11/21/2018

1

CE 413Highway and Traffic Engineering

Lecture 5

Geometric Design of Highways

Engr. Amjad Khan

MS Transportation Engineering (NUST)

The alignment of a highway is composed of horizontal andvertical elements

The horizontal alignment:

includes the straight (tangent) sections of the roadway

circular curves that connect their change in direction

The vertical alignment:

includes straight (tangent) highway grades

parabolic curves that connect these grades

Geometric Design of Highways

2

11/21/2018

2

Highway alignment is in reality a three-dimensionalproblem

Design & construction is difficult in 3-D so highway designis typically treated as two 2-D problems: Horizontalalignment, vertical alignment

Geometric Design of Highways

3

Geometric roadway design can be broken into three main parts: alignment, profile, and cross-section. Combined, they provide a three-dimensional layout for a roadway.

Horizontal Alignment

Corresponds to “X” and “Z” Coordinates

Plan view – Roughlyequivalent to the perspectiveof an aerial photograph ofhighway

Vertical Alignment

Corresponds to highwaylength and “Y” Coordinate

Presented in a profile view

Gives elevation of all pointsmeasured along the length ofa highway

Geometric Design of Highways

VerticalAlignment

Horizontal Alignment

4

11/21/2018

3

Geometric Design of Highways - Stationing

• Instead of using the coordinates system, highway positioning and length aredefined as the distance usually measured along the center line of thehighway from a specified point

• The notation for stationing distance is such that a point on highway 4250 ft(1295.3 m) from a specified origin (0+00 or 0+000) is said to be at station:

– 42+50 ft (42 stations and 50 feet)

– I + 295.300 meter( 1 station and 295.300 meters)

Horizontal Alignment

Vertical Alignment

5

The horizontal alignment consists of tangents and curves

The curves are usually segments of circles, which have radii that will provide for a smooth flow of traffic

The critical design feature of horizontal alignment:

horizontal curve that transitions the roadway between two straight (tangent) sections

focus on the design of directional transition of the roadway in a horizontal plan

A key concern in the directional transition is the ability of the vehicle to negotiate the horizontal curve

Horizontal Alignment

6

11/21/2018

4

Tangents Curves

Horizontal Alignment

7

Horizontal alignment to accommodate the cornering capabilityof a variety of vehicles (cars to combination trucks)

The design of the horizontal alignment entails the determination of:

the minimum radius of the curve

determination of the length of the curve

Side friction factor

Superelevation

Adequate stopping sight distance

Horizontal Alignment

8

11/21/2018

5

Horizontal Alignment

94/3/2015

Horizontal Alignment

104/3/2015

11/21/2018

6

Horizontal Alignment

114/3/2015

Horizontal Alignment

124/3/2015

11/21/2018

7

Tangent

Curve

Tangent to Circular Curve

Tangent to Spiral Curve

Horizontal Alignment

134/3/2015

Concept of Super-elevation

Centrifugal force and Centripetal Forces

o Centrifugal force (Latin for "center fleeing") describes the tendencyof an object following a curved path to fly outwards, away from thecenter of the curve. It's not really a force; it results from inertia i.e.the tendency of an object to resist any change in its state of rest ormotion

o Example: Mud flying off a tire; children pushed out on a roundabout

14

11/21/2018

8

Concept of Super-elevation

15

Concept of Super-elevation

Centrifugal force and Centripetal Forces

o Centripetal force is a "real" force that counteracts the centrifugalforce and prevents the object from "flying out", keeping it movinginstead with a uniform speed along a circular path

o Example: Satellite orbiting a planet

16

11/21/2018

9

Horizontal highway curve is a curve in plan to provide change in direction to the center line of a road. When a vehicle traverses a horizontal curve, the centrifugal force acts horizontally outwards through the center of gravity of the vehicle.

The centrifugal force is counteracted by the transverse frictional resistance developed between the tires and the pavement and weight of the vehicle.

Centrifugal force = ��²

�or

��²

��

The centrifugal force acting on a vehicle negotiating a horizontal curve has two effects1.Tendency to overturn the vehicle outwards about the outer

wheels 2.Tendency to skid the vehicle laterally outwards.

Concept of Super-elevation

Concept of Super-elevation

Super-elevation or banking is the transverse slope providedat horizontal curve to counteract the centrifugal force, byraising the outer edge of the pavement with respect to theinner edge, throughout the length of the horizontal curve.

11/21/2018

10

Concept of Super-elevation

C.GCentrifugal force = P

Weight = W

RA RB

FA = f RA FB = f RBCurve Direction

Concept of Super-elevation

C.GCentrifugal force = P

Weight = W

RA

RB

Curve Direction

θ

θ

θ

PSinθ

PCosθ

WCosθ

WSinθ

11/21/2018

11

At Equilibrium PCosθ = ����� + �� + ��PCosθ = ����� + ��� + ���PCosθ = ����� + � �� + ��PCosθ = ����� + � ����� + �����

Dividing by Wcosθ and rearranging�����

�����=

�����

�����+

������

�����+

������

�����

�

�= ���� + f + f

�

�����

�

�- f

�

����� = ���� + f

�

�(1- f����) = ���� + f

�

�=

������

������� As �

�=

��

��

��

��=

������

�������

��

��=

� ��

� � ��

Since ef ≈ 0 when max.allowable values of f and e are taken

��

��=

� ��

� ��

��

��= e + f

R =��

�(���)

Here V = velocity in ft/sece = superelevation rate in %R = radius in ft.g = 32.2 ft/sec2

11/21/2018

12

R =��

��(���)

Here V = velocity in miles/hr.e = superelevation rate in %R = radius in ft.g = 32.2 ft/sec2

Eq shows that to reduce R for a given velocity, either e or f or both should be increased.

Concept of Super-elevation

• AASHTO expression for superelevation after simplification

V 2 V 2

0.01e fv2

0.01e f

v2

15R 1 0.01ef gR

e = rate of roadway superelevation, %

f = side friction (demand) factor

v = vehicle speed, ft/s

g = gravitational constant, 32.2 ft/s2

V = vehicle speed, mph

R = radius of curve measured to a

vehicle’s center of gravity, ft

127R 1 0.01ef gR

e = rate of roadway superelevation, %

f = side friction (demand) factor

v = vehicle speed, m/s

g = gravitational constant, 9.81 m/s2

V = vehicle speed, Kmph

R = radius of curve measured to a

vehicle’s center of gravity, meter

11/21/2018

13

Superelevation Example -1

25

An existing horizontal curve on a highway has a radius of 465 ft, which restricts the posted speed limit on this section of the road to only 61.5% of the design speed of the highway. If the curve is to be improved so that its posted speed will be the design speed of the highway, determine the minimum radius of the new curve. Assume that the rate of superelevation is 0.08 for both the existing curve and the new curve to be designed.

Maximum Super-elevation

26

o The maximum rates of superelevation:

o Climate conditions: (i.e., frequency and amount of snow and ice)

o Terrain conditions (i.e., flat, rolling, or mountainous)

o Type of area (i.e., rural or urban)

o Frequency of very slow-moving vehicles whose operation mightbe affected by high superelevation rates

o No single maximum superelevation rate is universally applicable

o Design consistency: Using only one maximum superelevation rate within a region of similar climate and land use is desirable

11/21/2018

14

Side-Friction Factor

27

Achieving Superelevation

o The superelevation transition section consists of thesuperelevation runoff and tangent runout sections

o Tangent Runout: The tangent runout section consists ofthe length of roadway needed to accomplish a change inoutside-lane cross slope from the normal cross slope rateto zero (flat), or vice versa

o Superelevation Runoff: The superelevation runoff sectionconsists of the length of roadway needed to accomplish achange in outside-lane cross slope from zero (flat at) to fullsuperelevation, or vice versa

12

11/21/2018

15

13

Superelevation Runoff and Tangent Run out (Crown Runoff)

Fully superelevated cross section

Cross section with the adversecrown removed

Normal cross section

14

Tangent Runout Section

• Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero

For rotation about centerline

11/21/2018

16

15

Superelevation Runoff Section

• Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa

• For undivided highways with cross-section rotated about centerline

16

Source: CalTrans Design Manual online, http://www.dot.ca.gov/hq/oppd/hdm/pdf/chp0200.pdf

11/21/2018

17

17

Achieving Superelevation

18

11/21/2018

18

Achieving Superelevation

19

PC Superelevation runoff

Tangent runout

(Normal Crown)

(Adverse Crown)

(Full Superelevation)

Steps in Highway Rotation to Achieve Superelevation

o The outside lane(s) are rotated from their normal cross-slope to aflat condition

o The outside lane(s) are rotated from the flat position until they equal the normal cross-slope of the inside lanes.

o All lanes are rotated from the condition of step 2 to the full superelevation of the horizontal curve.

20