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j o u r n a l o f t r a ffi c and t r an s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 6 ; 3 ( 1 ) : 8 2e8 8
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journal homepage: www.elsevier .com/locate/ j t te
Original Research Paper
Toward an operating speed profile model for ruraltwo-lane roads in Egypt
Ibrahim H. Hashim a, Talaat A. Abdel-Wahed b,*, Yasser Moustafa b
a Faculty of Engineering, Menoufia University, Al Minufya, Egyptb Faculty of Engineering, Sohag University, Sohag, Egypt
a r t i c l e i n f o
Article history:
Received 4 March 2015
Received in revised form
1 July 2015
Accepted 30 September 2015
Available online 14 January 2016
Keywords:
Speed profile model
Operating speed
Consistency
Deceleration and acceleration
Horizontal curve
Tangent
* Corresponding author. Tel.: þ20 122 444557E-mail addresses: hashim1612@hotmail.c
Peer review under responsibility of Periodichttp://dx.doi.org/10.1016/j.jtte.2015.09.0052095-7564/© 2016 Periodical Offices of Changaccess article under the CC BY-NC-ND licen
a b s t r a c t
The geometric design, especially the horizontal and vertical alignments, of rural two-lane
highway facilities is considered one of the most important factors affecting the quality of
traffic service and safety. A consistent highway geometric design is defined to be one that
conforms to the driver's expectations. In order to calculate the main measures of design
consistency, an accurate operating speed profile model for road alignment is needed.
Studies have shown that operating speed models are country dependent due to varying
demographics, driver attitudes, habits, etc. This paper develops a speed profile model for
two-lane rural roads in Egypt. This includes the development of operating speedmodels for
horizontal curves and tangents, as well as the study of the characteristics and relationships
between acceleration and deceleration rates before and after horizontal curves. The study
uses a desert rural two-lane, two-way road sections that connect the city of Sohag with the
city of Hurghada, in Upper Egypt. All geometric characteristics were obtained from high-
way authority. Speed data regarding individual drivers traveling on selected two-lane rural
road sections were sampled using an on-board GPS system. The study confirms the finding
in previous research that curvature is the most important factor in determining the speed
on horizontal curves. Moreover, tangent length is the most important factor in determining
operating speeds at tangents. The acceleration and deceleration characteristics were
derived to gain an understanding of the behavior of individual vehicles traveling through
curves of varying radii and lengths as well as preceding tangent length. Several operating
speed models were developed for tangents and curves as well as for acceleration and
deceleration rates. Incredibly effective, these models can be used for design consistency
evaluations.
© 2016 Periodical Offices of Chang'an University. Production and hosting by Elsevier B.V. on
behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://
creativecommons.org/licenses/by-nc-nd/4.0/).
6; fax: þ20 93 2351895.om (I. H. Hashim), dr.talaat_ali@yahoo.com (T. A. Abdel-Wahed).
al Offices of Chang'an University.
'an University. Production and hosting by Elsevier B.V. on behalf of Owner. This is an opense (http://creativecommons.org/licenses/by-nc-nd/4.0/).
j o u rn a l o f t r a ffi c a nd t r an s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 6 ; 3 ( 1 ) : 8 2e8 8 83
1. Introduction
Highway geometry is one of the most important factors
affecting the efficiency and safety of highway systems.
Improving the geometry of two-lane highways should be a top
priority forhighwayauthorities, as they represent an important
component of any top network (Shawky and Hashim, 2010). In
Egypt, two-lane highway constitutes about 75% of all paved
rural highways (Hashim and Abdel-Wahed, 2011).
Improvements of those roads should be focused on the
locations where they will lead to the best possible reduction in
traffic casualties. Geometric consistency reduces the potential
of traffic casualties by correlating accident risk with geometric
alignment. It is defined as the conformance of a road'sgeometric features with driver's expectations (Nicholson,
1998). As design consistency increases, the number of crashes
decreases significantly (Dell'Acqua et al., 2013).
There are several methods to evaluate the consistency of a
highway design, namely alignment indices, driver workload,
and operating speed based measures (Hassan et al., 2001).
Among these methods, the operating speed approach is
known as the most efficient and quantifiable measure to
date. It is the most common vehicle operations based
consistency measure (Fitzpatrick et al., 2000a, 2000b).
Operating speed is defined as the speed at or below which
the majority of the drivers (e.g., 85%) are traveling without
being impeded by factors beyond the geometric features of the
road (Fitzpatrick et al., 2003). With the operating speed
approach, the design consistency evaluated based on one or
Fig. 1 e Red SeaeUp
a combination of two different ways. The first way is to
evaluate the consistency based on the difference of
operating speed between two successive elements of a road
(two curves or curveetangent). The second way is based on
the difference between the operating speed and design
speed values. If the operating speed differential between two
successive elements or the difference between the operating
speed and design speed is greater than a specified value, the
feature is considered inconsistent and the highway design is
considered poor (Lamm et al., 2002).
Therefore, the first step to evaluate design consistency is to
develop regression models that are used by highway de-
signers/practitioners. These models can predict the operating
speed of an element (i.e., curve, tangent). Consequently, the
speed differential between the two elements or the difference
between operating speed and design speed of an element can
be calculated. These models should be able to predict speed
values based on the geometric characteristics of the road el-
ements such as curve radius, curve length, deflection angle,
tangent length, etc. Vehicle acceleration and deceleration
rates, after or before negotiating horizontal curves, are also
important components in design consistency. These rates are
crucial in constructing the operating speed profile model.
Studies have shown that operating speed models and ac-
celeration or deceleration rates are country dependent or even
region dependent in larger countries, as they vary significantly
depending on the area under study (Lamm and Smith, 1994).
The reasons could be due to varying driver attitudes,
lifestyles, levels of motor law enforcement, etc. (Bird and
Hashim, 2005). Therefore, several models have been
per Egypt road.
Table 1 e Statistics of the geometric features.
Parameter Mean SD Minimum Maximum
Operating speed (km/h) 86.77 18.19 40.93 105.26
Radius (m) 486.60 196.97 59.00 823.00
Tangent length (m) 367.86 544.16 0.00 2406.33
Superelevation (%) �0.46 4.03 �6.00 6.00
Fig. 3 e Speed profiles in two directions of travel.
j o u r n a l o f t r a ffi c and t r an s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 6 ; 3 ( 1 ) : 8 2e8 884
developed to predict operating speed of horizontal curves and
tangents for several countries (Abbas et al., 2011).
Considering these factors, the objective of this study fo-
cuses on the development of operating speed models for
horizontal curves and tangents of rural two-lane roads in
Egypt. Another objective is to study the acceleration and
deceleration characteristics before and after horizontal curves
to create a speed profile model.
2. Previous studies
The literature review reveals that many studies have been
conducted to develop the operating speed models of hori-
zontal curves for two-lane highways (Dell'Acqua and Russo,
2010, 2011; Fitzpatrick et al., 2000a,b; Krammes et al., 1995;
Memon et al., 2008; Misaghi and Hassan, 2005). Many factors
affect the prediction of operating speed for horizontal curves,
such as horizontal curve's radius of length, and deflection
angle. Such studies confirm that a definite relationship exists
between operating speed and horizontal curve radius. Usu-
ally, when the horizontal curve radius decreases, the oper-
ating speed decreases. The radius of the next horizontal curve
and the grade and operating speed of the previous curve are
also used to predict the operating speed of horizontal curves
(Medina and Tarko, 2007).
It is also important to develop operating speeds for the
straight sections (tangents) that connect the horizontal
curves. Lamm et al. (2002) distinguishes between two types of
tangents according to their lengths. An independent tangent
that is long enough to be considered a design element, as its
length allows acceleration to occur up to the maximum
operating speed. The other type, known a non-independent
tangent, is not long enough for this, and may be ignored in
the design safety evaluation between successive elements.
Additional studies have developed operating speed models
Fig. 2 e External antenna mounted atop the test vehicle.
for independent tangents. A tangent is one of the elements
that affects the value of a speed reduction when a vehicle
enters a horizontal curve. Based on previous studies, the
operating speed of tangents was mainly dependent on the
length of the tangent (Polus et al., 2000).
In terms of acceleration and deceleration rates, speed data
were collected in Canada from horizontal curves with five
locations at each curve (Hassan, 2003). This paper uses the
operating speeds at each two successive locations in order
to calculate the deceleration and acceleration rates. In
conclusion, the deceleration and acceleration rates were
generally less than 0.85 m/s2. Drivers' speeds were not
constant along horizontal curves as drivers update their
speed based on the information they perceive and process
while negotiating the curves. Changes in acceleration and
deceleration rates may be indicative of design inconsistency,
and the issue should be examined by studying more curve
sites. Zuriaga et al. (2010) used a continuous speed profile to
determine the beginning and end points of deceleration and
the associated 85th percentile of deceleration rate using the
radius as an explanatory variable.
Considerable researches have used spot speeds, as
measured by radar speed guns, to predict operating speeds.
However, this method makes the measurements subject to
bias or human error (Nie, 2006). On the other hand, using in-
vehicle GPS equipment also allows for collection and
procession of speed data, and the data obtained lead to
more accurate and continuous speed profiles. This method
also enables the precise determination of minimum speeds
on horizontal curves, as well as the determination of the
maximum speeds at tangents used to calculate real
operating speeds. Perez et al. (2010), Cafiso and Cerni (2012),
and Memon et al. (2012) represent previous studies that used
in-vehicle GPS equipment to develop operating speed
models on two-lane two-way roads. The speed data used in
this study were also obtained using on-board GPS systems.
3. Data collection
3.1. Site selection and characteristics
This study uses a desert, rural, two-lane, and two-way road
sections that connect Sohag with Hurghada, Red SeaeUpper
Table 2 e Operating speed model of horizontal curves.
Location Model t-value R2 F Significant
Mid point of curve V85 ¼ 99:885� 3880:21r �11.43 0.704 130.69 0.000
Start point of curve V85 ¼ 101:564� 3480:88r �11.80 0.730 139.18 0.000
End point of curve V85 ¼ 101:18� 3969:90r �12.46 0.728 155.14 0.000
Note: V85 is the operating speed; r is the curve radius.
j o u rn a l o f t r a ffi c a nd t r an s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 6 ; 3 ( 1 ) : 8 2e8 8 85
Egypt road (Fig. 1). The total length of the studied road sections
is about 23 km with average daily traffic (ADT) equals
5000 veh/d. The road sections have a constant lane width of
3.75 m and were selected to cover the different roadway
characteristics of this type of road (e.g., different curve radii,
lengths, deflection angles and tangent lengths). The road
sections include 32 simple horizontal curves without spiral
transition curves between the tangents and circular
horizontal curves. The vertical alignments grades range
from �1% to 1%. Therefore, the effect of the vertical
alignment cannot be evaluated due to the range of vertical
alignment grades. Moreover, the road sections were chosen
for their distance from the influence of main intersections.
The speed limit of the road sections is 100 km/h which is the
national speed limit of rural desert roads in Egypt. The
experimental tests were conducted during day, in good
weather, and under good road surface condition. All
geometric data were obtained from “as built drawings”
obtained from General Authority for Roads, Bridges & Land
Transport (GARBLT). The summary statistics of the test
road's geometric features are given in Table 1.
3.2. GPS data collection
The survey was conducted using the GPS receiver SOKKIA
GRX-2 (double-frequency, GPS & GLONASS and operating
frequency range 400e470 MHz), which was placed on board of
the vehicle and supported by a fixedmaster station to perform
a post-differential correction to achieve high accuracy (cen-
timeters) of the spatial coordinates (Fig. 2).
To minimize conditions unrelated to the alignment
geometry, the experimental tests were conducted during
day-time, good weather conditions, low traffic flow. The
volunteer drivers, portraying various degrees of driving
Fig. 4 e Relationship between operating speed and curve
radius.
experience, were selected to represent the majority of the
natural driving population of the study area. Asking to drive
the test vehicle on the selected test routes following their
normal driving habits, drivers traveled in both directions
along road sections. The experiment's beginning and
completion points were disguised from the driver. Data
collection only started after the test driver had traveled for
some distance to allow test drivers to become familiar with
the specific test vehicle and the prevailing traffic conditions
of the road. The test driver sample consisted of 30 males
with ages ranging from 18 to 55.
The GPS antenna was mounted on the driver's side roof, as
this location minimizes multi-path errors and/or the loss of
signal due to satellite interruption caused by mountains. The
GPS unit was tuned to a mask angle of 10� above the horizon
for the current work. The relationships between speeds at
different points from both directions of travel are shown in
Fig. 3 (SohageHurghada and HurghadaeSohag).
4. Operating speed models
The study analysis comprised many mathematical forms of
the independent variables (i.e., curve radius, tangent length of
proceeding and following tangents and grade). These forms
are linear, inverse, square root. The criteria used to assess the
predictive accuracy of the models are listed as below.
� The coefficient of determination (R2) must be as high as
possible and significant at the 95% confidence level. R2
values only serve guides to the “goodness-of-fit”.
� Each independent variable should have regression co-
efficients that are significantly different from zero. Those
sign of each independent variable should logically denote
its effect on operating speed.
4.1. Curve models
The aim of this approach is to predict a single value for
operating speed at three different points of the curve: at its
center, at its start point, and at its end point. To do this, the
observed speeds in both directions were merged into a single
distribution, and the V85 percentile was computed for each
curve. Table 2 summarizes the best curve models using this
approach.
According to Table 2, the best curve model shows that the
bestmathematical form is the inverse of the curve radius (1/r).
From this table, the hypothesis that the coefficients of the
independent variable (1/r) are equal to zero is rejected at
95% confidence level since the t-values are greater than 1.96.
Table 3 e Operating speed model at the tangent.
Location Model t-value R2 F Significant
Middle of tangent V085 ¼ 84:34þ 0:593
ffiffiffiffiffiffi
TLp
5.34 0.851 28.45 0.003
Note: V085 is the maximum operating speed at the tangent.
j o u r n a l o f t r a ffi c and t r an s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 6 ; 3 ( 1 ) : 8 2e8 886
The independent variable's negative sign (1/r) means that
drivers tend to decrease their speeds as 1/r increases. The
resulting coefficients of determination (R2) and significance
of the F statistics reflect a relatively high goodness-of-fit for
the model and the significance of the models for using in
prediction. The table also shows that the operating speed of
the curve's middle is lower than operating speed of the
curve's beginning and end point. Fig. 4 indicates the
different operating speed values at various locations of
curve (i.e., start point, mid point, and end point) with
different curve radii values. The effect of road geometry is
shown using the same operating speed on a small radius
(i.e., r ¼ 100 m, r ¼ 200 m).
4.2. Tangent model
Only an independent tangent (tangent length TL � 200 m) is
used for modeling the relationship between operating speed
and tangent length. The best tangent models are summarized
into one model and shown in Table 3.
The best tangent models confirm that the best mathe-
matical form of a single independent variable is the square
root of the tangent length ð ffiffiffiffiffiffi
TLp Þ. The hypothesis that the co-
efficient of the independent variable ð ffiffiffiffiffiffi
TLp Þ is equal to zero is
rejected at 95% confidence level since the t-value is greater
than 1.96. Thismodel has a logical explanation for the effect of
the independent variable ð ffiffiffiffiffiffi
TLp Þ on the prediction of operating
speed on tangents. The positive sign of the independent var-
iable ð ffiffiffiffiffiffi
TLp Þ indicates that drivers tend to increase their speeds
asffiffiffiffiffiffi
TLp
increases. In other words, the longer the tangent
length, the higher the operating speed of the driver. The
resulting coefficient of determination (R2) and the significance
of the F statistic reflect a high goodness-of-fit for the model
and the significance of themodel for use in prediction. Finally,
this model is based on speeds in the range of 40e105 km/h.
Great care should be exercised in using this relationship
beyond the data used for its development.
Fig. 5 e Configuration of the five points.
5. Acceleration and deceleration models
Vehicle acceleration and deceleration characteristics before or
after negotiating horizontal curves are important components
in the analysis of design consistency. Studying these charac-
teristics is necessary to construct speed profile models of
roadway sections.
Speeds within this study were recorded to cover five main
points and are presented in Fig. 5. Using GPS technique based
on the configuration shown in Fig. 5, the maximum speed of
vehicles was surveyed along the tangent preceding the curve
(A), a point in the approach zone to the curve, the point
where speed started to decrease/to reach maximum speed
(B), and the start point (C), mid point (D) and end point (E) of
the curve (Fig. 5).
This configuration contributes to the study of the acceler-
ation and decelerations rates. For example, knowing the dis-
tances and operating speeds at points A (maximum speed on
tangent), B (speed in approach zone to curve), and C (speed at
start point of horizontal curve), we can calculate the acceler-
ation/deceleration rates and figure out the place where they
start. Fig. 6 depicts the idea behindmeasuring the speed at the
approach zone of a curve at point B. By the speeds at points B,
C, and A, it is possible to calculate the point where the
acceleration/deceleration starts.
Based on the Newton's Laws of Motion, using the operating
speed at every two successive points and the exact distance
between these two points, the acceleration or deceleration
rate can be calculated from the following equation.
acc=dec ¼ v12 � v2
2
25:92d1�2
where acc and dec are the acceleration and deceleration rates
(m/s2), v1, v2 are operating speeds at the first and second
points (km/h), respectively, d1e2 is the distance between the
two points (m).
Fig. 6 e Operating speed profile.
Table 4 e Deceleration and acceleration models.
Location Model t-value R2 F Significant
Deceleration from B to C dec ¼ �0:374þ 12:52ffiffi
rp 4.25 0.557 62.81 0.000
Acceleration from C to B acc ¼ �0:211þ 6:32ffiffi
rp 4.03 0.530 49.94 0.000
j o u rn a l o f t r a ffi c a nd t r an s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 6 ; 3 ( 1 ) : 8 2e8 8 87
Applying this equation, the deceleration and acceleration
models are determined at different locations, as shown in
Table 4.
The results show that there is a small deceleration rate
from the tangent point to the approach point (AeB), while
most of the deceleration took place in the approach zone
(BeC) just before the curve's starting point. Thus, the decel-
eration rates and the corresponding curve radii were used to
construct a relationship between them. According to Fig. 4,
the operating speeds along the curve (i.e., at the start, mid,
and end points) can be considered equal as indicated in Fig. 6.
The acceleration rate was obtained by calculating the
operating speeds at points C and B, respectively. The results
indicate that there was a small acceleration rate from the
curve point to approach point (CeB).
The developed equations have relatively fair goodness-of-
fit, as the R2 values are equal to 0.557 and 0.530, respectively.
The hypothesis that the coefficients of the independent vari-
able ð1= ffiffi
rp Þ are equal to zero is rejected at 95% confidence level
since the t-value is greater than 1.96. Also, the effect of the
independent variable ð1= ffiffi
rp Þ has a logical explanation, as when
the radius increases the deceleration and acceleration rates
decrease. Noting that great care should be exercised in using
this relationship beyond the data is used for its development.
Based on the results above, it is easier to model a rela-
tionship between deceleration rate and curve radius in the
approach distance just before entering the horizontal curve,
rather than modeling a similar relationship for acceleration
over the same distance. Collins and Krammes (1995) reported
that deceleration rates were more important than
acceleration rates based on the nature of curve related
accidents. Deceleration from a horizontal curve is more
safety-critical than acceleration from the same curve.
6. Conclusions
This study confirms the finding of previous research that the
curvature radius is the most important factor in determining
the driver's choice of speed on horizontal curves. On tangents,
the speed was mainly dependent on the tangent length. This
paper develops, operating speed models for tangents and
curves.Thesemodelsareveryusefulandcanbeusedtoevaluate
the design consistency of rural two-lane desert roads in Egypt.
The analysis in this study demonstrates that most of the
deceleration rates occur just before entering the horizontal
curve, but acceleration rates can be extended over a longer
distance upon leaving the horizontal curve. This can lead to
the conclusion that deceleration rates entering a horizontal
curve are usually higher than the corresponding acceleration
rates leaving a horizontal curve.
Detailed surveys also show that the acceleration values
after departing a curve and deceleration value before entering
a curve are different and do not take constant values as
assumed in most previous studies.
This study represents a step towards constructing a
speed profile model, as two continuous relationships were
established to predict acceleration and declaration rates as
a function of horizontal curve radius. Operating speed
models for horizontal curves and tangents were also
developed.
Finally, future research should be conducted to extend all
aspects of this research using comprehensive field data from
various regions and governorates in Egypt not only for desert
rural roads but also for agriculture roads. The calculation of
operating speeds, as well as acceleration and deceleration
rates, in this research was based on 85th percentile speed at
spot locations. However, to gain a more thorough under-
standing, the behavior of individual vehicles (drivers) through
road section is strongly recommended to be studied using the
current data. This may lead to the feasibility of developing a
continuous operating speed model to predict the speed at any
point along the roadway.
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