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Vertical alignment in roads
Presented to: Engr. Beenish Akbar khan. By: Humayoun
Table of contents• What is Vertical alignment?• Basic component of vertical alignment 1) grade 2)vertical curves• Types of vertical curves 1) sag vertical curves 2) crest vertical curves 3) unsymmetrical vertical curves• Types of vertical alignment• REFRENCE
What is vertical alignment?
• The vertical alignment is the rout of the road, defined is the series of horizontal tangents and curve. The profile is the vertical aspect of the road, including crest and sag curves, and the straight grades line connecting them.
What is vertical alignment?
• VPC: Vertical Point of Curvature• VPI: Vertical Point of Intersection• VPT: Vertical Point of Tangency• G1, G2: Tangent grades in percent• A: Algebraic difference in grades• L: Length of vertical curve
Basic component of vertical alignmentThere are two basic component of vertical alignment. (1): Grade ------ (2): vertical curves 1):GRADE:-
The grade of a highway is a measure of its incline or slope. The amount of grade indicates how much the highway inclined from the horizontal. For example, if the 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.
Grade contd. The illustration below shows a highway in profile ( fr- om 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 the left to right. The bottom of the triangle is the horizontal 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.
Grade contd. However, it is apparent that the road is not level but
rises from left to rightGrade contd.
To calculate the grade of a section of highway, divide the rise (height increase) by the run (horizontal distance)
Grade contd.
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
Grade contd. 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.
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 “critical length of 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.
EFFECT OF GRADE
Contd.
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.
Baldwin StreetContd.
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.
Dependency of vertical curves The design of the curve is
dependent on the following factors:
Vertical curves contd. 1) intended design speed for the roadway 2) Drainage 3) Slope 4) acceptable rate of change 5) Friction These curves are parabolic and are assigned
stationing based on a horizontal axis.
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.
Parabolic Formulation contd.
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.
Parabolic Formulation contd.
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
Parabolic Formulation contd. 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.
TYPE OF VERTICAL CURVES CONTD. Crest Vertical Curves :- 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.
Crest Vertical Curves cound.
Other types are: 1) unsymmetrical vertical curve. 2) symmetrical vertical curve.
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.
REFRENCES:
http://onlinemanuals.txdot.gov/txdotmanuals/rdw/vertical_alignment.htm
https://en.wikipedia.org/wiki/Grade_(slope)•
http://www.ehow.com/info_8640336_types-vertical-curves.html
• Images from Google search engine
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