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Vertical Alignment in road design
- 1. Alignment In Road Design Vertical alignment in road design
- 2. CONTENT • What Is Vertical Alignment ? • Basic Components Of Vertical Alignment Grade Vertical Curves • Type Of Vertical Curves Sag Vertical Curves Crest Vertical Curves Unsymmetrical Vertical Curves Symmetrical Vertical Curves • REFRENCES
- 3. WHAT SI VERTICAL ALIGNMENT? • The alignment is the route of the road, defined as a series of horizontal tangents and curves. The profile is the vertical aspect of the road, including crest and sag curves, and the straight grade lines connecting them.
- 4. BASIC COMPONENTS OF VERTICAL ALIGNMENT The two basic elements of vertical alignment are Grades and Vertical Curves. Grade Vertical Curves GRADE The grade of a highway is a measure of its incline or slope. The amount of grade indicates how much the highway is inclined from the horizontal. For example, if a section of road is perfectly flat and level, then its grade along that section is zero. However, if the section is very steep, then the grade along that section will be expressed as a number, usually a percentage, such as 10 percent.
- 5. GRADE CONTD. The illustration below shows a highway in profile (from the side). Notice that a right triangle has been constructed in the diagram. The elevation, or height, of the highway increases in the sketch when moving from left to right. The bottom of the triangle is the horizontal distance this section of highway covers. This horizontal distance, sometimes called the "run" of the highway, indicates how far a vehicle would travel on the road if it were level. However, it is apparent that the road is not level but rises from left to right. This "rise" is a measure of how much higher a vehicle is after driving from left to right along the road.
- 6. GRADE CONTD. To calculate the grade of a section of highway, divide the rise (height increase) by the run (horizontal distance). This equation, used to calculate the ratio of rise-to-run for highway grades, is the same ratio as the slope "y /x " encountered in a Cartesian coordinate system . In the example above, the rise of the highway section is 100 feet, while the run is 1,000 feet. The resulting grade is thus 100 feet divided by 1,000 feet, or 0.1. Highway grades are usually expressed as a percentage. Any number represented in decimal form can be converted to a percentage by multiplying that number by 100. Consequently, a highway grade of 0.1 is referred to as a "10 percent grade" because 0.1 times 100 equals 10 percent. The highway grade for a section of highway that has a rise of 1 kilometer and a run of 8 kilometers is ⅛, or 0.125. To convert the highway grade into a percentage, multiply 0.125 by 100, which results in a grade of 12.5 percent.
- 7. EFFECT OF GRADE The effects of rate and length of grade are more pronounced on the operating characteristics of trucks than on passenger cars and thus may introduce undesirable speed differentials between the vehicle types. The term “criticallengthof grade” is used to indicate the maximum length of a specified ascending gradient upon which a loaded truck can operate without an unreasonable reduction in speed (commonly 10 mph [15 km/h]). Figure 2-3 shows the relationship of percent upgrade, length of grade, and truck speed reduction.
- 8. FUN FACT The steepest roads in the world are Baldwin Street in Dunedin, New Zealand and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World Record lists Baldwin Street as the steepest street in the world, with a 35% grade (19°) overall and disputed 38% grade (21°) at its steepest section. 25000 balls of chocolate are rolled down the 350 m-long street in an annual charity Cadbury Jaffa Race. In 2001, a student was killed when the wheelie bin she rode down the street hit a trailer. The Pittsburgh Department of Engineering and Construction recorded a grade of 37% (20°) for Canton Avenue. The street has formed part of a bicycle race since 1983.
- 9. VERTICAL CURVES Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical curve provides a transition between two sloped roadways, allowing a vehicle to negotiate the elevation rate change at a gradual rate rather than a sharp cut. Dependencyof verticalcurves The design of the curve is dependent on the following factors: intended design speed for the roadway Drainage Slope acceptable rate of change Friction These curves are parabolic and are assigned stationing based on a horizontal axis.
- 10. PARABOLIC FORMULATION Two types of vertical curves exist: (1) Sag Curves and (2) Crest Curves. Sag curves are used where the change in grade is positive, such as valleys, while crest curves are used when the change in grade is negative, such as hills. Both types of curves have three defined points: PVC (Point of Vertical Curve), PVI (Point of Vertical Intersection), and PVT (Point of Vertical Tangency). PVC is the start point of the curve while the PVT is the end point. The elevation at either of these points can be computed as e_{PVC} and e_{PVT} for PVC and PVT respectively. The roadway grade that approaches the PVC is defined as g1 and the roadway grade that leaves the PVT is defined as g2. These grades are generally described as being in units of (m/m) or (ft./ft.), depending on unit type chosen. Both types of curves are in parabolic form. Parabolic functions have been found suitable for this case because they provide a constant rate of change of slope and imply equal curve tangents, which will be discussed shortly. The general form of the parabolic equation is defined below, where y is the elevation for the parabola. 11/29/20152K13-CE-02 10
- 11. PARABOLIC FORMULATION CONTD. At x = 0, which refers to the position along the curve that corresponds to the PVC, the elevation equals the elevation of the PVC. Thus, the value of c equals e_{PVC}. Similarly, the slope of the curve at x = 0 equals the incoming slope at the PVC, or g_1. Thus, the value of b equals g_1. When looking at the second derivative, which equals the rate of slope change, a value for a can be determined. Thus, the parabolic formula for a vertical curve can be illustrated. Where: epvc =elevation of the PVC g1 =Initial Roadway Grade (m/m) g2 =Final Roadway Grade (m/m) L =Length of Curve (m) Most vertical curves are designed to be Equal Tangent Curves. For an Equal Tangent Curve, the horizontal length between the PVC and PVI equals the horizontal length between the PVI and the PVT. These curves are generally easier to design.
- 12. TYPE OF VERTICAL CURVES SagVerticalCurves Vertical curves at the bottom of a hill are called sag curves. Sag vertical curves are used to connect two descending grades which form an upside down parabola, or a sag. Similar to crest vertical curves, the sight distance is the primary parameter needed to find the length of the curve. When designing sag curves however, you must take into account the positive change in grade which accounts for increased acceleration, or inertia. Using a dip in the road for example, sag vertical curves offer drivers a view of the roadway during daylight hours, but shorten the headlight views at night. For this reason, when calculating sag curves, an upward deviation of one degree is automatically assumed.
- 13. TYPE OF VERTICAL CURVES CONTD. Crest VerticalCurves Vertical curves at a crest or at the top of a hill are called also called summit curves. Crest vertical curves are used to connect two separate inclined sections. In calculating crest curves, you only need to find a correct length for the curve that will match the correct sight distance. The sight distance as well as the distance of the curve can be compared to each other in two different ways. The first is that the sight distance is less than the length of the curve and the second is that the length of the curve could be less than the sight distance.
- 14. TYPE OF VERTICAL CURVES CONTD. UnsymmetricalVerticalCurves Unsymmetrical curves are sometimes have unequal tangents and are called dog-legs. The process for solving an unsymmetrical curve problem is almost the same as that used in solving a symmetrical curve. However, you use a different formula for the calculation of the middle vertical offset at the PVI. Be aware that an unsymmetrical curve is made up of two different parabolas, one on each side of the PVI, having a common POVC opposite the PVI. SymmetricalVerticalCurves A symmetrical vertical curve occurs when the horizontal distance from the VPC to VPI is equal to the tangent length from VPI to VPT. A symmetrical vertical curve is useful when developing a freeway entrance when the ramp alignment is on a curve. The symmetrical vertical curve allows you to compensate for the changing skew between horizontal alignments.
- 15. GRADE CHANGE WITHOUT VERTICAL CURVES Designing a sag or crest vertical point of intersection without a vertical curve is generally acceptable where the grade difference (A) is: • 1.0 percent or less for design speeds equal to or less than 45 mph [70 km/h] • 0.5 percent or less for design speeds greater than 45 mph [70 km/h]. • When a grade change without vertical curve is specified, the construction process typically results in a short vertical curve being built (i.e., the actual point of intersection is “smoothed” in the field). Conditions where grade changes without vertical curves are not recommended include: • Bridges (including bridge ends) • Direct-traffic culverts • Other locations requiring carefully detailed grades.