Where, L_C = Length of curve & s = SSD

(b) When L_C < SSD

2. For two lane road

(a) when L_C > SSD

(b) when L_C < SSD

Grade Compensation

Grade compensation

Maximum value of grade compensation

Where, R = Radius of curve in meter.

Vertical Curve

Due to changes in grade in the vertical alignment of highway, it is necessary to introduce vertical curve at the intersections of different grades to smoothen out the vertical profile and thus ease off the changes in gradients for the fast moving vehicles.

The vertical curves used in highway may be classified into two categories:

(i) Summit curves or crest curves with convexity upwards

(ii) Valley or sag curves with concavity upwards.

Summit Curves (Crest Curve with Convexity Upward): Summit curves with convexity upwards are formed in any one of the case illustrated in fig. The deviation angles between the two interacting gradients is equal to the algebraic difference between them. Of all the cases, the deviation angle will be maximum then an ascending gradient meets with a descending gradient i.e., N = n₁ – (-n₂) = (n₁ + n₂)

(i) Length of summit curve for SSD

(a) when L > SSD

Where, L = Length of summit curve in meter

S = SSD (m)

N = Deviation angle

= Algebraic difference of grade

H = Height of eye level of driver above road way surface = 1.2 m

h = Height of subject above the pavement surface = 0.15 m

(b) When L < SSD

(ii) Length of summit curve for safe overtaking sight distance (OSD) or intermediate sight distance (ISD)

(a) When L > OSD

Where, S₀ = Overtaking or Intermediate sight distance

(b) When L < OSD

Valley Curves (Sag Curve with Concavity Upward): Valley curves or sag curves are formed in any one of the cases illustrated in fig. In all the cases the maximum possible deviation angle is obtained when a descending gradient meets with an ascending gradient.