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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://

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6; fax: þ20 93 2351895.om (I. H. Hashim), dr.talaat_ali@yahoo.com (T. A. Abdel-Wahed).

al Offices of Chang'an University.

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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.

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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.

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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

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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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