Explanation Given: The initial grade is + 2.5 % and final grade of the curve is − 1.0 % . The design speed is 55 mi / h . The PVT is at station 114 + 50 . The station of the PVT is 112 + 35 and is at elevation 245 ft . Formula used: The formula to calculate the minimum length of the vertical curve is given by L m = K A = K | G 1 − G 2 | ....... (I) Here, K is the rate of curvature, A is absolute value of the difference in grades, G 1 is the initial grade in percentage, G 2 is the final grade. The formula to calculate the stationing of vertical curve PVC is given by S P V I = S P V T − L m ........ (II) Here, S P V I is the station of PVI and S P V T is the station of PVT. The formula to calculate the coefficient b is given by b = G 1 ....... (III) The formula to calculate the coefficient is given by a = G 2 − G 1 2 L ....... (IV) Here, a is the coefficient, and L is the length of the curve in ft . The formula to calculate the distance between the point on the curve and PVC is given by D = Station of Point on the curve − Station of P V C ....... (V) The formula to calculate the elevation of high point is given by y = a x 2 + b x + c ....... (VI) Here, x is the distance from the beginning of the vertical curve in station or feet, c is the elevation of PVC, y is the elevation at a distance x from the beginning of the vertical curve in station. Differentiate equation (VI) to calculate the stationing of the high point of the curve. d y d x = d d x ( a x 2 + b x + c ) = 2 a x + b ....... (VII). Calculation: The value of rate of vertical crest curvature from "table 3.2" book "Principles of highway engineering and traffic analysis" for the design speed of 55 mi / h is K = 247 . Substitute 247 for K , 2.5 % for G 1 and − 1.0 % for G 2 in equation (I). L m = 114 | 2.5 − ( − 1.0 % ) | = 399 ft Substitute 114 + 50 for S P V I and 399 ft for L m in equation (II). S P V C = ( 114 + 50 ) − 399 ft 100 = 110 + 51 Substitute 2.5 % for G 1 in equation (III). b = + 2.5 % Substitute 2