Lec 05 Highway Engineering - Curve Superelevation

Lecture 05 46

Highway Eng. Superelevation 14 15

Dr. Firas Asad

In this lecture; ---------------------

A- Definition and Justifications.

B- Min. Radius of Circular Curve.

C- Superelevation Section (Runoff

& Runout).

D- Superelevation Attainment .

Superelevation is the banking ()

of a roadway around a curves to

counterbalance the centripetal force

of a vehicle traversing a

horizontal curve.

The provision of superelevation - one edge of

a roadway higher than the other - will

prevent vehicles from overturning or sliding

off the road. The side friction between

pavement and tires also help in

counterbalancing the centripetal (outward

pull) force.

Superelevation at Horizontal Curves

The information listed in this lecture is mainly taken from the Policy on Geometric Design of Highways and Streets (AASHTO, 2011), Iraqi Highway Design Manual (SORB, 2005) and Traffic and Highway Engineering (Garber and Hoel, 2009).

A- Superelevation: Definition and Justification

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Dr. Firas Asad

When a vehicle is moving around a circular

curve the centripetal force will attempt to pull

the vehicle outside the curve. In flat curves

(with large radii) this force can be fully

counterbalanced by the side friction.

However, for sharper curves, only side friction

will not be enough to prevent vehicles from

sliding outwards and hence superelevation is

needed.

The minimum radius of a circular curve R for a

vehicle travelling at V kph can be determined

by considering the equilibrium of the vehicle

with respect to its moving up or down the

incline. If is the angle of inclination of the

highway, the component of the weight down

the incline is W sin , and the frictional force

also acting down the incline is . W cos .

There are limitations for values of highways cross slopes. The minimum rate of

cross slope applicable to the travelled way is determined by drainage needs. In

contrast, the maximum amount of superelevation should not be exceeded for

preventing slow-moving vehicle from sliding or overturning to the inside of the

curve when the road is covered with rain, snow, or ice.

According to AASHTO, the minimum rate of cross slope, also called normal crown is

(1.5 2)% while the maximum amount of superelevation is (10 12)%.

B. Minimum Radius of Circular Curve

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Dr. Firas Asad

Where is the coefficient of side friction. The centrifugal force is R

Vg

W 2. .

Other forces acting on the car are its weight W and force exerted against the wheel

by the roadway surface. These forces are the normal force N, and friction forces F,

so: F N. Appling equilibrium by algebraic summing for forces parallel to the

roadway gives:

sin).(cos2

WFR

Vg

W+= ; since F = N and

).(sincos

2

RV

gWWN +=

But, superelevation e = tan . ------ >

sin).(sincos().(cos22

WR

Vg

WwfR

Vg

W++= ----- >

gRVfefe

gRV 22 .++=

fefe

gRV

.1

2

+

= ------ > The term ef is small compared to one, and may be omitted, so

the relationship can be simplified to

)(127

2

feVR+

= Where: V: speed in km/hr and R: radius in m.

It can be obviously noted that minimum radius of the circular curve Rmin is occurred

when applying maximum values for the rate of superelevation emax and coefficient

of side friction max.

Coefficients of side friction for different design speed are as following (AASHTO):

Design speed km/hr 50 65 80 100 110

Max. f 0.19 0.16 0.14 0.12 0.10

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Dr. Firas Asad

Generally, maximum rates of superelevation are:

(10 12)% for rural highway;

8 % for rural highway with snow or ice effect;

(4 6) % for urban street.

According to AASHTO recommendations and for design purposes use (6-8) % for

rural highways and (4-6) % for urban one.

EXAMPLE PROBLEM: A) What is the minimum radius of curvature allowable for a

roadway with a 100 km/h design speed, assuming that the maximum allowable

superelevation rate and the pavement coefficient of friction are both 0.12? B) What

is the actual maximum superelevation rate allowable under AASHTO recommended

standards for a 100 km/h design speed, if the maximum value of and minimum

curve radius allowed by AASHTO for this speed are 0.12 and 490m respectively?

Round the answer down to the nearest whole percent.

Sol.)

A) Minimum radius of curvature for 100 km/h design speed:

Rmin. = )(127

2

feV+

= )12.012.0(127

1002

+= 328 m

B) Actual maximum superelevation rate for AASHTO recommended standards for

100 km/h is:

e = fR

V

127

2

= 12.0)490(127

1002 = 0.0406 ---- >

Rounding, emax = 0.04 = 4%.

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Dr. Firas Asad

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Dr. Firas Asad

C. Superelevation Transition Section

The superelevation transition length is comprised of superelevation runoff and

tangent runout. For reasons of safety and comfort, the pavement rotation in the

superelevation transition section should be effected over a length that is sufficient

to make such rotation imperceptible to drivers. To be pleasing in

appearance, the pavement edges should not appear distorted to the driver.

As shown previously in the Horizontal Alignment lecture, transition (spiral) curve

may be used to provide smooth transition from the tangent to the main circular

curve. When a transition curve is not used, the roadway tangent directly adjoins the

main circular curve. This type of transition design is referred to as the tangent-to-

curve transition.

The figure below shows the locations of superelevation runoff and tangent runoff

for curves Uwith and without U spiral transition sections.

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Dr. Firas Asad

C-1 Superelevation Runoff.

The superelevation runoff section consists of the length of roadway needed to

accomplish a change in outside-lane cross slope from zero (flat) to full

superelevation, or vice versa. Its length usually ranges within (30-200)m.

I- In alignment design with spirals: the superelevation runoff is effected over the

whole of the transition curve. The

1) Location with respect to end of curve:

length

II- In the tangent-to-curve design (no spiral): the location of the superelevation

runoff with respect to the point of curvature (PC) must be determined. Normal

practice is to divide the runoff length between the tangent and curved sections and

to avoid placing the entire runoff length on either the tangent or the curve (see the

figure). Generally, the proportion of runoff length placed on the tangent varies from

0.6 to 0.8 (i.e., 60 to 80 percent) with a large majority of highway agencies in the

USA using 0.67 (i.e., 67 percent) as a single value for all street and highway curves.

Table below shows AASHTO recommendations.

of the superelevation runoff should be

equal to the spiral length for both the tangent-to-spiral (TS) transition at the

beginning and the spiral-to-curve (SC) transition at the end of the circular curve. In

this design, the whole of the circular curve has full superelevation. In case of the

length of spiral is less than the runoff length, it is appropriate to use the

superelevation runoff instead of the length of spiral curve.

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Dr. Firas Asad

: Experience indicates that relative gradients of

0.80 and 0.35 % provide acceptable runoff

lengths for design speeds of 20 and 130 kph,

respectively. Current practice is to use max.

relative gradient value 0.50% or a longitudinal

slope of 1:200 at 80 kph.

n1: is equal to one-half the total number of lanes

for undivided streets or highways where the

cross section is rotated about the highway

centerline

For pleasing appearance and comfort, the length of superelevation runoff Lr where

no spiral used should be based on a maximum acceptable difference between the

longitudinal grades of the axis of rotation and the edge of pavement (relative

gradient, ).

2) Length of superelevation runoff (Tangent-to-Curve transition):

According to AASHTO, the minimum length of runoff should be determined as:

The application of the max. relative gradient () provides runoff lengths for 4-lane

undivided roadways that are double those for 2-lane roadways; those for 6-lane

undivided roadways would be tripled. This may be desirable but it is often not

practical to provide such lengths in design. Empirically, it is recommended that min.

superelevation runoff lengths be adjusted downward using adjustment factors as

listed in the table below.

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Dr. Firas Asad

Minimum length of tangent runout (Lt).

The length of tangent runout is determined

by the amount of adverse cross slope to be

removed and the rate at which it is

removed. To effect a smooth edge of

pavement profile, the rate of removal

should equal the relative gradient used to

define the superelevation runoff length.

Based on this rationale, the following

equation should be used to compute the

minimum tangent runout length:

C-II Tangent Runout.

The tangent runout section consists of the length of roadway needed to accomplish

a change in outside-lane cross slope from the normal cross slope rate to zero (flat),

or vice versa.

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Dr. Firas Asad

According to AASHTO, the table below listed minimum superelevation runoff and

tangent runout lengths for different design speeds.

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Dr. Firas Asad

D. Superelevation Attainment.

It is essential that, the change from a crowned cross-section to a superelevated on

to be achieved without causing any discomfort to motorists or creating unsafe

condition. One from four methods can be used to achieve this change on undivided

highway:

1- A crowned pavement is rotated about the profile centerline;

2- A crowned pavement is rotated about the profile inside edge;

3- A crowned pavement is rotated about the profile outside edge;

4- A straight cross-slope pavement is rotated about the profile outside edge.

Selection of the method is depending on:

A- which one will provide pleasant appearance;

B- which one will provide drainage requirements;

C- Cost of cut and fill and paving material.

The change in cross slope begins by removing the adverse cross slope from the lane

or lanes on the outside of the curve on a length of tangent just ahead of tangent-to-

spiral point TS (the tangent runout). Between the TS and SC, the spiral curve and the

superelevation runoff are coincident and the traveled way is rotated to reach the

full superelevation at the spiral-to-curve point SC. This arrangement is reversed on

leaving the curve. In this design, the whole of the circular curve has full

superelevation.

The figure below shows diagrammatic profiles showing the four methods of

attaining superelevation for a curve to the right.

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Dr. Firas Asad

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Dr. Firas Asad

Documents

Lec 05 Highway Engineering - Curve Superelevation