Transportation Research Part C 31 (2013) 99–111

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Transportation Research Part C

journal homepage: www.elsevier .com/locate / t rc

New highway geometric design methods for minimizingvehicular fuel consumption and improving safety

0968-090X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.trc.2013.03.002

⇑ Corresponding author. Tel.: +1 443 885 1446; fax: +1 443 885 8218.E-mail addresses: mwkang@southalabama.edu (M.-W. Kang), shaghayegh.shariat@morgan.edu (S. Shariat), manoj.jha@morgan.edu (M.K. Jha)

1 Tel.: +1 251 460 6174; fax: +1 251 461 1400.2 Tel.: +1 202 569 5996.

Min-Wook Kang a,1, Shaghayegh Shariat b,2, Manoj K. Jha b,⇑a Department of Civil Engineering, University of South Alabama, 150 Jaguar Drive, Shelby Hall, AL 36688, United Statesb Department of Civil Engineering, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, United States

a r t i c l e i n f o

Article history:Received 9 February 2012Received in revised form 8 March 2013Accepted 8 March 2013

Keywords:Green highway infrastructure designHighway alignment evaluationOptimizationFuel consumptionSight distanceSafety

a b s t r a c t

This paper proposes separate computational methods for evaluating (1) fuel efficiency, (2)sight distance deficiencies and (3) expected accident costs for a given highway alignment,depending on its detailed geometric characteristics. A fuel consumption model is devel-oped based on two important concepts: (i) variability in the amount of fuel consumedby vehicles depending on variability in highway geometry and (ii) minimization of the fuelconsumption by ensuring conditions suitable for driving at cruising speed. The methodsestimate the fuel consumption by integrating vehicle propulsive force necessary to main-tain the cruising speed from the beginning to the end of an alternative highway being eval-uated. A sight distance model that not only automatically calculates available sightdistance (ASD) and stopping sight distance (SSD), but also evaluates sight distance defi-ciency of alternative alignments is proposed. The total sight distance deficiency of an alter-native alignment is estimated based on (i) the length of the road segments whereASD < SSD and (ii) the significance of sight distance restriction. A crash prediction modelproposed in the Highway Safety Manual (HSM) is adopted to evaluate and compare alter-native alignments from safety perspective. A case study is presented to demonstrate theeffectiveness of the developed methods. These methods will be integrated into a highwayalignment optimization model (HAO) previously developed by the authors to evaluatenumerous possible alternative alignments of a new highway system through tradeoffsamong various relevant decision criteria. Those criteria may include vehicle fuel efficiency,sight distance, and safety, besides various cost factors, such as the construction cost, main-tenance cost, user cost, and environmental impact cost. Such an integrated modelingframework will help evaluate green and environmentally sustainable highways. Manyextensions of the work remain to be worked in the future, for example: (1) the effects ofgain in propulsive force when traveling down from the crest of a curve; and (2) variabilityin fuel consumption rate based on vehicle type, gradient, critical length of grade, weather,and other factors.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The hike in fuel prices prompts us to develop new methods to evaluate highway alignment alternatives that minimizevehicular fuel consumption while improving safety and facilitating driver comfort. An increased level of vehicular fuel con-sumption not only taxes the society, but also causes increased levels of environmental pollution, thereby creating hazard to

.

100 M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111

human health. In previous works (Trietsch, 1987; Fwa et al., 2002; Easa et al., 2002; Jong and Schonfeld, 2003; Jha and Schon-feld, 2004; Jha et al., 2006; Cheng and lee, 2006; Lee et al., 2009; Kang et al., 2009, 2010, 2012), optimization methods havebeen developed to evaluate alignment alternatives, primarily from cost minimization perspective. Many optimization meth-odologies, such as genetic algorithm (GA), dynamic programming, linear programming, and heuristics with mixed integerprogramming, have been developed to compute optimal alignments of a planned highway. The decision criterion (i.e., objec-tive) for optimizing highway alignments in these models is normally minimization of total construction costs, which includeearthwork cost, land acquisition cost, pavement cost, etc. However, optimizing alignments based only on minimization of thetotal construction cost may not consider other important stakeholders’ objectives, such as minimization of fuel consumptionand travel time costs for road users (i.e., motorists) and minimization of environmental cost.

Recently, Kang et al. (2010) proposed a mathematical model that evaluates traffic impact of alternative alignments to anexisting road network in optimizing highway alignments. The model extends a GA-based alignment optimization model,called HAO model (Jong and Schonfeld, 2003; Jha and Schonfeld, 2004; Jha et al., 2006; Kang et al., 2009, 2012) to includea user travel time cost in the objective function of the model, by formulating the highway alignment optimization problemas a bilevel program. It showed that there would be a significant variation in the alignment optimization results with andwithout consideration of the user cost. The effect of alternative alignments to environmentally sensitive areas (i.e., howmuch the sensitive areas are affected by the alternative) is also considered in the optimization process of the model.

Fuel consumption and highway safety are other important decision criteria to be considered in highway alignment opti-mization because the selection of alternative alignments that lead to better vehicular fuel economy and safety are highlydesirable. Many vehicular fuel consumption models (Zaniewski, 1983; Ahn et al., 2002; Boriboonsomsin and Barth, 2009)and accident prediction models (Zegeer et al., 1992; Vgot and Bared, 1998; AASHTO, 2010) have been developed untilnow. Highway geometric characteristics such as grade, horizontal curve radius, and superelevation are employed to estimatethe vehicular fuel consumption and accident frequency of a given highway. However, none of them are effectively taken intoaccount as a decision criterion in the highway alignment optimization process reported in previous works. This paper pro-poses useful mathematical models to be integrated with the alignment optimization process in order to evaluate variousalternative alignments in terms of vehicular fuel consumption, sight distance, and safety, besides the construction cost.

Sight distance is one of the major elements that must be considered in the geometric design to obtain safe and comfort-able highways (Hassan et al., 1997). Many analytical models (Hassan et al., 1997; Hassan and Easa, 1998; Taignidis, 1998;Lovell, 1999; Taignidis and Kanellaidis, 2001; Hassan, 2003; Easa, 2009) have been developed to determine available sightdistance (ASD) on a highway and identify road segments where ASD is less than required sight distance (e.g., stopping sightdistance, SSD). A new mathematical method that not only automatically calculates all ASDs at both night and daytimes, butalso measures the significance of sight distance deficiency of a highway is proposed in the present paper through a carefulreview of the previous models.

2. Evaluating vehicle fuel efficiency

The amount of fuels consumed by vehicles varies significantly depending on the highway geometry. The fuel consump-tion directly affects the cost of vehicle operation; furthermore, it influences greenhouse gas and pollutant emissions if fossilfuels are used. Thus, evaluating the effect of highway geometry on vehicle fuel consumption is highly desirable to find fuelefficient and environmentally friendly highways. Through a real-world experiment by Boriboonsomsin and Barth (2009), itwas verified that road grade can have significant effects on the fuel economy of light-duty vehicles. Pavement surface rough-ness and distance of roadway segments with varying grades also account for vehicle fuel consumption. Taking into accountall these roadway-related factors, a vehicle fuel consumption model which is sensitive to highway geometry is developed inthe present study.

2.1. Vehicle resistance

Several types of resistance act on a motor vehicle (i.e., a passenger car in this paper) while it is in motion (see Fig. 1). Theseinclude rolling resistance (RR), grade resistance (RG), curvature resistance (RC), and air resistance (RA). The curvature resis-

Air resistance (RA)

Rolling resistance (RR)

(RG)Grade resistance

Propulsive force delivered from engine (FP)

o

o

Vehicle weight (mg)

Fig. 1. Resistance forces acting on moving vehicles.

M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111 101

tance is normally taken as zero for a high-speed highway because its effect on the vehicle is negligible due to several geo-metric treatments on horizontal curves (such as superelevation, widening, and spiral transition). According to numerous pre-vious studies (e.g., Schwarzkopf and Leipnik, 1977), the fuel consumption of a motor vehicle is approximately minimized byoperating at cruising speed. This is again confirmed recently by Chang and Morlok (2005) according to which the optimalspeed profile for fuel consumption of a motor vehicle, under different roadway characteristics, is achieved at cruising speed.Thus, vehicle propulsive force (FP) necessary to overcome the total resistances at the cruising speed is given in the simplestform as:

FP ¼ RR þ RG þ RA ð1ÞRR ¼ mgCr cosðcÞ ð2ÞRG ¼ mg sinðcÞ ð3Þ

RA ¼AqCa

2

� �V2 ð4Þ

where m is the vehicle mass; g, the gravitational constant, 9.8 m/s2; Cr, the coefficient of rolling resistance, which varies withroad surface type and condition; c, the grade angle in degree; A, the vehicle cross-sectional area; q, the air density; Ca, the airdrag coefficient and V is the vehicle cruising speed.

Other resistances (such as mechanical resistance), vehicle engine efficiency and transmission efficiency are not consid-ered in calculation of vehicle propulsive force, but need to be considered for its more accurate estimation. The basic resis-tance formula is adapted from Vuchic (1981).

2.2. Evaluating vehicle fuel consumption

Fig. 2 shows a conceptual scenario in which vehicle fuel consumption can be estimated with the propulsive force requiredto maintain a cruising speed. As shown in the figure, the profile of the propulsive force significantly varies depending on thehighway geometry. On a level terrain, a relatively low propulsive force is needed for the vehicle to maintain a cruising speedbecause only the rolling and air resistances act on the vehicle operation. A much higher propulsive force is required for driv-ing on upgrade sections because of the grade impact (i.e., grade resistance). No propulsive force may be necessary for drivingon downgrade sections because a negative grade resistance acts on the vehicle and it nullifies the effect of other resistances.The length of the road segment where no propulsive force is necessary, is dependent on the steepness and the length of thedown grade section. Note that some of the additional fuel consumption expected on hilly roads may be avoided with a regen-erative propulsion system that recovers and stores energy when going downhill.

A computational model that estimates the amount of fuel consumed by a vehicle traveling over a highway is proposedhere with consideration of highway geometric conditions (e.g., grades, length, and location of crest and vertical curves), roadsurface type and condition, and speed. Knowing that the fuel consumption is approximately proportional to total propulsivework (WP) performed by the vehicle (Chang and Morlok, 2005), a formula that estimates the total fuel consumed (SFuel) by thevehicle operating at cruising speed from the start and end of a highway can be expressed as:

SFuel ¼ rFuelWP ð5Þ

(b) Propulsive force profile

(a) Vertical profile

Fig. 2. Vehicle propulsive force required to maintain a cruising speed for an example highway.

102 M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111

WP ¼Z xend

xstart

FPdx ¼Z xend

xstart

½RR þ RG þ RA�dx

¼Z xend

xstart

ðmgCr cosðcÞÞ þ ðmg sinðcÞÞ þ AqCa

2

� �V2

� �dx

ð6Þ

where rFuel is the fuel consumption rate (e.g., l/J); WP, the total propulsive work and Xstart, Xend are the start and end points of ahighway being evaluated.

The propulsive work is the work performed by the vehicle as the vehicle moves along its path. Thus, if the propulsive forceof the vehicle at point x is defined as FP(x), then the total propulsive work performed by it for a certain distance can be esti-mated by integrating the force for that distance (see, shaded areas shown in Fig. 2b). Note that Eq. (6) is for the propulsivework of a passenger car. It could simply be updated with additional form of resistance forces for other types of vehicles (e.g.,bus and truck) if traffic composition information (i.e., the fraction and types of vehicles used in a highway) is given. It shouldbe also noted that the fuel consumption rate (rFuel) in Eq. (5) may vary at different power levels and under different environ-mental conditions (e.g. temperatures). It can also vary with the vehicle type, propulsion type, age, and maintenance history.

The underlying assumption in evaluating a new highway alignment in terms of fuel efficiency is that the traffic conditionof the highway is uncongested. Please note that our focus here is to evaluate the effect of highway geometry on vehicle fuelconsumption, not the effect of traffic volume. Thus, to find fuel efficient highway alignments, it is assumed that vehicles tra-vel at cruising speed without interference from other vehicles over the entire section of the highway in uncongested trafficconditions. Delay cost and vehicle operating cost with consideration of traffic mix and traffic growth over the design life ofthe highway are estimated separately in the alignment optimization model as user cost, which is one of the life-cycle costcomponents. Interested readers may refer to the authors’ previous publication (Kang et al., 2012) for more about the life-cy-cle cost considered in the alignment optimization model.

3. Evaluating sight distance

3.1. Measuring ASD on horizontal alignments

Many studies have been reported in the literature dealing with various aspects of sight distance associated with horizon-tal, vertical, and 3-dimensionsal curves (Hassan et al., 1997; Lovell, 1999; Taignidis and Kanellaidis, 2001; Hassan, 2003;Easa, 2009; Olson et al., 1984; Jha et al., 2011; Kuhn and Jha, 2011). Some studies (Jha et al., 2011) have proposed new 3-dimensional methods of road design based on a polynomial function that eliminates the need of separate processing of hor-izontal and vertical alignments. The sight distance across the inside of horizontal curves is typically restricted by sightobstructions such as, retaining walls, buildings and longitudinal barriers. Thus, a particular review that analyzes whetherenough sight distance is provided on each individual curve of a horizontal alignment should be made for its proper design.A new methodology is proposed in this section, by which the available sight distance (ASD) for any vehicle location on hor-izontal curves is calculated. The available sight distance on horizontal alignments (denoted as ASDhor) is calculated based onthe following procedure. Note that notations used in this procedure are shown in Fig. 3.

Step 1: Create vector AC�!

that connects vehicle’s current point (A) and the farthest point (C) that the driver can see, mea-sured along the roadway.Create vector AB

�!that connects vehicle’s current point (A) and the end of SSD (B), measured along the roadway.

Step 2: Check if there is any obstacle blocking AC�!

and AB�!

:� If no obstacle blocks both AC

�!and AB

�!(i.e., Case H1 in Fig. 3), then

– ASDhor becomes the MSD which is predetermined (i.e., ASDhor = MSD)

� Else if an obstacle only blocks AC�!

(i.e., Case H2 in Fig. 3), then– Domain of D becomes the road segment between B and C.– Find a vector whose origin is A and destination D is located in between B and C as well as that just touches the edge

of the obstacle.– ASDhor becomes less than MSD but greater than or equal to SSD (i.e., SSD 6 ASDhor < MSD)

� Else if the obstacle blocks AB�!

(i.e., Case H3 in Fig. 3), then– Domain of D becomes the road segment between A and B.– Find a vector whose origin is A and destination D is located in between A and B as well as that just touches the edge

of the obstacle.– ASDhor becomes less than SSD (i.e., ASDhor < SSD < MSD)

Step 3: Move vehicle location (A) for a short distance interval (e.g., 1 m) along the roadway. Repeat Steps 1 and 2 until itreaches the endpoint of the roadway.

The SSD is the sum of (i) the distance traveled during the brake reaction time and (ii) the distance needed to brake thevehicle to a stop. According to AASHTO (2004), the SSD can be expressed as:

Fig. 3. Line-of-sight at horizontal curve sections.

M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111 103

SSD ¼ 0:278Vt þ V2

254 a9:81

� �� G

� � ð7Þ

where t is the brake reaction time, 2.5 s; V, the design speed, km/h; a, the deceleration rate, 3.4 m/s2 as recommended inAASHTO (2004) and G is the percent grade� of tangent divided by 100, decimal. �May use the average grade (Gm) if the vehi-cle is on vertical curves (Taignidis and Kanellaidis, 2001).

3.2. Measuring ASD on vertical alignments

3.2.1. ASD on graded tangentsDrivers’ vision is physically infinity in the daytime if no obstacle blocks their line-of-sights. However, it is significantly

reduced at night because it totally depends on vehicle’s headlight capability. For driving on highways at nighttime withoutlighting, the length of visible roadway is the roadway segment length that is directly illuminated by the headlights of thevehicle (AASHTO, 2004). According to Federal Motor Vehicle Safety Standard (FMVSS), ‘‘Every motor vehicle, except motorcy-cles, must be equipped with one or more lamps which, shall display a white or amber light visible from a distance of 300 meter(1,000 feet) to the front of the vehicle.’’ It should be noted however that the 300 m criteria relates to the ability of a driverto see the headlight from a distance of 300 m, not his ability to see an object placed on the road surface 300 m ahead. Undernormal nighttime conditions, a driver would be able to discern a dark object in the roadway from a distance of only about45 m (150 feet) under low-beam and 200 m (650 feet) under high-beam headlight illumination (Ruma, 2002). Although thehigh-beams are rarely used in the roadway due to oncoming traffic, this paper adopts 200 m as the value of driver’s maxi-mum available sight distance on tangent sections at night time (i.e., MSDnight = 200 m).

3.2.2. ASD on sag vertical curvesSight distance on a sag vertical curve is restricted at night because the portion of roadway lighted ahead depends on the

position of the headlight and the direction of the light beam (AASHTO, 2004). As recommended in AASHTO (2004), a head-light height of 600 mm above the road and a 1� upward angle of the light beam from the longitudinal axis of the vehicle are

Fig. 4. Headlight sight distance on a sag vertical curve.

104 M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111

assumed in the calculation of available sight distances on a sag vertical curve at night. Formulas for this ASD calculation canbe derived for five cases below based on (i) the vehicle position and (ii) the intersection point of the light beam with theroadway.

Let x coordinate of BVC be 0 (i.e., XBVC = 0) in a sag vertical curve, and let XEVC = Lseg as shown in Fig. 4. Given the x coor-dinate of vehicle’s position (denoted as XC), the end of the headlight beam position (denoted as XH) with reference to XBVC canbe calculated, by equating (i) the parabolic curve equation and (ii) the line-of-headlight beam equation, which is derivedfrom the derivative of the vertical alignment equation with the assumed headlight height and angle. Taking all these intoconsideration, XH is calculated as:

Case SV1: if

XC < 0 and XH 6 Lseg XH ¼tanðaÞ þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitanðaÞ2 þ 4 G2�G1

200Lseg

�HC

r2 G2�G1

200Lseg

� ð8Þ

Case SV2: if

XC < 0 and XH > Lseg XH ¼HC þ G2�G1

200

� �Lseg

G2�G1100

� �� tanðaÞ

ð9Þ

Case SV3: if

0 6 XC < Lseg and XH 6 Lseg XH ¼

G2�G1100Lseg

�XC þ tanðaÞ þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiG2�G1100Lseg

�XC þ tanðaÞ

�2þ 4 G2�G1

200Lseg

�HC

r" #

2 G2�G1200Lseg

� ð10Þ

Case SV4: if

0 6 XC < Lseg and XH > Lseg XH ¼HC þ G2�G1

200

� �Lseg

G2�G1100Lseg

�ðLseg � XCÞ � tanðaÞ

ð11Þ

Case SV5: if

XC P Lseg and XH > Lseg XH ¼ XC þMSDnight ð12Þ

Thus, the available headlight sight distance on a sag vertical curve (denoted as ASDseg) is calculated as:

ASDseg ¼ XH � XC ð13Þ

3.2.3. ASD with overhead structures on sag vertical curvesIn order to calculate ASD on a sag vertical curve in the presence of overhead structures (denoted as ASDover), the same

procedure developed for ASDhor is used. The only difference in this case is that driver’s line-of-sight is measured on a vertical

M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111 105

alignment with the assumption of 2400 mm eye height (HE) and 600 mm object height (HO) for a truck driver recommendedby AASHTO (2004). Given (i) the maximum distance that the driver is able to see in a normal condition (i.e., MSD), (ii) thelocation of the vehicle on the vertical alignment, and (iii) overhead structure location, ASDover is calculated by measuringthe length of driver’s line-of-sight vector that just touches the bottom of the overhead structure and ends at a point aheadof him (see vector AD

�!in Fig. 5). Similar to the ASDhor, three possible cases (i.e., Case O1 where ASDover = MSD; Case O2 where

SSD 6 ASDover < MSD (as described in Fig. 5); and Case O3 where ASDover < SSD < MSD) are considered to calculate the ASDover.

3.2.4. ASD on crest vertical curvesIn order to calculate the ASD on a crest vertical curve (denoted as ASDcrest), this paper adopts a model developed by Taig-

nidis (1998). That model precisely and automatically calculates ASDcrest, based upon driver’s and object’s location on or off ofit. Let x coordinate of BVC in the crest vertical curve be 0 (i.e., XBVC = 0). Then, the length of the crest vertical curve (denoted asLcrest) becomes x coordinate of EVC (i.e., XEVC = Lcrest). Denoting XC and XS vehicle and object locations with reference to XBVC,respectively, Taignidis’s model can be rewritten as follows:

Case CV1: if

0 6 XC 6 Lcrest and XS 6 Lcrest ASDcrest ¼ ð200KHEÞ1=2 þ ð200KHOÞ1=2 ð14Þ

Case CV2: if

0 6 XC 6 Lcrest and XS > Lcrest ASDcrest ¼ ð200KHEÞ1=2 þ 200KHO þ ðLcrest � XC � ð200KHEÞ1=2Þ2

2ðLcrest � XC � ð200KHEÞ1=2Þð15Þ

Case CV3: if

XC < 0 and XS 6 Lcrest ASDcrest ¼ ð200KHE þ X2CÞ

1=2 þ ð200KHOÞ1=2 ð16Þ

Case CV4: if

XC < 0 and XS > Lcrest ASDcrest ¼ ð200KHE þ X2CÞ

1=2 þ 200KHO þ ðLcrest � XC � ð200KHE þ X2CÞ

1=2Þ2

2ðLcrest � XC � ð200KHE þ X2CÞ

1=2Þð17Þ

where K is the rate of vertical curvature; K = Lcrest /|G2 � G1|; HE, the driver’s eye height, 1080 mm and HO is the object height,600 mm.

3.3. Sight distance evaluation function

For the entire section of a highway being evaluated, the ASD should be greater than or, at least, equal to the SSD corre-sponding to the design speed in order for drivers to control the operation of their vehicles safely. Otherwise, there will be ahigh probability of an accident, such as striking an unexpected object in the traveled way (AASHTO, 2004). For this reason,the length of the road segment where ASD < SSD (i.e., the length of the road segment with SSD restriction, denoted as ldef) isconsidered an important criterion for evaluating existing or planned highways (Olson et al., 1984). It should be noted how-

Road distance

Elev

atio

n

Overhead structure

MSD

SSDASDover

A

BVC EVC

PVC

B

C

D

HE

HO

ACAB ADHS

Fig. 5. Available sight distance under overhead structure.

106 M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111

ever, that this criterion cannot reflect how significant the ASD deficiency is at that road segment. In order to overcome such alimitation, a simple evaluation function is proposed in the present study as follows:

CPSD ¼Xndef

i¼1

b0 þ b1 � ðAdefi Þb2

h ið18Þ

Adef ¼R ldef

0 ðddef Þdx if ddef > 00 otherwise

(ð19Þ

where CPSD is the significance of the sight distance deficiency for a highway being evaluated. Note that the value of CPSD is 0 ifthere is no road segment with SSD restriction in the entire section of the highway; ndef, the total number of segments whereASDMin is less than SSD in the highway; ddef, the sight distance deficiency; ddef = SSD � ASDMin; ldef, the length of the road seg-ment where ASDMin < SSD; ASDMin, the minimum available sight distance at any point on the highway; b0, b1, b2 are the coef-ficients used for the sight distance penalty function, CPS and Adef is the total sight distance deficiency of the highway beingevaluated.

The procedure for estimating Adef is described as follows:

Step 1: Plot the profiles of all available sight distances (e.g., ASDhor, ASDseg, ASDcrest, and ASDover, etc.) of the highway beingevaluated.Take the minimum of all the available sight distances and plot it; ASDMin = Min (ASDhor, ASDseg, ASDcrest, ASDover).Step 2: Plot SSD profile on the ASDMin profile.Identify the road segments where ASDMin is less than SSD.Calculate the sight distance deficiency (i.e., ddef as shown in Fig. 6) for each point on the road segment with SSDrestriction.Step 3: Calculate the total sight distance deficiency (Adef), by integrating ddef for the length of the road segment with SSDrestriction (ldef).Apply the total sight distance deficiency (Adef) in the evaluation function shown in Eq. (18) to penalize the highway align-ment that has a sight distance problem.

Note that a crash speed concept introduced by Taignidis (1998) is also useful as a criterion to measure the severity of SSDrestriction when evaluating existing or planned highways; it is defined as the speed at which the vehicle is expected to col-lide with a stationary object on a crest vertical curve having restricted SSD.

4. Evaluating level-of-safety

It is a known fact that despite a highway being designed in accordance with proper standards, crashes do occur sincethere are many factors contributing to the occurrence of a crash. According to AASHTO (2010), crashes have three generalcategories of contributing factors, which include human, vehicle, and roadway environment. Among them, only the roadwayenvironment is controllable in a highway design process from a safety perspective. The other categories of the crash contrib-uting factors are difficult to quantify in the highway design stage. For this reason, the level-of-safety of a planned highway isevaluated based on the geometric conditions in the present study.

ddef

Adef

Available sight distance (ASDMin)Stopping sight distance (SSD)

Sigh

t dis

tanc

e

Roadway distance (x)

MSD

ldef

Fig. 6. Total sight distance deficiency of a road segment where ASDMin is less than SSD.

M.-W. Kang et al. / Transportation Research Part C 31 (2013) 99–111 107

A crash prediction model proposed in the Highway Safety Manual (HSM) by AASHTO (2010) is adopted in the presentstudy for evaluating alternative alignments of a planned highway from safety point of view. The HSM model can estimatetotal predicted average crash frequency of the planned highway. It combines a safety performance function (SPF) with aset of crash modification factors (CMFs) and a calibration factor. CMF represents the relative change in crash frequencydue to a change in one specific geometric condition when all other conditions and site characteristics remain constant(AASHTO, 2010). Thus, a CMF may serve as an estimate of the effect of a particular geometric design of a particular condition.The SPF, which is the basis of the HSM model, predicts total crash frequency for base conditions of the planned highway.Adjustment of the base SPF with a calibration factor or the use of a particular SPF developed with data obtained from actualsites is recommended for satisfactory result of crash frequency prediction. It is important to note however, that the base SPFmay be directly used with CMFs without calibration if it is used to compare alternatives of a planned highway, which havethe same facility type, geographical location, driver populations, climate, and land-use, but are different in geometric con-ditions. The safety evaluation function combined with the base SPF for planned highways adopted from the HSM (AASHTO,2010) can be expressed as follows:

CSA ¼ UAcc � Npredicted rs ð20ÞNpredicted rs ¼ Nspr rs � Cr � ðflw � fsw � fhc � fse � fgd � fncÞ ð21ÞNsprrs ¼ AADT � L� 365� 10�6 � e�0:312 ð22Þ

fhc ¼Ynhc

k¼1

fhckð23Þ

fse ¼Ynhc

k¼1

fsekð24Þ

fgd ¼Yngd

j¼1

fgdjð25Þ

where CSA is the predicted accident cost of an alternative highway alignment being evaluated; UAcc, the accident unit cost ($/crash) as a net perceived value (NHTS, 2000); Npredicted rs, the predicted total crash for a planned rural two-lane, two-wayhighway for a specific year. Eq. (21) is adopted from the HSM by AASHTO (2010); Nspr rs, the predicted total crash for baseconditions of a planned rural two-lane, two-way highway. Eq. (22) is adopted from the HSM by AASHTO (2010); AADT is theAverage annual daily traffic volume (veh/day); L, the length of the alternative highway alignment in miles; Cr, the calibrationfactor for roadways of a specific type developed for a particular geographical area, flw, the CMF for lane width; fsw, the CMF forshoulder width and type; fhc, the CMF for horizontal curves. CMF values are multiplicative and applied to each horizontalcurve in the highway alignment; fse, the CMF for superelevation of horizontal curves. CMF values are multiplicative and ap-plied to each horizontal curve in the highway alignment; fgd, the CMF for the vertical grades. CMF values are multiplicativeand applied to each individual grade segment on the highway alignment; fnc, the CMF for density of roads being crossed bythe highway alignment; nhc, the total number of horizontal curves in the highway alignment and ngd is the total number ofgrade segments in the highway alignment.

CMFs for geometric design features considered in the safety evaluation function include: length and width of the high-way, horizontal curve radius, superelevation rate used in the horizontal curve, presence of spiral transition curve, up anddowngrades of the highway vertical alignment, etc. Other CMFs, such as roadside design and existence of lighting and cen-terline rumble strips are not considered here because their conditions are assumed to be the same for all alternatives beingevaluated. Base conditions of a rural two-lane, two-way highway that brings default CMF values (AASHTO, 2010) are:

� 12 ft lane width and 6 ft shoulder width;� Paved travel lanes and shoulders.� Undivided highway without centerline rumble stripes and two-way left-turn lane (TWTL).� Straight alignment on level terrain (i.e., no horizontal and vertical curves).� Total number of roads being crossed by the planned highway is less than 5 per mile (i.e., 3/km).

5. Example

A case study is presented here to see how the proposed models (i.e., the fuel consumption model, sight distance model,and safety model) work properly in evaluating an example highway alignment. The example alignment is hypotheticallydrawn as an alternative of a highway being planned. Note that a part of the example highway does not satisfy (intentionally)the design standards (AASHTO, 2004) in order to demonstrate the functionality of the proposed sight distance model. Thegeometry of the example highway with a couple of obstacles along it is shown in Fig. 7a and b. As shown in the figure, abig roadside obstacle is located inside of the first horizontal curve and an existing highway overpasses the example highwayat its second sag vertical curve. The geometric specification of the example highway with other parameters used in thisexample is shown in Table 1.

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The sight distance profiles resulting from the proposed sight distance model are shown in Fig. 7c. A SSD profile based on80 km/h design speed is plotted together with all ASDs on horizontal and vertical alignments of the example highway. Thereare two road segments where ASD < SSD in the example highway; one is because of a short crest vertical curve at about sta-tion 1 + 900 and the other is due to a short sag vertical curve at about station 2 + 360. Thus, the example alternative is dis-qualified from the sight distance perspective. A penalty from Eq. (18) can be applied to penalize its disqualification if the

Roadsideobstacle

Fig. 7. Evaluation of an example highway in terms of vehicle fuel efficiency, sight distance, and safety.

Table 1Geometric specifications and other parameters used in the example.

Roadway environment– A rural two-lane, two-way, undivided highway – Two horizontal curves with 1000 m curves radius; 200 m long

spiral transitions at both sides of each curve; 6% superelevation– 80 km/h design speed– 3.6 m lane with– 1.8 m paved shoulder for each direction– 2891 m length (1.8 mile) – Two crest and two sag vertical curves– A grade separation with an existing road

Vehicle and others– Vehicle (passenger car) mass: 1760 kg – AADT: 10,000 veh/day– Projected frontal area of the vehicle: 2.276 m2 Assumption: passenger cars only– Coefficient of rolling resistance: 0.013 – Fuel consumption rate: 3.1 � 10–8 l/J– 0.5 air drag coefficient Note: 1 gallon gasoline � 114,000 BTU– 1.202 air density 1 BTU � 1055 J (N m)

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proposed sight distance model is incorporated into the highway alignment optimization process. Note that no sight distanceissue is found because of the overpass structure.

At the short crest vertical curve (i.e., the second crest vertical curve in Fig. 7a), the minimum value of estimated ASD forboth night and daytime is 79 m which is less than the value of SSD (121 m) corresponding to the design speed with an in-stant grade at the curve. The length of the SSD restriction and the total area of sight distance deficiency at this road segmentare 133 m and 4251 m2, respectively. At the second sag vertical curve with the overpass structure, only the nighttime ASD(i.e., headlight sight distance at night) on the vertical curve is below the SSD; the minimum values of ASD and SSD at thisroad segment are 124 and 135 m, respectively. The length of the SSD restriction and the total area of sight distance deficiencyat this segment are 54 m and 407 m2, respectively.

Fig. 7d shows the propulsive force of a passenger car calculated along the example highway while maintaining a cruisingspeed of 80 km/h. The propulsive force is estimated here based on the total resistance, which includes the rolling, grade, andair resistances (see Eqs. (1) and (6)). It should be noted that the propulsive force become zero at some points of down gradesbecause the grade resistance becomes negative and nullifies the effect of the other resistances. For example, the propulsiveforce becomes zero at about station 0 + 667, which is about 10 m after the highest point (at station 0 + 657.3) of the first crestvertical curve. The force becomes positive at about station 1 + 478 just before station 1 + 482.5, which is the lowest point ofthe first sag vertical curve. Note that the propulsive force is calculated at 1 m interval in this example.

The fuel consumption of a passenger car is shown in Fig. 7e. It is computed with (i) a given fuel consumption rate (seeTable 1) and (ii) the propulsive work performed by the vehicle as the vehicle moves along the example highway. FromEqs. (5) and (6), it is estimated that, in total, 0.7 l of gasoline is consumed by the vehicle for traveling over the highwayat 80 km/h cruising speed. Note that this would be underestimated because the power loss of the vehicle due to the internalresistance leading from the running gear, wheel bearings, and suspension system is not considered in the estimation.

The HSM models, Eqs. (21) and (22) are employed to estimate the predicted total crash for the example highway. 0.017per year of crashes are predicted for the example highway based on its geometric and traffic information shown in Table 1.The total accident cost of the highway can also be estimated if the information of unit accident cost ($/crash) and analysisperiods were given.

6. Conclusion

The methodology proposed in this paper for evaluating a planned highway allows a quick and precise review of vehicularfuel consumption, sight distance deficiency, and safety level of that highway. A fuel consumption model is developed basedon highway geometric characteristics (e.g., grades, length, and location of crest and vertical curves), speed, and road surfacetype and condition. The output of the fuel consumption model is the amount of fuel consumed by the vehicle while it travelsalong a highway at cruising speed. The model may be useful in finding fuel efficient and environmentally friendly highwaysbecause the vehicular fuel consumption directly affects not only the cost of vehicle operation but also generates greenhousegas and pollutant emissions.

The proposed sight distance model automatically draws graphs depicting the profiles of all ASDs on horizontal and ver-tical alignments at both night and daytimes as well as a SSD profile corresponding to the design speed and road grades. Fur-thermore, it calculates the significance of the sight distance deficiency of a highway having road segments with SSDrestriction. The model can be used in the highway alignment optimization process to penalize alternative highways and dis-qualify them from further evaluation if sight distance is found inadequate. The HSM crash prediction model (AASHTO, 2010)is adopted to evaluate alternative highways in terms of the highway safety. Note that calibration of the crash predictionmodel may not be necessary if it is used to just compare alternative highway alignments which have the same facility type,geographical location, driver populations, climate, and land-use, but are different in geometric conditions.

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7. Future work and model limitations

The proposed methods will be integrated with the highway alignment optimization model previously developed by theauthors (Jha et al., 2006 and Kang et al., 2012). The integration will be performed by integrating the evaluation parameters ofthe fuel, sight distance, and safety methods to the objective function of the optimization model. After the integration work iscompleted, numerous possible alternative alignments of a new highway can be generated and evaluated through tradeoffsamong all relevant decision criteria, which include vehicle fuel efficiency, sight distance, and safety, besides the constructioncost, maintenance cost, user cost, and environmental impact, which are already considered in the optimization model.Accordingly, a trade-off solution balanced with all important decision criteria is searched through the alignment optimiza-tion process. The proposed model may also be used to evaluate existing highways; however, some limitations need to beresolved. These will be addressed as the model continues through the development process, and will be incorporated intofuture versions of the model. Model limitations acknowledged by the authors are:

� The proposed fuel consumption model is designed to evaluate the fuel consumption of the vehicles traveling on relativelyhigh-speed highways with consistent design speeds. It may not be suitable to apply along highway curved sections wheredeceleration and re-acceleration are needed due to varying design speeds (or varying speed limits).� The fuel consumption model is for passenger cars only. It will be updated with consideration of other types of vehicles.� The fuel consumption model does not yet consider the effect of intersections and junction points with existing roads.� The fuel consumption rate is assumed to be constant in this study and not sensitive to temperature, road steepness, crit-

ical length of grade, and other factors. Sensitivity of fuel consumption to such factors will be modeled in future works.� The sight distance model only considers vertical curves when calculating nighttime ASDs. The effect of horizontal curves

on the nighttime ASDs calculation should also be considered in the future because objects around a horizontal curve mayalso not be illuminated at nighttime.� Sight distance is evaluated separately in the proposed model for horizontal and vertical alignments. Incorporating it with

a three-dimensional sight distance model, which simultaneously considers horizontal and vertical curves (Jha et al., 2011)would consider the impact of roadside obstacles on ASD calculation.

Acknowledgements

This work was jointly carried out at the Center for Advanced Transportation and Infrastructure Engineering Research (CA-TIER)–Morgan State University and the University of South Alabama, Mobile.

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