Welcome

1. Welcome Highway Engineering Code No. (CM 304) Lec. 5 and 6 Dr.Khaledali

2. Design of Highways Vertical Profile

3. Maximum and Minimum Gradients 3% - Mixed Traffic 5% - Passenger Cars only 7% - Exceptional in hilly terrain Factor Affecting the Design of Vertical Curves • Intersecting grades • Speed • Type of vertical curve

4. Types of Vertical Curves • Summit (Crest) Curves • Sag Curves Summit Sag Sag

5. Vertical Curve Characteristics Algebraic difference of gradients, percent G1= approaching gradient G2= leaving gradient PVI = Point of intersection (Mid-Point, MP) PVC= Point of curve PVT= Point of tangent L= Length of vertical curve (horizontal projection)

6. Critical point on the Curve (Highest or Lowest Point) • if the gradients on either sides are equal, the critical point lies on the bisector of the two gradients • if gradients on either sides are not equal, the critical point lies on the side of the flatter gradient

7. Design of Vertical Curves Length of Summit Curve Case 1: S<L for stopping (non-passing) sight distance: h1 =1.22 m , h2 = 0.10 m for passing sight distance: h1 =1.22 m , h2 = 1.37 m

8. Case 2: S>L for stopping (non-passing) sight distance: for passing sight distance:

9. Example II-5 Determine the vertical curve length to provide. a. Non passing sight distance. b. Passing sight distance. in the following cases: