roads_3_2010

9/27/2010

1

ROADSROADSDESIGN OF

ALIGNMENT

LECTURE 3

The ALIGNMENT should

be

SAFE

ECONOMIC

AESTHETIC

determined mainly by alignment

building and transportation costs

road of good alignment explores the landscape driver tires less

The REQUIREMENTSof the alignment

are realized through the

design speedand the

sight distances

Cross

Section

Design speed Alignment

Functional

classification

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DESIGN SPEED

the maximum safe speed

that can be maintained over a specified section of highway

base of the design of the alignment

determined by the function and the surroundings of the road

conditions are so favorable that the design features of the highway govern-no traffic-no extreme weather conditions

STOPPING SIGHT

DISTANCE

distance traveled while the driver perceives a situation and comes to a stop

''' UUU +=

reaction distance

breaking distance

REACTION DISTANCE

distance traveled while the driver perceives a situation and applies the break

'U

t = 2s

speed does not change!

[ ]m 28,06,3

' tvtv

U ⋅⋅=⋅=

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BREAKING DISTANCE

distance traveled, while the kinetic energy of the vehicle is consumed by the breaking force

''U

kinetic energy of the vehicle

2

2

22

0039,06,322

vQv

g

QMs⋅⋅=⋅=

BREAKING FORCE

affected by the longitudinal coefficient of kinetic friction (f1) and the weight of the vehicle

''U

value of f1 is affected by the characteristics of surface and of the breaking

1fQ ⋅

dry pavement, light breaking: 0,6 – 0,8wet pavement, hard breaking: 0,3 – 0,35icy pavement: 0,1 – 0,15

kinetic friction is now understood not to be caused by surface roughness but by chemical bonding between the surfaces

GRADE RESISTANCE''U

good approximation for angles used in road engineering practice

[ ] [ ] [ ]

100tgsin

eQQQE kNkNkN

e ⋅=⋅≈⋅= αα

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The kinetic energy

of the vehicle is consumed by the breaking force and the grade resistance along the breaking distance

''U

kinetic energygrade resistance

upgrade/downgrade

")100

(0039,0 1

2 Ue

QQfQv ⋅±=⋅

breaking distance

breaking force

BREAKING DISTANCE''U

")100

(0039,0 1

2 Ue

QQfQv ⋅±=⋅

][

100

0039,0"

1

2

me

f

vU

±

=

BREAKING DISTANCE

could be determined in the relation of breaking deceleration

b

vU

UbMMvMs

⋅=

⋅⋅=⋅

=

26"

"6,322

2

2

22

breaking deceleration

fQbg

QbM ⋅==⋅

affected by the coefficient of kinetic friction

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5

][

100

0039,028,0

1

2

me

f

vtvU

±

+⋅⋅=

STOPPING SIGHT

DISTANCE

''' UUU +=

reaction distance breaking distance

The spatial alignment of the

road is designed through its projections separately and together

horizontal alignment

vertical alignment

cross sectional alignment

HORIZONTAL

ALIGNMENT

tangent

curve

transition curve

designed in the layout

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TANGENT

Good sight conditionsbut

aesthetically rigidFavorable in flat areas, thoug hard to fit into the landscape in hilly areas

GOOD SIGHT

CONDITIONS

overtaking and

intersections

OVERTAKING SIGHT

DISTANCE

distance necessary for safe

overtaking manouvre

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OVERTAKING

usually t = 9 s is needed

overtaking vehicle travels vvvvtttt·9999 s s s s distance

… and the opposite vehicle as well!!!

SAFE OVERTAKING

time needed for overtaking

should be increased by 2s

overtaking vehicle travels vvvvtttt·11 s 11 s 11 s 11 s distance

… and the opposite vehicle as well!!!

OVERTAKING SIGHT

DISTANCE

distance between overtaking and

opposite vehicle

tt

e vv

U ⋅=⋅⋅= 66,3

112

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The overtaking sight

distance is six times thedesign speed

te vU ⋅= 6

The TANGENT is

aeshtetically rigid

hard to fit to the landscape

The TANGENT assures

good sight conditions

by night the blinding effect of headlights could be dangerous

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The TANGENT is boring

driver tires and looses

attention, which is dangerous

Tangents are used

ONLY IF the advantages are shown up and the disadvantages are not

too large

The

minimal length of tangents

6·vtlength of overtaking sight distance

advantages to show up, to be able to overtake

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The

maximallength of tangents

20·vt

disadvantages not tobe too large

CURVE

Fits well to the landscape, but the dynamics and sight conditions are affected by the

radius

CURVE

applicability affected by the radius and the clear length of the curve

dynamics

aesthetics

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In curves

an outwardcentrifugal force acts

on the vehicles overrolling

slipping

The minimal

applicable radius is determined by

the design speed

Rmin

one consequence of functional classification on geometrical parameters

By superelevating

the outer edge of the pavement

the dynamics of vehicles

could be improved

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Outward force on a vehicle

on superelvated pavementcentrifugal force

R

vQ

Rg

vQ

R

sMP

1276,3

2

2

22 ⋅=

⋅⋅

⋅=⋅=

járműtömege

speed [m/s]

speed [v/h]

weight of vehicles

radius of curve

Slipping equilibrium

centrifugal force

lateral coefficient of friction

weight of vehicles

αααα sinsincoscos 22 ⋅+⋅⋅+⋅⋅=⋅ QPfQfP

usually 0.1

( ) αααα sintgcos cos127

22

2

⋅⋅++⋅⋅=⋅⋅

PffQR

vQ


The previuosly calculated expression is substituted instead of Pof Pof Pof P

setting out Q·cos(α) from first and third term


Q ·sin(α)Q·cos(α)

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( ) αααα sintgcos cos127

22

2

⋅⋅++⋅⋅=⋅⋅

PffQR

vQ


simplifying by Q and cos(α)


( ) αα tgtg 127

22

2

⋅⋅++= PffR

v

tg(α)



( ) αα tgtg 127

22

2

⋅⋅++= PffR

v

<<1 <<1

their product is in 0.01 order

negligible

negligation is for for for for safetysafetysafetysafety

Applicable minimum radius

[ ]m

100127 2

2

min

+⋅

=q

f

vR

Design speed

Su

pe

rele

vatio

n

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The minimal radius

only in REASONABLE cases could be applied

fi. geometrical restrictionsfi. traffic calmings

strive for dynamical alignment

f coefficient of friction consists of

f1 longitudinal component andf2 lateral component

41

absolute value of vectorialsum is nearly constant

At BRAKING

the value of f1 component increases, the value of f2 component decreases

42

danger of slipping!!!

Do not brake in curves!!!Do not brake in curves!!!Do not brake in curves!!!Do not brake in curves!!!

absolute value of vectorial sum is nearly constant

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CLEAR LENGTH OF CURVE

should be longer than the distance travelled in 3 s

aesthetics – to avoidthe break in theperspective view

dynamics – to avoid thesudden change incurvature

tt

R vv

Í ⋅=⋅= 8,06,3

3min

The CURVES eliminates

the disadvantages of tangents, while achiving

their advantages in case of

appropiate radius

TRANSITION

CURVE

continuous transition between the tangent and the curve

curve drawn by the vehicle at uniform steering and uniform speed

curve is offsetcurve starts sooner

Layout

Curvature

diagram

Layout

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TRANSITION

CURVE

clothoid curve is applied

the break in the change of curvature is not disturbing, because the track is not fixed

linear change of curvature

Curvature

diagram

Layout

CLOTHOID

natural formula

(constant)

;1

1

2pLRlr

R

rL

l

=⋅=⋅

=from similar triangles of curvature diagram

parameter of transition curve

!!!!!!!!!!!!

Curvature

diagram

Layout

48

CLOTHOID

major parameters

could ne determined byTaylor-polinom

20

LX =

R

LR

⋅=∆

24

2

20

RY

∆=

charts or computer

R

L

⋅=

2τ

LX =

RR

LY ∆⋅=

⋅= 4

6

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The minimal length of the

transition curve is determined by

dynamicalaesthetical recognizability

aspects, and the

length of superelevation runoff

DYNAMICAL ASPECT

the change of unbalanced lateral acceleration should be even and

should not exceed the physiological limit

51

Forces acting on vehicle in

transition curve

ααα sincoscos ⋅−⋅=⋅⋅ QPaM

due to superelevation

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52

Forces transformed

ααα sincoscos ⋅−⋅=⋅⋅ QPaM

what balances somepart of lateralacceleration?

100127

2 qQ

R

vQa

g

Q⋅−

⋅

⋅=⋅

M P sin(α)cos(α)

/cos(α)

53

The unbalanced lateral

acceleration 100127

2 qQ

R

vQa

g

Q⋅−

⋅

⋅=⋅

2,1013

1001272

2

q

R

v

qg

R

vga

−⋅

=

=⋅

−⋅

⋅=

Value of unbalanced lateral acceleration:a = 1,5 – 1,8 m/s2: nem észrevehetőa = 2,0 – 2,5 m/s2: normálisa = 3,0 – 3,5 m/s2: észrevehetőa = 4,0 – 5,0 m/s2: eltűrt

Maximal value of temporal

change of lateral acceleration

==

3s

m 4,0

t

ak

physiological considerations motion sickness

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Time needed for the change of

lateral acceleration

k

q

kR

v

k

at

⋅−

⋅⋅==

2,1013

2

2,1013

2 q

R

va −

⋅=

==

3s

m 4,0

t

ak

Minimal length of transition curve

in case of even change of lateral acceleration

k

q

kR

v

k

at

⋅−

⋅⋅==

2,1013

2

k

vq

kR

vL

vtstL

⋅⋅

⋅−

⋅⋅⋅=

⋅=⋅=

2,106,3136,3

6,33

DYNAMICAL ASPECT

dynamically necessary minimal length and parameter of transition curve

k

vq

kR

vL

⋅

⋅−

⋅⋅=

378,46

3

min

minmin LRp ⋅=

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AESTHETICAL ASPECT

the length of the transition curve should be equal to the clear length of curve

favourable but not obligatory

1:1:1:: 21 =LÍHL

RECOGNISABILITY

ASPECT

the transition curve should be so long, that the driver will be able to recognize

RRRLRp

RLR

⋅≈⋅⋅≥⋅=

⋅≥≥

3.01.0

1.0

minmin

not too shortnot too long

before curves of long radius no transition curve is applied

INSERTION OF

SUPERELEVATION RUNOFF

the transition curve should be so long, that the superelevation runoff could be inserted

it will be discussed in the next lecture

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The relation and order of

the elements of the horizonat alignment is

essential from dynamical

and safety considerations

Between two tangents curves

with transition curves are applied

except for the curves of large radius

The curve with transition curves

is symmetrical, if the parameters are equal

The figure and the formulas will be asked in the test

see the project!!!

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If the angle between tangents is

too small, and the clear length of curve can not be inserted, the composed curve consists only of transition curves

τα

γ

⋅=

=

2

azaz ,0

0=γ

τα ⋅= 2

should be avoided!!!

Curves of small angle

could be applied

only if the length of the curve

exceeds 500 m

m 500≥⋅= αarcRIh

to avoid composed curves of transition curves

α < 6º

The geometrical parameters

of the elements of the horizontal alignment are affected by the adjacent elements

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The radii of

adjacent curves should not differ significantly

( )3:1 2:1: 21 ≤RR

Suddenly decreasing radius is dangerous!!!

Radius

Ra

diu

s

The curves connecting without

tangent sections are called compund curves

Between curves of the same direction tangient section should be applied!!!

Only in very exceptional cases could be other soultions applied!!!

Curves of opposite direction

connects by inflection if there are no tangent between them

Start points of transition curves are the same

At this point the tangent cuts the curve

( )

2:

[m] 03.0

21

21

≤

+⋅≤∆

pp

ppl

Small overlap or gap possible

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TWO-CENTERED CURVES

curves of the same direction without transition curve

2:

m 250radius)(smaller

21

2

≤

≥

RR

R

Sudden change of curvatureShould be avoidedcould be applied only with very strict conditions

TWO-CENTERED CURVE

WITH TRANSITION CURVE

Should be avoidedthough more favorable than the two-centered curve

Transition curve between the curves

The goal is to achieve

a continuous, curvilinear road, which molds with the rolling terrain features

Avoid using curves separated by long tangents

Achieve a continuous, curvilinear road

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HORIZONTAL ALIGNMENTThe alignment of tangents,curves nad transition curves based on dynamical, economical and aesthetical

aspects

… to be continued next week

Documents

roads_3_2010