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Alberta InfrastructureHIGHWAY GEOMETRIC DESIGN GUIDE AUGUST 1999

BASIC DESIGN PRINCIPLES B-1

CHAPTER B

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Section SubjectPage

Number Page Date

B.1 INTRODUCTION ..................................................................................................... B-5 August 1999B.2 SIGHT DISTANCE ................................................................................................... B-5 August 1999

B.2.1 General Considerations ............................................................................... B-5 August 1999B.2.2 Criteria for Measuring Sight Distance ....................................................... B-6 August 1999B.2.3 Stopping Sight Distance............................................................................... B-6 August 1999B.2.4 Passing Sight Distance ................................................................................. B-8 April 1995B.2.5 Non-Striping Sight Distance ....................................................................... B-11 April 1995B.2.6 Decision Sight Distance ............................................................................... B-12 April 1995

B.3 HORIZONTAL ALIGNMENT................................................................................ B-13 April 1995B.3.1 Introduction .................................................................................................. B-13 April 1995B.3.2 General Controls........................................................................................... B-13 April 1995B.3.3 Maximum Safe Side Friction Factors ......................................................... B-27 April 1995B.3.4 Maximum Superelevation........................................................................... B-27 April 1995B.3.5 Minimum Radius.......................................................................................... B-27 April 1995B.3.6 Rates of Superelevation for Design ............................................................ B-28 April 1995

B.3.6.1 Speed to be Used for Superelevation....................................... B-28 April 1995B.3.6.2 Superelevation Rates.................................................................. B-28 April 1995

B.3.7 Development of Superelevation ................................................................. B-35 April 1995B.3.8 Spiral Curves................................................................................................. B-39 April 1995

B.3.8.1 Form and Properties................................................................... B-39 April 1995B.3.8.2 Basis of Design ............................................................................ B-39 April 1995

B.3.8.2.1 Comfort .................................................................. B-41 April 1995B.3.8.2.2 Superelevation Runoff.......................................... B-41 April 1995B.3.8.2.3 Aesthetics ............................................................... B-42 April 1995

B.3.8.3 Design Values for Spiral Parameters........................................ B-42 April 1995B.3.9 Passing Sight Distance and Stopping Sight Distance on Horizontal

Curves............................................................................................................ B-42 April 1995B.4 VERTICAL ALIGNMENT....................................................................................... B-45 April 1995

B.4.1 General Controls for Vertical Alignment .................................................. B-45 April 1995B.4.2 Maximum Gradient...................................................................................... B-46 April 1995

B.4.2.1 Vehicle Operating Characteristics on Grades........................ B-46 April 1995B.4.3 Minimum Gradient ...................................................................................... B-47 April 1995

B.4.3.1 Rural Highways ........................................................................ B-47 April 1995B.4.3.2 Curbed Roadways .................................................................... B-47 April 1995

B.4.4 Vertical Curves ............................................................................................. B-48 April 1995B.4.4.1 K Parameter ............................................................................... B-48 April 1995B.4.4.2 Crest Vertical Curves................................................................ B-48 April 1995B.4.4.3 Sag Vertical Curves................................................................... B-53 April 1995

B.5 CLIMBING AND PASSING LANES..................................................................... B-55 April 1995B.5.1 Introduction .................................................................................................. B-55 April 1995

Table of Contents Continued...

Alberta InfrastructureJUNE 1996 HIGHWAY GEOMETRIC DESIGN GUIDE

B-2 ALIGNMENT ELEMENTS

Table of contents continued.....

Chapter Section SubjectPage

Number Page Date

B.5.2 Geometric Features of Climbing and Passing Lanes................................. B-55 April 1995

B.5.2.1 Lane Width.................................................................................. B-55 April 1995B.5.2.2 Shoulder Width ........................................................................ B-55 April 1995B.5.2.3 Superelevation............................................................................ B-55 April 1995B.5.2.4 Tapers .......................................................................................... B-55 April 1995B.5.2.5 Proximity to Intersections ......................................................... B-55 April 1995B.5.2.6 Start and End Points and Length ............................................. B-55 April 1995B.5.2.7 Sight Distance at Start and End Points .................................... B-56 April 1995

B.5.3 Climbing Lanes .............................................................................................. B-59 April 1995B.5.3.1 Climbing Lane Warrant for Two-Lane Undivided

Highways .................................................................................... B-61 April 1995B.5.3.2 Climbing Lane Warrant for Four-Lane Divided

Highways .................................................................................... B-68 April 1995B.5.3.3 Determining Length and Location of Climbing Lanes.......... B-68 April 1995

B.5.4 Passing Lanes ................................................................................................. B-80 April 1995B.5.4.1 Passing Lane Warrant................................................................ B-80 April 1995B.5.4.2 Considerations for Location and Spacing of Passing

Lanes............................................................................................ B-83 April 1995B.6 TYPICAL HIGHWAY TRANSITIONS................................................................... B-84 April 1995

B.6.1 Introduction.................................................................................................... B-84 April 1995B.6.2 Construction Practices at Typical Highway Transitions .......................... B-84 April 1995

B.7 TEMPORARY HIGHWAY DETOUR .................................................................... B-89 August 1999B.7.1 Introduction.................................................................................................... B-89 August 1999B.7.2 Guidelines for Surfacing of Detour ............................................................. B-89 August 1999

B.7.2.1 Design Speed of Detour ............................................................ B-90 June 1996B.7.2.2 Horizontal Alignment Guidelines ........................................... B-90 June 1996

Alberta InfrastructureHIGHWAY GEOMETRIC DESIGN GUIDE JUNE 1996

ALIGNMENT ELEMENTS B-3

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Figure DescriptionPage

Number

B-2.4 Elements of and Total Passing Sight Distance - Two-Lane Highways .............................................. B-10B-3.2a Illustration of Design Form...................................................................................................................... B-15toB-3.2l Illustration of Design Form...................................................................................................................... B-26B-3.6 Methods of Distributing Superelevation and Side Friction................................................................. B-34B-3.7a Superelevation Transition (Case I) ......................................................................................................... B-36B-3.7b Superelevation Transition (Case II) ........................................................................................................ B-37B-3.7c Superelevation Transition (Case III)....................................................................................................... B-38B-3.8.2 Minimum Spiral Parameter Considerations.......................................................................................... B-40B-3.9a Lateral Clearances on Horizontal Curves for Passing Sight Distances.............................................. B-43B-3.9b Lateral Clearances on Horizontal Curves for Stopping Sight Distance ............................................. B-44B-4.4.2a Minimum Stopping Sight Distance on Crest Vertical Curves............................................................. B-50B-4.4.2b Passing Sight Distance.............................................................................................................................. B-51B-4.4.2c Minimum Non-Striping Sight Distance on Crest Vertical Curves ..................................................... B-52B-4.4.3 Minimum Stopping Sight Distance on Sag Vertical Curves................................................................ B-54B-5.2 Climbing/Passing April 1995 Lanes for Various Pavement Widths.................................................. B-57B-5.2.7 Typical Signing for Passing and Climbing Lanes and Decision Sight

Distance Requirement at Merge Taper................................................................................................... B-58B-5.3 Collision Involvement Rate of Trucks for Which Running Speeds are

Reduced Below Average Running Speeds of all Traffic ...................................................................... B-60B-5.3.3a Climbing Lane Design Example.............................................................................................................. B-69B-5.3.3b Performance Curves for Heavy Trucks 180 g/w. (Deceleration) ....................................................... B-70B-5.3.3c Performance Curves for Heavy Trucks 180 g/w. (Acceleration) ....................................................... B-71B-5.3.3d Performance Curves for Heavy Trucks 200 g/w. (Deceleration) ....................................................... B-72B-5.3.3e Performance Curves for Heavy Trucks 200 g/w. (Acceleration) ....................................................... B-73B-5.3.3f Performance Curves for Heavy Trucks 150 g/w. (Deceleration) ....................................................... B-74B-5.3.3g Performance Curves for Heavy Trucks 150 g/w. (Acceleration) ....................................................... B-75B-5.3.3h Performance Curves for Heavy Trucks 120 g/w. (Deceleration) ....................................................... B-76B-5.3.3i Performance Curves for Heavy Trucks 120 g/w. (Acceleration) ....................................................... B-77B-5.3.3j Performance Curves for Heavy Trucks 60 g/w. (Deceleration) ......................................................... B-78B-5.3.3k Performance Curves for Heavy Trucks 60 g/w. (Acceleration) ......................................................... B-79B-6.1a Typical Highway Transitions (Two-Lane Undivided, Four-Lane Divided) 38m Centreline

to Centreline Spacing................................................................................................................................ B-85B-6.1b Typical Highway Transitions (Two-Lane Undivided, Four-Lane Divided) 30m Centreline

to Centreline Spacing................................................................................................................................ B-87B-7.2.2a Typical Cross-Section for Detours ......................................................................................................... B-93B-7.2.2b Typical Plan View of Bridge Detour (3 Curves) 60 Km/h Design Speed.......................................... B-94B-7.2.2c Typical Plan View of Bridge Detour (4 Curves) 60 Km/h Design Speed.......................................... B-95



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Table DescriptionPage

Number

B.2.3 Minimum Stopping Sight Distance (SSD).............................................................................................. B-7B.2.4 Minimum Passing Sight Distance ........................................................................................................... B-10B.2.6 Calculation of Decision Sight Distance for Design ............................................................................... B-13B.3.3 Maximum Safe Side Friction Factors ...................................................................................................... B-27B.3.6a Values for Superelevation and Spiral Parameters Related to Design

Speeds and Circular Curve Radii. (e max = 0.06 m/m) ....................................................................... B-29B.3.6b Values for Superelevation and Spiral Parameters Related to Design Speeds

and Circular Curve Radii (e max = 0.08 m/m)...................................................................................... B-31B.3.7 Length Required for Superelevation Runoff on Simple Curves ......................................................... B-35B.3.8.2.2 Maximum Relative Slope Between Outer Edge of Pavement and Centreline

for Two-Lane Roadway............................................................................................................................ B-41B.4.3 Minimum Gradient ................................................................................................................................... B-47B.4.4 Minimum Vertical Curve Criteria........................................................................................................... B-49B.5.3.1a Critical Length of Grade in Metres for a Speed Reduction of 15 km/h............................................. B-61B.5.3.1b Volume Warrants for Truck Climbing Lanes on Two-Lane Highways - Passing

Opportunity = 100%.................................................................................................................................. B-64B.5.3.1c Volume Warrants for Truck Climbing Lanes on Two-Lane Highways - Passing

Opportunity = 70%.................................................................................................................................... B-65B.5.3.1d Volume Warrants for Truck Climbing Lanes on Two-Lane Highways - Passing

Opportunity = 50%.................................................................................................................................... B-66B.5.3.1e Volume Warrants for Truck Climbing Lanes on Two-Lane Highways - Passing

Opportunity = 30%.................................................................................................................................... B-67B.5.4.1a Percent of the Hour with Gaps Available for Overtaking as a Function of Volume........................ B-80B.5.4.1b Passing Lane Warrant .............................................................................................................................. B-82B.7.2 Guidelines for Surfacing of Detours ...................................................................................................... B-89B.7.2.2a Geometric Parameters of Detours .......................................................................................................... B-91B.7.2.2b Superelevation for Detours ..................................................................................................................... B-92



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Roads are traditionally designed in three views: plan,profile and cross-section. The highway designengineer will often design each view independently,perhaps including a sight distance calculation.Drivers, however, have a different appreciation forroad appearance since they see the road from variousangles. Some road features will be in view from allpoints for a considerable length, while other featureswill be in view momentarily.

Generally, when topography is rugged or rolling,considerable construction cost savings can be madewhen the design speed is lowered at selectedlocations. In rugged or rolling terrain, whenreductions in design speed are considered, thehorizontal alignment standard is generally morecritical than the vertical alignment standard. Theposted highway speed is not frequently lowered dueto vertical alignment deficiencies unless they occur athazardous locations such as intersections. However,horizontal alignment deficiencies may necessitatelower posted speed. Consequently, it is important toattach a high priority to meeting horizontal alignmentstandards while exercising more flexibility withvertical alignments. The examination of differentalternative vertical alignments is encouraged tomaximize the benefits considering construction costs,road user costs and safety. Notwithstanding theabove, vertical alignment standards should not becompromised near intersections due to the importanceof intersection sight distance.

Certain combinations of horizontal and vertical curvescan result in an apparent distortion in the alignment orgrade although the horizontal and vertical curvescomply to the design standards outlined in Table A.7.

Although this guide does not identify all concepts ofgood design form, Figures B-3.2a through B-3.2lillustrate various bad design forms that areaesthetically displeasing to drivers and should beavoided.

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The ability to see ahead is of utmost importance in thesafe and efficient operation of a vehicle on a highway.The path and speed of motor vehicles on highwaysand streets are subject to the control of drivers whoseability, training and experience are quite varied. Forhighway safety, sufficient sight distance must beprovided so that drivers can avoid strikingunexpected objects on the roadway surface. Certaintwo-lane highways should also have sufficient sightdistance to enable drivers to safely occupy theopposing traffic lane during passing manoeuvres.Two-lane rural highways should generally providesuch passing sight distance at frequent intervals andfor substantial portions of their length. Conversely, itis normally impractical to provide passing sightdistance on two-lane urban streets or arterials. Thelength and interval of passing sight distance should becompatible with highway function. Generally, for two-lane undivided rural arterial highways, it is desirableto provide passing sight distance over at least70 percent of the length.

Sight distance is discussed in five steps:

1. Stopping sight distances (the distances requiredfor stopping, applicable on all highways).

2. Passing sight distances (the distances required forpassing manoeuvres, applicable only on two-lanehighways).

3. Non-striping sight distances (the distancesrequired for the pavement markings to allowpassing) on two-lane highways.

4. Decision sight distances (the distances needed fordecisions at complex locations).

5. The criteria for measuring these distances for usein design.

The design of alignment and profile to provide thesedistances and to meet these criteria are described later

Alberta InfrastructureAUGUST 1999 HIGHWAY GEOMETRIC DESIGN GUIDE


in this chapter. The special conditions related to sightdistances at intersections are discussed in Chapter D.

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For passenger vehicle sight distance calculations, theheight of the driver’s eye is considered to be 1.05mabove the road surface. This height is based onsurveys of actual vehicles and drivers and willaccommodate the vast majority of vehicle/drivercombinations. This height of eye is used in measuringstopping, passing and decision sight distances.

An eye height of 1.8m is adopted for single unitvehicle (SU) and the BUS design vehicle.

An eye height of 2.1m is adopted for all large trucks ortruck-trailer combinations based on the height oftypical highway tractors.

For pavement marking purposes (non-striping sightdistance), a height of eye = 1.15m and height of object= 1.15m is adopted for simplicity.

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For stopping sight distance an object height of 0.38m isused. This value is based on the legal minimum heightfor a vehicle tail light in Canada.

This height was adopted based on the rationale that adriver may not make the decision to stop for an objectless than 0.38m. from the road surface. In previousyears, the height of 0.15m was the standard, but it wasdetermined that drivers may not stop for objects ofthat height. A driver will, however, stop for an objectthat is 0.38m in height.

The average tail light height typically seen on Albertaroads is considerably greater than 0.38m. However,0.38m is used to ensure that the worst scenario isaccommodated by the stopping sight distance model.

The height of object used for passing sight distanceand intersectional sight distance is 1.3m. Thisrepresents the full height from road surface to roof ofa design passenger vehicle.

The height of object used in non-striping sightdistance is 1.15m.

The height of object used in decision sight distance isselected based on circumstances. For example, theobject height is zero if the driver needs to see the roadsurface.

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Sight distance is the length of roadway ahead visibleto the driver. The minimum sight distance availableon a roadway should allow a vehicle, travelling at anassumed running speed (which is based on the designspeed), to stop before reaching a stationary object inits path. Although greater length is desirable, sightdistance at every point along the highway should be atleast the distance required for a vehicle to stop.

Stopping sight distance is the distance a vehicle travelsfrom the instant the driver sights an object anddecides to stop, to the instant the vehicle comes to acomplete stop after applying the brakes. This distancedepends upon perception-reaction time, height of thedriver’s eye, height of object, coefficient of friction forthe highway surface and the initial vehicle speed. Fordesign purposes, the following criteria have beenadopted by Alberta Infrastructure to determine theseminimum values:

• A fixed perception-reaction time of 2.5 seconds • Eye height of 1.05m • Object height of 0.38m • Coefficient of friction for wet pavement (based on

American Association of State Highway andTransportation Officials 1990 and TransportationAssociation of Canada 1986 values)

• Assumed running speed equals design speed up

to 100km/h. For design speeds of 110 km/h andhigher, the assumed running speeds are based onthe 85th percentile running speeds recorded onAlberta highways in good conditions.

These criteria and the resulting minimum values aretabulated in Table B.2.3.

The derived minimum stopping sight distancesdirectly reflect passenger car operation and might bequestioned for use in design for truck operation.Trucks as a whole, especially the larger and heavierunits, require longer stopping distances thanpassenger cars. This is assuming that the braking



capability of the vehicles is the limiting factor indetermining the stopping distance.

There is a factor that tends to balance the additionalbraking lengths for given truck speeds with those forpassenger cars. The truck operator is able to see thevertical features of the obstruction from farther awaybecause of the higher position of the truck seat.Separate stopping sight distances for trucks andpassenger cars, therefore, are not used in highwaydesign standards.

There are several situations that should be treated withcaution. Every effort should be made to provide stoppingsight distances greater than the minimum design valuewhen horizontal sight restrictions occur on downgrades,particularly at the ends of long downgrades. Even whenthe horizontal sight obstruction is a cut slope, the truckoperator’s greater height of eye is of little value on long

downgrades. Truck speeds may closely approach orexceed those of passenger cars. Although the averagetruck operator tends to be more experienced and quickerto recognize hazards than the average passenger caroperator, under conditions of restricted horizontal sightlines it is best to supply a stopping sight distance thatexceeds the values in Table B.2.3.

Another situation where trucks may have difficultystopping is in the vicinity of underpasses due torailway grade separations, interchanges etc. Thestructure may restrict the sight lines for traffic(particularly trucks) on the lower elevation roadway.Additional sight distance should be provided wherepossible to avoid problems in these areas.

Minimum vertical crest and sag curvatures whichsatisfy stopping sight distance criteria are given inSection B.4.4.

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DesignSpeed

AssumedRunning

Perception-Reaction Friction

BrakingDistance

ComputedValue

Min. SSDfor Design

(km/h) Speed(km/h)

Time(s)

Distance(m)

Factor (m) (m) (Rounded)(m)

40 40 2.5 27.8 0.38 16.6 44.4 4550 50 2.5 34.7 0.36 27.3 62.0 6560 60 2.5 41.7 0.34 41.7 83.4 8570 70 2.5 48.6 0.32 60.2 108.8 11080 80 2.5 55.6 0.31 81.2 136.8 14090 90 2.5 62.5 0.30 106.2 168.7 170

100 100 2.5 69.4 0.30 131.1 200.5 200110 108 2.5 75.0 0.29 158.2 233.2 235120 115 2.5 79.9 0.28 185.8 265.7 270130 115 2.5 79.9 0.27 192.7 272.6 275

Minimum stopping sight distance (SSD):SSD perception / reaction distance braking distance= +

= +Vt V

f3 6 254

2

.

Where V is the assumed running speed, (km/h)t is the perception/reaction time (sec)f is the coefficient of longitudinal friction

Braking distance is derived from the general expressions:u v ad a gf2 2 2= − =andWhere u is the final speed

v is the initial speeda is accelerationd is distance travelled during acceleration

g is acceleration due to gravity

In this case u = 0, therefore:

f

v

f

v

gf

vd

gfdv

254

2

)81.9(2

2

1000

3600

2

2

2

220

===

−=

Where d is the braking distance (m)ν is the initial speed (km/h)g is 9.81 m/s2

Alberta InfrastructureAPRIL 1995 HIGHWAY GEOMETRIC DESIGN GUIDE


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Most rural highways are two-lane and two-way, sodrivers must use the opposing traffic lane to passslower vehicles. To pass safely, the driver should beable to see that the opposing traffic lane is clear for asufficient distance ahead. A driver should have timeto complete or terminate the manoeuvre withoutinterfering with the smooth flow of traffic in eitherdirection.

Many passes are accomplished without the driverseeing a safe passing section ahead, but design basedon such manoeuvres does not have the desired safetyfactor. Because many cautious drivers would notattempt to pass under such conditions, design on thisbasis would reduce highway usefulness.

Passing sight distance for use in design should bedetermined on the basis of the length needed tocomplete a safe passing manoeuvre. While there maybe occasions to consider multiple passes, where two ormore vehicles pass or are passed, it is not practical toassume such conditions in developing minimumdesign criteria. Instead, sight distance is determinedfor a single vehicle passing a single vehicle. Longersight distances occur naturally in design and theselocations can accommodate an occasional multiplepassing.

Certain assumptions for traffic behavior are necessarywhen computing minimum passing sight distances ontwo-lane highways for design use and some offer awide choice. The assumed control for driver behaviorshould be that practised by a high percentage ofdrivers, rather than the average driver. Suchassumptions follow:

1. The overtaken vehicle travels at uniform speed.

2. The passing vehicle has reduced speed and trails theovertaken vehicle as it enters a passing section.

3. When the passing section is reached, the driverrequires a short period of time to perceive the clearpassing section and start the manoeuvre.

4. Passing is accomplished under what may be termed adelayed start and a hurried return in the face ofopposing traffic. The passing vehicle acceleratesduring the manoeuvre, and its average speed duringoccupancy of the left lane is 16 km/h higher than thatof the overtaken vehicle.

5. When the passing vehicle returns to its lane, thereis a suitable clearance length between it andoncoming vehicles.

Some drivers accelerate at the beginning of a passingmanoeuvre to an appreciably higher speed and thencontinue at a uniform speed until passing is complete.Many drivers accelerate at a fairly high rate until justbeyond the vehicle being passed and then completethe manoeuvre either without further acceleration orat reduced speed. For simplicity, extraordinarymanoeuvres are ignored and passing distances aredeveloped with the use of observed speeds and timesthat fit the practices of a high percentage of drivers.

The minimum passing sight distance for two-lanehighways is determined as the sum of the fourdistances (shown in the diagram at the bottom ofFigure B-2.4):

d1 - Distance traversed during perception andreaction time and during the initial accelerationto the point of encroachment on the left lane

d2 - Distance travelled while the passing vehicleoccupies the left lane

d3 - Distance between the passing vehicle at the endof its manoeuvre and the opposing vehicle

d4 - Distance traversed by an opposing vehicle fortwo-thirds of the time the passing vehicleoccupies the left lane, or 2/3 of d2 above.

The minimum passing sight distances given in TableB.2.4 have been developed based on extensive fieldobservations of driver behavior during passingmanoeuvres. The average speed differential of 16km/h between overtaken vehicles and passingvehicles is based on these observations.

Initial manoeuvre distance (d1). The initialmanoeuvre period has two components, a time forperception and reaction, and an interval during whichthe driver brings the vehicle from the trailing speed tothe point of encroachment on the left or passing lane.To a great extent the two overlap. As a passing sectionof highway comes into view, a driver desiring to passmay begin to accelerate and manoeuvre the vehicletoward the centreline of the highway while decidingwhether or not to pass. Studies show that the averagepassing vehicle accelerates at less than its maximumpotential, indicating that the initial manoeuvre periodcontains an element of time for perception and

Alberta InfrastructureHIGHWAY GEOMETRIC DESIGN GUIDE APRIL 1995


reaction. However, some drivers may remain innormal lane position while deciding to pass. The exactposition of the vehicle during initial manoeuvre isunimportant because differences in resulting passingdistances are insignificant.

Distance while passing vehicle occupies left lane(d2) In studies, passing vehicles have been found tooccupy the left lane from 9.3 to 10.4 seconds. Thesestudies involved extensive field observations of driverbehavior during passing manoeuvres, documented byPrisk3 during the years 1938 to 1941. The distance d2travelled in the left lane by the passing vehicle iscomputed by the following formula:

d t2 2= v

3 6.

Where t2 = time passing vehicle occupies the leftlane (seconds)

v = average speed of passing vehicle(km/h)

3 Prisk, C.W., “Passing Practices on Rural Highways”,HCB Vol. 21, Washington, D.C., Highway ResearchBoard, 1941.

Clearance length (d3) The clearance length betweenthe opposing and passing vehicles at the end of themanoeuvres found in the passing study varied from33m to 92m. This length increases with increaseddesign speed.

Distance traversed by an opposing vehicle (d4)Passing sight distance includes the distance traversedby an opposing vehicle during the passing manoeuvreto minimize the chance of a passing vehicle meetingan opposing vehicle while in the left lane.Conservatively, this should be the distance traversedby an opposing vehicle during the time it takes tocomplete a pass, or the time that the passing vehicleoccupies the left lane. Such a distance is questionablylong. During the first phase of the passing manoeuvre,the passing vehicle has not yet pulled alongside thevehicle being passed. Even though the passing vehicleoccupies the left lane, its driver can return to the rightlane if an opposing vehicle is seen. It is unnecessary toinclude this trailing time interval in computing thedistance traversed by an opposing vehicle. This timeinterval, which can be computed from the relativepositions of passing and passed vehicle, is about one-third the time the passing vehicle occupies the leftlane. Therefore, the passing sight distance element forthe opposing vehicle is the distance it traverses duringtwo-thirds of the time the passenger vehicle occupiesthe left lane. The opposing vehicle is assumed to betravelling at the same speed as the passing vehicle, sod4 = 2d2/3.



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The design values for minimum passing sight distancefor each design speed are listed in Table B.2.4.

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Design Speed(km/h)

Minimum Passing SightDistance (m)

40 27550 34060 42070 48080 56090 620100 680110 740120 800130 860

Note: Passing Sight Distance is based on height ofdriver’s eye at 1.05m and height of opposingvehicle at 1.30m.

These maximum passing sight distances for designshould not be confused with other distances used aswarrants for placing no-passing zone pavementmarkings on paved highways. Such values, describedin Section B.2.5, are substantially less than designdistances and are derived for traffic operating-controlneeds that are based on different assumptions fromthose for highway design.

Minimum vertical curvatures which satisfy passingsight distance criteria are given in Section B.4.4.



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Non-striping sight distance is the limiting value usedto determine when no-passing pavement markings(barrier lines ) are required. Although passing sightdistance is a desirable condition on two-lanehighways, non-striping sight distance is still adequatefor safe passing manoeuvres.

The non-striping sight distance for each design speedis substantially less than the passing sight distance.The principal reason for the difference is that manydrivers consider roadways marked according topassing sight distance requirements to be toorestrictive. A safe passing manoeuvre can often beexecuted where full passing sight distance is notavailable depending on the timing of oncomingvehicles.

To explain the difference between passing sightdistance and non-striping sight distance, reference ismade to the passing model described in Section B.2.4for passing sight distance. In the case of passing sightdistance, if an oncoming vehicle comes into view atthe critical moment, that is at the end of the firstphase, the driver has sufficient time to complete thepass safely. In the case of non-striping sight distance,if an oncoming vehicle appears at the critical moment,there is only sufficient time available to safely abortthe pass.

The non-striping sight distance value chosen fordesign in Alberta is based on the Uniform TrafficControl Devices for Canada (UTCDC) manualprepared by TAC, and the current Alberta standardsfor pavement marking. Both Alberta and TAC use aneye height and object height of 1.15m in their model.

Alberta currently installs a barrier line where the sightdistance is less than 425m. TAC suggests 475m for aspeed of 110 km/h. Speed is defined as the higher ofthe 85th percentile speed and the posted speed limit.Alberta’s daytime 85th percentile running speed forpassenger cars on two lane highways is currentlyapproximately 110 km/h, and has been rising slightlyover the last few years. Because of the high runningspeeds, it is best to use a non-striping sight distancethat allows for a 110 km/h speed for design purposes.

Efforts should be made to achieve at least minimumnon-striping sight distance on the flatter crest curvesto maximize passing opportunities and consequentlyimprove the level of service. This is especiallyimportant on higher volume highways in rollingterrain.

In general, designers should strive to achieve at least75 percent of the length of a highway as barrier-free.Higher percentages are desirable on higher volumeroads. Information obtained from videolog shows thatapproximately 73 percent of Alberta’s paved two-lanehighways are presently barrier free. Bear in mind thatbarrier lines are used at intersections andclimbing/passing lanes even where there is no sight-line restriction.

For design purposes, a sight distance of 480m is usedfor non-striping to allow for a running speed of110 km/h. This speed is commonly encountered ontwo-lane undivided rural highways in Alberta whichare posted for 100 km/h. If 480m is used, rather than475m, the resulting K values will be a convenientnumber (250) while offering an additional factor ofsafety. K values are explained in detail in SectionB.4.4.

Distances immediately above the minimum non-striping sight distance values may cause a false feelingof safety for passing because of the absence of barrierlines. Also, frequent barrier lines are likely to appearunreasonable to the driver. It is, therefore, importantthat the sight distances only slightly greater than thenon-striping values be increased as much aseconomically possible.

If it is not feasible to provide the non-striping values,it may be desirable to reduce the length of verticalcurve to approach the stopping sight distance. Thisaccomplishes three things: it shortens the total lengthof the no-passing zone, it may make the restrictivemarking appear more reasonable to the driver, and itmay provide a more economical design.

Minimum crest vertical curvatures that satisfy non-striping sight distance criteria are given in SectionB.4.4.



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Minimum stopping sight distance is usually sufficientto allow reasonably competent and alert drivers tocome to a hurried stop under ordinary circumstances.However, this distance is often inadequate whendrivers must make complex or instantaneousdecisions, when information is difficult to perceive, orwhen unexpected or unusual manoeuvres arerequired. Limiting sight distance to that provided forstopping may also preclude drivers from performingevasive manoeuvres that are often less hazardous andotherwise preferable to stopping. Even with anappropriate complement of standard traffic controldevices, stopping sight distance might not providesufficient visibility distance for drivers to corroborateadvance warnings and to perform the necessarymanoeuvres. It is evident that there are manylocations where it would be prudent to provide longersight distance. In these circumstances, the use ofdecision sight distance instead of minimum stoppingsight distance provides the greater length that driversneed.

Decision sight distance is the distance required for adriver to:

• detect an information source or hazard which isdifficult to perceive in a roadway environmentthat might be visually cluttered

• recognize the hazard or its threat potential• select appropriate action• complete the manoeuvre safely and efficiently.

Because decision sight distance gives driversadditional margin for error and affords them sufficientlength to manoeuvre their vehicles at the same orreduced speed, rather than simply to stop, it issubstantially greater than minimum stopping sightdistance.

Drivers need decision sight distance whenever there islikelihood for error in either information reception,decision making, or control actions. Examples ofcritical locations where these kinds of errors are likelyto occur, and where it is desirable to provide decisionsight distance are:

• interchanges and intersections

• locations where unusual or unexpectedmanoeuvres are required

• changes in cross section such as at rest areas andlane drops

• areas of concentrated demand where sources ofinformation compete; for example, from roadwayelements, traffic, traffic control devices, andadvertising signs.

The decision sight distances in Table B.2.6 are used forappropriate sight distance at critical locations andserve as criteria in evaluating suitability of the sightdistance lengths at these locations. Because of theadditional safety and manoeuvrability these lengthsyield, decision sight distances instead of minimumstopping sight distances are provided at criticallocations. If it is not feasible to provide these distancesbecause of horizontal or vertical curvature, specialattention should be given to the use of suitable trafficcontrol devices for providing advance warning ofconditions likely to be encountered.

A range of decision sight distance values applicable tomost situations has been developed. The rangerecognizes the variation in complexity that occurs atvarious sites. For less complex situations, valuestoward the lower end of the range are appropriate andfor more complexity, values at the upper end are used.The calculations for decision sight distance are givenin Table B.2.6.

Decision sight distance should be considered for crestsnear major intersections and for ramp exits. Eachmajor intersection or ramp exit should be checked on asite specific basis, and analyzed individually todetermine if decision sight distance is achieved. Othersight distance requirements must also be met.

For measuring decision sight distance, the height ofeye of 1.05m is used together with an appropriateheight of object depending on the anticipatedprevailing conditions. In some circumstances, thedriver needs to see the road surface, in which case theobject height is zero.

Because of the variation in height of eye, minimumcrest vertical curves which satisfy decision sightdistance requirements are not given.



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TimePre-manoeuvre Time Decision Sight Distance

DesignSpeed(km/h)

Detectionand

Recognition(s)

DecisionResponse

andInitiation

(s)

Manoeuvre(lane change)

(s)Total

(s)Calculated

(m)

Roundedfor Design

(m)40 1.5-3.0 4.2-6.5 4.5 10.2-14.0 113-155 110-16050 1.5-3.0 4.2-6.5 4.5 10.2-14.0 141-194 140-19060 1.5-3.0 4.2-6.5 4.5 10.2-14.0 170-233 170-23070 1.5-3.0 4.2-6.5 4.5 10.2-14.0 198-272 200-27080 1.5-3.0 4.2-6.5 4.5 10.2-14.0 226-311 230-31090 2.0-3.0 4.7-7.0 4.5 11.2-14.5 280-362 280-360100 2.0-3.0 4.7-7.0 4.0 10.7-14.0 297-389 300-390110 2.0-3.0 4.7-7.0 4.0 10.7-14.0 327-427 330-430120 2.0-3.0 4.7-7.0 4.0 10.7-14.0 357-466 360-470130 2.0-3.0 4.7-7.0 4.0 10.7-14.0 386-505 390-500

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The horizontal alignment of a road is usually a seriesof tangents and transition spirals. Where a transitioncurve is omitted, the tangents connect with a circularcurve. Curvilinear alignment is horizontal alignmentin which long flat curves are connected by longtransitions, generally without connecting tangents.

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The following are general controls and considerationsfor horizontal alignment. These controls are notsubject to empirical or formula derivation, but theyare important for attainment of safe, smooth-flowingand aesthetically pleasing highways.

Note: Specific controls for horizontal alignment arediscussed in the following sections.

1. Alignment should be as directional as possibleand consistent with topography. Effort should bemade to preserve developed properties andcommunity values. The use of winding alignment,composed of short curves, should be avoidedsince it tends to cause erratic operation andaccidents. While the aesthetic qualities ofcurvilinear alignment are important, passing sightdistance requirements on two-lane highways

necessitate long tangents to provide passingopportunities.

2. The use of the minimum radius of curvatureshould be avoided, if possible, to establish analignment based on the selected design speed. Useflat curvature generally, reserving the minimumradius for critical locations.

3. Consistent alignment should be provided. Sharpcurves should not be introduced at the ends oflong tangents or at other locations where highapproach speeds are anticipated. Where physicalrestrictions dictate curvature of a lower standardthan the project design speed, the critical curveshould be approached by successively sharpercurves. In this way erratic operation and accidentscan be minimized because the driver will not besurprised by a sudden need to slow down.

4. For small deflection angles, curves should be longenough to avoid the appearance of a kink. Curvesshould generally be long enough to provide anaesthetically pleasing alignment (refer to FigureB-3.2e). A deflection angle of 30 minutes requiresa curve; smaller deflections do not. For smallerdeflection curves (between 30’ and 10), that occuron rural roads in open country, a minimum curvelength of 350m should be used to maintain apleasing appearance. For the purpose ofdetermining curve length, where spiral curves areapplied, 50 percent of the spiral length is regardedas part of the curve.


ALIGNMENT ELEMENTSB-14

The longer the distance a curve is viewed from,the more kinky its appearance, and in these casesthere is a greater need to lengthen the curve.Curves that do not require any superelevation, i.e.normal crown curves are very desirable for smalldeflections.

5. Sharp curves should not be introduced on steephills. With the absence of physical objects abovethe roadways, a driver may have difficultyestimating the radius and may fail to adjust to theconditions.

6. A broken back curve consists of two curves in thesame direction joined by a short tangent. This typeof alignment appears unpleasant and is potentiallyhazardous to drivers who do not expectsuccessive curves in the same direction. The use ofspiral transition curves, which provide somedegree of continuous superelevation, is preferable.The term broken back is usually applied when thelength in metres of the connecting tangent is lessthan four times the design speed in kilometres perhour.

7. Long spirals should be used whenever possiblerather than compounding circular curves. If it isnecessary to compound circular curves without aspiral between them, the ratio of the longer radiusto the shorter radius should not exceed 1.5.

8. Abrupt alignment reversal must be avoided.When reverse curves are too close it is difficult tosuperelevate them adequately, resulting inhazardous and erratic vehicle operation.Alignment reversal can be suitably designed byincluding back-to-back spirals of sufficient lengthfor the applicable design speed with enoughtangent length between the spiral curves to allowfor tangent runout.

9. Where feasible, a curve beginning or ending neara bridge should be located so the superelevationtransition does not occur on the structure.

10. Horizontal alignment should be co-ordinated withvertical alignment to avoid the appearance ofinconsistent distortion.

Figure B-3.2a through B-3.2l are illustrations of designform which show good and bad examples of theconcepts.



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The friction co-efficient, at which side skidding isimminent, depends upon a number of factorsincluding: vehicle speed, type and condition ofroadway surface, and type and condition of tires.

On any curve, it can be expected that some driverswill travel in excess of the design speed. In makinglane changes or passing manoeuvres, a path of smallerradius than the control line is possible. Recognizingthis, a safety factor has been incorporated into sidefriction factors. From available data and experience,the American Association of State Highway andTransportation Officials has established maximumsafe side friction factor values for use in highwaycurvature design. These values are primarily based onan empirical relationship between side friction factorand design speed. The maximum safe values for eachdesign speed are shown in the following table.

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Design Speed(km/h)

Safe SideFriction Factors

40 0.1750 0.1660 0.1570 0.1580 0.1490 0.13100 0.12110 0.10120 0.09130 0.08

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The maximum rates of superelevation usable forhighway design are controlled by several factors:

1. Climatic conditions• Frequency and amount of snow and icing

2. Terrain conditions• Flat versus mountainous

3. Type of area• Rural or urban

4. Frequency of very slow moving vehicles thatwould be subject to uncertain conditions.

In Canada, provincial highway authorities typicallychose either 0.06m/m or 0.08m/m as the maximumsuperelevation rate for rural highways. For thefollowing reasons, there has been a recent trendtowards adoption of 0.06 m/m as the maximum rate.

1. Adoption of the 0.06 m/m maximum tableresults in better horizontal alignments in caseswhere the minimum radii are used. Use of theminimum radii shown on the 0.08 m/mmaximum table can result in sharp curves notconsistent with driver expectations in a ruralenvironment. Use of isolated sharp curves in agenerally smooth high speed rural alignment isdiscouraged because it breaks one of thecardinal rules of highway design, that is, nosurprises.

2. Use of the 0.06 m/m maximum table is expectedto improve operational characteristics forvehicles traveling at lower speeds duringadverse weather conditions, or for other reasons,while not adversely affecting higher speedvehicles. This is especially important forhighways located where winter conditionsprevail several months of the year.

A maximum superelevation rate of 0.06 m/m isrecommended for all rural roads.

In an urban environment, superelevation is generally notapplied on local streets, and is used only occasionally oncollector streets. Topographic considerations may suggestthe use of superelevation on collector streets, and to alesser extent on local streets, to provide a better elevationmatch between street facilities and adjacentdevelopments. Maximum superelevation rates in thesecases are in the range of 0.02m/m to 0.04m/m. Forfurther information on urban design refer to the mostrecent TAC publication on this subject.

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The minimum allowable radius is a limiting value fora given design speed determined from the maximumrate of superelevation and the maximum side frictionfactor. For that design speed, use of sharper curvaturewould call for superelevation beyond the limitconsidered practical or for operation with tire frictionbeyond the safe limit or some combination of both.


ALIGNMENT ELEMENTSB-28

The formula for calculating the radius is:

Rmin = V

e f

2

127( )max +

Where Rmin is the minimum radius of the circularcurve (m)

V is the vehicle speed (km/h)

emax is the maximum roadwaysuperelevation (m/m)

f is the maximum side friction factor

Minimum radii for corresponding design speeds areshown in Tables B.3.6a and B.3.6b.

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For design purposes, the speed to be used for selectingthe superelevation rate is based on the expected 85thpercentile running speed on the completed facility. InAlberta, this is generally 10 km/h higher than theposted speed. Therefore in general where the postedspeed on undivided highways is 100 km/h, the speedto be used for superelevation is 110 km/h. Similarlyon divided highways where the posted speed isgenerally 110 km/h, the speed to be used forsuperelevation is 120 km/h. Notwithstanding theabove, horizontal alignments on divided highways inAlberta are generally set out based on a design speedof 130 km/h to allow for a possible increase in speeds(posted and running) that may occur in the future.

Where the design speed is less than 110 km/h, it isgenerally appropriate to use the full design speed forsetting the superelevation rate as the 85th percentilerunning speed may match or exceed the design speed.

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The recommended superelevation rates for variousradii for each design speed are given in Tables B.3.6aand B.3.6b. These tables are based on the form ofsuperelevation distribution and side friction describedas Method 5 in the 1990 AASHTO publication entitledA Policy on Geometric Design of Highways andStreets. The values shown in the tables are alsoconsistent with those currently recommended byTAC.

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Design superelevation rates can be read directly fromTables B.3.6a and B.3.6b. When superelevation is used,the minimum rate should not be less than the rate ofcrossfall of the normal crown rate per travel lane, thatis, normally 0.02m/m for paved roads and 0.03m/mfor gravel roads.

Table B.3.6a (emax = 0.06 m/m), which is normallyused on all rural highway curves, includes an insettable entitled Values for Superelevation on HorizontalCurves Containing Major Intersections. The tableprovides values for superelevation related to designspeed and circular curve radii for curved alignmentscontaining major intersections. An intersection isconsidered major if intersection treatment, that isflaring or channelization, is provided. In addition toproviding superelevation rates, the inset table alsoindicates those curves on which intersections may bepermitted. It is noted that intersections on curve areundesirable for safety reasons and should be avoidedwhere possible.

However, intersections on curves may be permittedwhere the combination of design speed and radius (asshown on this special inset table), or the radius isgreater than 4000m. Also, for design speeds from40 km/h to 90 km/h, which are not covered by theinset table, intersections are generally permitted onlyif e is less than or equal to 0.038m/m.



The following paragraphs describe in more detail thevarious methods of distribution of e and f over a rangeof curves that are available. Although Method 5 iscurrently used by AI, this does not imply that othermethods are not acceptable or that there is noflexibility. The form of distribution of e and f iscurrently under review by AI.

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For a given design speed, there are five methods forcounteracting centrifugal force on curves by use of eand f, or both. These methods follow, and theirresulting relation is illustrated in Figure B-3.6.

1. Superelevation and side friction are directlyproportional to the degree of curve (D), that is, astraight-line relation exists between D = O and D= Dmax.

2. Side friction is such that a vehicle travelling atdesign speed has all centrifugal force counteractedin direct proportion by side friction on curves upto those requiring fmax. For sharper curves, fremains at fmax and e is then used in directproportion to the continued increase in curvatureuntil e reaches emax .

3. Superelevation is such that a vehicle travelling atdesign speed has all centrifugal force counteracted indirect proportion by superelevation on curves up tothat requiring emax. For sharper curves, e remains atemax and f is then used in direct proportion to thecontinued increase in curvature until f reaches fmax .

4. Method 4 is the same as Method 3, except that it is basedon average running speed instead of design speed.

5. Superelevation and side friction are in acurvilinear relation with degrees of curve, withvalues between those of methods 1 and 3.

Table B.3.6a shows the comparative relations ofsuperelevation versus degree of curve for thesemethods. Table B.3.6b shows the corresponding valueof side friction for a vehicle travelling at design speed.Figure B-3.6 shows the value of side friction for avehicle travelling at the corresponding averagerunning speed.

To favor the overdriving characteristics that occur onflat to intermediate curves, it is desirable that thesuperelevation approximate that obtained by Method4. Overdriving on such curves is not dangerousbecause superelevation counteracts nearly allcentrifugal force at average running speed, andconsiderable side friction is available for greaterspeed. On the other hand, it also is desirable to favourMethod 1, which avoids a substantial part of the rangeof curves with maximum superelevation. UsingMethod 5, a curved line (curve 5, as shown within thetriangular working range between curves 1 and 4 inFigure B-3.6) represents a superelevation and sidefriction distribution reasonably satisfying both aspects.Curve 5, of parabolic form, represents a practicaldistribution over the range of curvature.

There is some flexibility when applying superelevation inurban areas due to the willingness of drivers to accepthigher friction values than on open highways and due toother controls that frequently apply. For current practicefor application of superelevation to urban roadways,refer to the most recent TAC publication dealing with thissubject.



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To superelevate two-lane highways the pavementshould generally be rotated about its centreline. Incases where centreline rotation would causedrainage problems or adversely affect the profile ofguard rails or retaining walls, either inside oroutside edge of pavement may be used as the pointof rotation.

For multi-lane divided highways with depressedmedian widths greater than 13m, superelevationmay be attained by rotating travel lane centrelines.Where there is a possibility of future widening of afour-lane divided highway to a six-lane dividedhighway by adding lanes to the inside of eachroadway, superelevation should be developed byrotation about the inside edge of the futurepavement. Figures B-3.7a, B-3.7b and B-3.7c illustratethe desirable methods of developing superelevationfor both simple and spiral curves.

It should be noted that simple curves are rarely usedin new construction. Spiral curves are required on allnew roadways except where superelevation is notrequired (see Table B.3.6a) or on the flatter curves onlocal roads (see Table H.3.3.1a). When appropriate,simple curves may be used on existing paved roadsto avoid the need to make minor realignments. Theuse of simple curves to tie in to existing pavedalignments is considered a design exception.

When spiral transition curves are used, the adversecrown should be completely removed at the

beginning of the spiral. For two-lane undivided andfour-lane divided highways, transition from normalcrown to where the adverse crown is removed isaccomplished by means of a 30m tangent runout. Forsix-lane or eight-lane divided highways, the tangentrunout length is to be determined using a slope onthe outside pavement edge in relation to thecentreline of one m in 400m, as suggested in TAC.From the beginning of the spiral curve to thebeginning of the circular curve, the slope of thepavement edge is governed by the spiral parameterrequirements and pavement width. Vertical curvesshould be used whenever a change in grade occursat the shoulder line, at the beginning of the spiralcurve, and at the beginning of the circular curve.

To superelevate simple circular curves, two-thirds ofthe full superelevation should be in place at thebeginning of the circular curve, with the remainingthird developed on the circular curve. Transition,from normal crown to where the adverse crown isremoved, is accomplished by means of a 30mtangent runout. The length, Lr, over which thesuperelevation is applied, is determined by referenceto Table B.3.7.

Where a transition occurs near the end of a bridge,the horizontal alignment is usually adjusted, ifpossible, to keep the superelevation transition off thebridge and maintain the normal cross-fall or constantsuperelevation throughout the structure.

On curves where the adverse crown is removed, butwhere the superelevation required does not exceedthe crown slope, the superelevation should beadjusted to equal the crown slope.

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e Length of Runoff, Lr (m) for Design Speed (km/h)(m/m) 50 60 70 80 90 100 110 120 130

0.02 30 30 30 30 30 30 30 30 300.03 30 30 30 30 40 40 40 40 500.04 30 40 40 40 50 50 50 60 600.05 40 50 50 50 60 60 70 70 700.06 50 60 60 70 70 80 80 80 900.07 60 60 70 70 80 90 90 90 1000.08 70 70 80 80 90 100 110 110 120

The above runoff lengths, Lr, are required for two-lane and four-lane undivided pavements. For six-laneundivided pavements, use 1.3 times the tabularvalues.



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Spiral curves provide a gradual change in curvaturefrom a straight to a circular path. The advantages ofspiral curves are as follows:

1. Spiral curves provide a natural path for amotorist to follow, allowing centrifugal force toincrease and decrease gradually as the vehicleenters and leaves the circular portion of thecurve. This minimizes encroachment uponadjoining traffic lanes, promotes speeduniformity and increases safety.

2. The spiral curve length provides a desirablearrangement for superelevation runoff. Achange from normal to a fully superelevatedcross-slope is applied along the spiral curvelength.

3. Where the pavement section is to be widenedaround a circular curve, the spiral facilitates thetransition in width. Spirals simplify the designprocedure and provide flexibility so thatwidening of sharp curves can be applied, in part,on the outside of the pavement without areverse-edge alignment.

4. Highway appearance is improved by theapplication of spirals. Breaks that appear at the

beginning and end of circular curves, which canbe further distorted by superelevation runoff,should be avoided.

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Spiral curves are defined by three values: R (radius), L(length) and A (the spiral parameter). The square ofthe spiral parameter is the rate of change of lengthwith respect to curvature; that is, the reciprocal ofradius. This is expressed mathematically as follows:

R varies with LRL is constantRL = A2 where A is a constantL = A2/R

In the above expression, each term (L, A and R) isexpressed in units of length. All spiral curves are thesame shape and vary only in size. The spiralparameter is a measure of the spiral flatness — thelarger the parameter, the flatter the spiral.

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As illustrated in Figure B-3.8.2, spiral design is basedon three considerations: comfort, superelevationrunoff and aesthetics. For any given design speed andradius, the highest value of spiral parameter, asdetermined by this criterion, is adopted for design.

Alberta InfrastructureHIGHWAY GEOMETRIC DESIGN GUIDE JUNE 1996


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A vehicle travelling along a spiral curve from tangentto the end radius at a constant speed experiences acentripetal force which varies at a constant rate alongthe transition length. For a given speed and endradius, the change rate of the centripetal force is afunction of the spiral length — the shorter the spiral,the more rapid the rate of change. If it is very short,passengers will experience discomfort. The rate ofchange of centripetal force is proportional to the rateof change of radial acceleration and this is a measureof the severity of the discomfort. Tolerable radialacceleration varies between drivers. As a basis fordesign, the maximum value used to provide theminimum acceptable comfort and safety suitable forpassengers is 0.6 metres per second cubed. Theminimum spiral parameter, based on comfort, can becalculated for each design speed using the followingexpression.

Note: The minimum spiral parameter based oncomfort considerations is independent of theradius, as illustrated in Figure B-3.8.2 by thecomfort line paralleling the X-axis(representing the radius).

A = 0.189 V1.5

Where A is the spiral parameter (m)V is the design speed (km/h)

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As a vehicle traverses a spiral curve, the decreasingradius requires a corresponding increase insuperelevation. In order to ensure a gradual change inthe resulting radial acceleration, the superelevation isapplied over the length of the spiral by raising orlowering the edge of pavement relative to some fixedprofile control line. The slope of the outer edge ofpavement, if permitted to become excessive relative tothe profile control line, creates an aestheticallyunpleasant kink in the vertical alignment of thepavement edge. The upper limiting values for relativeslope between the outer edge of pavement andcentreline (that is, profile control) for two-lanepavements at various design speeds are shown inTable B.3.8.2.2.

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Design Speed(km/h)

Relative Slope (%)

40 0.7050 0.6560 0.6070 0.5680 0.5190 0.47100 0.44110 0.41120 0.38130 0.36

Utilizing the maximum permissible values for relativeslope from Table B.3.8.2.2, the minimum length ofspiral, L, can be found from the following expression:

Lwes

= 1002

Where L is the length of spiral (m)w is the width of pavement (m)e is the superelevation being developed

(m/m)s is the relative slope (%)

For a given design speed and radius, superelevationand relative slope are known, and minimum lengthscan be calculated. From minimum length and radius,the minimum spiral parameter can be calculated,using the expression:

A2 = RL

Where A is the spiral parameterR is the radius (m)L is the length of spiral (m)



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Short spiral curves are visually unpleasant. It isgenerally accepted that the length of the spiral curveshould be such that driving time is at least twoseconds. For a given radius and speed, therefore, theminimum length FORMULAE and minimum spiralparameter can be calculated using the expression:

A2 = 0.56RV

Where A is the spiral parameterR is the radius (m)V is the design speed (km/h)

The minimum spiral requirement for design is thehighest of the three values required for comfort,runoff, and aesthetics. For smaller radii the comfortcriterion controls, for the next larger set of radii therelative slope criterion controls, and for the largerradii the aesthetic criterion controls.

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Spiral A parameter values for design are shown inTables B.3.6a and B.3.6b for maximum superelevationrates of 0.06 m/m and 0.08 m/m, respectively. Foreach design speed and radius, minimum and

desirable A parameters are given. On two-lanepavements desirable values should be used wheneverpossible. For three-lane and four-lane pavementsdesirable values are to be used, and on six-lanepavements desirable values multiplied by 1.15 are tobe used. Spiral A parameter values are shownrounded to the nearest whole metre.

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The minimum lateral clearances required on curvesfor each design speed to provide safe passing sightdistance and stopping sight distance for a wide rangeof radii, are given in Figures B-3.9a and B-3.9b. Theco-ordinates were calculated using the values shownin Table B.2.4 and in Table B.2.3, respectively.

Horizontal stopping sight distance should beprovided along the entire road length. This may onlyinvolve the changing of a backslope, the removal oftrees and hedges, or setback of a bridge handrail.Exceptions should be made only in rare cases, wherethe cost of such provision would be excessive, andthen only with approval of a design exception.Horizontal sight distance for passing should beprovided as frequently as possible.



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The following general controls should be consideredin design of vertical alignment, in addition to thespecific controls related to sight distance, vehicleperformance, drainage, etc., that are detailed later inthis chapter.

1. A smooth gradeline with gradual changes,consistent with the type of highway and terrain,should be preferred over a line with numerousbreaks and short lengths of grades. Detaileddesign values are the maximum grade and thecritical length of grade, but the manner in whichthey are applied and fitted to the terrain on acontinuous line determines the suitability andappearance of the finished product.

2. The roller-coaster or the hidden-dip type ofprofile should be avoided. Such profilesgenerally occur on relatively straight horizontalalignment where the roadway profile closelyfollows a rolling natural ground line. Examplesof these undesirable profiles are evident onmany older highways. They are unpleasantaesthetically and more difficult to drive. Hiddendips contribute to passing manoeuvre problemsfor drivers. The passing driver is deceived by theview of the road or street beyond the dip thatappears to be free of opposing vehicles. Evenwith shallow dips, this type of profile isdisconcerting because the driver does not knowif there are oncoming vehicles hidden beyondthe rise. This type of profile is avoided by use ofhorizontal curves or by more gradual grades.

3. Undulating gradelines, involving substantiallengths of grade, should be appraised for theireffect on traffic operation. Such profiles permitheavy trucks to operate at higher overall speeds

than is possible when an upgrade is notpreceded by a downgrade. However, they mayencourage excessive speeds of trucks withattendant conflicts with other traffic.

4. A broken-back gradeline (two vertical curves inthe same direction separated by short section oftangent grade) generally should be avoided,particularly in sags where the full view of bothvertical curves is not pleasing. This effect is verynoticeable on divided roadways with openmedian sections.

5. On long grades it may be preferable to place thesteepest grades at the bottom and lighten thegrades near the top of the ascent. Another optionis to break the sustained grade by short intervalsof lighter grade instead of a uniform sustainedgrade that might be only slightly below theallowable maximum. This is particularlyapplicable to low-design-speed highways.

6. Where at-grade intersections occur on roadwaysections with moderate to steep grades, it isdesirable to reduce the gradient through theintersection to less than three percent. Such aprofile change is beneficial for all vehiclesmaking turns and serves to reduce the potentialhazards.

7. Sag vertical curves should be avoided in cutsunless adequate drainage can be provided.

8. Generally, to ensure a smooth gradeline, aminimum Vertical Point of Intersection (VPI)spacing of 300m is used. A minimum length ofvertical curve of 120m is used also to ensure thatthe parabolic shape is achieved using a surveycontrol with 20m stations. Asymmetric paraboliccurves may be used in special cases to suitterrain. This is achieved by using a differentlength for the second half of the curve comparedto the first half; that is, the K value will change.



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Table A.7 provides the desirable maximum gradientthat should be used for each design designation. Thedesirable maximum gradient is three percent ondivided highways and RAU-213.4 roadways, fivepercent on undivided highways with pavementwidth from nine metres to 11.8m, and six percent onundivided two-lane eight metre roadways. Highermaximums are permitted on local roads due to thelower speeds and lower volumes. The use of thesedesirable maximum gradients will contribute towardsvery uniform vehicle speeds on the higher standardroadways with greater speed variation on the lowerdesign designation roadways. With all other factorsbeing equal, this would result in higher levels ofservice on the higher designation facilities.

The desirable maximum gradients shown in TableA.7 provide maximum gradients that should not beexceeded whenever practical. However, themaximum gradient is site specific. On alignmentswhere construction costs increase substantiallydepending on the maximum gradient, an economicanalysis should be undertaken to determine thesuitable maximum gradient for that roadway section.This is why an absolute maximum gradient is notsuggested in Table A.7. The economic analysis shouldinclude road user costs for collisions and vehiclerunning costs over the design life of the highway aswell as construction costs, highway maintenancecosts, and any other costs that are impacted by thechoice of maximum gradient. It should be noted thatthe choice of maximum gradient may have a bearingon whether or not a climbing lane or truck runawaylane is required and this should be included in theeconomic analysis. For economic analysis purposes,the department uses a guide entitled Benefit-CostAnalysis which was prepared by K.E. Howery,P. Eng., and Applications Management ConsultingLtd. This guide presents the analysis methods andunit costs to be used for collisions and other road usercosts to ensure uniformity for various evaluations.This guide can be obtained from Planning ServicesBranch.

An additional consideration that will not be apparentspecifically from the economic analysis is level ofservice. Level of service can be downgradedconsiderably by the choice of a maximum gradientexceeding three percent on a long grade withsignificant truck traffic, especially where a climbinglane is not warranted on a two-lane roadway.

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Passenger cars The practices of passenger caroperators with respect to grades vary greatly. Thereis a general acceptance that nearly all passenger carscan readily negotiate grades as steep as four to fivepercent without appreciable loss in speed below thatnormally maintained on level highways, except forcars with high weight/horsepower ratios, includingsome compact and subcompact cars.

Studies show that operation on a three percentupgrade, compared with that on the level, has only aslight effect on passenger car speeds underuncongested conditions. On steeper grades, thespeeds decrease progressively with an increase in theascending grade. On downgrades, passenger carspeeds generally are slightly higher than on levelsections but local conditions govern.

Trucks The effect of grades on truck speeds is muchmore pronounced than on passenger car speeds.Average speed of trucks on level sections of highwayapproximates the average speed of passenger cars.Trucks display up to about a five percent increase inspeed on downgrades and about a seven percent ormore decrease in speed on upgrades as compared tooperation on the level. On upgrades the maximumspeed that can be maintained by a truck dependsprimarily on the length and steepness of the gradeand the mass/power ratio, which is the gross vehicleweight in grams divided by the engine horsepower inwatts. The effect of rate and length of grade on thespeed of typical heavy trucks is shown in TableB.5.3.1a through Table B.5.3.1e in the climbing lanesection of this chapter. Performance characteristics forvarious different mass:power ratios are shown. It hasbeen found that trucks with a mass:power ratio ofabout 180g/W have acceptable operatingcharacteristics from the standpoint of the highwayuser. Such a mass/power ratio assures a minimumcrawl speed of about 43 km/h on a long three percentupgrade. There is evidence that the automotiveindustry finds a mass/power ratio of this magnitudeacceptable as a minimum goal in the design ofcommercial vehicles. There is also evidence that thecarrier operators are voluntarily recognizing this ratioas a minimum performance control in the loadsplaced on trucks of different power. The overallresult is that mass/power ratios of trucks onhighways have improved in recent years; that is,truck performance has improved.



A mass/power ratio of 180g/W should be used ingeneral for the design truck for the purpose ofsimulation of vehicle performance on grade forAlberta highways. Field surveys of truck ratings haveshown the 180g/W generally provides for more than85 percent of the trucks in the traffic stream.Additional performance charts are provided forspecial situations; for example, where the designtruck is a log haul truck or where at least 20 percentof the heavy vehicles consist of seven or eight axletrucks, as may be the case on divided highways,200g/W should be used. For light trucks or recreationvehicles 60g/W is appropriate; that is, it should onlybe used where at least 85 percent of the heavyvehicles are recreational vehicles or light trucks (twoaxles). Similarly, the 120g/W and 150g/W areappropriate where the design vehicle is a three axleor five axle truck, respectively.

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Level grades (0 percent) on uncurbed rural highwaysare considered perfectly acceptable provided that theroadway surface is adequately crowned to drain thesurface laterally. A two percent crown is standard forpaved roadways and three percent for gravelsurfaces. Although a level grade is acceptable on theroadway surface, some positive drainage is requiredin the roadside ditch to ensure that ponding does notoccur. A different gradient in the ditch compared tothe road surface can be built using a design ditch.This is achieved by adjusting the ditch depth. Thispractice is also known as false grading. Table B.4.3provides the desirable and absolute minimumgradients for narrow and wide roadside ditches.Flatter gradients are permitted on the wider ditchesbased on the assumption that the ditch bottom will

slope away from the roadway. Since this cross-slopehelps keep water away from the subgrade, a smallervalue for longitudinal gradients may be used. Forwide ditches the desirable minimum longitudinalgrade is 0.2 percent and absolute minimum is 0.05percent. Where the longitudinal ditch gradient isquite flat, designers should consider using a fivepercent cross-slope on the ditch bottom (slopingaway from the subgrade) to provide a drierembankment.

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On curbed pavements where drainage is adjacent tothe travel lanes, longitudinal gradients must be set toeliminate excessive water accumulation on thepavement. A minimum grade for the usual case is0.5 percent, but an absolute minimum of 0.35 percentmay be used where the pavement surface isaccurately crowned and supported on firm subgrade.

Table B.4.3 gives the standard minimum longitudinalgradients for roadways and ditches on all classes ofroads.

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GRADIENTRoadway

TypeDesirable

Minimum %Absolute

Minimum %Rural Highways Longitudinal Gradient for

DitchWide Ditches(greater than 3m)

0.2 0.05

Narrow Ditches(less than 3m)

0.5 0.2

Urban Roadways(curbed)

Longitudinal Gradient forRoadway Surface

Roadway Surface 0.5 0.35



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The K parameter is a coefficient for defining the rateof gradient change. For example, a K value of 90means a horizontal distance of 90m is required forevery one percent gradient change.

For metric curve calculation the length of a verticalcurve is based on the K value, using the formula:

L = KA

Where L is the horizontal length of thevertical curve (m)

A is the algebraic difference ingradient between the twointersecting gradelines (%)

K is a coefficient, as described above

Table B.4.4 provides a summary of all the minimumvertical curve K parameters based on stopping, non-striping and passing sight distance criteria. Thedecision sight distance K values are not includedbecause the vertical curvature depends on the heightof object which is variable (depending on what thedriver needs to see to make a decision).

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Minimum crest vertical curves that satisfy stopping,non-striping and passing sight distancerequirements are given in Table B.4.4. Theseminimum curvatures are expressed in terms of the Kparameter for each design speed.

Minimum crest curve K values which satisfystopping sight distance requirements were derivedbased on an eye height of 1.05m, object height of

0.38m and using the unrounded minimum stoppingsight distances (see Table B.2.3). These values aregiven for minimum curve lengths for each designspeed, but in practice a higher value should be usedwhenever possible.

The designer should use crest vertical curves thatprovide passing sight distance on two-lane highwayswherever economically practicable. This will resultin improved traffic flow, increased capacity andprobably some reduction in the number of collisions.Minimum crest vertical curves that satisfy passingsight distance requirements were derived based onan eye height of 1.05m, height of opposing vehicle of1.30m and using minimum passing sight distances asshown in Table B.2.4.

Passing sight distance is desirable on crest verticalcurves; however, where it is not economicallyfeasible to provide passing sight distance, theprovision of non-striping sight distance is of somebenefit. Non-striping sight distance is still adequateto allow drivers to complete safe passes; however,drivers must be prepared to abort a pass if anoncoming vehicle comes into view at the criticalmoment, that is, when actual passing is about tooccur. Section B.2 includes further information aboutthe differences between passing sight distance andnon-striping sight distance.

Using a K value greater than the minimum stoppingsight K but less than the minimum non-striping Kwill increase the length of the barrier line; that is, itwill increase the length of the no passing zone on thecrest vertical curve.

Figures B-4.4.2a, b and c show the models andformulae used to determine the crest verticalcurvature K parameters.



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Design Assumed MINIMUM K VALUES OF VERTICAL CURVESSpeed Running Speed Vertical Crest Curves Vertical Sag Curves (SSD)(km/h) (km/h) SSD NSSD* PSD Headlight

ControlComfortControl

40 40 5 - 80 7 550 50 10 - 125 12 760 60 15 - 190 20 1070 70 25 - 245 25 1380 80 35 - 335 35 1790 90 55 - 410 40 21100 100 75 250 495 50 26110 108 100 250 585 60 30120 115 130 250 685 70 35130 115 140 - 790 70 35

height of eye (m) 1.05 1.15 1.05 1.05 - height of object (m) 0.38 1.15 1.3 0 -

SSD = Stopping Sight DistanceNSSD = Non-Striping Sight DistancePSD = Passing Sight Distance

* Although a “K” value of 250 should be used on new construction as a desirable parameter where passing is tobe permitted, a lower “K” value may also allow passing. Using the current AI practice for marking barrierlines, based on a sight distance of 425 m and eye height = object height = 1.15 m, a “K” value of 197 m mayallow passing. Also where the crest curve is less than 425 m long, passing may be permitted even on sharpercrests (this can be established from the profile plan or through measurements taken in the field).



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The minimum vertical curvature on sag curves,shown in Figure B-4.4.3, is based on providingstopping sight distance within the headlight beam.This is described as headlight control and is onlyappropriate for roadways that are not illuminated.Headlight control is based on the followingassumptions: headlight beams slope upward at anangle of one degree from the plane of the vehicle,height of headlights is 0.6m above the drivingsurface, and the object (to be stopped for) comes intoview when the vehicle is the minimum stoppingsight distance away.

On illuminated sag curves, it is acceptable to usecomfort control rather than headlight control toselect K values for sag vertical curves. These valuesare normally exceeded where feasible, inconsideration of possible power failures and othermalfunctions to the streetlighting systems. Thecomfort K value is based on the radial accelerationexperienced by occupants of vehicles travelling atthe assumed running speed at the bottom of the sagvertical curve. The maximum acceptable radialacceleration adopted by Alberta Infrastructure is0.3m/s2, based on TAC. The comfort K valuesshown in Figure B-4.4.3 and Table A.7 are based onthis allowable radial acceleration.



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Auxiliary lanes are additional lanes that can beprovided at selected locations along highways tofacilitate turning, deceleration, acceleration, passingor low velocity climbing (climbing lanes). Auxiliarylanes for turning, deceleration, or acceleration arenormally provided at intersection treatments andtherefore are included in Chapter D. Climbing lanesand passing lanes are generally required due to thecharacteristics of the vertical and horizontalalignment, together with other factors, and thereforeare covered in this chapter.

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The following geometric criteria should be met inprovision of climbing or passing lanes.

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The width of the auxiliary lane should be the sameas the through lane, that is, 3.7m for designdesignation of RAU-211.8 and higher or 3.5m fordesign designations of RAU-210 and lower.

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The shoulder adjacent to the auxiliary lane should beequal to the lesser of 1.5m or the standard shoulderwidth on that design designation of highway.

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Superelevation on the climbing lane portion of theroadway surface should generally be the same as onthe adjacent through lane. However, whereoperating speeds of heavy vehicles can be expectedto be much lower than design speed, the designermay use judgment in selecting a lowersuperelevation rate. Superelevation on the passinglane portion of the roadway surface should be thesame as the adjacent through lane.

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The taper at the beginning and end ofclimbing/passing lane should be 60:1. The 60:1 taperon the diverge should promote use of the right handlane by all vehicles except those intending toovertake slower vehicles.

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Locations that include or are in close proximity tointersections should be avoided because of possibleoperational difficulties. Where these situationscannot be avoided, a site specific analysis should beundertaken to determine the intersection treatmentrequired. The treatment may require construction ofan additional lane or relocation of the intersection.

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The full width of a climbing lane should begin whenthe design truck has experienced a 15 km/h speedreduction. It should not be terminated until thedesign truck has regained the speed that it had at thebeginning of the climbing lane.

A climbing lane could be started earlier or endedlater if this would result in a noticeableimprovement in traffic operations; for example, onroadways where the passing demand is high (due tohigh volume and/or high percentage of heavyvehicles) and the length of grade is short. Where ithas been decided that a climbing lane should belengthened, it is generally preferable to add to thebeginning of the climbing lane. Beginning a climbinglane earlier (that is, before heavier vehicles havedecreased their speed by 15 km/h) will allowfollowing vehicles to pass without having todecelerate to 80 km/h. This results in a moreefficient climbing lane when the passing demand ishigh and a generally higher level of service for theroadway. It is preferable that the length of climbinglane be minimized to less than two to three km toprovide greater cost-effectiveness. Very longclimbing lanes, especially on lower volume roads,tend to be under-utilized.

The desirable length of a passing lane is between 1.5km and 2.0 km. This range is long enough to beadequate for dispersing queues while still beingshort enough to be cost effective.



With long continuous grades, it is occasionallyimpractical to continue a climbing lane for thecomplete length required for the design truck toregain the entry speed. In this case, it is necessary toterminate the extra lane prematurely. It is importantto ensure that there is good sight distance usingdecision sight distance criteria at the end point. It isalso good practice to provide an extra wide shoulder(3.5m) for some length after the termination point.This length of wide shoulder should be sufficient toallow a vehicle travelling in the upgrade direction tocome to a safe stop in an emergency situation,assuming the vehicle is at a reduced speed on theupgrade as shown by the design vehicleperformance charts. The designer may use theappropriate stopping sight distance as a guide. Thewide shoulder will serve as an escape lane andshould reduce the occurrence of collisions at themerge area. The merge area can be very problematicfor recreational vehicles and trucks, especially if thelane is ended prematurely. Under thesecircumstances, the absence of an escape lane canreduce the utilization and effectiveness of a climbinglane.

Very long passing or climbing lanes are especiallyundesirable on high volume two-lane highwaysbecause of the restricted passing for the opposingtraffic stream. Current pavement marking guidelinesin Alberta suggest that a double solid barrier line(prohibiting passing in the single lane direction) bepainted at all passing/climbing lane locations onundivided highways where the AADT exceeds 4000.Where the AADT is less than 4000, passing ispermitted in the single lane direction provided thatpassing sight distance is available. This is illustratedon Figure B-5.2.7.

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Decision sight distance should be available fordrivers of passenger vehicles to see the pavementsurface in the first half of the taper at the terminationof a climbing lane or passing lane. A similar sightdistance is desirable but not essential at thebeginning of climbing or passing lanes. Whenmeasuring the decision sight distance, a height ofeye 1.05m (corresponding to a passenger vehicle)and a height of object of 0 (corresponding to theroadway surface) should be used. The range ofdecision sight distances suggested for thetermination of an auxiliary lane is shown onTable B.2.6.

For the purpose of measuring decision sightdistance, the object can be assumed to be 120m pastthe beginning of taper at the termination of theclimbing lane. The reasons for selecting this locationare as follows:

1. A driver seeing the pavement surface at thispoint will know that there is a taper. (That is, thedriver will already have seen the two arrows onthe pavement, the end of the auxiliary lane lineand the narrower pavement.)

2. The decision sight distance requirement includes

four seconds for a manoeuvre (lane change)which could occur on the first half of the taper (avehicle travelling at 110 km/h will travelapproximately 120 m in four seconds).

For example, for a design speed of 110 km/h, thedriver of a passenger vehicle should be able to seethe pavement surface over the first 120m of taperfrom a point 210m - 310m before the taper begins.This should enhance the safety of mergingoperations. Figure B-5.2.7 illustrates the generallayout of a climbing/passing lane including typicalsigning and pavement markings and the decisionsight distance requirement.



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Level of service and safety of operation on two-lanehighways are impacted by the extent and frequencyof passing sections. They are also adversely affectedby heavily loaded vehicles operating on grades ofsufficient length to result in speeds that couldimpede following vehicles. Because of the highnumber of accidents occurring on grades involvingheavy vehicles, climbing lanes are commonlyincluded in new construction of busier highwaysand additional lanes on existing highways arefrequently built as safety improvement projects. Thejustification for these safety improvements isdemonstrated by a plot of accident involvement ratefor trucks on two-lane roads versus speed reduction.See Figure B-5.3.

It is desirable to provide a climbing lane as an extralane on the upgrade side of a two-lane highwaywhere the grade, traffic volume and heavy vehiclecomponent combine to degrade traffic operationsfrom those on the approach to the grade. Whereclimbing lanes have been provided, there has been ahigh degree of compliance in their use by truckdrivers. On highways with low volumes, only theoccasional car is delayed. Climbing lanes, althoughdesirable, may not be justified economically evenwhere the critical length of grade is exceeded. Awarrant system is used to identify those cases wherea climbing lane is called for based on safety andoverall cost-effectiveness.



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Climbing lanes should normally be provided onlywhen both the speed reduction warrant and trafficvolume warrant are met on a particular upgradesegment of roadway.

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A 15 km/h speed reduction is experienced by thedesign truck.

For the purpose of calculating the speed reduction oftrucks on gradient the following assumptions areused: • The truck entry speed is 95 km/h • The mass power ratio for the design truck is

180 g/W.

The truck entry speed is based on mean speedrecorded for trucks on two-lane highways inAlberta. The mass/power ratio is based on a surveyof the Alberta trucking industry together with a spotsurvey taken at provincial vehicle inspection

stations. The 180 g/W rating, which correspondsapproximately to 300lbs/hp used by many U.S.Transportation Departments, is based on the 85thpercentile mass/power ratio, that is, 85 percent ofthe heavy vehicles in the upgrade traffic streamshould be able to perform as well or better than thedesign truck.

Exceptions to the standard design truck mass/powerratio should only be made where records of theactual mass/power ratio of the trucks in the trafficstream indicate that a different value would moreclosely represent the 85th percentile heavy vehicle.An example of this may be a predominantlyrecreational route where more than 85 percent of theheavy vehicles are recreational, in which case alower mass/power ratio (probably 120 g/W) wouldbe appropriate.

Table B.5.3.1a may be used as a quick reference todetermine if the speed reduction warrant is met on aparticular grade. The truck performance curvesshould be used together with other considerations todetermine the exact start and end point of theclimbing lane.

GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

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Design Truck Mass/Power Rating Grade in PercentageMetric Imperial 2 3 4 5 6 7 860 g/W (100lb/hp) N/A N/A 740 410 240 190 180120 g/W (200 lb/hp N/A N/A 440 280 240 200 160150 g/W (250 lb/hp) 730 360 280 220 170 140 -180 g/W (300 lb/hp)* 550 340 260 210 160 120 -200 g/W (325 lb/hp) 520 320 260 210 160 120

Note: * 180 g/W is normally used for 2 lane highways.

1. Length of specified grade at which the designated designtruck speed is reduced by 15 km/h from its entry speed(entry speed assumed to be 95 km/h)

2. Conversion factor: 1 g/W = 1.645 lb/hp

3. Values shown above have been rounded.



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The volume warrant for climbing lanes onundivided roadways is shown in Tables B.5.3.1bthrough B.5.3.1e. This volume warrant is based ontwo conditions:

1. The heavy traffic (T) must exceed 150 veh/day 2. The level of service on the grade must drop

below LOS A in the design hour on the two-laneroadway, that is, if the level of service on thegrade in the design hour is LOS A, a climbinglane is not required.

Note: T is defined as the total number of tractortrailer-combinations and single unit trucksplus half of the recreational vehicles plushalf of the buses. Buses and recreationalvehicles generally perform better than truckson grades.

If the traffic volume required for the warrant isprojected to occur in the first half of the design life,the climbing lane shall be considered warranted, thatis, it is not necessary to justify a climbing lane basedon existing traffic volume.

On particular projects, it may be possible to showthat the construction of climbing lanes is costeffective even though the traffic volume does notmeet the general warrant. In this case, theconstruction of climbing lanes would be consideredgood design.

The daily volume to be used for design purposes isgenerally the AADT, unless the ASDT or AWDT ismore than 15 percent greater than AADT, in whichcase the higher number should be used.

The reasons for recommending this volume warrantare as follows:

1. It is necessary to choose a minimum volume forwhich climbing lanes would be built. Use of thelevel of service criteria alone could result in somevery low volume roads warranting climbing lanes,even though they are not cost effective, based oncollision reduction or road user savings. A volumeof 150 heavy vehicles per day was chosen becausethis represents one heavily loaded vehicletravelling in the upgrade direction for every 10minutes in the design hour, that is, 150 heavyveh/day = 22 heavy vehicles/hour = 11 loaded

heavy vehicles/hour = 6 loaded heavyvehicles/direction/hour. This is based on theassumption that the design hour volume equals 15percent of the AADT. The presence of one loadedheavy vehicle travelling in the upgrade directionevery 10 minutes in the design hour (30th highesthour of the design year) does not represent aserious congestion problem nor would it normallybe a serious safety problem.

2. A warrant which is based on volume only without

consideration of length of grade, steepness andtraffic composition would be too simplistic.Alberta’s warrant considers all those variables byusing the level of service on the upgrade and theminimum number of heavy vehicles.

3. A review of the geometry and traffic conditions at

91 existing climbing lanes on Alberta’s primary andsecondary highway system shows that neither thevolume nor the level of service criteriarecommended in this warrant are too high. In fact,there are some climbing lanes in Alberta that havelower volume and higher level of service thanrequired by the warrant.

Although 150 heavy vehicles/day is suggested as ageneral warrant, it is noted that inclusion of climbinglanes in low volume situations should be considered ifshown to be cost-effective. Construction of climbinglanes may be less costly on new construction projects oron projects where the existing or proposed shoulder iswide. The benefits of providing climbing lanes may begreater if:

1. There is a high percentage of loaded trucks in theupgrade traffic stream

2. If the geometry of the highway, prior to the grade,

is very restrictive for passing, thus resulting in ahigh demand for passing.

To be considered cost-effective, the benefits(considering road user costs, time savings andreduction in collision costs) should be sufficient to givea four percent internal rate of return on the extrainvestment required for construction of the climbinglane. The four percent internal rate of return shouldresult before the end of the design life of theimprovement. This is usually 20 years but may be less iffuture twinning is scheduled. The department’s BenefitCost Analysis guidelines should be followed for theeconomic analysis.



The following is an example of the use of theclimbing lane warrant for two-lane highways.

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Listed below is the geometric and traffic informationfor a particular segment of two-lane roadway whereconstruction of a climbing lane is being considered.

Design Designation: RAU-211.8-110Length of Grade: 500mAverage Gradient: 3%Percentage of PassingZones on UpgradeSegment: 50%, i.e., on a 2 lane

roadway 50% of thecentreline would bepainted as a barrierzone.

Design Truck: 180 g/WDesign/Existing AADT: 2000/1333 Based on

20 year design lifeand 2.5% annualgrowth notcompounded.

Traffic Composition: TRTL: 8%SU: 3%RV: 6%BUS: 2%PV: 81%

Design Hour Factor (K) 0.15, i.e., DesignHour Volume =Design AADT x 0.15= 300

Step 1: Check Speed Reduction Warrant

According to Table B.5.3.1a, a 15 km/hspeed reduction would have occurredafter 340 m at three percent using a180 g/w design truck. Therefore, speedreduction warrant is definitely met on a500 m long three percent grade. The

speed distance charts should be used tolocate the points at which the 15 km/hspeed reduction occurs on both thedeceleration and acceleration portions ofthe vertical alignment.

Step 2: Check Traffic Volume Warrant

Based on the traffic composition, a valuefor T is calculated as shown below:

T = TRTL + SU + 1/2 (RV + BUS)= 8 + 3 + 1/2 (6 + 2)= 15%

Because the percentage of passing zones on thesegment in question is 50 percent, Table B.5.3.1d isused as the volume warrant. The assumptions usedare all consistent with this design designation andthe traffic characteristics shown.

The minimum volume required to warrant aclimbing lane for a three percent grade of 500 mlength with T = 15% is 1,871 AADT.

The existing AADT is 1333.

The design AADT is 2000, that is after 20 years with2.5 percent annual growth not compounded.

The projected AADT for the 16th year is 1,866; thatis, 1333 x [1 + 16 (0.025)].

The projected AADT for the 17th year is 1,899; thatis, 1333 x [1 + 17 (0.025)].

The volume warrant for this grade is only achievedin the 17th year and therefore a climbing lane is notwarranted at this time.

Note: If the volume warrant was met on or beforethe 10th year, a climbing lane would bewarranted.



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The addition of climbing lanes to four-lane dividedhighways need not be considered if the AADT is lessthan 12,000, regardless of grades or percentages oftrucks, because of the generally high level of serviceprovided by a four-lane divided facility with thistraffic volume. If the AADT exceeds 12,000 and thedesign truck experiences a speed reductionexceeding 15 km/h, the level of service on theupgrade segment in the design hour should becompared to the level of service on the approachsegment. If there is a reduction of at least onecomplete level of service when going from theapproach segment to the upgrade, a climbing lane iswarranted.

There has been little application of climbing lanes todivided highways in Alberta to date, due to thegenerally high level of service that exists onprovincial divided facilities.

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Once the need for a climbing lane has beenestablished by satisfying the speed reduction andtraffic volume warrants, the exact start and endpoints and length are determined using the truckperformance curves (Figures B-5.3.3b throughB-5.3.3k).

The following example illustrates the use of thetruck performance curves.

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The vertical alignment and truck performancecurves are shown on Figure B-5.3.3a. The designtruck is assumed to have a mass/power ratio of 180g/W, as this is the standard truck. The dashed linessuperimposed on the performance curves of FigureB-5.3.3a show the plot of the design truck speedthroughout the alignment section as follows.

1. Entry speed = 95 km/h (assumed) at PI #1 (pointof intersection)

2. Truck decelerates to 52 km/h at PI #2 due to

800m upgrade at four percent 3. Truck decelerates to crawl speed (26 km/h) due

to 600m upgrade at six percent

The design truck now experiences a grade changewhose algebraic difference exceeds four percent; thatis, +6% - (-2%) = +8%.

When the algebraic difference exceeds four percent,the vertical curve connecting the grades isapproximated through the average gradesconnecting the quarter points on the semi-tangentsof the vertical curve. These quarter points act as newPI’s for the purpose of estimating the design vehiclespeed. In this example, the length of the verticalcurve is 800m. Therefore the quarter points occur at200m on either side of the real PI and the gradeconnecting the quarter points has been estimated attwo percent. This approximated grade, 400m inlength, reduces the length of the preceding andfollowing grades by 200m each. (The dashed linenow enters the acceleration portion of the chart, asthe design truck accelerates on the two percentupgrade).

4. Truck accelerates from crawl speed (26 km/h) to47 km/h on the 400m, two percent upgrade

5. Truck accelerates from 47 km/h to 75 km/h at PI

#4 on the 400m, two percent downgrade 6. Truck accelerates from 75 km/h to 80 km/h (the

merge speed) on a 300m, zero percent grade.

As per the plot shown on Figure B.5.3.3a, theclimbing lane should begin when the design truckspeed reaches 80 km/h (this occurs at 1+260). The60:1 taper should be introduced before this point.The end point of the climbing lane can be placedanywhere after the merge speed has been achieved,that is, after 3+500, provided that the decision sightdistance is available. The merge taper is placed afterthe end of climbing lane.



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Passing lanes are additional parallel auxiliary lanesprovided, on two-lane undivided highways, for theexclusive purpose of improving passingopportunities. Passing lanes should be considered asa cost-effective geometric improvement on two-laneroads where: the length and location of passingzones on the existing highway are less thandesirable, and the traffic volume is high enough thatthe level of service is noticeably low. Passing lanesshould also be considered on new construction ormajor realignment projects to achieve the desiredlevel-of-service. Passing lanes may also be a cost-effective solution where:

1. Volumes on a two-lane highway are increasingand will soon warrant twinning

2. Where the provision of passing lanes may

postpone the construction of a divided facility,for example for five to 10 years.

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To establish the need for passing lanes on an existingtwo-lane undivided rural highway, the net passingopportunity (NPO) concept is to be used.

The following is a brief description of the net passingopportunity concept and how it should be applied:

Net passing opportunity is a function of bothpassing opportunities provided by highwaygeometry and the number of gaps in the opposingtraffic stream. The probability of time gaps greaterthan 30 seconds available for overtaking, known asP(GAO), can be estimated using the followingformula:

P(GAO) = e(-0.0023381 Vopp)

Where Vopp = opposing traffic volume invehicles per hour

Values for P(GAO) for various values of Vopp havebeen tabulated in Table B.5.4.1a. The net passingopportunity for one direction on a particularsegment of highway in the hour of interest is equalto the product of the P(GAO) for that hour and thepercentage of passing zones (% PZ) availableaccording to pavement markings.

NPO = P(GAO) × (% PZ)

NPO = Net Passing Opportunity

P(GAO) = Percentage of the hour with gaps(greater than 30 seconds)

available for passing

% PZ = percentage of the road segmentwhere passing is allowed bypavement markings.

For example NPO = 0.792 x 0.730 = 0.578 = 57.8%;that is, the net passing opportunity is 57.8% on aroadway with 73% passing zones if the probability ofgaps is 79.2% (this corresponds to an opposingvolume of 100 veh/h).

To establish a warrant for provision of passing lanes, eachdirection of travel should be examined separately. This isbecause the NPO in one direction may be very low whileit is satisfactory in the other direction, depending ontraffic and geometric conditions.

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Opposing Volume, Vopp(veh/h)

Probability ofTime Gaps

Available forOvertaking

P(GAO)50 0.890100 0.792150 0.704200 0.627250 0.557300 0.496400 0.393500 0.311600 0.246

Note: P(GAO) = e(-0.0023381 Vopp)

For passing lane warrant purposes the Design HourVolume (DHV) for the roadway segment of interestis to be used. The DHV is calculated as follows:DHV = K (Design AADT). Where the K value isunknown, 0.15 may be assumed. The DHV willnormally correspond to the 30th highest hourlyvolume in the design year (approximately).

To obtain values for NPO based on opposing volumeand percent no passing zones, Table B.5.4.1b may be



used. It should be noted that the AADT valuesshown in Table B.5.4.1b have been calculated usingAADT = DHV/0.15. AADT values, assumingvarious directional splits (50:50, 55:45, and 60:40)have been provided at the top of Table B.5.4.1b. Ifthe traffic conditions in the design hour on thehighway being studied differ from above, make theappropriate adjustments.

Alberta’s passing lane warrant is shown in TableB.5.4.1b and can be summarized as follows:

1. If NPO ≥ 40%, the percentage of passing zones issatisfactory.

2. If 40% > NPO ≥ 30% , the percentage of passing

zones is marginal. 3. If NPO < 30%, the passing improvement is

warranted.

In Alberta, there is considerable variation in thepercentage of passing zones available on variousprojects. The network-wide average availability is73 percent on the paved roadways that have beenvideologged. The roadways with higher trafficvolumes tend to have better geometry and thereforemore passing zones.

For warranting purposes, designers should considerthe net passing opportunity for traffic derived fromthe higher volume directional split in the designhour because this is the direction with the highestpassing demand.

The directional split in the design hour has asignificant impact on the net passing opportunity fora given AADT. This is why three lines are providedon Table B.5.4.1b to show the various AADT valuesthat correspond to the three directional splits. Adesigner should use project specific trafficinformation where it is available, otherwise a 50:50split should be assumed.

Passing demand is proportional to the square of theone way stream flow according to Wardrop’sformula; that is:

PQ

V

2

= 0 562

. σ

Where P = overtaking demand (overtakings/km/h)

Q = stream flow (veh/h)V = mean unimpeded speed (km/h)σ = standard deviation of the

unimpeded speed distribution (km/h)

Therefore, with a 60:40 split, the passing demand inthe high volume direction is 2.25 times higher thanthe passing demand in the low volume direction.

The construction of passing lanes is only onesolution to the problem of a less than desirable levelof service. Other possible solutions are geometricimprovements, such as horizontal and/or verticalrealignments (to provide more passing zones) ortwinning, which would provide unlimitedpercentage of passing zones for both traffic streams.On existing paved roadways, the provision ofadditional passing opportunities throughconstruction of passing lanes may be more cost-effective than realignment and general gradewidening. However, in many cases geometricimprovements may be desirable to reduce road-usercosts or necessary for safety reasons.

On higher volume rural roadways, especially above5000 AADT with K = 0.15 (that is, DHV > 300), it willbe difficult to achieve a high level of service in thedesign hour without twinning. Therefore, passinglanes would have limited application. Passing lanesmay, however, be cost effective on high volumeundivided roadways if they can be used totemporarily alleviate traffic problems and hencedelay the need to twin for a period, for example fiveto 10 years. If passing lanes can be installed onexisting RAU-213.4 roadways by altering thepavement markings and without doing any gradewidening, this can be a very cost effectiveimprovement. However, the shoulders will be lessthan the desirable width. Therefore, this type ofimprovement should be considered as an interimmeasure only (less than five years).

Care must be taken when designing passing lanes toensure that the overall two-directional Net PassingOpportunity is significantly improved by theaddition of the passing lanes at the proposedlocations. Otherwise, the cost effectiveness will bequestionable.



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1. Passing lane locations should be chosen with aview to minimizing unnecessary costs. Locationsrequiring large culverts, bridge widenings,major cuts or major fills should be avoidedwhere possible unless the construction ofpassing lanes is beneficial in terms of balancingearthwork quantities.

2. Locations that include or are in close proximity

to intersections should be avoided because ofpossible operational difficulties. Where thesesituations cannot be avoided, the intersectionshould be relocated or a site specific analysisundertaken to determine the intersectiontreatment required.

3. It is important to ensure that the two-way

percent passing zones will be improved as aresult of passing lane construction. It must beremembered that if the existing AADT exceeds4000, the pavement will be marked with adouble barrier line through the passing lanesection. Therefore, no passing will be allowedfor the opposing traffic flow. Consequently, it isimperative to locate passing lanes in sections oflimited passing zones to ensure overall passingopportunities are improved, especially wherethe existing AADT exceeds 4000.

4. The addition of passing lanes should not result

in an imbalance in percentage of passing zones

between the two directions of travel on anundivided roadway. To achieve a balance, itmay be necessary to add passing zones for eachdirection of travel alternately.

Where passing lanes are being added to bothsides of a two-lane highway, it is generallypreferable to place a passing lane after a zone ofrestricted passing rather than before. This isreferred to as the tail-to-tail configuration. Theafter location allows the platoons, which havebeen built up over the zone of restricted passing,to be dissipated on the passing lane. Also, driverfrustration in the zone of restricted passing maybe alleviated by signs advising of the upcomingpassing lane.

5. Passing lane locations should be selected basedon review of geometric and traffic conditions inboth the upstream and downstream directions.Passing lanes in close proximity to four-lanesections, or downstream from climbing lanes,are not particularly effective in improving theoverall level of service.

6. Generally passing lanes should not exceed about

25 percent of the highway section length for eachdirection of travel. For example, on a 40 kmsection of highway, up to five passing lanes eachtwo km in length, could be constructed in eachdirection. This provides an average spacing ofsix km between the beginning of successivepassing lanes in the same direction.



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Typical highway transitions from four-lane divided totwo-lane undivided and the reverse are shown inFigures B-6.1a and B-6.1b. Figure B-6.1a showstransitions based on a 38m centreline offset whileFigure B-6.1b shows transitions based on a 30mcentreline offset.

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On projects where twinning of an existing two-lanefacility is expected to continue over the nextconstruction season or within the next five years, aparallel alignment section of the new two-lane, one-way roadway, should be built. This extension(grading and base course) beyond the point at which

transition back to a two-lane undivided highwayoccurs is called a stub. The stub of the new roadwayshould continue until there is a physical separationbetween the temporary transition section and thenew two-lane, one-way roadway. The stub shouldproceed with the -0.02 m/m cross-slope, extendingacross the temporary transition section, until the gorehas occurred between the two roadways. Beyond thegore, the transition roadway section may be rotated,attaining the proper cross-slope (-0.02 m/m), at thepoint where transition back to a two-lane undividedhighway is complete. Superelevation on the curvedportion of the transition is usually kept to twopercent to match the future crown. However, it isbuilt low to allow for one additional lift of ACP.

The benefit of this construction procedure is thattraffic on the transition lane is not disrupted whenconstruction resumes on the next twinned portion.There is also a cost savings in not having toreconstruct the transition portion of the highway.


CROSS-SECTION ELEMENTS B-89

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Temporary highway detours that are to be open forpublic use in Alberta must be designed and builtunder the supervision of a professional engineer asper the Engineering, Geological and GeophysicalProfessionals Act.

The following guidelines should be used wheretemporary detours are required to accommodate trafficon existing highways due to bridge construction orother activities. Designers may exceed the standardsshown here for efficiency or safety but lower standardsfor the geometric elements are generally notappropriate. The guidelines provide advice on thefollowing topics.

• Guidelines for surfacing of the detour;

• Appropriate design speed for the detour;

• Minimum geometric parameters that should beused for each design speed on a detour;

• Horizontal alignment guidelines.

A typical cross-section and two typical detour plansare also provided.

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Detour surfacing requirements generally depend on theroad type, the duration of the detour, the time of yearand the expected daily traffic volume during the timethe detour will be in place.

In winter conditions gravel surfacing is generallyadequate structurally due to the frozen groundconditions. Asphalt stabilized base-course (ASBC) isnot a good option for detours built in winter becausethe material is not readily available. In spring andsummer conditions ASBC (alone) does not providesufficient structural strength for heavy trucks andtherefore a gravel surface with dust abatementtreatment is more appropriate. A paved surface on adetour is generally only warranted where the dailytraffic volumes exceed 4000, the detour will be in placefor a long duration, or no alternate routes areavailable. A "long duration" is typically defined asmore than 3 weeks on a divided highway or morethan 4 months on an undivided highway.

In some cases the department may stipulate the type ofsurface required on a detour however, where this is notthe case, Table B.7.2 is suggested as a guide. Thesurfacing options are asphalt concrete pavement, orroad gravel with dust abatement treatment.

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Road Type

Short Duration< 4 Months

Long Duration> 4 Months

AADT Detour Surfacing AADT Detour Surfacing

Divided Primary Highway All Gravel/Pavement All Pavement

Undivided Primary> 4000 Gravel > 4000 Pavement/Gravel

Highway< 4000 Gravel < 4000 Gravel

Secondary Highway orLocal Road

All Gravel All Gravel


B-90 CROSS-SECTION ELEMENTS

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Design speed of the detour is selected based on thetraffic volume and the expected duration of the detour.

Generally a 60 km/h minimum design speed isappropriate for all detours. Detours that are designedfor 60 km/h may be posted for 50 km/h. A 40 km/hposted speed may be used if necessary to reduce vehiclespeeds in the construction zone. Higher design speedsmay be appropriate in some cases, for example wherethe traffic will use the detour for a long duration orwhere the detour itself is long. A 50 km/h design speedmay be appropriate for lower volumes (AADT < 500) orshort duration detours.

Illumination, using at least two overhead streetlights,one at each detour entrance to the highway, is generallyprovided on all detours where any hazard is involved.

Where a temporary structure is required on the detourto accommodate the flow of water, the contractor’sengineer should select the size based on an engineeringassessment and professional judgement unless a sizehas been specified by the Department. Detour crossingstructures should generally be designed to handle a 1 in5 year flood if the structure will be in placed during thestream’s typical flood season.

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At the conclusion to the permanent highway the detourshould begin with 40 m long 20:1 tapers. This providesa visual cue to the driver. A horizontal curve can beginat the end of taper without any spiral transition. A

curve in the opposite direction may be joined directly tothe end of this curve, without spiral transitions ortangents between curves.

The maximum deflection angles and minimum radii areshown in Table B.7.2.2a. The minimum radii have beenselected based on a maximum superelevation of 0.05m/m and maximum side-friction factors for the limit ofcomfortable driving as recommended for low-speedurban design. These friction factors are chosen becausedetours do not have to provide the same level ofcomfort that is appropriate on the open highway,however, they must be safe. The purpose of using a 0.05m/m superelevation rate is to safely accommodate thefull range of speeds, including very low speeds coupledwith adverse weather/road conditions. When roadconditions are good and speeds are higher the surfacewill still provide an adequate margin of safety againstsideslipping. Table B.7.2.2b "Superelevation for Detour"has been developed to show recommended "e" valuesfor each radius for design speeds from 40 km/h to 90km/h. For higher design speeds the 0.06 m/msuperelevation table in Section B.3.6 may be used. Thedistribution of e and f through the range of curvesshown in Table B.7.2.2b is based on Method 5 asdescribed in AASHTO’s 1994 publication "A Policy onGeometric Design of Highways and Streets". Method 5represents a practical distribution over the range ofcurvature.

Figures B-7.2.2b and B-7.2.2c show typical plan views ofbridge detours using three-curve and four curve layoutsrespectively. The four-curve layout is appropriatewhere a temporary bridge structure (overhead trusstype) requiring a tangent approach is utilized.


CROSS-SECTION ELEMENTS B-91

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Design Speed of Detour (km/h) 50 60 70 80 90

Max. Deflection (degrees) for first curvejoining the highway 30 25 20 15 10

Max. Grade (%) �- Primary Highways or Secondary

Highways > 200 AADT

8 8 8 8 7

Max. Grade (%) �- Secondary Highways or Local Roads < 200 AADT

10 10 9 8 7

Stopping Sight Distance (m) * 45 65 85 110 140

Min. Crest K. *(based on stopping sight distance) 5 10 15 25 35

Min. Sag K *(based on comfort control) 7 10 13 17 21

Max. Superelevation (m/m) Use 0.05 m/m as a maximum on the detour

Superelevation Use Table B.7.2.2b Superelevation for Detours

Min. Radius (m) ** 75 120 185 250 350

Min. Width (m) 9 m if AADT < 2000, 10 m if AADT > 2000

See notes on Figure B-7.2.2a

Sideslope on unprotected fills + 3:1 3:1 3:1 3:1 3:1

� Grades higher than the suggested maximum may be permitted as directed by the Engineer.

* Based on 10 km/h less than the design speed.

** Based on a maximum superelevation of 0.05 m/m and maximum side friction factors for "limit of comfort",as per low-speed urban design.

+ Where traffic is protected from the slope by traffic barrier, a steeper slope may be used behind the barrierbased on stability of soil.

Note: Adequate warning and decision sight distance (based on the design speeds of the highway) should beprovided on the approaches to the detour. The guidelines for construction zone signs and other traffic controldevices should also be followed.



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Design Speed (km/h)

Radius (m) 40 50 60 70 80 90

4500 NC NC NC NC NC NC

4000 NC NC NC NC NC RC

3000 NC NC NC NC RC RC

2000 NC NC NC RC RC RC

1500 NC NC RC RC 0.024 0.028

1000 NC RC 0.021 0.026 0.031 0.036

750 RC 0.021 0.026 0.032 0.036 0.041

500 RC 0.027 0.034 0.041 0.044 0.048

350 0.025 0.034 0.041 0.048 0.048 0.050

250 0.031 0.040 0.046 0.049 0.050 -

220 0.034 0.043 0.048 0.050 - -

185 0.037 0.046 0.049 0.50 - -

150 0.041 0.048 0.050 - - -

120 0.045 0.049 0.50 - - -

100 0.047 0.050 - - - -

75 0.049 0.050 - - - -

45 0.050 - - - - -

Notes: 1. The maximum superelevation rate for temporary detours is 0.05 m/m. 2. Simple circular curves are adequate for temporary detours, i.e., spiral transitions are not required.



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