Introduction to Transportation Engineering Alignment Design Vertical Alignment Instructor Dr. Norman Garrick Hamed Ahangari May 2014

Basic Elements Horizontal Alignment Vertical Design Cross Section

3 Horizontal Alignment Vertical Alignment Crest Curve Sag Curve G1G1 G2G2 G3G3

Design of Vertical Curves

Parabolic Curve 5 BVC EVC L G2G2 G1G1 L/2 PI Change in grade: A = G 2 - G 1 G is expressed as % Rate of change of curvature: K = L / |A| Rate of change of grade: r = (g 2 - g 1 ) / L Equation for determining the elevation at any point on the curve y = y 0 + g 1 x + 1/2 rx 2 where, y 0 = elevation at the BVCg = grade expressed as a ratio x = horizontal distance from BVCr = rate of change of grade (ratio)

A B El. 100 ` El. 200

Alignment Standard related to Design Speed Design Speed (mph) Minimum Radius of Horizontal Curve (ft) Maximum Percentage of Grade Minimum Length of Vertical Curve for each 1% of Algebraic Differences Site Engineering by Steven Storm

` A B El. 200 El

` A B El

Longitude Profile Distance Elevation B (1150,200) A (0,100)

Distance B (1150,200) A (0,100) Elevation G1=10% h=40’,d=400’ h=20’,d=320’ G2=6.25% h=40’,d=430’ G3=9.3%

Distance B (1150,200) A (0,100) Elevation G1=10% G2=6.25% G3=9.3%

Vertical alignment Step 1: First provide the longitude profile of the road which contain earth elevations. Step 2: Based on the maximum allowable slope and topographic condition, determine vertical tangents. Step 3: Calculate the parabolic vertical curve specifications.

Example We want to design a road which connect point A and B Design Speed is 30 mph Provide vertical alignment for this road

` A B