# Geometric Design of Highways

Geometric Design of Highways – Highway Engineering

- Geometric Design for transportation facilities includes the design of geometric cross section, horizontal alignment, vertical alignment, intersections, and various design details.
- maximize the comfort
- safety,
- economy of facilities
- while maximizing their environmental impacts
- geometric cross section
- vertical alignment
- horizontal alignment
- super elevation
- intersections
- various design details.
- The primary consideration in the design of cross sections is drainage.
- Highway cross sections consist of traveled way, shoulders (or parking lanes), and drainage channels.
- Shoulders are intended primarily as a safety feature.

Shoulders provide:

- accommodation of stopped vehicles
- emergency use,
- and lateral support of the pavement.
- Shoulders may be either paved or unpaved.
- Drainage channels may consist of ditches (usually grassed swales) or of paved shoulders with berms of curbs and gutters.
- Two-lane highway cross section, with ditches.

Two-lane highway cross section, curbed.

Divided highway cross section, depressed median, with ditches.

Divided highway cross section, raised median, curbed.

Standard lane widths are normally 3.6 m (12 ft), although narrower lanes are common on older roadways, and may still be provided in cases where the standard lane width is not economical. Shoulders or parking lanes for heavily traveled roads are normally 2.4 to 3.6 m (8 to 12 ft) in width; narrower shoulders are sometimes used on lightly traveled road.

The vertical alignment of a transportation facility consists of

tangent grades (straight line in the vertical plane), vertical curves. Vertical alignment is documented by the profile. Tangent grades are designated according to their slopes or grades. Maximum grades vary depending on the type of facility, and usually do not constitute an absolute standard. The effect of a steep grade is to slow down the heavier vehicles (which typically have the lowest power/weight ratios) and increase operating costs.

Vertical tangents with different grades are joined by vertical curves.

Symmetrical Vertical Curve

Vertical curves are normally parabolas centered about the point of intersection (P.I.) of the vertical tangents they join. Vertical curves are thus of the form

where y = elevation of a point on the curve

yo = elevation of the beginning of the vertical curve (BVC)

g1 = grade just prior to the curve

x = horizontal distance from the BVC to the point on the curve

r = rate of change of grade

The rate of change of grade, in turn, is given by

where g2 is the grade just beyond the end of the vertical curve (EVC) and L is the length of the curve.

Vertical curves are classified as sags where g2 > g1 and crests otherwise. Not that r (and hence the term rx2 /2) will be positive for sags and negative for crests.

If grades are in percent, horizontal distance must be in stations

If grades are dimensionless ratios, horizontal distances must be in meters.

The grade of any point in the vertical curve is a linear function of the distance from the BVC to the point. That is,

A –2.5% grade is connected to a +1.0% grade by means of a 180-m vertical curve. The P.I. station is 100 + 00 and the P.I elevation is 100.0 m above sea level. What are the station and elevation of the lowest point on the vertical curve?

Design standards for vertical curves establish their minimum lengths for specific circumstances

based on sight distance,

on comfort standards involving vertical acceleration,

or appearance criteria.

In most cases, sight distance or appearance standards will govern for highways.

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 the vertical curve length.

For crest vertical curves, the minimum length depends on the sight distance, the height of the driver’s eye, and the height of the object to be seen over the crest of the curve.

When S≤L

When S≥L

where S = sight distance (from Table)

L = vertical curve length

A = absolute value of the algebraic difference in grades, in percent, |g1-g2|

h1 = height of eye

h2 = height of object

- For stopping sight distance, the height of object is normally taken to be 150mm. for passing sight distance, the height of object used by AASHTO is 1300 mm. Height of eye is assumed to be 1070 mm.
- For sag vertical curves, stopping sight distance is based on the distance illuminated by the headlights at night.
- Design standards are based on an assumed headlight height of 600 mm and an upward divergence of the headlight beam of 1°.
- As in the case of crest vertical curves, the formulas for minimum length of vertical curve depend on whether the length of the curve is greater or less than the sight distance.
- For sag vertical curves, the formula is
- Design charts of tables are used to determine minimum length of vertical curve to provide stopping sight distance for both crest and sag vertical curves, and passing sight distance on crests. These may be found in the AASHTO Policy on Geometric Design of Highways and Streets.
- Finally, vertical curve lengths may be limited by the need to provide clearances over or under objects such as overpasses or drainage structures.
- VERTICAL CURVES PASSING OVER OBJECTS(e.g. Overpass)
- SAG CURVE – Minimum Lengths
- CREST CURVE – Maximum Lengths
- VERTICAL CURVES PASSING UNDER OBJECTS(e.g. Drainage
- SAG CURVE – Maximum Lengths
- CREST CURVE – Minimum Lengths
- Horizontal alignment for linear transportation facilities such as highways and railways consists of horizontal tangents, circular curves, and possibly transition curves. In the case of highways, transition curves are not always used.
- Horizontal alignments with and without transition curves.
- Horizontal tangents are described in terms’ of their lengths (as expressed in the stationing of the job) and their directions. Directions may be either expressed as bearings or as azimuths and are always defined in the direction of increasing station. Azimuths are expressed as angles turned clockwise from due north; bearings are expressed as angles turned either clockwise or counterclockwise from either north or south.
- Horizontal curves are normally circular. Figure in the next slide illustrates several of their important features. Horizontal curves are also described by radius, central angle (which is EQUAL to the deflection angle between the tangents), length, semitangent distance, middle ordinate, external distance, and chord. The curve begins at the tangent-to-curve point (TC) and ends at the curve-to-tangent point (CT).
- Design standards for horizontal curves establish their minimum radii and, in some cases, their minimum lengths. Minimum radius of horizontal curve is most commonly established by the relationship between design speed, maximum rate of superelevation, and curve radius. In other cases, minimum radii or curve lengths for highways may be established by the need to provide stopping sight distance or by appearance standards.
- Transition curves are used to connect tangents to circular curves.
- tangent to spiral point (TS),
- spiral to curve point (SC),
- curve to spiral point (CS),
- spiral to tangent point (ST).
- The purpose of superelevation or banking of curves is to counteract the centripetal acceleration produced as a vehicle rounds a curve. The term itself comes from railroad practice, where the top of the rail is the profile grade.

A commonly used mixed-unit version of the equation is:

where V is in km/h and R is in meters. Alternatively,

Compute the minimum radius of a circular curve for a highway designed for 110 km/h. The maximum superelevation rate is 12%. Value of f(from AASHTO table) is 0.11.

Geometric Design of transportation facilities must provide for the resolution of traffic conflicts.

In general, these conflicts may be classified as:

- Merging conflicts – Occurs when vehicles enter a traffic stream
- Diverging conflicts – Occurs when vehicles leave the traffic stream
- Weaving conflicts – Occurs by merging then diverging
- Crossing conflicts – Occurs when they cross paths directly
- Time-sharing Solutions
- Space-sharing Solutions
- Grade separation Solutions
- Except for freeways, all highways have intersections at grade, so that the intersection area is a part of every connecting road or street.
- In this area, crossing and turning movements occur.
- Some intersection are channelized – to minimize traffic accidents, speed control, prevention of prohibited turns, refuge may be provided for pedestrians

Unchannelized T

Unchannelized Y

Flared T

Unchannelized

3-leg intersections

Y with turning roadways

Channelized Are classified according to the way they handle left-turning traffic.

INTERCHANGE CONFIGURATION – are selected on the basis of structural cost, right-of-way costs, and ability to serve traffic.

ON-RAMP (entrance to highway)

ON-RAMP (entrance to highway)

OFF-RAMP (exit to highway)

OFF-RAMP (exit to highway)

- Diamond Interchange
- Employ diamond ramps which connect to the cross road by means of an at grade intersection.
- Left turns are accomplished by having vehicles turn left across traffic on the cross road.
- Cloverleaf Interchange
- Employ loop ramps, in which vehicles turn left by turning 270 degrees to the right.
- Partial Cloverleaf Interchange (Parclo)
- Involves various combinations of diamond and loop ramps.
- Trumpet Interchange