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.

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.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.

2. Transport Research Arena Europe 2010, Brussels
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

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 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.
m * 2
F
R
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.
F  N * sin( )  N * f s * cos( )
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.
2
 tan( )  f s
R* g
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.
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 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.

6. Transport Research Arena Europe 2010, Brussels
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

7. Transport Research Arena Europe 2010, Brussels
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

8. Transport Research Arena Europe 2010, Brussels
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.

9. Transport Research Arena Europe 2010, Brussels
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