Length of Summit Curves (Vertical curve)

Read: Length of the Transition Curves

Length of Summit Curves

• Design criteria for the length of Summit Curves:      Summit curves are the vertical curves having convexity upwards. These curves are introduced for the driving comfort and aesthetic purposes. In summit curves we do not need any transition curves because centrifugal acceleration is not acting laterally outward or inward but, its acting upward. 

The rate of introduction of providing the superelevation is not the criteria. 
If we provide the circular curve without the transition curve, since the centrifugal force is upward, driver will not face the sudden jerks.  The main criteria for the design of the length of the summit curves is the sight distance.

Length of the curve is governed by the stopping sight distance and the overtaking sight distance.

On the basis of the Stopping sight distance(SSD):

Suppose length of the transition curve is given as Ls and SSD is denoted by S. Stopping sight distance criteria has two cases:

1. L > S , When length of the curve is more than the stopping sight distance SSD.
2. L < S, When length of the curve is less than the stopping sight distance SSD.

For both the cases IS has given the empirical formulas and you have to check both of them

Read: Length of the Transition Curves

Case 1:  L>S

  In this case ,     L=   (NS^2)/ [ (2H)^(1/2) + (2h)^(1/2)]
Where, 
N = Change in grade
S = Stopping sight distance
H = Height of the eye of the driver, taken as 1.2 m
h = Height of the object, taken as 0.15 m.
 putting these values    L =  (NS^2)/ 4.4

Case 2 : L<S  

In this case check this formula   L = 2S – [ (2H)^(1/2) + (2h)^(1/2)] / N

On the basis of overtaking sight distance(OSD):

For this criteria, use the same formulae as given above for the SSD,  but use the object height as that of the eye level of driver. That means, take H= 1.2 m and h= 1.2 m, too.

Case 1 : L > S,  then,    L = (NS^2)/ [ (2H)^(1/2) + (2H)^(1/2)]  = NS^2/ 9.6

Case 2: L < S,  then,   L = 2S – [ (2H)^(1/2) + (2h)^(1/2)] / N   = 2S – 9.6/N