Length of Summit Curves (Vertical curve)

Hi,
 Today, I am going to put here the details and engineering behind the length of the Summit Curves required for the vertical alignment of the highways.

• 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. 

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

Length of the road 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 less than the stopping sight distance.
2. L<S - When length of the curve is more than the stopping sight distance.

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

• L>S :  

In this case check this formula    L=   (NS^2)/ [ (2H)^(1/2) + (2h)^(1/2)]
Here, 
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

• L<S : 

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

Here, 

all terms denote the same as above so,

  L = 2S -4.4/N.

• On the basis of overtaking sight distance(OSD):

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

• L> S:      then,    L=   (NS^2)/ [ (2H)^(1/2) + (2H)^(1/2)]  = NS^2/ 9.6
• L<S:     then,   L = 2S - [ (2H)^(1/2) + (2h)^(1/2)] / N   = 2S - 9.6/N

you have to use trial method to check both the cases.

Thanks for your kind visit!