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

2. Basic Elements Horizontal Alignment Vertical Design Cross Section

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

4. Design of Vertical Curves

5. 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)

6. A B El. 100 ` 140 120 130 110 150 170 180 190 160 El. 200

7. 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 201001210 302501020 40450835 50750770 6011005150 7016004200 Site Engineering by Steven Storm

8. ` A B El. 200 El. 100 140 120 130 110 170 160 150 180 190

9. ` A B El. 200 120 150 180 130 170 110 140 160 190 0+00 1+00 2+00 3+00 4+00 5+00 6+00 7+00 8+00 9+00 10+00 11+50 11+00

10. Longitude Profile Distance Elevation 100200 300400500600 700800 900 10001100 100 120 140 160 180 200 B (1150,200) A (0,100)

11. Distance 100200 300400500600 700800 900 10001100 100 120 140 160 180 200 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%

12. Distance 100200 300400500600 700800 900 10001100 100 120 140 160 180 200 B (1150,200) A (0,100) Elevation G1=10% G2=6.25% G3=9.3%

14. 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.

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

16. ` A B