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- 1. Transport Research Arena Europe 2010, Brussels Safer Curves on Multiple Lane Roads Johan Granlund IPMA certified Senior Project Manager Vectura Consulting AB Röda vägen 1, Box 874, SE-781 28 BORLÄNGE, SWEDEN johan.granlund@vectura.seAbstractMany road users have crashed at high speed in sharp curves during slippery road conditions. Toreduce the skid risk following high lateral forces, outercurves are banked into superelevation.Road designers are guided by design codes into what superelevation values to select among,given a reference speed and curve radius. Curve design codes are based on analysis of corneringforces acting on AASHO’s point-mass model of a vehicle. While the design codes typically yieldcurves with acceptable safety level, there is a systematic problem with skid accidents on multiplelane curves. This paper discusses a causal factor and recommends changes in curve design codesas well as actions to improve safety in existing unsafe curves. Current road design practiseapproximates the vehicle travelled path (and thus lateral force) by the road curvature, which isreasonable on small roads. On multiple lane roads however, many drivers are changing lane alsoin sharp curves since no oncoming traffic is present. When shifting lane quickly, the vehicleexperience a transient “curve radius” much sharper than indicated by the road curve radius. Thiscan yield higher lateral force than the road design code have considered. Then the superelevationmay be insufficient - when the road is slippery - to outbalance the cornering force. As a rule bythumb, sharp curves on multiple lane roads with high speed traffic should have maximumallowed cross slope in order to increase stability.
- 2. Transport Research Arena Europe 2010, Brussels1. IntroductionHorizontal road curves were recognised as a problem thousands of years ago. Evidence is presentin the book of the prophet Isaiah: “A voice of one calling in the desert; -Prepare the way for theLord, make straight paths for him. Every valley shall be filled in, every mountain and hill madelow. The crooked roads shall become straight, the rough ways smooth”.Since the introduction of the automobile, cornering is made at highway speeds and is associatedwith lateral forces that may bring instability and thus crash risk. Therefore it is not surprising thathorizontal curvature correlates strongly with crash rates on rural highways. After analysing 34000 road crashes in the United States, Gupta & Jain (1975) found that curvature actually is amore important factor than road width, vertical clearance as well as sight distance. They alsonoted that especially head-on collisions, collisions with fixed objects and rollover crashes occurdisproportionately on curved road sections.There is good agreement in the road safety research community that sharper curves cause moreaccidents (Charlton & de Pont 2007). Crash rates in curves have been found to be typically 2 to4.5 times higher than on straight road sections (Johnston 1982; Leonard et al. 1994). Trucksshow the highest raise in crash rates between straight and curved road sections. Single sharpcurves in highways with long straight sections as well as improperly banked curves (especially“flat curves”) create some of the most hazardous situations (Haywood 1980). A study of all fatalsingle crashes during four years in Sweden showed that outercurves count for five times morecrashes than innercurves (Lindholm 2002). The EU project Roadex found that hazardousimproper cross slope is several times more frequent in outercurves than in innercurves (Granlund2008). This finding is to be explained by road history. Ancient dirt roads were built with acrown, with cross slopes to the nearest roadside to maximize rain water drainage. The roadsection was the same in both straight sections and curves. There was simply no need for bankingup superelevation in outercurves, since the non-motorized carriages didn’t reach speed levelswhere side forces become high. As dirt roads have been upgraded to tarmac roads, many ancientoutercurves have not yet been updated with enough superelevation to meet the needs of themotorized road users.Also on modern highway curves, systematic problem with instability-accidents can be found.One case is sharp high speed multiple lane curves. This is exemplified by the 90 km/h curve onEuropean Highway Nr 4 in Skönsberg, see Figure 1. Every third car crash in Sundsvall occurs inthe Skönsberg area; see the crash map in Figure 2 and note that crash dots are piled in the curve.Figure 1 The Skönsberg Curve on E4 Highway North of Sundsvall City, Sweden
- 3. Transport Research Arena Europe 2010, Brussels Figure 2 Crashes Reported by the Rescue Department of Sundsvall During 10 Years According to the Swedish Traffic Accident Data Acquisition (STRADA) database, at least 82 % of the reported crashes in Skönsberg have involved skidding. 65 % have taken place with the road being reported as slippery due to rain, snow or ice. 29 % of all crashed vehicles were actively reported as making a lane-change. These figures are extremely disproportionate, since the E4 highway is dry most of the time and only a small fraction of our driving time is spent on changing lane on the highway. What is the reason for the disproportionate crash rate in multiple lane curves such as in Skönsberg, and how can the crash risk be reduced? 2. Reducing the Crash Risk in Multiple Lane Curves The objective of this paper is to discuss a cause to the excessive crash rates observed in sharp multiple lane curves. The paper will also recommend changes in curve design codes as well as actions to improve safety in existing unsafe curves on multiple lane roads. In addition the paper will also pinpoint the need for improved education of motor vehicle drivers. 3. Design of Cross Slope in Horizontal Curves Modern design of cross slope (a k a cross fall) in curves is based on the principle that it shall join force with the side friction between tyre and road, so they together outbalance the lateral force caused by driving through a curve at highway speed. In outercurves this is achieved by banking the cross slope into sufficient superelevation. 3.1 The Exciting Lateral Force As described by Newton’s second law of mechanics, cornering vehicles undergo centripetal acceleration acting toward the centre of the curvature. As seen in Formula 1, the associated lateral1 force F is a product of vehicle mass m [kg] and squared vehicle speed v [m/s], divided by the curve radius R [m]. For a vehicle with given reference speed, the lateral force depends1 In Figure 3 the centripetal acceleration is substituted by a corresponding centrifugal force in the opposite direction. Even though people in a cornering vehicle perceive a “centrifugal force”, it is fictive (not real) on the vehicle. This paper follows the practice set used in many road design manuals, by referring to the (fictive) centrifugal force, rather than to the fundamentally correct centripetal acceleration with opposite direction.
- 4. Transport Research Arena Europe 2010, Brusselsonly on the curve radius. Smaller radii (tighter curves) yield higher lateral forces. For tightcurves, even a minor increase in radius results in a large decrease of the lateral force. m * 2F RFormula 1, Lateral Acceleration Force Acting on a Cornering VehicleFigure 3 shows the factors influencing the cornering forces acting on a vehicle as described bythe AASHO point mass model used in road design manuals worldwide (Psarianos et al, 1995).These are the gravitational force G [N], the normal force N [N], the lateral force F [N], the sidefriction demand factor fs [-], and the tangent of the angle corresponding to pavementsuperelevation/banking/cross slope [%].Figure 3 Vehicle Cornering ForcesNote that the total road grip between tyre and pavement can be divided into a tangential part(braking friction, longitudinal direction) and a radial part (side friction, lateral direction). Theside friction is the part of the total road grip normally utilized when cornering.3.2 The Reaction Forces Needed to Balance the RideIf the lateral force F is not balanced by reaction forces, the vehicle ride will become unstable andthe risk of a traffic accident (run-off, skidding and rollover modes) will increase. There are tworeaction forces that may balance the lateral force F. One is the horizontal component of thenormal force; N * sin(). The other is the horizontal component of the side friction developedbetween the vehicles tyres and the pavement surface friction force, N * fs * cos(). This can beexpressed by the equation in Formula 2.F N * sin( ) N * f s * cos( )Formula 2, Lateral Equilibrium; Initial Setup
- 5. Transport Research Arena Europe 2010, BrusselsAfter division by cos (), substitution with N = m * g (g being the gravitation constant) and withF as per Formula 1, elimination of m and recalling that cos() is close to 1 for small angles(from a mathematical point of view, pavement cross slopes are small angles), the equation is,with good approximation, expressed as Formula 3. 2 tan( ) f sR* gFormula 3, Lateral Equilibrium; Final ExpressionNow recall that tan(α) represents the cross slope. Clearly, Formula 3 shows that a prerequisitefor steady cornering is that the sum of the cross slope and the side friction demand factor is highenough to outbalance the effect of vehicle speed, of the vehicle’s curved path and of gravity.Correct application of cross slope reduces the need for side friction, while incorrect cross slope -such as a crowned section in an ancient outercurve - increases the need for side friction.Cross slope design codes all over the world are fundamentally based on the equilibriumexpressions above. Most codes are presenting design charts, showing what cross slope to use asfunction of road curve radius and for given speeds. However, these design charts may differ,depending on what value of the side friction supply factor fs that has been applied. In Sweden,the used supply factor fs corresponds to the friction number between a good summer tyre (lockedwheel) and rain wet road in good condition, after deduction with 2/3 to add a safety margin(VGU). The supply factor used in Sweden is a function of speed and is calculated as perFormula 4.f s 0.28 * e 0.0096*3.6*Formula 4, The Side Friction Supply Factor used in Sweden [VGU]In cold climate with icy winter roads and winter (Mud + Snow) tyres, such as in northernScandinavia, lower side friction supply factor fs may be relevant. As seen in Formula 3, a lowerfs results in a demand for higher superelevation for a given speed and radius. In the USA, thefactor fs are set to a speed-depending value where 95 % of the drivers slow down by 3 - 5 km/hin the curve (NCHRP report 439).The design chart for cross slope in 90 km/h curves in Sweden is based on a side friction supplyfactor fs of 0.12, as given by Formula 4. (As per NCHRP report 439, American 90 km/hhighway curves are designed with a similar value - 0.13 - for the factor fs). The resultingSwedish design chart is showed in Figure 4. Note that the Swedish code only allows certaindiscrete values of cross slope. Since a curve with 1000 m radius may have 2.5 % or 4.0 % or 5.5% cross slope and still fulfil “Good” standard (“God”, in Swedish), it is of course not hazardousto have - let’s say - 3.2 % or 4.6 % cross slope in such a curve. A design chart that calls forunnecessary cross slope adjustments of the existing cross slope (for example 4.6 %) just to meetone of a few allowed discrete values, with no relevance what so ever to Newton´s laws ofphysics, has of course extremely poor benefit/cost ratio when restoring old paved roads.
- 6. Transport Research Arena Europe 2010, BrusselsFigure 4 Cross Slope Design Chart for 90 km/h Roads in Sweden [VGU]4. Testing How a Lane-change within a Curve Affects Travelled CurvatureThis work is searching for a causal factor behind the excessive crash rates in sharp multiple lanecurves. The curve cross slope has been designed under the assumption that the travelled curvedpath follows the road curvature. Could the main risk be that some vehicles experience muchhigher lateral force, as their drivers make a quick lane-change within the curve (poor driving)?Then this kind of curves should be designed with maximum allowed superelevation, in order tocompensate for the higher-than-considered lateral force.To test the idea above, the curve was measured several times with a laser/inertial Profilograph.The advanced Profilograph is normally used for accurate measurements of road alignment and ofroad surface condition. Here the Profilograph was used to record travelled curvature during adouble lane-change, as compared to normal driving within the same lane through the wholecurve. Two types of double lane-changes were tested; one very smooth (over long distance) andone quick and thus quite aggressive. All measurements were done at 90 km/h.5. Travelled Curvature Peaked During the Quick Lane-ChangeThe Profilograph data is reported in Figure 5. In the reference-case, without changing lane (blueline), the travelled curvature reached approximately 3 [km-1]. The two lane-changes both startedas the curvature reached its stationary level. The smooth lane-change (green line), the curvaturedid not increase significantly. The quick double lane-change took about 55 m less than thesmooth lane-change. While being shorter, the quick lane-change resulted in travelled curvaturepeaking up to about 4 [km-1]. This is some 35 % worse than indicated by the road curvatureitself, which is the curvature used when designing the cross slope. This result confirms that quicklane-change can be a key factor behind the disproportionate crash rate seen in sharp multiple lanecurves.Another observation is that the Skönsberg curvature (= 1000 / Radius) reach values of about 3[km-1] already without lane-change. This corresponds to such sharp radius as 300 – 350 m.Already a radius of 350 m is on the edge of being unacceptably sharp for a 90 km/h road, whencomparing with the design tolerances also for “poor” standard (“låg” standard in Swedish) givenin Figure 4. Obviously the current speed limit of 90 km/h should be reduced at least when the
- 7. Transport Research Arena Europe 2010, Brusselsroad is slippery, since the curve is sharper than allowed when designing 90 km/h curves inSweden.Figure 5 Travelled Curvature With/Without a Double Lane-ChangeThe measured combination of cross slope and curvature was analyzed in a new chart that wasdeveloped in the Roadex project (Granlund, 2008). This chart is basically a transform of thecross slope design chart in Figure 4. Cross slope rates are given as function of curve radius in thetraditional design chart. An important difference with the new chart, is that cross slope rates aregiven as function of curvature (=1000/Radius). This makes it possible to plot data measured bothfrom curves and from straight sections, where the radius goes into +/- infinity. Furthermore acopy of the chart has also been “flipped”, so data from both innercurves (+) and outercurves (-)can be investigated in the same resulting chart. The chart in Figure 6 show tolerance boxes for 90km/h; properly banked curves have all their data within the green boxes. Each data pointcorresponds to average values over 1 m. The plotted data reveal that the Skönsberg curve is notonly too sharp, but also too flat even when driving without lane-change. Clearly, the Skönsbergcurve would be safer if redesigned with maximum allowed cross slope of - 5.5 % in Sweden.Figure 6 Paired Cross Slope and Curvature Data from the Southbound Fast Lane
- 8. Transport Research Arena Europe 2010, Brussels6. Conclusions and RecommendationsCurve cross slope design codes are based on analysis of cornering forces acting on AASHO’spoint-mass model of a vehicle. A systematic problem with skid accidents on multiple lane curveshas been identified. Current road design practise approximates the vehicle travelled path (andthus lateral force) by the road curvature, which is reasonable on small roads. On multiple laneroads however, many drivers are changing lane also in sharp curves. When shifting lane quickly,the vehicle experience a transient “curve radius” much sharper than indicated by the road curveradius. This can yield higher lateral force than the road design code have considered. Results inthis work show that in a sharp curve, a lane-changing vehicle was exposed to 35 % higher lateralforce than given by the road curvature itself. Without considering this driving mode whendesigning the curve, the selected superelevation may be insufficient - when the road is slippery -to outbalance the cornering force.Curve design codes should be revised to include the following rule by thumb:-Sharp curves on multiple lane roads with high speed traffic should be designed withmaximum allowed cross slope.However, maximized cross slope is only recommended for sharp curves. In soft curves,excessive superelevation may be detrimental in the critical final moment of the double lane-shift.When applying enhanced cross slope in sharp multiple lane curves, the maximum allowedsuperelevation values (for example 12 % in the USA and 8 % in Norway) should not beexceeded.The geometry of existing curves can efficiently be evaluated with a new type of chart, wheremeasured data for cross slope is paired with data for curvature (see Figure 6). The new chartgives clear information on if the road has too sharp or improperly banked curves. Thisinformation should be used to decide speed limit reduction, posting warning signs (preferablyusing intelligent sensors recording vehicle speed and road slipperiness), intensified frictionmaintenance and curve redesign such as increasing the cross slope or straightening the curve.In order to improve the Benefit-to-Cost ratio for road renovation, the design chart for cross slopeused in Sweden should be revised. It is of no value to demand a few fixed cross slope values;target cross slopes should be expressed as a range instead. For highway speed stability reasons,the maximum allowed superelevation in Swedish hairpin curves should be raised into 8 %, as inNorway and in “winter-white” areas of the USA too (see NCHRP 439).The Profilograph measurements in the E4 Skönsberg Curve show that a smooth double lane-change resulted in lateral forces similar to those experienced during cornering without lane-change. The quick lane-change resulted in 35 % higher lateral force in the sharp curve. (Tests notshowed here, made in a smoother curve on highway E4, resulted in an even larger relativeincrease of lateral force but with absolute values smaller than in the sharp Skönsberg curve).These results illustrate the risk with making quick lane-changes. There is a need for improvededucation of motor vehicle drivers, making them aware of the importance of avoiding quicklane-changes in curved sections on multiple lane roads.
- 9. Transport Research Arena Europe 2010, Brussels7. References 1. Gupta, R. C., & Jain, R. P. (1975). Effect of certain roadway characteristics on accident rates for two-lane roads in Connecticut. Transportation Research Record, 541: 50−54. 2. Charlton, S. G., & de Pont, J. J. (2007). Curve speed management. Land Transport New Zealand, Research Report 323. Internet 2009-10-14: http://www.ltsa.govt.nz/research/reports/323.pdf 3. Johnston, I. R. (1982). Modifying driver behaviour on rural road curves: A review of recent research. Proceedings of 11´th Australian Road Research Board (ARRB) Conference, 11(4): 115−24. 4. Leonard, J., Bilse, D., & Recker, W. (1994). Superelevation rates at rural highway intersections. Report no. RTA-53P434. Irvine CA: University of California Institute of Transportation Studies. 5. Haywood, J. C. (1980). Highway alignment and superelevation: Some design-speed misconceptions. Transportation Research Record, 757: 22−25. 6. Lindholm, M. (2002). Analys av singelolyckor med dödlig utgång på det statliga vägnätet. Swedish National Road Administration, publication 2002:109. Internet 2009- 10-14: http://publikationswebbutik.vv.se/upload/1436/2002_109_analys_av_singelolyckor_med _dodlig_utgang_pa_det_statliga_vagnatet_exklusive_motorvagar_1997_2000.pdf 7. Granlund, J. (2008). Health Issues Raised by Poorly Maintained Road Networks. The Roadex Project. Internet 2009-10-14: http://www.roadex.org/Publications/docs-RIII- EN/Health%20Issues%20-%20RIII.pdf 8. Psarianos, B., Kontaratos, M. & Katsios, D. (1995). Influence of Vehicle Parameters on Horizontal Curve Design of Rural Highways. International Symposium on Highway Geometric Design Practices, Boston, Massachusetts, USA. Internet 2009-10-14: http://onlinepubs.trb.org/onlinepubs/circulars/ec003/ch22.pdf 9. Vägars och Gators Utformning (VGU). Vägverket, publication 2004:80. Internet 2009-10-14: http://www.vv.se/Startsida-foretag/vagar/Planering/Vagplanering- och-projektering/Vag--amp-gatuutformning/Dokument-vag-amp-gatuutformning/Vagar- amp-gators-utformning-VGU/ 10. Superelevation Distribution Methods and Transition Designs. (2000). Transportation Research Board, NCHRP Report 439

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