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.se

Abstract

Many road users have crashed at high speed in sharp curves during slippery road conditions. To

reduce 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 cornering

forces acting on AASHO’s point-mass model of a vehicle. While the design codes typically yield

curves with acceptable safety level, there is a systematic problem with skid accidents on multiple

lane curves. This paper discusses a causal factor and recommends changes in curve design codes

as well as actions to improve safety in existing unsafe curves. Current road design practise

approximates the vehicle travelled path (and thus lateral force) by the road curvature, which is

reasonable on small roads. On multiple lane roads however, many drivers are changing lane also

in sharp curves since no oncoming traffic is present. When shifting lane quickly, the vehicle

experience a transient “curve radius” much sharper than indicated by the road curve radius. This

can yield higher lateral force than the road design code have considered. Then the superelevation

may be insufficient - when the road is slippery - to outbalance the cornering force. As a rule by

thumb, sharp curves on multiple lane roads with high speed traffic should have maximum

allowed cross slope in order to increase stability.

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1. Introduction

Horizontal road curves were recognised as a problem thousands of years ago. Evidence is present

in the book of the prophet Isaiah: “A voice of one calling in the desert; -Prepare the way for the

Lord, make straight paths for him. Every valley shall be filled in, every mountain and hill made

low. The crooked roads shall become straight, the rough ways smooth”.

Since the introduction of the automobile, cornering is made at highway speeds and is associated

with lateral forces that may bring instability and thus crash risk. Therefore it is not surprising that

horizontal curvature correlates strongly with crash rates on rural highways. After analysing 34

000 road crashes in the United States, Gupta & Jain (1975) found that curvature actually is a

more important factor than road width, vertical clearance as well as sight distance. They also

noted that especially head-on collisions, collisions with fixed objects and rollover crashes occur

disproportionately on curved road sections.

There is good agreement in the road safety research community that sharper curves cause more

accidents (Charlton & de Pont 2007). Crash rates in curves have been found to be typically 2 to

4.5 times higher than on straight road sections (Johnston 1982; Leonard et al. 1994). Trucks

show the highest raise in crash rates between straight and curved road sections. Single sharp

curves 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 fatal

single crashes during four years in Sweden showed that outercurves count for five times more

crashes than innercurves (Lindholm 2002). The EU project Roadex found that hazardous

improper cross slope is several times more frequent in outercurves than in innercurves (Granlund

2008). This finding is to be explained by road history. Ancient dirt roads were built with a

crown, with cross slopes to the nearest roadside to maximize rain water drainage. The road

section was the same in both straight sections and curves. There was simply no need for banking

up superelevation in outercurves, since the non-motorized carriages didn’t reach speed levels

where side forces become high. As dirt roads have been upgraded to tarmac roads, many ancient

outercurves have not yet been updated with enough superelevation to meet the needs of the

motorized 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 on

European Highway Nr 4 in Skönsberg, see Figure 1. Every third car crash in Sundsvall occurs in

the 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

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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 depends

1 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.

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only on the curve radius. Smaller radii (tighter curves) yield higher lateral forces. For tight

curves, even a minor increase in radius results in a large decrease of the lateral force.

R

mF

2*

Formula 1, Lateral Acceleration Force Acting on a Cornering Vehicle

Figure 3 shows the factors influencing the cornering forces acting on a vehicle as described by

the 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 side

friction demand factor fs [-], and the tangent of the angle corresponding to pavement

superelevation/banking/cross slope [%].

Figure 3 Vehicle Cornering Forces

Note 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). The

side friction is the part of the total road grip normally utilized when cornering.

3.2 The Reaction Forces Needed to Balance the Ride

If the lateral force F is not balanced by reaction forces, the vehicle ride will become unstable and

the risk of a traffic accident (run-off, skidding and rollover modes) will increase. There are two

reaction forces that may balance the lateral force F. One is the horizontal component of the

normal force; N * sin(). The other is the horizontal component of the side friction developed

between the vehicle's tyres and the pavement surface friction force, N * fs * cos(). This can be

expressed by the equation in Formula 2.

)cos(**)sin(* sfNNF

Formula 2, Lateral Equilibrium; Initial Setup

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After division by cos (), substitution with N = m * g (g being the gravitation constant) and with

F 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.

sfgR

)tan(*

2

Formula 3, Lateral Equilibrium; Final Expression

Now recall that tan(α) represents the cross slope. Clearly, Formula 3 shows that a prerequisite

for steady cornering is that the sum of the cross slope and the side friction demand factor is high

enough 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 equilibrium

expressions above. Most codes are presenting design charts, showing what cross slope to use as

function 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 (locked

wheel) 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 per

Formula 4.

*6.3*0096.0*28.0 ef s

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 northern

Scandinavia, lower side friction supply factor fs may be relevant. As seen in Formula 3, a lower

fs results in a demand for higher superelevation for a given speed and radius. In the USA, the

factor fs are set to a speed-depending value where 95 % of the drivers slow down by 3 - 5 km/h

in the curve (NCHRP report 439).

The design chart for cross slope in 90 km/h curves in Sweden is based on a side friction supply

factor fs of 0.12, as given by Formula 4. (As per NCHRP report 439, American 90 km/h

highway curves are designed with a similar value - 0.13 - for the factor fs). The resulting

Swedish design chart is showed in Figure 4. Note that the Swedish code only allows certain

discrete 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 hazardous

to have - let’s say - 3.2 % or 4.6 % cross slope in such a curve. A design chart that calls for

unnecessary cross slope adjustments of the existing cross slope (for example 4.6 %) just to meet

one of a few allowed discrete values, with no relevance what so ever to Newton´s laws of

physics, has of course extremely poor benefit/cost ratio when restoring old paved roads.

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Figure 4 Cross Slope Design Chart for 90 km/h Roads in Sweden [VGU]

4. Testing How a Lane-change within a Curve Affects Travelled Curvature

This work is searching for a causal factor behind the excessive crash rates in sharp multiple lane

curves. The curve cross slope has been designed under the assumption that the travelled curved

path follows the road curvature. Could the main risk be that some vehicles experience much

higher 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 to

compensate 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 of

road surface condition. Here the Profilograph was used to record travelled curvature during a

double lane-change, as compared to normal driving within the same lane through the whole

curve. Two types of double lane-changes were tested; one very smooth (over long distance) and

one quick and thus quite aggressive. All measurements were done at 90 km/h.

5. Travelled Curvature Peaked During the Quick Lane-Change

The Profilograph data is reported in Figure 5. In the reference-case, without changing lane (blue

line), the travelled curvature reached approximately 3 [km-1

]. The two lane-changes both started

as the curvature reached its stationary level. The smooth lane-change (green line), the curvature

did not increase significantly. The quick double lane-change took about 55 m less than the

smooth lane-change. While being shorter, the quick lane-change resulted in travelled curvature

peaking up to about 4 [km-1

]. This is some 35 % worse than indicated by the road curvature

itself, which is the curvature used when designing the cross slope. This result confirms that quick

lane-change can be a key factor behind the disproportionate crash rate seen in sharp multiple lane

curves.

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, when

comparing with the design tolerances also for “poor” standard (“låg” standard in Swedish) given

in Figure 4. Obviously the current speed limit of 90 km/h should be reduced at least when the

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road is slippery, since the curve is sharper than allowed when designing 90 km/h curves in

Sweden.

Figure 5 Travelled Curvature With/Without a Double Lane-Change

The measured combination of cross slope and curvature was analyzed in a new chart that was

developed in the Roadex project (Granlund, 2008). This chart is basically a transform of the

cross slope design chart in Figure 4. Cross slope rates are given as function of curve radius in the

traditional design chart. An important difference with the new chart, is that cross slope rates are

given as function of curvature (=1000/Radius). This makes it possible to plot data measured both

from curves and from straight sections, where the radius goes into +/- infinity. Furthermore a

copy 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 90

km/h; properly banked curves have all their data within the green boxes. Each data point

corresponds to average values over 1 m. The plotted data reveal that the Skönsberg curve is not

only too sharp, but also too flat even when driving without lane-change. Clearly, the Skönsberg

curve 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

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6. Conclusions and Recommendations

Curve cross slope design codes are based on analysis of cornering forces acting on AASHO’s

point-mass model of a vehicle. A systematic problem with skid accidents on multiple lane curves

has been identified. Current road design practise approximates the vehicle travelled path (and

thus lateral force) by the road curvature, which is reasonable on small roads. On multiple lane

roads 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 curve

radius. This can yield higher lateral force than the road design code have considered. Results in

this work show that in a sharp curve, a lane-changing vehicle was exposed to 35 % higher lateral

force than given by the road curvature itself. Without considering this driving mode when

designing 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 with

maximum 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 allowed

superelevation values (for example 12 % in the USA and 8 % in Norway) should not be

exceeded.

The geometry of existing curves can efficiently be evaluated with a new type of chart, where

measured data for cross slope is paired with data for curvature (see Figure 6). The new chart

gives clear information on if the road has too sharp or improperly banked curves. This

information should be used to decide speed limit reduction, posting warning signs (preferably

using intelligent sensors recording vehicle speed and road slipperiness), intensified friction

maintenance 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 slope

used 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 in

Norway 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 not

showed here, made in a smoother curve on highway E4, resulted in an even larger relative

increase 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 improved

education of motor vehicle drivers, making them aware of the importance of avoiding quick

lane-changes in curved sections on multiple lane roads.

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7. References

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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

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_dodlig_utgang_pa_det_statliga_vagnatet_exklusive_motorvagar_1997_2000.pdf

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EN/Health%20Issues%20-%20RIII.pdf

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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.

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och-projektering/Vag--amp-gatuutformning/Dokument-vag-amp-gatuutformning/Vagar-

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10. Superelevation Distribution Methods and Transition Designs. (2000). Transportation

Research Board, NCHRP Report 439