Safety Effects of Horizontal Curve Design on Motorcycle Crash Frequency on Rural Two-Lane Undivided Highways in Florida

Transcription

1 Safety Effects of Horzontal Curve Desgn on Motorcycle Crash Frequency on Rural Two-Lane Undvded Hghways n Florda Chunfu Xn Department of Cvl and Envroment Engneerng, Unversty of South Florda 0 E. Fowler Avenue, ENC00, Tampa, FL 0 Tel: () -, Emal: chunfu@mal.usf.edu Zhenyu Wang (Correspondng Author) Center for Urban Transportaton Research, Unversty of South Florda 0 E. Fowler Avenue, CUT00, Tampa, FL 0 Tel: () -, Emal: zwang@cutr.usf.edu Pe-Sung Ln Center for Urban Transportaton Research, Unversty of South Florda 0 E. Fowler Avenue, CUT00, Tampa, FL 0 Tel: () -0, Emal: ln@cutr.usf.edu Chanyoung Lee Center for Urban Transportaton Research, Unversty of South Florda 0 E. Fowler Avenue, CUT00, Tampa, FL 0 Tel: () -0, Emal: cylee@cutr.usf.edu Ru Guo Center for Urban Transportaton Research, Unversty of South Florda 0 E. Fowler Avenue, CUT00, Tampa, FL 0 Tel: () 00-, Emal: ru@cutr.usf.edu Word count:,00+ tables/fgures x 0 words (each) =,00 words November, 0

2 Xn, Wang, Ln, Lee, Guo 0 0 ABSTRACT The assocaton between horzontal curve desgn (e.g., radus and type) on rural two-lane undvded hghways and motorcycle crash frequency s not well-documented n exstng reports and publcatons. Ths study amed to nvestgate the effects of the desgn parameters and assocated factors on the occurrence of motorcycle crashes consderng the ssue of unobserved heterogenety. A random parameters negatve bnomal regresson model was developed based on motorcycle crashes, whch were collected on, horzontal curves along two-lane undvded hghways n Florda for a perod of years (00 0). Four normally-dstrbuted random parameters (logarthm of curve radus, reverse curves, pavement condton, and rough pavement ndcator) were dentfed to represent ther heterogenety caused by unobserved factors over tme, space, and/or ndvduals. The major conclusons are the followng: () An ncrease n curve radus, on average, sgnfcantly and near-logarthmcally decreases the motorcycle crash frequency on rural two-lanes undvded hghways. Ths effect s more sgnfcant when the curve radus s less than,000 ft. ().% of reverse curves tend to decrease the motorcycle crash frequency on rural two-lane undvded hghways; the remanng.% have an opposte effect. On average, the lkelhood of motorcycle crashes on reversecurves s reduced by %. () The crash modfcaton functon (CMF) for curve radus on rural two-lane undvded hghways was establshed, gven the radus of,000 ft as the baselne, as a power formula, CMF = (Radus/000) Keywords: Motorcycle, Crash frequency, Horzontal curve, Random parameters, Un-observed heterogenety, Negatve Bnomal, Crash Modfcaton Functon/Factor

3 Xn, Wang, Ln, Lee, Guo INTRODUCTION In the Unted States, although motorcycles comprse only % of regstered vehcle and less than % of vehcle mles traveled, the percentage of motorcyclst fataltes as a porton of total traffc deaths grew from % n 000 to % n 0 (). As shown n a Natonal Hghway Traffc Safety Admnstraton (NHTSA) report, motorcyclsts n the US are 0 tmes more lkely than car passengers to be fatally njured n traffc crashes (). As the state wth the second hghest number of regstered motorcycles, Florda has experenced a sgnfcant ncrease n the number of motorcyclst fataltes, from a record low of n 00 to 0 n 0. Accordng to the Florda Department of Health, n 0, Florda hosptalzaton charges from motorcycle crashes exceeded $00 mllon (). It s worth notng that motorcycle crashes are over-represented on horzontal curves n Florda, especally for fatal crashes. Curved roadway segments comprsng around % of total mleages n Florda accounted for % of fatal sngle-motorcycle crashes and % of ncapactatng sngle-motorcycle crashes (). Horzontal curves on rural two-lane undvded (RTU) hghways are more dangerous to motorcyclsts compared to other roadway facltes. Zegeer et al. () ndcated that crash rates on horzontal curves are..0 tmes greater than those on tangents of rural two-lane hghways. In addton, t has been estmated that there are more than 0 mllon horzontal curves n the US on two-lane hghways alone (). The causes of safety hazards to motorcyclsts on RTU horzontal curves are () () the relatvely hgh speed and low standards of horzontal algnment desgn on RTU hghways; () complex rdng maneuvers requred for negotaton of curves, e.g., turnng maneuvers n lmted space, counterweghtng technques, etc.; () reduced sght dstance on curves that weaken rder percepton; and () for some rders, the attracton of sharp curves to rsk-seekng behavor for aggressve rders, especally on RTU hghways. These factors may cause erroneous rdng behavors (e.g., underestmaton of curve sharpness, excessve speed, erroneous lean angle, flawed trajectory, etc.) when negotatng curves, resultng n an ncreased number of motorcycle crashes on RTU curves. However, the occurrence of motorcycle crashes s a jont consequence from a complex process nvolvng varous factors, some of whch can be observed (usually obtaned from polce accdent reports or roadway characterstcs nventores) and others cannot. The safety effect of a contrbutng factor may be random rather than fxed f heterogenety (over tme, space, or ndvduals) exsts n unobserved factors that are related to the contrbutng factor (). Many efforts have been made to address motorcycle safety n terms of crash frequency ( ) and njury severty (,, 0 ). Prevous studes on the factors contrbutng to motorcycle crash occurrence (frequency or crash rate) are summarzed n Table. Only a few studes were found to nvestgate the relatonshp between horzontal curve desgn parameters and motorcycle crash occurrence. Schneder et al. () evaluated the mpacts of horzontal curves and other geometrc characterstcs on the frequency of motorcycle crashes along rural two-lane hghways n Oho usng the negatve bnomal model wth the full Bayesan estmaton. They found that both the radus and length of each horzontal curve sgnfcantly nfluence the occurrence of motorcycle crashes, and an ncrease of % n the radus tends to decrease average sngle-motorcycle crash frequency by 0.%. Gabauer and L (0) nvestgated motorcycle-tobarrer crash frequency on horzontally-curved roadway sectons n Washngton and concluded that curve length, traffc volume, and locaton of adjacent curves can sgnfcantly affect the occurrence of motorcycle-to-barrer crash. Chen et al. () conducted a motorcycle safety nvestgaton at an ext ramp secton and concluded that ramp type, ramp length, and reverse curvature are the major factors contrbutng to motorcycle crashes. In summary, the safety effects

4 Xn, Wang, Ln, Lee, Guo 0 of RTU horzontal curve desgn parameters on motorcycle crash frequency were not welldocumented. Thus, t s essental to seek nsght nto the assocaton of horzontal curve desgn parameters (e.g., curve radus, length, and type) and motorcycle crash frequency. TABLE Summary of Prevous Studes on Motorcycle Crash Frequency Category Factors Effectveness & References Curve Characterstcs Geometrc Characterstcs Pavement Characterstcs Traffc Characterstcs Curve radus Curve type Segment length Number of lanes Lane wdth Shoulder wdth Access densty Pavement roughness Annual average daly traffc (AADT) Truck volume Speed % ncrease n radus tends to decrease average sngle-motorcycle crash frequency by 0.% (). Horzontal curves of 0 ft or less ncrease average motorcycle-tobarrer crash frequency by factor of 0 compared to curves not meetng ths crteron (0). Isolated curves curves havng no adjacent curved sectons wthn 00 ft of ether curve end ncrease rsk of motorcycle-to-barrer crashes (0). % ncrease n curve length results n ncrease n average frequency of snglemotorcycle crashes by 0.% (). Long horzontal curves ncrease motorcycle-tobarrer crashes (0). Increasng road length ncreases motorcycle crash frequency (). 0.-mle ncrease of ramp length wll lead to % ncrease n motorcycle crashes occurrng on ramps (). Greater number of lanes decreases lkelhood of ntersecton-related motorcycle crashes ( ); addtonal lane ncreases number of motorcycle crashes occurrng on four-legged sgnalzed ntersectons by ~% (). Wder lane decreases lkelhood of ntersecton-related motorcycle crashes (, ). Narrow shoulder ( ft) ncreases average sngle motorcycle crashes by.% (). Lkelhood of motorcycle crashes decreases wth ncrease of shoulder wdth (, ). Hgher access densty ncreases motorcycle crash frequency (, ). Lkelhood of motorcycle crashes ncreases wth ncrease of Internatonal Roughness Index of pavement (). % ncrease n AADT results n ncrease of sngle-motorcycle crash frequency by 0.% (). Increasng AADT ncreases rsk of motorcycle-to-barrer crashes (0), lkelhood of ntersecton-related motorcycle crashes (,,, ), and motorcycle crash frequency (,, ). % ncrease n heavy vehcle traffc may ncrease motorcycle accdents by ~% (). 0 km/h ncrease n approach speed expected to cause % ncrease n nonsgnalzed ntersecton-related motorcycle crashes (); mph ncrease n posted speed lmt wll result n % ncrease n ramp-related motorcycle crashes (). Hgher mposed speed lmts ncrease lkelhood of ntersecton-related motorcycle crashes (,, ). Hgher speed or greater speed varaton ncrease lkelhood of motorcycle crashes (, ). The prmary objectve of ths study was to nvestgate the effects of horzontal curve desgn parameters on the occurrence of motorcycle crashes along RTU hghways n Florda. Ths study amed to () quantfy the effects of horzontal curves on the occurrence of motorcycle crashes, () dentfy factors contrbutng to motorcycle crash frequency on horzontally-curved segments on RTU hghways, and () address the unobserved heterogenety ssues n curverelated motorcycle crashes usng a random-parameters model. DATA COLLECTION The data set developed for ths study was compled from two major sources. Data from the frst source, the Florda Roadway Characterstcs Inventory (RCI) database, whch contans

5 Xn, Wang, Ln, Lee, Guo comprehensve roadway nformaton, was scanned, and, horzontal curves wth a 00-ft buffer on each end were dentfed. Among these horzontal curves,, horzontal curves are located on RTU hghways. Curves n whch a sgnalzed ntersecton was present were excluded. Informaton on geometry, traffc, and pavement data were extracted from the RCI database for each dentfed RTU curve. The types of horzontal curve are classfed as reverse curve and nonreverse curve. A reverse curve conssts of two jonted smple curves, but curvng n opposte drectons. A non-reverse curve could be a smple curve or a compound curve that conssts of two or more smple curves wth deflectons n the same drecton mmedately adjacent to each other. The types of horzontal curves are shown n Fgure. 0 0 Sngle Curve Compound Curve Reverse Curve FIGURE Types of Horzontal Curves The second source was the Crash Analyss and Reportng (CAR) system mantaned by the Florda Department of Transportaton (FDOT). In total, motorcycle crashes for years (00 0) were spatally matched to the dentfed RTU horzontal curves. The descrptve statstcs of the collected data are shown n Table. TABLE Descrptve Statstcs of Curvature, Geometrc, Pavement, and Traffc Varables Varable Descrpton (number of observatons:,) Mean Std. Dev. Mn. Max. Dependent Varable: number of motorcycle crashes per years Curve characterstcs Logarthm value of curve radus n log (ft) Reverse curve ndcator ( f reverse curve, 0 otherwse) Curve length n mles Geometrc characterstcs Shoulder wdth n ft.. Auxlary lane ndcator ( f auxlary lane exsts n curve segment, 0 otherwse) Grade ndcator ( f vertcal grade s present, 0 otherwse) Access densty: number of junctons per mle.0. 0 Pavement characterstcs -year average pavement condton (scale 0 ) Pavement roughness ndcator ( f -year average nternatonal roughness ndex (IRI) s greater than n./m, 0 otherwse) Traffc characterstcs Average annual daly traffc (AADT) n thousands of vehcles per day.. 0..

6 Xn, Wang, Ln, Lee, Guo STATISTICAL METHODOLOGY A wde range of statstcal regresson methodologes has been developed to descrbe the relatonshp between crash frequency and a set of explanatory varables. These methodologes were comprehensvely revewed and assessed by two revewed papers (, ). In ths study, the random-parameters negatve bnomal (RPNB) model was used to assess the factors that determne the occurrence of motorcycle crashes. Negatve Bnomal (Posson-Gamma) Model The negatve bnomal (NB) model s an extenson of the Posson model to address overdsperson n crash data (, ). The Posson regresson model can be wrtten as: y EXP( λ ) λ P( y ) = () y! where P (y) s the probablty of curve segment havng y crashes per a gven perod and λ s the Posson parameter for curve segment, whch s equal to curve segment th expected number of crashes per a gven perod, E[y]. The Posson regresson model can be estmated by specfyng the Posson parameter λ as a functon of explanatory varables by typcally usng a log-lnear functon: λ = EXP βx ) () ( where X s a vector of explanatory varables and β s the vector of regresson coeffcents (). In ths study, the Posson model s not approprate because the mean (0.) of motorcycle crashes s sgnfcantly less than the varance (0. = 0. ). To address ths over-dsperson ssue, the NB model can be derved as λ = EXP β + ε ) () ( X where EXP(ε) s a gamma-dstrbuted error term wth mean and varance α. The addton of ths term allows the varance to dffer from the mean as VAR[y] = E[y][ + αe[y]]= E[y] + αe[y]. The negatve bnomal probablty densty functon can be descrbed as P( y ) = α + λ ( α ) α Γ [( α ) + y ] ( ) y Γ α! ( α ) λ + λ where Г( ) s a gamma functon. Random-Parameters Negatve Bnomal Model The occurrence of a motorcycle crash s a complcated outcome that nvolves complex nteractons between human factors and roadway characterstcs, vehcle features, traffc attrbutes, and envronmental condtons (). Sample data for crash modelng usually are retreved from polce accdent reports and RCI fles; t s mpossble to nclude all factors nfluencng the occurrence of a traffc crash n these databases over tme, space, and ndvduals. The unobserved factors, correlated wth the observed varables, potentally can cause the ssue of n ()

7 Xn, Wang, Ln, Lee, Guo unobserved heterogenety that s, dfferences among crash observatons that are not measured. Tradtonal statstcal methods (e.g., NB model) cannot address the ssue of unobserved heterogenety and may lead to based and nconsstent parameter estmaton, erroneous nferences, and neffcency predctons (). To resolve ths ssue, the random-parameters negatve bnomal (RPNB) model was developed to allow some parameters to vary across crash observatons, rather than fxed n tradtonal models. The equaton of regresson coeffcents for random parameters model s gven as β = β + () ϕ where φ s a randomly dstrbuted term wth mean 0 and varance σ. Wth ths, the loglkelhood functon can be shown as LL ( β ) ln f ( ϕ ) P( y ϕ ) d = ϕ () ϕ where f( ) s the probablty functon of the φ. Snce Equaton cannot be derved to a closed form, the smulated maxmum lkelhood approach wth a Halton sequence was used to estmate the model parameters (). Model Interpretaton Unlke fxed parameters, the sgn of a random parameter cannot be used drectly to nterpret the effect of the parameter. Alternatvely, the probablty of whch parameter s postve or negatve was used to ndcate dfferent nfluences on the occurrence of motorcycle crashes. Assume a random parameter (β ) obeys a gven dstrbuton wth parameter θ, the probablty of ts coeffcent β < 0 can be calculated as P ( β < 0) = F( β < 0 θ ) P( β > 0) = F( β < 0 θ ) where F( ) s the cumulatve dstrbuton functon of the parameter β. The parameter effects can be nterpreted as the lkelhood of the parameter to decrease motorcycle crash frequency s P(β < 0) and the lkelhood to ncrease motorcycle crash frequency s P(β > 0). Margnal effects were used to quantfy the mpacts of an explanatory varable n the estmated model. For a contnuous varable, magnal effects reflect the effect of a one unt change n the kth explanatory varable (xk) on the expected number of accdents (λ) per a gven perod for the th observaton (). They can be computed as ME λ xk = λ x k MODEL ESTIMATION The software package NLOGIT () was used to estmate the NB and RPNB models based on the collected data. In the estmaton of the RPNB model, several assumptons (normal, lognormal, trangular, unform dstrbuton) on the random parameters dstrbuton were tested for dfferent varables usng the smulated maxmze lkelhood approach. Fnally, four normally- () ()

8 Xn, Wang, Ln, Lee, Guo 0 dstrbuted random parameters (curve radus, reverse curve, pavement condton, pavement roughness) were dentfed after 00 Halton draws. A lkelhood rato test wth the null hypothess that two models are statstcally equvalent was performed between the NB and RPNB models (), as shown n Equaton. NB [ LL( β ) LL( β )] χ = RPNB () NB where LL( β ) s the log lkelhood at convergence of the NB model (-0.0) and RPNB LL( β ) s the log lkelhood at convergence of the RPNB model (-0.). The ch-square statstc for the lkelhood rato test wth four degrees of freedom gave a value greater than the % confdence lmt (χχ =.0). It ndcates that the RPNB model s statstcally superor to the correspondng NB model. The estmated RPNB model, along wth average margnal effects, s presented n Table. TABLE Random-Parameters Negatve Bnomal Regresson Model for Motorcycle Crash Frequency on Rural Two-Lane Undvded Hghways Varable Descrpton Estmated t- Margnal Parameter Statstc Effect Constant Curve characterstcs Logarthm value of curve radus n log(ft) Standard devaton of parameter dstrbuton (0.0) (.) Reverse curve ndcator ( f a reverse curve presents, 0 otherwse) Standard devaton of parameter dstrbuton (0.) (.) Curve length n mle Geometrc characterstcs Auxlary lane ndcator ( f auxlary lane s present n curve segment, otherwse) Grade ndcator ( f vertcal grade s present, 0 otherwse) Access densty: number of junctons per mle Pavement characterstcs -year average pavement condton (scale 0 ) Standard devaton of parameter dstrbuton (0.0) (.) Pavement roughness ndcator ( f -year average nternatonal roughness ndex (IRI) s greater than n./m, 0 otherwse) Standard devaton of parameter dstrbuton (0.0) (.) Traffc characterstcs Average annual daly traffc (AADT) n thousands of vehcles per day Overdsperson parameter α 0.. Number of observatons Log-lkelhood wth constant only -. Log-lkelhood at convergence -0. McFadden pseudo R-squared (ρ ) 0.

9 Xn, Wang, Ln, Lee, Guo DISCUSSION Curve Radus and Type The logarthm of the curve radus s a random parameter that s normally dstrbuted, wth a mean of -0.0 and standard devaton of 0.0. Ths ndcates that ncreasng the curve radus nearly always decreases the motorcycle crash frequency (less than 0.0% of the dstrbuton would have a postve value) but wth varyng magntude across the populaton of RTU roadway segments. The ncrease of curve radus can reduce the rsk factors for motorcyclsts, such as speed varaton, poor sght dstance, and complexty of negotaton maneuvers. Schneder et al. () found a smlar result, that sharper curves mght attract motorcyclsts who exhbt greater rsk-takng behavor. The reverse curve ndcator produced a normally-dstrbuted negatve parameter wth a mean of -0.0 and a standard devaton of 0., suggestng that for.% of roadway segments, the presence of reverse curves tends to result n a decrease n motorcycle crash frequency. For the remanng roadway segments, the presence of reverse curves tends to result n an ncrease n motorcycle crash frequency. Ths s perhaps because a great porton of motorcycle rders (~.%) would become more alert and take safety-orentaton behavors (e.g., slow speed) to compensate for the dffculty of negotatng reverse curves. Other rders stll suffer the rsk caused by reverse curve, such as frequent adjustments of rdng posture, poor sght dstance, etc. Gabauer and L (0) reported a smlar fndng, that the solated curves (smple curves) ncrease the rsk of motorcycle-to-barrer crashes but ther effects are fxed. Margnal effects show that the presence of reverse curves results n an average 0.0 decrease n the number of motorcycle crashes per years. Fgure presents the expected motorcycle crash frequency (per years) by curve radus and type, holdng other factors at ther average over sample observatons. The relatonshp between motorcycle crash frequency and curve radus s near-logarthmc. The expected motorcycle crash frequency decreases rapdly wth an ncrease n radus f the curve s sharp (radus <,000 ft). When the radus exceeds,000 ft but s less than,000 ft, the decrease slope s smaller than sharp curves but stll hgher than a flat curve (radus >,000 ft). It s also obvous that the presence of reverse curve can sgnfcantly decrease the motorcycle crash frequency at each radus level.

10 Xn, Wang, Ln, Lee, Guo Expected Motorcycle Crash Frequency (-years) Radus of Horzontal Curve (feet) Non-reverse Curves Overall Curves Reverse Curves FIGURE Expected Motorcycle Crash Frequency by Curve Radus and Curve Type Curve Length Snce some geometrc factors (e.g., shoulder wdth) may vary wth the ncrease n curve length, curve length was not treated as an exposure varable that be assumed to have a lnear relatonshp wth expected crash frequency. The RPNB model shows that the length of horzontal curve s a postve fxed parameter, whch ndcates that the average number of motorcycle crashes ncreases wth an ncrease n curve length because motorcycle rders would gan more exposure tme wth ncrease of curve length. Ths fndng s n lne wth several prevous studes (, ). The margnal effects show that a -mle ncrease n curve length on RTU hghways results n an average ncrease of 0. motorcycle crashes per years. Geometrc Characterstcs Auxlary lanes, lnkng access ponts and, consequently, ncreasng potental traffc conflcts, were found to ncrease the probablty of motorcycle crash occurrence on RTU curves. Margnal effects show that the presence of auxlary lanes would ncrease the average number of motorcycle crashes on RTU hghways by 0.0 (per years). The vertcal grade varable produced a postve fxed parameter that ncreases motorcycle crash frequency by 0.0 crashes per years. The nteracton between horzontal curves and vertcal slope can sgnfcantly decrease the sght dstance and ncrease the complexty of rdng maneuvers. The safety effects of horzontal curve and grade combnatons on rural two-lane hghways were dscussed n a prevous study () n whch the authors found that short horzontal curves at sharp vertcal curves are assocated wth hgher crash frequences for all vehcles. The number of junctons (access ponts) per mle on horzontal curves s a postve fxed parameter, snce hgh access densty may ntroduce more traffc conflcts. Ths fndng also s consstent wth prevous studes (, ). Margnal effects show that each addtonal juncton per mle can result n an ncrease of 0.00 motorcycle crashes per years on RTU roads.

11 Xn, Wang, Ln, Lee, Guo Pavement Characterstcs The pavement condton varable ranges from 0 (completely deterorated) to (excellent pavement condton). Ths varable produced a normally-dstrbuted negatve parameter, wth a mean of 0. and a standard devaton of 0.0, suggestng that for nearly all RTU curves, the number of motorcycle crashes ncreases when the pavement condtons become better. Ths fndng seems counterntutve and could be related to a varety of unobserved factors. For example, one possble unobserved factor s related to motorcyclst rsk-compensaton behavor; that s, motorcycle rders who beleve pavement qualty s good tend to take rsky behavors, such as hgher speed and less alertness. Smlar fndngs about the effects of good pavement condton tendng to ncrease vehcle crash frequency were found n two prevous studes (, 0). Another ndcator of pavement condton s the Internatonal Roughness Index (IRI), whch measures roughness of road surface. In Florda, the IRI s measured n nches per mle, wth lower values ndcatng a smoother surface. The RPNB model shows that a rough-pavement (IRI > n./m) s a random postve parameter, wth a mean of 0.00 and a standard devaton of 0.0, suggestng that 0.% of RTU curves wth rough pavement tend to ncrease motorcycle crash frequency. Traffc Volume AADT has a postve fxed parameter, ndcatng that a growth of,000 vehcles per day ncreases the expected number of motorcycle crashes by 0.0 per years. Ths fndng s consstent wth prevous studes (,, ). CRASH MODIFICATION FUNCTION The crash modfcaton functon (CMF) for horzontal curve radus descrbes the rsk of curve radus n terms of motorcycle crash frequency relatve to a baselne. Assumng that the curve radus of,000 ft s the baselne, the crash modfcaton functon can be derved from the estmated model (Table ) as CMF where ( R X ) 0.0 λ ( R X ) EXP( 0.0 LN( R ) + β X ) R = = (0) λ( R X ) EXP( 0.0 LN( R ) + β X ) = λ s the expected number of motorcycle crashes along curve segment wth radus R ; R0 s,000 ft, the baselne of CMF; -0.0 s the estmated parameter of radus n Table ; X represents the vector of the other varables; and β s the vector of estmated parameters for the other varables. The curve of the CMF for horzontal curve radus s shown n Fgure. The CMF curve has a smlar nonlnear tendency wth the curve of curve radus expected motorcycle crash frequency. The safety performance n reducng motorcycle crashes s more sgnfcant n the low range of curve radus. For example, the expected motorcycle crash frequences for horzontal curves of 0, 00, and,000 ft are, respectvely,.0,., and.0 tmes as many as the frequency for the radus,000 ft. In other words, f decreasng the radus from,000 ft to 0 ft, 00 ft, and,000 ft, the expected motorcycle crash frequency wll ncrease by 0%, %, and 0%, respectvely. If ncrease the radus from,000 ft to,000 ft, the percent of expected motorcycle crash frequency s only decreasng by %.

12 Xn, Wang, Ln, Lee, Guo. Crash Modfcaton Factor - CMF CMF=(R/000) Radus of Horzontal Curve-R (ft) FIGURE Crash Modfcaton Functon by Curve Radus The crash modfcaton factor for reverse curve ndcates the relatve change of expected motorcycle crash frequency comparng reverse curves wth non-reverse curves (smple or compound curves, Fgure ). λ( Reverse X ) ( Non reverse X ) EXP( β X ) CMF = = = EXP λ EXP( β X ) where ( Reverse X ) ( Non reverse X ) ( 0.0) 0. λ s the expected number of crashes along a reverse curve; λ s the expected number of crashes along a non-reverse curve; -0.0 s the estmated parameter of reverse curve n Table ; X represents the vector of the other varables; and β s the vector of estmated parameters for the other varables. The crash modfcaton factor of curve type ndcates that the number of motorcycle crashes would decrease % when a reverse curve s present on RTU roads. CONCLUSIONS AND RECOMMENDATIONS Ths study quantfed the effects of horzontal curve parameters and contrbutng factors on the occurrence of motorcycle crashes on rural two-lane undvded (RTU) roads usng the random parameters negatve bnomal (RPNB) model. Based on the dscusson, the followng conclusons can be obtaned: Horzontal curve radus sgnfcantly nfluences motorcycle crash occurrence on RTU roads. Although curve radus s a random parameter, nearly all RTU curves (>%) tend to decrease motorcycle crash frequency wth an ncrease n curve radus. The average margnal effects of horzontal curve radus suggest a logarthmc assocaton between curve radus and motorcycle crash frequency: the expected motorcycle crash frequency decreases (ncreases) rapdly wth an ncrease (decrease) n curve radus when the curve ()

13 Xn, Wang, Ln, Lee, Guo radus n a low range; ths trend (decrease) becomes progressvely slower wth the radus ncrease. Based on the developed RPNB model, the crash modfcaton fucton (CMF) for horzontal curve radus on RTU roads was establshed as a power functon of the quotent 0 of curve radus CMF for Radus = ( R 000) 0.. Reverse curve was dentfed as a random parameter. On.% of roadway segments, the presence of a reverse curve tends to result n a decrease n motorcycle crash frequency. On average, the presence of a reverse curve decreases the expected motorcycle crash frequency on RTU roads by % (CMF for Reseverse Curve = % = %). The presence of auxlary lanes, vertcal slope, hgh access densty, and growth of AADT can sgnfcantly ncrease the number of motorcycle crashes. Pavement condton and rough pavement ndcator were found to have random effects on motorcycle crashes casued by unobserved factors over tme, space, and ndvduals. The number of motorcycle crashes tends to ncrease on nearly all RTU curves wth good pavement condtons and 0.% of RTU curves wth rough pavement. Ths fndng revealed motorcylst sgnfcant rsk-compensaton behavors wth hgh-qualty pavement on horzontal curves. It s nterestng to compare the effects of horzontal curve desgn between frequency and severty. A random parameter negatve bnomal (RPNB) model, predctng the frequency of all motorcycle crashes on rural two-lane undvded horzontal curves, shows that sharp curves (radus<,00 ft) are more lkely to ncrease both the lkelhood of motorcycle crash occurrence and the probablty of motorcycle crash severe njury on horzontal curves. Curve type has dfferent mpacts: reverse curves tend to decrease the lkelhood of motorcycle crash frequency on curves and ncrease the probablty of severe njury n a sngle-motorcycle crash on curves. Smlarly, good pavement condtons tend to ncrease motorcyclst safety-compeston effects, thus rasng both motorcycle crash frequency and severty on horzontal curves. Recommendatons A strategc framework from Es (Engneerng, Educaton, and Enforcement) s necessary to be developed for addressng the motorcycle safety ssues dentfed n ths study. As descrbed n FHWA-SA--0 Low-Cost Treatments for Horzontal Curve Safety 0 (), varous engneerng countermeasures (e.g., pavement markngs, traffc control sgns, pavement treatments, roadsde mprovements, ITS devces) have been developed to alert motorsts of the presence and/or rsk of horzontal curves and control ther speed/trojectory n curve negotaton. However, these treatments that am to mprove vehcle safety on curves are not necessarly amed to be motorcycle-frendly because of the specal characterstcs and sgnfcant rsk-compensaton of motorcycles and motorcyclsts. Addtonal assessments on these treatments are requred for mplementng motorcycle-frendly treatments to mprove road safety on horzontal curves. Educaton programs (e.g., tranng courses, educaton campagns, safety coaltons) are effectve for mprovng motorcyclst behavors n curve negottaton, whch s the prmary contrbutng factor n a motorcycle crash. Educaton programs am to () ncrease rder awareness on the rsk of horzontal curves, () mprove rder sklls n negotaton wth horzontal curves, and () allevate njury severty by usng safety equpment. Enforcement, especally for speedng, also s effectve n reducng motorcycle crash and fataltes on horzontal curves.

14 Xn, Wang, Ln, Lee, Guo ACKNOWLEDGMENT The authors express ther grattude to FDOT project managers Joel Provenzano and Alan El- Urfal for ther assstance and support n ths research. The authors also thank Tna Hatcher and Ed Hutchnson from the FDOT Statstcs Offce for ther valuable help n data collecton. REFERENCES. Rettng, R., and H. Rothenberg. Motorcylst Traffc Fataltes by State-0 Prelmnary Data. Governors Hghway Safety Assocaton, 0.. Natonal Hghway Traffc Safety Admnstraton (NHTSA). Traffc Safety Facts 0 Data: Motorcycles. DOT-HS--. NHTSA, U.S. Department of Transportaton, 0.. Smart Rde Florda. Crash Data. Traffc Safety Offce, Florda Department of Transportaton, Florda. Accessed Jul. 0, 0.. Wang, Z., C. Lee, and P.-S. Ln. Modelng Injury Severty of Sngle-Motorcycle Crashes on Curved Roadway Segments. Presented at rd Annual Meetng of Transportaton Research Board, Washngton DC., 0.. Zegeer, C. V., J. M. Twomey, M. L. Heckman, and J. C. Hayward. Safety effectveness of hghway desgn features. Volume II: Algnment. FHWA-RD--0. FHWA, U.S. Department of Transportaton,.. Torbc, D. J., D. W. Harwood, D. K. Glmore, R. Pfefer, T. R. Neuman, K. L. Slack, and K. K. Hardy. A gude for reducng collsons on horzontal curves. NCHRP Report 00-. NCHRP, Transportaton Research Board of the Natonal Academes, 00.. Shankar, V., and F. Mannerng. An exploratory multnomal logt analyss of snglevehcle motorcycle accdent severty. Journal of Safety Research, Vol., No.,, pp... Mannerng, F. L., V. Shankar, and C. R. Bhat. Unobserved heterogenety and the statstcal analyss of hghway accdent data. Analytc Methods n Accdent Research, Vol., 0, pp... Schneder IV, W., P. Savolanen, and D. Moore. Effects of horzontal curvature on snglevehcle motorcycle crashes along rural two-lane hghways. In Transportaton Research Record: Journal of the Transportaton Research Board, No.. Transportaton Research Board of the Natonal Academes, Washngton D.C., 00, pp.. 0. Gabauer, D. J., and X. L. Influence of horzontally curved roadway secton characterstcs on motorcycle-to-barrer crash frequency. Accdent Analyss and Preventon, Vol., 0, pp. 0.. Chen, H., C. Lee, and P.-S. Ln. Motorcycle Safety Investgaton at Ext Ramp Secton from Crash Data and Rder s Percepton. Journal of Transportaton Technologes. Vol., No., 0, pp. 0.. Machsus, H. S., A. Wcaksono, and L. Djakfar. The Predcton Models of Motorcycle Accdents on Surabaya Arteral Roads Usng Generalzed Lnear Models. Mddle-East Journal of Scentfc Research, Vol., No., 0, pp... Harnen, S., S. V Wong, R. S. Radn Umar, and W. I. Wan Hashm. Motorcycle crash predcton model for non-sgnalzed ntersectons. IATSS research, Vol., No., 00, pp... Jehan, M., G. Mazloomdoust, and K. Ghoser. A Comprehensve Engneerng Analyss of Motorcycle Crashes n Maryland. MD-0-SP0BJ. Natonal Transportaton Center, Morgan State Unversty, Maryland, 00.

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16 Xn, Wang, Ln, Lee, Guo Curve Safety 0. FHWA-SA--0. FHWA, U.S. Department of Transportaton, 0.