lec 6_vertical alignment

8/6/2019 Lec 6_Vertical Alignment

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Dr. Lina Shbeeb

Vertical alignment

Transportation Engineering


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Dr. Lina Shbeeb

Vertical alignmentVertical Curves are used to provide a gradual change from

one tangent grade to another, so that vehicles may smoothlynavigate changes in grade as they travel the highway.


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Dr. Lina Shbeeb

Vertical alignment Vertical alignment consists of grade tangents

connected with parabolic curves. The desirable maximum grades and gradient

changes depend on the facility type and vehiclecharacteristics.

The desirable grade as function of facility type: 2% for freeways

6% for local street

Higher grades are unavoidable at location with difficulttopography.

The length of vertical curve is measured along thehorizontal alignment. A point on the curve isspecified by its station location on the horizontalalignment and its elevation from a datum.


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Dr. Lina Shbeeb

Maximum grades by highway function


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Dr. Lina Shbeeb

Vertical alignment Grades vertical slope from reference station

upgrade positive

downgrade - negative

Crest, sag curves


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Dr. Lina Shbeeb

Vertical alignment Vertical point of intersection (VPI): The point where the grade

line intersect Vertical point of tangency (VPT): The point where the grade

vertical curve ends

Vertical point of curvature (VPC) The point where the grade

vertical curve beigns


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Dr. Lina Shbeeb

Vertical design element It important to find the vertical elevation at each station

particularly VPC,VPI and VPT.

External distance E needs to be calculated to estimate

their elevation.


8/20

Dr. Lina Shbeeb

Vertical alignment

Total change in grade

Vertical curvature

External distance

Vertical offset

High(low) point of curve

Elevation of any P

12 GGA !

|| A

LK !

ftALE800

!

2

4

!

L

xEy

0X u

!21

1

GG

LGX

yxG

!

100

1VPCofelevation

X is the distance along

the horizontal alignment

from PVC to the point of

interest


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Dr. Lina Shbeeb

General considerations

Reasonable upgrades without significant

loss in speed is 4-5 %

@ 70 mph design speed max grade is5%

@ 30 mph design speed max grade is 7-

12%


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Dr. Lina Shbeeb

Vertical alignment example A 600-ft curve connects a +4% grade to a 2% grade

at station 25+60.55 and elevation 648.64 ft. Calculate

the location and elevation of the VPC, the middle of the

curve, the VPT, and the curve elevation at stations

24+00 and 27+00

?? ? ?

?


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Vertical alignment example

Total change in grade

Vertical curvature

External distance

Vertical offset

High(low) point of curve

Elevation of any P

%612

!! GGA

1006

600!!!

|| A

LK

ftAL

54800

6006

800.!

!!

2

4

!

L

x

y

400

21

1!

!

!

6

(4)600

GG

LGX

2

1

4100

!

L

xx

G

VPCofelevation


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Dr. Lina Shbeeb

Vertical alignment example


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Dr. Lina Shbeeb

Calculation of vertical curve length

In most cases, sight distance will govern forhighways. The equations used to calculate

minimum lengths of vertical curves based on

sight distance depend on whether the sight

distance is greater than or less than thevertical curve length.


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Dr. Lina Shbeeb

Crest Vertical Curves, S > L


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Dr. Lina Shbeeb

Crest Vertical Curves, S < L


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Dr. Lina Shbeeb

Crest Vertical Curves

For first condition: S < L

For second condition: S > L

where L = minimum length of vertical curve

S = sight distance

A = algebraic difference in grades (gradient)

h1 = height of eye above roadway surface

h2 = height of object above roadway surface

A

HHSL

2

21 )(2002

!

2

21

2

)(200 HH

ASL

!


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Dr. Lina Shbeeb

Crest Vertical Curves

If the height of eye, h1, is 3.5 ft and height of object,

h2, is 0.5 ft respectively, as used for SSD, then

For first condition: S < L


ASL

13292 !

1329

2

SAL !


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Dr. Lina Shbeeb

Sag vertical curve: headlight sight distance

Headlight beam of automobile at 2 ft ( or 600 mm),

with 1o upward divergence from longitudinal axis of

roadway.

S is actually the distance between the vehicle and

point where the 1o angle of light beam intersects the

surface of the roadway. For first condition: S < L


A

ShSL

)tan(2002

F!

)tan(200

2

Sh

SAL

F!


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Dr. Lina Shbeeb

Headlight Sight Distance

For safety the length of a sag vertical curve

should be long enough so that the light beam

distance is nearly the same as the SSD. Therefore SSD is used for "S" in the above

equations.


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Dr. Lina Shbeeb

Vertical Curves The procedures for designing a crest vertical curve

are the following:

Step 1: Determine the minimum length of curve to

satisfy sight distance requirements

Step 2: Determine from the layout plans the station

and elevation of the PVI, that is the point where thegrades intersect.

Step 3: Compute the elevations of the PVC (or BVC)

and end of vertical curve (EVC or PVT).

Step 4: Compute the offsets y from the tangent tothe curve at equal distances, usually 100 feet or 20 m

apart.

Step 5: Compute elevations on the curve.

lec 6_vertical alignment

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