Highway Alignment Principles

BASIC PRINCIPLES OF HIGHWAY ALIGNMENT

Concepts, basic principles

a. Horizontal AlignmentFundamentalsHorizontal curvesSuperelevation

b. Vertical AlignmentFundamentalsCrest Vertical CurvesSag Vertical CurvesExamples

c. Other Stuff - coordination

- The alignment of a highway is a three dimensional problem withmeasurement in x, y, and z dimensionsBASIC PRINCIPLES OF HIGHWAY ALIGNMENT

DESIGNING STANDARDSBASIC PRINCIPLES OF HIGHWAY ALIGNMENT

- safety,- smoothness and- capacity

All of values (curves, superelevation, grades) represent minimum or maximum.

comfort predictability estheticforgiving

Requirements which are involved for highway alignment (generally):

MOST IMPORTANT: LESS IMPORTANT:

FOR DESIGNING WE ARE USING STANDARDS(CZECH CSN, GERMANY HBS, POLAND WPD)

BASIC PRINCIPLES OF HIGHWAY ALIGNMENT

design speed (tool used to determine geometric features ofa new road during road design - most important tool)sight distance (for stopping or overtaking, in curves)axis of the road (position)horizontal curves (radius)transverse slope (cross slope)drainage gradient (resulting slope)superelevation (changing the slope between straight

and curve)location of vertical axis (vertical curves, gradients)lenght of gradient (lenght vs. slope)coordination of horizontal and vertical alignmentothers (depends on used design standard)

BASIC DESING ELEMENTS

DESIGN SPEEDDesign speed is a selected speed used to determine the

various geometric design features of the roadway.USAGE:

The selected design speed should be a logical one with respect to the anticipated operating speed, topography, the adjacent land use, and the

functional classification of the highway.

In selection of design speed, every effort should be made to attain a desired combination of safety, mobility, and efficiency within the

constraints of environmental quality and others (aesthetics).

Once the design speed is selected, all of the highway features should be related to it to obtain a balanced design.

Above-minimum design criteria for specific design elements should be used (on lower speed facilities urban roads, use of above-minimum design criteria may encourage travel at speeds higher than the design

speed).

DESIGN SPEEDSome design features, such as curvature,

superelevation, and sight distance, are directly related to design speed.

Other features, such as widths of lanes and shoulders and clearances to walls and rails, are not directly related

to design speed, but they do affect vehicle speeds. Thus, when a change is made in design speed, many elements of the highway

design will change accordingly.

DESIGN SPEED TYPICAL RANGE

(DEPENDS ON TYPE OF COMMUNICATION,

TERRAIN)

DESIGN SPEED

classification appropriate technical road category Motorways (highways) D 33,5/120, 100 a 80; D 27,5/120, 100 a 80 Motorwyas (expressways)

R 33,5/120, 100 a 80; R 27,5/120, 100 a 80; R 25,5/120, 100 a 80

I.class roads S 24,5/100, 80 a 70; S 20,75/90, 80 a 70 S 11,5/90, 80 a 70 S 9,5/80, 70 a 60*)

II.class roads S 9,5/80, 70 a 60 S 7,5/70, 60 a 50

III.class roads S 7,5/70, 60 a 50; S 6,5/60 a 50 S 4,0/40 a 30**)

*) can not use for international roads (marked E) **) mostly for reconstruction of III. class roads

S 11,5/70: S road, type of communication (D, R highway, motorway)11,5 space among guard rails or marker posts70 - design speed

EXAMPLE CZECH STANDARD (HIGHWAYS, MOTORWAYS AND ROADS)

DESIGN SPEEDEXAMPLE AASHTO

Minimum Design Speeds for Rural Collectors

Rural arterials other than freeways, should be designed for speeds of 60 to 120 km/h [40 to 75 mph] depending on terrain, driver expectancy and, in the

case of reconstruction projects, the alignment of the existing facility.- design speeds of 100 to 120 km/h [60 to 75 mph] are normally used in level

terrain- design speeds of 80 to 100 km/h [50 to 60 mph] are normally used in rolling

terrain,- design speeds of 60 to 80 km/h [40 to 50 mph] are used in mountainous

terrain.

DESIGN SPEEDEXAMPLE UK STANDARD

Design Speeds for Urban RoadsWithin the UK the design speed for an urban highway is chosen on the basis of itsspeed limit. The value chosen will allow a small margin for speeds greater thanthe posted speed limit. For speed limits of 48, 64, 80 and 96km/hr, design speedsof 60B, 70A, 85A and 100A respectively are employed.

The suffixes A and B indicate the higher and lower categories respectivelywithin each speed band.

DESIGN SPEEDChanging the design speed

RULE: In the design of a highway segment, it is desirable to select a uniform design speed (for the as

longest as possible segment of a highway).However, changes in terrain and other physical controls may dictate a change in design speed on certain sections. If so, the introduction of a lower design speed should not be done abruptly but should be effected

over sufficient distance to permit drivers to gradually change speed before reaching the highway section with the lower design speed.

Warning: Where it is appropriate to reduce horizontal and vertical alignment features, many drivers may not perceive the lower speed

condition ahead, and therefore, it is important that they be warned well in advance - the changing condition should be indicated by such

controls as speed-zone and curve-speed signs.

SIGHT DISTANCESight distance is defined as the length of carriageway

that the driver can see in both the horizontal and vertical planes.

Two types of sight distance are detailed:stopping distance and overtaking distance

Stopping sight distance - is defined as the minimum sight distance required bythe driver in order to be able to stop the car before it hits an object on thehighway. It is of primary importance to the safe working of a highway.

Overtaking sight distance - is of central importance to the efficient working of agiven section of highway. Overtaking sight distance only applies to singlecarriageways. Full overtaking sight distances are much larger in value thanstopping sight distances. Therefore, economic realities dictate that they can onlybe complied with in relatively flat terrain where alignments, both vertical andhorizontal, allow the design of a relatively straight and level highway.

SIGHT DISTANCEStopping Sight Distance (SSD)

The distance itself can be subdivided into three constituent parts:The perception and reaction distance (l1) length of highway travelled whiledriver perceives hazard + length travelled during the period of time taken by thedriver to apply the brakes and for the brakes to functionThe braking distance (l2) length of highway travelled while the vehicle actuallycomes to a halt.The safety distance (bv) distance between stopped vehicle and obstruction (CZstandard)Reaction time:Czech 1,5 sUK 2 sUS 2,5 s

Notice:- depends on design /standard speed and longitudinal slope- must be ensure on all roadways


The perception and reaction distance (l1) calculation:

6,3)(snr vt where: vn design speed [km/h],

tr reaction time

The braking distance (l2) calculation:

sfgv

vn

sn

01,06,32 22

)(

where: vn design speed [km/h], gn normal gravitational acc. 9,81 m/s2, fv breaking force coefficient (coefficient of

friction for wet pavement)s longitudinal slope [%].

The safety distance (bv) calculation: Equal to the rounded result to the nearest higher 10 m if vn(s) 80 km/h andnearest higher 5 m if vn(s) < 80 km/h.This safety distance is calculated in czech standard.


CZECH STANDARD


AASHTO - US

Stopping Sight Distance on Level Roadways Stopping Sight Distance on Grades


UK

Stopping sight distances for different design speeds according to UK standard

SIGHT DISTANCEOvertaking / Passing Sight Distance (OSD / PSD)

Full overtaking sight distance is made up of three components: lp, bv2 and l4:lp - distance travelled within the passing manoeuvre (Overtaking Time) made upfrom decision lenght l1, overtaking distance (measured separately) l2 and distancetravelled within returning to origin lane l3bv2 - distance between the overtaking and opposing vehicles at the point in timeat which the overtaking vehicle returns to its designated lane (Safety Time)l4 - distance travelled by the opposing vehicle within the overtaking time (ClosingTime). - have to be ensure only on two lane

roads- have to be ensure on as longest as possible part of communication- depends on design/standard speed


Full overtaking sight distance calculation:

2)(

2)( 32112,1

vsnsn

P bvvv

D

where: vn design speed [km/h], v speed difference between overtaking and overtaken

car [km/h]; value is between 15 24 km/h.

bv2 equal to the rounded result to the nearest higher 50 m


CZECH STANDARD

UK STANDARD

There is no full overtaking sight distance (OSD) for a highway with a design speed of 100 (CZ) /120 (UK) km/hr since this design speed is not suitable for a

single carriageway road (undivided roads).single carriageway road

double carriageway road


CZECH STANDARD Passing Sight Distance for Design of Two-Lane Highways

AASHTO - US

SIGHT DISTANCEComparison of Design Values for Passing Sight

Distance and Stopping Sight Distance

AXIS OF THE ROAD, HORIZONTAL CURVESTWO BASIC ELEMENTS: TANGENTS AND CURVES

Tangents (straights) Curves

AXIS OF THE ROAD, HORIZONTAL CURVESHORIZONTAL TANGENT POLYGON

CONSISTS OF: - STRAIGHTS- CURVES

Two basic principles should be respected:a) Lengths of sides of the tangent polygon

should be balanced (no short sides followed by long sides)

b) Central angles should be in proportionto the lengths of the polygon sides

DUMB DESIGN

AXIS OF THE ROAD, HORIZONTAL CURVESSTRAIGHTS

Straight - the shortest connection of two points.BUT NOT THE BEST SOLUTION EVERY TIME

WHY: - Driving on straight roads is very boring - the driver doesnt pay so much attention to the situation on a road, increases speed of a vehicle and his driving can be dangerous.

- Drivers are dazzled by cars going in the opposite direction at night.- In the spring and autumn mostly at early and late time of the day drivers could be

sun glared- There is not many straights in the nature

IF IT IS NECESSARY :MAXIMAL LENGHT OF STRAIGHTSHOULD BE BETWEEN 3 5 km

(but the lenght is not limited in Czech standards)

AXIS OF THE ROAD, HORIZONTAL CURVESCURVES

a) Plain circular arcsb) Circular arcs with transition curves c) Transition curves clothoidsd) Compound curves

A horizontal curve - is an arc connecting two straight parts (tangents) of the highway.

- The highway engineer must design a horizontal alignment toaccommodate (suit to) a variety of vehicles corneringcapabilities that range from mini - cars (via Mr.Beansminicooper) to long trucks

TYPES OF CURVES:

AXIS OF THE ROAD, HORIZONTAL CURVESStraight

Curve

Tangent to Circular Curve

Tangent to Spiral Curve toCircular Curve


DERIVING THE MINIMUM RADIUSThe values for horizontal curvature are derived from the design speed, superelevation rate,

and side friction factors.Figure illustrates:- the forces acting on a vehicle of weight G as it is

driven in arc of radius R.- the angle of incline of the road (superelevation)

is termed as .- p denotes the side frictional force between the

vehicle and the highway (p=tg )- Fo is the centrifugal force acting horizontally on the

vehicle and equals:

where G/g is the mass of the vehicle, Rv .

gG= F

2

o

As all the forces should be equilibrium, they can be resolved along the angle of inclination of the road:

(Centrifugal force resolved parallel to highway) denoted as Fb= (Weight of vehicle resolved parallel to highway) + (Side friction factor) as Tb


DERIVING THE MINIMUM RADIUSAs all the forces in should be in equilibrium, they can be resolved along the angle of

inclination of the road:(Centrifugal force resolved parallel to highway) denoted as Fb

(Weight of vehicle resolved parallel to highway) + (Side friction factor) as TbFb Tb ,

,sin.F cos .G f sin .G cos . ob oFwhere: - fb is side friction factor

. )sin . Rv .

gG + cos.G( f sin . G cos .

Rv .

gG 2

b

2

than:

.p fg p . f -1 Rv

bb

2

and after resolving:


The basic equation is:

, p fg v Rb

2

min

Where: Rmin - minimum radius of curve (m)p - superelevation ratef - side friction factorV - vehicle speed (m/s)

DERIVING THE MINIMUM RADIUS:

, p

V0,3 R2

nmin

or:

Where: Rmin - minimum radius of curve (m)p - superelevation rate (in %)V - vehicle speed (km/h)

Notice: f is out it is small value

AXIS OF THE ROAD, HORIZONTAL CURVESCURVES - TYPES

PLAIN CIRCULAR CURVESA simple curve has a constant circular radius which achieves the desired deflectionwithout using an entering or exiting transition. This is the most frequently used curvebecause of their simplicity for design, layout, and construction as shown.Plain circular arc in highway design can be used only if the offset of the circle in theclothoid R 0,25.This condition means that the minimal radius of the plain circle arc must be R 800m or at least R 0,375 2nV NOTICE:

For small radii and low design speed (prevailing design conditions for local communications) you can use only circular curves without restrictions

above.

AXIS OF THE ROAD, HORIZONTAL CURVESCURVES - TYPESTRANSITION CURVES

These curve types are mainly used to connectcurved and straight sections of highway. (theycan also be used to ease the change betweentwo circular curves where the difference inradius is large).The radius of curvature of a transition curvegradually decreases from infinity at the intersectionof the tangent and the transition curve to thedesignated radius R at the intersection of thetransition curve with the circular curve so theclothoid is a curve which radius of theosculating circular decreases withlength of a curve WHY IT ISUSING ???


It is difficult for drivers to travel imediately from a tangent section (straight) to acircular arc, because of:

CURVATORY OF TANGENT SECTION IS 0, while CURVATORY OF CIRCULAR ARC IS CONSTANT

Than the connecting between tangent and arc is not continuous andcould disturb drivers

WHY IT IS USING???

Use of transition curves provides for a number of benefits:- Provides an easy path for drivers to follow: centrifugal and centripetal forces are

increased gradually- Provides a desirable arrangement for superelevation runoff- Provides a desirable arrangement for pavement widening on curves- Enhances highway appearance (travel looks better)


Figure illustrates the situation where transition curves are introduced between the tangents and a circular curve of radius R. Here, the circular curve must be shifted inwards from its initial position

by the value S (R) so that the curves can meet tangentially. This is the same as having a circular curve of radius (R + S) joining the tangents replaced by a

circular curve (radius R) and two transition curves. The tangent points are, however, not the same. In the case of the circular curve of radius (R + S), the tangent occurs at B, while for the

circular/transition curves, it occurs at T .


WHY IT IS USING???

NO TRANSITION WITH TRANSITIONesthetics


OFFTRACKING, WIDENING IN CURVEOfftracking is the characteristic, common to all vehicles, typically to the

larger design vehicles, in which the rear wheels do not follow precisely the same path as the front wheels when the vehicle negotiates a horizontal

curve or makes a turn.In that cases it is necessary to widenthe pavement on sharp curves toaccommodate off-tracking of largervehicles.Widening of the carriageway is doneonly if the radius of the circular is lowerthan 250 m.


OFFTRACKING, WIDENING IN CURVE

Where curves are introduced with clothoid transitions, the widening occurs overthe length of the clothoid. On alignments without spirals, the widening isdeveloped over the same distance that the superelevation transition occurs. Thecenterline pavement marking and the center joint (if applicable) should be placedequidistant from the pavement edges.

The widened portion of the pavement is normally placed on both sides of the curve (according to czech standard).

TRANSVERSE SLOPE (CROSS SLOPE)

1. Gutter; 2. Shoulder; 3. Sub-base; 4. Base course; 5. AsphaltCross slope or camber is a geometric feature of pavement surfaces:

it is the transverse slope with respect to the horizon.

It is a very important safety factor:Cross slope is designed to provide a drainage gradientso that water will run off the surface to a drainage systemsuch as a street gutter or ditch.

Inadequate cross slope will contribute to aquaplaning!!!

TRANSVERSE SLOPE (CROSS SLOPE)

In horizontal curves, the cross slope isbanked into superelevation to reducesteering effort and lateral force required togo around the curve.

On straight sections of normal two-lane roads, the pavement cross section is usually highest in the center and drains to both sides.

TRANSVERSE SLOPE (CROSS SLOPE)VALUES

According to Czech standards:Basic cross slope in straight is 2,5 % (2% extraordinary) for high-type pavements.

For low-type pavements in straight 3 % (and more for i.g. gravel).

High-type pavements are those that retain smooth riding qualities and good non-skid properties in all weather under heavy traffic volumes and loadings with littlemaintenance required.

Low-type pavements are those with treated earth surfaces and those with looseaggregate surfaces.

According to AASHTO:Normally, cross slopes range from 1,5 to 2 % for high-type pavements.

A cross slope of 3 to 7 % is desirable for low-type pavements.

DREINAGE GRADIENTFLOW FIRECTION

Drainage gradient (M) is a term in road design, defined as the

combined slope due to road surface cross slope (P) and longitudinal

slope (S).(drainage gradient resulting slope in close czech

translation)

Most road design manuals require drainage gradient to

exceed 0,5% (minimal value), in order to drain water and prevent

excessive skid accidents.

Rural roads

Urban roads

DREINAGE GRADIENTEffect of insufficient gradient

Due to the normal cross slope and the interaction with grade, road sections with insufficient drainage gradient are few and short (still, they account for an

unacceptable number of skid accidents).

These hot spots are found at the entrances and exits of banked curves, where the cross slope changes direction in order to create superelevation. As the outside edge of the

curve is raised (or superelevated) to create the bank, it passes through a point where the cross slope is absolutely

flat. If there is not enough longitudinal grade, water will collect at these spots.

Problem segments may be found at the summits (or sags) of vertical curves,

where the longitudinal slope is close to or at zero value.

DREINAGE GRADIENTMinimizing insufficient drainage gradient

Roads should be designed so that sections where the cross slope change direction (and sign), are located where the road is going uphill or downhill. Otherwise the pavement will get an area with too little drainage gradient (<

0,5%), resulting in unacceptable skid accident risk.

When designing road curves in a flat landscape, it may be necessary to design long wave undulations on purpose. These "synthetic" longitudinal

gradients can then be used to reach a sufficient drainage gradient, in sections where the cross slope is close to zero.

Another option to minimize crash risk due to low drainage gradient at entrance or exit of banked outercurves, is to move the superelevation

further from the curve and out to a straight road section. This results in a banked straight lane.

Other option is to within the superelevation transition section increase the cross slope "tilt rate" within the zone where the cross slope is between

- 0,5 % to + 0,5%.

SUPERELEVATIONsuperelevation = roadway banking

It is normal practice for horizontal curves to be superelevated. This allows a component of the vehicle weight to provide some of the centripetal force

that is needed for the vehicle to move in a circular path.All the forces should be in equilibrium :

(Centrifugal force resolved parallel to highway) denoted as Fb (Weight of vehicle resolved parallel to highway) + (Side friction factor) as Tb

Fb Tb , ,sin.F cos .G f sin .G cos . ob oF

, p fg v Rb

2

min Where: Rmin - minimum radius of curve (m)

p - superelevation ratef - side friction factorV - vehicle speed (m/s)

than:

SUPERELEVATION

Selection of p (superelavationrate) and fb (side friction factor)Practical limits affecting superelevation (p):

- Climate- Constructability- Adjacent land use

Side friction factor (fb) variations (changes):- Vehicle speed- Pavement texture- Tire condition

SUPERELEVATION

Superelevation rates pCzech stadndard recommends the use of superelevation rates between 2,5 and 7 . Maximum ratesacross other world standards varies from region to region. Values of superelevation rates are affected by aclimate, terrain, development density or frequency of slow moving vehicles.

EXAMPLE:USA restrictions

(COMPARE WITH CZECH STANDARDS)

SUPERELEVATIONSide friction factor fb

Design values of the side friction factor (also coefficient of side friction) vary with design speed.Design values represent wet pavements and tires in reasonable but not top condition. Values alsorepresent frictional forces that can be comfortably achieved. They do not represent the maximum sidefriction that is achieved the instant before skidding.

EXAMPLE:AUSTRALIA

SUPERELEVATIONSide friction factor fb

EXAMPLE:AASHTO

SUPERELEVATIONSuperelevation rates using minimal p

However, there are situations where the application of superelevation can cause pavement drainage problems. In some situations when the grade is nearly flat, water will not run off the

road properly at places where the crossfall is also nearly flat (0%).

It is normal practice to superelevate all curves to a value that is at least equal to the normal crossfall on straights (this is normally 2,5% in order to ensure adequate surface

drainage).

Problems with drainage of the pavement surface may be overcome by modifying thecombination of the grading, the superelevation and the application of the superelevation:

If the horizontal curve radius is large enough, there may be scope to leave the curve unsuperelevated (called adverse superelevation).

design/ standard

speed in km/h

30 40 50 60 70 80 90 100 110 120 130

MinimalRadiii with

basic transverse slope 2,5%

(2%)

250 450 700 950 1300 1700 2200 2700 3200 3800 4500

SUPERELEVATIONMinimum Length of Superelevation on Horizontal Curves

The superelevation ramp is mainly designed in the length of the clothoid

a . p-p

12

sL Or the lenght is given by:

Where: s slope of superelvation rampa - distance between edge of pavement and the axis of superelevation

in mp1 crossfall of pavement at the beginning of superelevationp2 crossfall of pavement at the end of superelevation

design speedin km/h

max s (%) min s (%)a 4,25 m a 4,25 m a 4,25 a 4,25 m

50 1,2 1,4

0,1 a0,07 a

( max s)60 a 70 1,0 1,2

80 a 90 0,7 0,85

100 a 120 0,6 0,7

tab. Max. and min. slope of a superelevation ramp (s)

s

SUPERELEVATIONAchieving superelevation

Superelevation development length could be defined as the length required to rotate the pavement from the point of normal crossfall to the point where the full

superelevation for the curve is achieved.This superelevation development length has two components:1. Tangent run - out

This is the length from the point of normal crossfall to the point of zero crossfall.2. Superelevation runoff length

This is the length from the point where the pavement has been rotated tozero crossfall to the point where the full curve superelevation has beenachieved.

Inside edge

outside edg

eNormal crown Relative gradientTangent Run-ou

t Runoff

Supperelevation runoff

4%

0%

8%

SUPERELEVATIONAchieving superelevation - methods

1) Rotate pavement about centerline (b, d, g, h)2) Rotate about inner edge of pavement (the outer edge of the inner horizontal

marking) (a, c, h)3) Rotate about outside edge of pavement (for dividing roadways e, g, f)


Cross section (-1-) is the normal crown sectionwhere the transitioning begins (with basictransversal slope 2,5 %)Cross section (-2-) is reached by rotating half thepavement until it is level.Cross section (-3-) is attained by continuing torotate the same half of pavement until a planesection is attained across the entire pavementsection, at a cross slope equal to the normal crownslope.Cross section (-4-) is achieved by further rotation ofthe planar section, the entire pavement section, toattain the full superelevation at a cross slope.

0

0z

h + 2h

L . h . 2= L

Rotate pavement about centerline

100p . s= h

200p . s= h 00


Cross section (-1-) is the normal crown sectionwhere the transitioning begins (with basictransversal slope 2,5 %)Cross section (-2-) is reached by rotating half thepavement until it is level.Cross section (-3-) is achievedeby continuing torotate the same half of pavement until a planesection is attained across the entire pavementsection, at a cross slope equal to the normal crownslope.Cross section (-4-) is achieved by further rotation(but by the inner edge) of the pavement to the fullvalue of superelevation.

100p . s= h

TANGENT RUN OUT IS THE SAME FOR BOTH METHODS

Rotate pavement inner edge of the pavement

200p . s= h 00

SUPERELEVATIONSome important factors have to be consider when

designing horizontal alignment:- Horizontal alignment should be as smooth and as direct as possible

while responsive to the topography. Flatter curvature with shorter tangents is generally preferable to sharp curves connected by long tangents. Angle points should be avoided.

- Maximum length of straights is not limited, but recommended length of straights is between 3 5 km. Also recommended is to have no straights if it is possible.

- Broken back curvature (a short tangent between two curves in same direction) should be avoided because drivers do not expect to encounter this arrangement on typical highway geometry.

- If compound circular curves are required in an effort to fit the highway to the terrain or to other constraints, large differences in radius should be avoided. The radius of the largest curve should not be more that 1.5 times the radius of the smaller curve (except for highway ramps). On ramps, the ratio of the larger curve to the smaller curve should not exceed 2:1.

SUPERELEVATIONSome important factors have to be consider when

designing horizontal alignment:- Horizontal curves should be avoided on bridges whenever possible. These

cause design, construction, and operational problems. Where a curve is necessary on a bridge, a simple curve should be used on the bridge and any curvature or superelevation transitions placed on the approaching roadway.

- Plain circular arc can be used if the displacement (shift) of the circular in the clothoid R0,25m. The minimal radius of the plain circular arc must be R 800 m or at least R 0,375 m.

- Broken back curves should be avoided because they are unsightly and drivers do not expect succeeding curves to be in the same direction. If it is necessary there must be insert straight of minimal length above 2 vn (design speed).

- If possible, the minimum distance between reverse plain circular arc should be at least 2 x vn (design speed). When it isn't possible to obtain the desired distance between reverse curves, than the transition curves may be placed there.

- Transition curves should be design as clothoids with parameter (A):

notice: using of other curves is also allowed

Ro A 3

Ro

VERTICAL ALIGNMENTVERTICAL TANGENT POLYGON

CONSISTS OF: - STRAIGHTS- CURVES

The design of the vertical alignment is started after completing of the horizontal alignment:The design of vertical alignment consists of: 1.Drawing of terrain into the longitudinal section 2.Design of the vertical alignment by using vertical polygon (according to the same principles as at the horizontal alignment see dumb design) 3.Rounding polygon sides by vertical parabolic curves

VERTICAL ALIGNMENTVERTICAL TANGENT POLYGON

Vertical alignment terminology:si slope in percentVi point of intersection of the two adjacent grade lines

V1 SAG, V2 - SUMMITli length of segment with same grade (projection onto horizontal surface

corresponds to plan distance)Hi elevation of each point of intersection and start and end pointshi elevation difference betwee start and end point of the segment with same

grade

shli

i

i 100

VERTICAL ALIGNMENTVERTICAL CURVES

A vertical curve - is an arc which provides a gradual change between two adjacent grade lines

CURVE IS PARABOLIC ONLY !!! 21 s -s 200

R T

R 2t= y

2

n

100s R= x 1 1 100

s R= x 2 2

R 2x= y

2

x

VERTICAL ALIGNMENTSome important factors have to be consider when

designing vertical alignment:- Longitudinal slope is mainly leading by type of terrain and

design speed.- Minimum value of longitudinal slope is about 0,5 %

(exceptionally 0,3 %)- Lengths of sides of the tangent polygon should be

balanced. The lengths should correspond to the lengths of vertical curves tangents.

- Avoid vertical straight between two curves in the same direction.

- Polygon sides breaks must be round by vertical parabolic (second degree) curves.

- Parabolic curves have to agree with length of sight distance (minimal value of vertical curve radius is derived from minimal sight distance).

Balance curvature and grades- Use of steep grades to achieve long tangent and flat curves, or

excessive curvature to achieve flat grades, are both poor designs.

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT

Balance curvature and grades- Vertical curvature superimposed

(like cascades) on horizontalcurvature generally results in amore pleasing facility. Successivechanges in profile not incombination with horizontalcurvature may result in a seriesof dips not visible to the driver.


Curvature in the horizontal plane should be accompanied bycomparable length of curvature in the vertical plane.

(horizontal curvature should lead vertical curvature a bit)


Curvature in the horizontal plane should be accompanied bycomparable length of curvature in the vertical plane.


- If a vertical crest curve overlaps either the beginning or the end of ahorizontal curve, drivers have little time to react to the horizontalcurve once it comes into view. This condition can be unsafe,especially at night, if the driver does not recognize the beginning orending of the horizontal curve. Safety is improved if the horizontalcurve leads the vertical curve, that is, the horizontal curve is madelonger than the vertical curve in both directions.

No vertical curve overlapping beginning or end of the horizontal curve


Unexpected combinations of curves and tangents in both thehorizontal and vertical planes should be avoided

- i.e., "broken back" curves in vertical or horizontal alignment


Horizontal curvature should lead vertical curvature - i.e., the horizontal curve should be longer than the vertical curve and the

ZZ/KZ and TK/KT (or TP with transitions) should not be at the same point.

Horizontal alignment

Vertical alignment


rounding by the concave parabolic curve is covered with horizontal arc

rounding starts ahead the horizontal arc

DESIGN PRINCIPLES FOR COORDINATION VERTICAL AND HORIZONTAL ALIGNMENT

Ideally the vertices of horizontal curves (KK) and vertical curves(VZ) should coincide (same position) or be within 1/4 phase of

each other.

Horizontal alignment

Vertical alignment


The alignment designs should enhance attractive scenic views ofthe natural and manmade environment, such as rivers, rockformations, parks, and outstanding man-made structures.


Fitting the Road to the Terrain


the driver can see before the peak of the parabolic curve towhich side the road turns.

clothoid is not used with clothoid


In the next two pictures it can be seen the influence of the radius of concave curve in the horizontal straight on the optical deformation.

If the radius is small, the road seems to be like broken.


Similarly as in the horizontal alignment the sequence of vertical curves with a shortinterstraight causes deformation - it can be seen on old roads where the interstraight is designed for a bridge.

Sequence of convex and concave curves with small radius in a horizontal straight is also not a good solution lost road.

Direct connection of convex and concave curves (inflex point) also does not look well.


small radius of vertical curvesThis sequence is sometimes called flying road for its big visual deformation.

Twice lost road



OTHER MISTAKES

EFFECTS OF ROAD CATEGORY, ALIGNMENT AND GRADIENT

ON CAPACITY

EFFECTS OF ROAD CATEGORY

The primary parameter for determining the capacity of a roadway is the number of travel lanes.

NUMBER OF LANES

COMPARE THE CAPACITY

EFFECTS OF ROAD CATEGORY

The ideal width for a roadway is about 3,5 m (3,25 3,75 m).

Narrower lane width = decreasing capacity

Wider lane width = increasing capacity

LANE WIDTH

Narrower lanes are acceptable only on low volume and low speeds.Below a lane width of about 2,5 m capacity deteriorates rapidly.

EFFECTS OF ROAD CATEGORYShoulders portion of the roadway contiguous with the traveled way that

accommodates stopped vehicles, emergency use and lateralsupport of sub base, base and surface courses.

Provides a refuge for temporarily stopped vehicles, increasing sight distance on horizontal curves, improving capacity and operations, space for snow removal and storage, more space for signs or guardrails, improved drainage on a traveled way

Normal shoulders width is 0,5 m (unpaved) 1,5 m (paved) - see lecture 1

Shoulders on the roadway= more comfortable operations (sight distances) = increasing capacity

SHOULDER WIDTH

A tightly and close curving alignment in rural areas can cause a reduction in free-flow speeds* and decreasing ofcapacity.

*Free-flow speed:(1) The theoretical speed of traffic, when density is zero, that is, when no vehicles are present;(2) the average speed of vehicles over an urban street segment without signalized intersections, under

conditions of low volume; (3) the average speed of passenger cars over a basic freeway or multilane highway segment under

conditions of low volume.

EFFECTS OF ALIGNMENTCURVES

LOWER SPEED = LOWER CAPACITY HIGHER SPEED = HIGHER CAPACITY

Tight and close curves causes poor sight lines and forward visibility. This delimits overtaking of slow moving vehiclesand reduces overall capacity.

EFFECTS OF ALIGNMENTCURVES

NO OVERTAKING OF SLOW MOVING VEHICLES = LOWER CAPACITY

OVERTAKING IS ALLOWED = HIGHER CAPACITY

Heavy vehicle speed heavily deteriorates on a combination of gradient and length of gradient.

EFFECTS OF GRADIENTSLOPES (GRADIENTS)

LENGTH OF GRADIENT

S

P

E

E

D

EXAMPLE:Original speed 80 kphLength of gradient 1500 mGradient 6

35 kph

Additional climbing lanes (for heavy trucks low speed vehicles) are designed on long steep gradients

EFFECTS OF GRADIENTSLOPES (GRADIENTS)

Normal traffic lanes

Documents

Highway Alignment Principles