Explanation Given: The design speed of equal-tangent crest curve is 70 mi / h . The height of driver's eye is 3 ft . The height of an object for which the designed curve was avoided is 1 ft . The current assumed design standard for stopping distance is 0.5 g . The station of P V C is 43 + 48 , and elevation of the P V C is 848 ft . The initial grade is + 2 % . The final grade is − 1 % . Formula used: The formula to calculate the stopping sight distance ( S S D ) for the vertical curve is given by S S D = V 1 2 2 g ( a g ± G ) + ( V 1 × t r ) ...... (I) Here, S S D is the stopping sight distance for the vertical curve, V 1 is the initial vehicle speed, g is the gravitational constant, a is the deceleration rate of the vehicle, G is the roadway grade in percent, and t r is the perception or reaction time. The formula to calculate the minimum length of the vertical curve is given by L m = K A = K | G 1 − G 2 | ...... (II) Here, L m is the minimum length of the vertical curve in feet, K is the horizontal distance required to effect a 1 % change in the slope of the vertical curve, G 1 is the initial grade of the vertical curve, G 2 is the final grade of the vertical curve and A is the absolute value of the difference in grades. The formula to calculate the minimum length of the vertical curve is given by L m = A × S S D 2 200 ( H 1 + H 2 ) 2 ...... (II) Here, A is the absolute value of the difference in grades, H 1 is the height of the driver eye, and H 2 is the height of the object to be avoided by stopping before a collision. The formula to calculate the rate of vertical curvature ( K ) is given by K = L m A = A × ( S S D ) 2 200 ( H 1 + H 2 ) 2 A = ( S S D ) 2 200 ( H 1 + H 2 ) 2 ...... (III) The formula to calculate the stationing of high point is given by x hl = K × | G 1 | ....... (IV) Here, x hl is the distance from the point of the vertical curve ( P V C ) to the high or low point. The equation of the vertical curve is given by y = a x 2 + b x + c ...... (V) Here, y is the roadway elevation at distance x from the beginning of the vertical curve P V C in stations, x is the distance from the beginning of the vertical curve station, a and b are the coefficients and c is the elevation of the P V C . Differentiate equation (V) with respect to x to find the station of the high point on the vertical curve. d y d x = d ( a x 2 + b x + c ) d x d y d x = 2 a x + b ...... (VI) The relation between b and G 1 is given by b = G 1 The formula to calculate the coefficient a by using the above relation is given by a = G 2 − G 1 2 L ...... (VII) Calculation: Assume the grade of roadway as zero. Put 0.5 g for g which is equal to 16.10 ft / s 2 . Substitute 70 mi / h for V 1 , 2.5 s for t r , 16.10 ft / s 2 for g , 11.2 ft / s 2 for a and 0 for G in equation (I). S S D = ( 70 mi / h ) 2 2 ( 16