vertical alignment

2. Vertical alignment in roads
Presented to:
Engr. Beenish Akbar khan.
By:
Humayoun

3. 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

4. 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.

5. 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

6. Basic component of vertical alignment
There 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.

7. 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.

8. 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)

9. 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

10. 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.

11. 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.

12. EFFECT OF GRADE
Contd.

13. 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.

14. Baldwin Street
Contd.

15. 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:

16. 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.

17. 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.

18. 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.

19. Parabolic Formulation contd.

20. 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

21. 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.

22. 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.

23. Crest Vertical Curves cound.
Other types are: 1) unsymmetrical vertical curve.
2) symmetrical vertical curve.

24. 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.

25. 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