The elevation of various points of the curve gives the relative difference in the level at different points on the curve. Also shown in the figure are length of the curve, start of the curve and also the end of the curve. To provide easy movement of vehicles and also to smooth out the vertical profile the vertical curves are introduced at the intersection of the grades. Usually two type of vertical curves are used in the geometric design of roads. They are crest curves or summit curves and sag curves or valley curves. The crest curves have the convexity upwards and when a fast moving vehicle travels along the curve, upward action of the centrifugal force against the gravity and would relieve a part of the pressure on the tyres. This phenomenon would eliminate the discomfort experienced by the passengers wouldn't feel the discomfort while passing over these curves (Garber and Hoel, 2001). The process of aligning the vertical curves along the road is influenced by various factors like the vehicle speed, acceleration, stopping sight distance and comfort in travel (Wright and Dixon, 2004).
The design of the summit curve is governed only by sight distance considerations. Though the circular crest curve is an ideal choice as the sight distance available throughout the length of a circular curve is constant most of the designs prefer parabolic curve. This is because the deviation angles in the vertical curves of highways are very small and between the same tangent points a simple parabola is congruent with a circular arc. In addition, easiness in computation of the ordinates besides the better rising comfort given by crest curves gives preference to parabolic curves (DRMB, 1993). When the parabolic crest curves are adopted the equation is given as y=ax2 , where a = N /2L. The N in the equation is the deviation angle and L is the length of the curve. Since the crest curves are long and flat , the length of the curve L is taken as equal to the horizontal projection. During the process of the design of the parabolic crest curves it is necessary to consider the stopping sight distance and overtaking sight distance separately. As indicated earlier, it is essential to provide sight distances atleast equal to the stopping distances at all points on the highways to avoid the accidents due to inadequate sight distance (Garber and Hoel, 2001).
Figure 2 : The length of the crest curve is greater than the stopping side distance
Length of the summit curves for stopping side distance.
The two situations that need to be considered in the determination of length of the curve for stopping side distance (SSD) are (i) When the length of the curve is greater than the side distance (L > SSD) and (ii) When length of the curve is less than the side distance (L < SSD) (Mannering et al, 2005).
For L > SSD (Figure 2), the length of the vertical crest curve is given as
Where, L is the length of the vertical crest curve in metre, S is the stopping side distance in metre, N is the deviation angle which is equal to algebraic difference in grades, radians or tangent of the deviation angle, H is the height of the eye level of the driver above the road surface in metre, h is the height of the object above the pavement surface in metre. The value of H