11. Contract or Grant No. Lubbock, Texas

Transcription

1 Tee hnalr c eport D ocwnentaton Page 1. ReportNo. 2. Government Accesson No.. Recpent's Catalog No. TX S. Ttle and Subttle 5. Report Date Proposed Geometrc Desgn for Two-Lane, Two-Way Hghway ntermttent October 199 Passng Secton (Texas SuperTwo) 6. Performng Organzaton Code TECH 7. Author(s). Performng Organzaton Report No. Douglas D. Gransberg, Sanjaya Senadheera, Emn Slay, S.M.Z. Rahman, and nterm Research Report 951-S lker Karaca 9. Performng Organzaton Name and Address 10. Work Unt No. (TRAS) Texas Tech Unversty Departments of Engneerng Technology and Cvl Engneerng Box Contract or Grant No. Lubbock, Texas Project S 12. Sponsorng Agency Name and Address 1. Type of Report and Perod Cover Texas Department of Transportaton Fnal Report Research and Technology P. 0. Box Sponsorng Agency Code Austn, TX Supplementary Notes Study conducted n cooperaton wth the Texas Department of Transportaton. Research Project Ttle "Development of an mproved Two-Lane, Two-Way Hghway Geometrc Secton" 16. Abstract The focus of ths project s to use a standard methodology to evaluate the Super-Two concept for mprovng the geometres of two-lane, two-way rural hghways. Ths concept modfes exstng lane usage by provdng some form of alternatve passng lanes on a reconfgured -foot cross secton. The study ncludes the determnaton of sgnng and strpng requrements. t also ncludes developng crtera for a test roadway and proposed geometrc desgn requrements. 17. KeyWords 1. Dstrbuton Statement Super Two, Two-Lane, Two-Way Rural Hghway, Passng Lanes No restrctons. Ths document s avalable to the publc through the Natonal Techncal nformaton Servce, Sprngfeld, Vrgna Securty Classf. (of ths report) 20. Securty Classf. (of ths page) 21. No. ofpages 22. Prce Unclassfed Unclassfed 250 Form DOT F (-72)

2 Proposed Geometrc Desgn For Two-Lane, Two-Way Hghway ntermttent Passng Secton (Texas Super Two). by: Douglas D. Gransberg, Ph.D., P.E., C.C.E. Research Supervsor Sanjaya Senadheera, Ph.D. Co-Prncpal nvestgator Emn Slay, S.M.Z. Rahman, and llker Karaca Research Assstants Report Number: TX-9n -951-S Project Number: Research Sponsor: Texas Department of Transportaton Texas Tech Unversty Departments of Engneerng Technology and Cvl Engneerng Box 107 Lubbock, Texas October, 199 Project 7 916

3 MPLEMENTATON STATEMENT The results of ths project wll yeld the documentaton necessary to readly produce constructon project plans for use n plot projects n the Chldress Dstrct. f the desgn proves successful, TxDOT hghway desgn crtera would then be augmented wth a md-range alternatve to provdng a full four-lane hghway. Ths opton wll prove to be partcularly attractve n those areas where traffc volumes are margnal and rght-of-way costs are hgh. The Super Two desgn would provde a soluton for the problem of safe passng wthout the necessary sght dstances. Addtonally, as the desgn was prolferated across the State, drver behavor would be altered to operate on the roadway as t was desgned. The best means to convey the fmdngs of ths research s through the project summary report and the desgn drawngs. DSCLAMER The contents of ths report reflect the vews of the authors, who are solely responsble for the facts and the accuracy of the data presented heren. The contents do not necessarly reflect the offcal vew or polces of the Texas Department of Transportaton. Ths report does not consttute a standard, specfcaton, or regulaton. ACKNOWLEDGEMENTS The authors would lke to take ths opportunty to acknowledge the valuable contrbutons of the followng members of the Texas Department of Transportaton: Doug Echorst, P.E., Project Drector, Odessa Dstrct Robert Stuard, P.E., Project Coordnator, Austn Dstrct Davd Casteel, P.E., Project Advsor, Chldress Dstrct Greg Brnkmeyer, P.E., Project Advsor, Traffc Operatons Dvson Dan Rchardson, P.E., Project Advsor, Ablene Dstrct Susan Knght, P.E., Project Advsor, Ablene Dstrct Danny Brown, P.E., Project Advsor, Chldress Dstrct Wthout ther help, professonal gudance, and drecton, the work would have been much more dffcult and tme consumng. Project 7-916

4 Prepared n cooperaton wth the Texas Department of Transportaton and the U.S. Department of Transportaton, Federal Hghway Admnstraton. v

5 AUTHOR'S DSCLAMER The contents of ths report reflect the vews of the authors who are responsble for the facts and the accuracy of the data presented heren. The contents do not necessarly reflect the offcal vew of polces of the Department of Transportaton or the Federal Hghway Admnstraton. Ths report does not consttute a standard, specfcaton, or regulaton. PATENT DSCLAMER There was no nventon or dscovery conceved or frst actually reduced to practce n the course of or under ths contract, ncludng any art, method, process, machne, manufacture, desgn or composton of matter, or any new useful mprovement thereof, or any varety of plant whch s or may be patentable under the patent laws of the Unted States of Amerca or any foregn country. ENGNEERNG DSCLAMER Not ntended for constructon, bddng, or permt purposes. TRADE NAMES AND MANUFACTURERS' NAMES The Unted States Government and the State of Texas do not endorse products or manufacturers. Trade or manufacturers' names appear heren solely because they are consdered essental to the object of ths report. v

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7 Techncal Report Documentaton Page Table of Contents Ttle Page mplementaton Statement Dsclamer Acknowledgments Table of Contents Lst of Tables Lst of Fgures Report ntroducton Background Applcaton of Queung Theory to Super-Two Geometrc Desgn Arrval and Servce Rate Computaton Beneft-Cost Analyss Constructon Costs Case Study-Parametrc Calculatons of Tme Savngs Desgnng the Super-Two Secton Case Study Desgn Example Feld Traffc Study of Case Study Area Conclusons Recommendatons Appendx A: Lterature Revew Appendx B: Applcaton of Queung Theory n Two-Way, Two-Lane Rural Hghways Appendx C: Geometrc Desgn Standards Appendx D: Economc Evaluaton of Super-Two Hghway Desgn Geometry Appendx E: Traffc Study Appendx F: Traffc Data Sheets Bblography lll V v A-1 B-1 C-1 D-1 E-1 F-1 Bb-1 1 Project 7-916

8 Lst of Tables Table 1 Mnmum Passng Secton Length Based on ADT and Percent of Trucks 1 Table 2 Number of Passng Sectons per 100 Klometers on ADT and Percent Trucks 1 Table B-1 Servce Rate (5.2 vehlmn) B-7 Table B-2 Servce Rate (7.05 vehlmn) B- Table C-1 Number of Passng Lanes per100 km based onadt and Truck Percentage C-2 Table C-2 Lengths of Passng Lane for varable ADT and Truck Percentage C-5 Table C- Lengths of Dverge Taper, Ld, wth respect to Desgn Speed and Lane Wdth C-6 Table C- Lengths of Lane Merge Taper, Lm, wth respect to Desgn Speed and Lane Wdth C- Table C-5 Passng Lane Frequency for varable ADT and Truck Percentage C-10 Table D-1 Levels of Servce and Maxmum Servce Volumes on Two-Lane Hghways under Unnterrupted Flow Condtons D-7 Table D-2 Combned Effect of Lane Wdth and Restrcted Lateral Clearance on Capacty and Servce Volume oftwo-lane Hghways wth Unnterrupted Flow D- Table D- Truck Adjustment Factors for Each Level of Servce on Dfferent Terrans D-9 Table D- Passng Lane Length accordng to ADT and Truck Percentage D- Table D-5 Number of Passng Lanes per 100 klometers accordng to ADT and Truck Percentage D-5 Table E-1 Traffc Count Summary Sheet on 07/17/9 Frday-ntersecton at US 7 & 179 (TX) E-5 Table E-2 Summary of Queue Formaton on 07/17/9 Frday- ntersecton at US 7 & 179 (TX) E-5 Table E- Traffc Count Summary Sheet on 07/17/9 Frday US 6 before Frst Passng Lane E-6 Project 7-916

9 Table E- Summary of Queue Formaton on 07/17/9 Frday US 6 before Frst Passng Lane E-6 Table E-5 Table E-6 Traffc Count Summary Sheet on 07/1/9 Saturday-ntersecton at US 7 & 179 (TX) E-7 Summary of Queue Formaton on 07/1/9 Saturday ntersecton at US 7 & 179 (TX) E-7 Table E-7 Traffc Count Summary Sheet on 07/1/9 Saturday- US 6 before Frst Passng Lane E- Table E- Summary of Queue Formaton on 07/1/9 Saturday US 6 before Frst Passng Lane E- Lst of Fgures Fgure 1 Exstng Rural Two-Lane, Two-Way Cross sectonal Geometrc Secton 2 Fgure 2 Proposed Super-Two Cross Sectonal Geometrc Secton 2 Fgure Super Two Beneft Cost Rato vs. Average Daly Traffc 11 Fgure Super Two Beneft Cost Rato vs. Truck Percentage 12 Fgure 5 Case Study Map 15 Fgure 6 Super Two Desgn for US 7 from Dalhart to Texlne 16 Fgure A-1 Type A Desgn wth Contnuous nteror Alternatng Passng Lane A-7 Fgure A-2 Type B Desgn wth Separated Passng Sectons A- Fgure A- Type C Desgn wth Overlappng Sectons A-9 Fgure A- TypeD Desgn wth solated Passng Secton A-9 Fgure B-1 Queue n a Sngle Channel B-2 Fgure B-2 Watng Tme vs. ADT (Servce Rate= 5.2 veh/mn) B- Fgure B- Watng Tme vs. ADT (Servce Rate= 7.05 veh/mn) B-10 Fgure C-1 Cross Secton of a Rural Road n Texas C-12 Project 7-916

10 Fgure C-2 Cross Secton for Texas Super Two Fgure C- Lane Confguraton for Texas Super Two Fgure C- Sgnng and Pavement Markng for Texas Super Two Fgure C-5 Layout of Super Two sectons from Chldress to Hamln for the Example Problem Fgure D-1 Current Two-Lane Rural Hghway Cross-Secton Fgure D-2 Proposed Super-Two Cross-Secton Fgure D- B/C Rato to ADT Levels Fgure D- B/C Rato to Truck Percentage Fgure D-5 Number of Cars n Queue at Dfferent ADT Levels Fgure D-6 Passng Lane Frequency Fgure D-7 Senstvty of B/C Rato Fgure D- Passng Lane Length C-1 C-1 C-15 C-16 D- D- D-29 D-0 D-0 D-1 D-2 D-2 Project 7-916

11 ntroducton PROPOSED GEOMETRC DESGN OF TWO-WAY, TWO-LANE DGHW AY NTERMTT ANT PASSNG SECTON (TEXAS SUPER TWO) Two-lane rural roads are of great mportance n the Amercan Hghway System. There are more than mllon mles (. mllon klometers) of two-lane rural hghways n the Unted States, and they comprse about 97% of the total rural system and 0% of all U.S. roadways. t s estmated that 6 % of rural travel and 0 % of all travel occur on these rural two-lane roads. Fundng s lmted consderng the extensveness of the rural hghway system and envronmental concerns, and research for ways to mprove the servce of these roadways s essental. Because of the low ADT levels carred on these rural hghways, low-cost mprovement methods such as constructon of Super sectons are advantageous over the classcal methods nvolvng major modfcatons such as four-lane sectons, extensve modfcaton of road geometry. The purpose of the study s to justfy the mplementaton of ntermttent passng lanes on rural two-way, two-lane hghways where passng opportuntes are lmted. n ths study, passng lane length and the dstance between passng lanes are correlated to two major parameters: ADT and percentage of trucks. Passng opportuntes are modeled to decrease wth ncreasng oncomng traffc. n addton, as ADT ncreases, delay tme savngs ncrease. Also, the ncrease n the percentage of trucks creates more delay whch results n a need for more passng lanes. A hgh percentage of trucks also causes operatonal problems n terms of reduced level of servce, ncreasng passng attempts, aborted passes and drver frustraton. An economc analyss s performed to reveal the beneft-cost ratos (B/C) for dfferent stuatons. Reducton of queues and enhanced passng opportuntes yeld travel tme savngs and a predcted reducton n accdents. Taken together, these output parameters form the benefts accrued by mplementng Super Two hghway desgn. Super Two geometry s essentally an attempt to provde mproved hghway capacty for those two lane rural hghways whose ADT does not justfy an upgrade to a full four lane cross secton. Ths study used as ts bass a typcal two-lane hghway cross-secton of about 1. meters ( feet) shown n Fgure 1. Fgure 2 depcts the Super Two cross-secton that requres a wdenng of 60 centmeters (2 feet) to furnsh a small shoulder on the passng sde of the cross-secton. Texas drvers are known to pull out onto the shoulder to let a faster movng vehcle pass on a rural road. Thus, the change to the Super Two cross-secton essentally strpes the road the way Texas drvers actually drve t. The requrement for a shoulder s added to ensure that the economc analyss s conservatve and comes from dscussons wth numerous TxDOT constructon and mantenance engneers who feel that the shoulder s desrable as a protecton for the pavement's edge. Project Pagel

12 Shoulder CJ Opposng Lane ~ D Traffc Lane n Shoulder "".. "" ~ 1.0 m.70.. ~ "".00 _ Fgure 1. Exstng Rmal. Two-Lane, Two-Way, Cross-sectonal Geometrc Secton. Shoulder ~... ~ "" Opposng Lane ~ "" Passng Lane m Fgure 2. Proposed Super Two Cross-sectonal Geometrc Secton. Truck Lane.25 Shoulder ~ _..... Background The recent statutory change n the speed lmt has had a dramatc mpact on rural two-lane, twoway traffc. n years past, heavy trucks tended to utlze the nterstate hghway system because at the 55 mle per hour (mph) ( klh) speed lmt, t provded the least path of resstance. Whle actual dstance drven were somewhat greater, trp tmes were roughly equal when compared to the use of rural hghways owng to the delays encountered whle drvng through towns. The new speed lmt changed that equaton. By beng able to travel at greater speeds, truck traffc can now realze a benefcal tme savng by takng more drect routes to ther ultmate destnatons by usng the rural hghways. Thus, the percentage of truck traffc has ncreased. Wth ths ncrease n large vehcles comes an ncrease n the number of passng movements requred by passenger vehcles on rural hghways. Ths condton s a drect functon of the allowable speeds for the varous types of vehcles. Whle passenger vehcles may travel at speeds up to 70 mph (112 klh), trucks are restrcted to 60 mph (96 klh) and school buses are Project Page2

13 requred to drve no faster than 50 mph (0 k/h). Ths relatve speed devaton creates a condton where drvers n open terran lke that n West Texas are tempted to execute potentally unsafe passng movements for three reasons. Frst, because the terran s relatvely flat they beleve that they have the necessary passng sght dstance when n many cases they do not. Secondly, because the traffc s generally lght, they are more confdent that they can execute ths movement safely. Thrd and most crtcally for ths study's purpose, they know that they must execute a passng movement at some pont n tme f they do not want to follow a slow movng vehcle to the next town because there are no alternatves. Ths condton s further exacerbated by a drvng behavor pecular to Texas. t s customary n rural areas to pull over onto the shoulder and permt a faster movng vehcle to pass wthout havng to pull completely nto the oncomng lane of traffc. n fact, ths practce has been carred to the pont where a vehcle n the oncomng lane who sees a passng movement beng executed ahead of t wll also pull onto the shoulder, thus temporarly makng a three-lane road out of a two lane one. Whle ths certanly speaks well for the courtesy of West Texas drvers, ths habt creates unsafe condtons n and of tself, not to menton the structural damage ncurred to the paved shoulders. n order to change ths drvng habt, two condtons must exst. Frst, the drver must know that an opportunty to pass a slower movng vehcle wll occur n a reasonable amount of drvng tme, and secondly, the drver must also know that the safe passng opportunty wll occur ndependently from the status of oncomng traffc. The deal soluton to ths problem s to wden these rural roads and provde a four-lane hghway. However, between $1.0 and $2.0 mllon per mle of constructon cost, ths s not economcally feasble (Hembach, et. al, 197). The logcal alternatve s to determne at what volumes the addtons of perodc passng lanes are justfed, and develop several possble desgn alternatves to provde ths capacty. Most states provde passng lanes on two-lane roads where passng sght dstances are mpossble to attan on hlls and around long radus horzontal curves. Nevertheless, only a few have expermented wth provdng these lanes on terran wth adequate sght dstances. New Mexco s one nearby state that has expermented wth ths concept. US Hghway 6/7 between Raton and Clayton utlzes a Super Two style desgn (Eyler, et. al, 1996) wth wdened sectons that permt passng at fve to eght mle ( to 1 km) ntervals. Thus, passenger vehcles know that a passng secton wll be avalable every two to fve mnutes. A traffc study was conducted on that hghway n New Mexco and ts extenson nto Texas where no Super Two exsts to verfy that ths change n hghway geometry ndeed enhances level of servce. Detals are contaned n Appendx E to ths report. Several foregn countres have also taken a smlar nterest n enhancng the safety of ther hghways wthout ncurrng the constructon costs of buldng four-lane hghways. Appendx A to ths report contans the detals of ntermttent passng lane desgn geometry currently n use n Canada, Mexco, and Germany. The recent enactment of the North Amercan Free Trade Agreement (NAFT A) makes the study of the Mexcan and Canadan Super Two standard desgns very mportant. At ths pont n the study, t appears that the Mexcan secton wll be most easly adapted to use n Texas. Consderng the relatve proxmty of Mexco and the relatve percentage of Mexcan traffc as opposed to Canadan traffc, modelng the Texas Super Two desgn after the Mexcan approach makes a lot of sense. The German desgn sprngs from a severe restrcton on the amount of avalable rght-of-way n European countres. Therefore, t Project Page

14 seeks to mnmze the requred cross-secton. t only requres a total of 12 meters (0 feet) from shoulder to shoulder, but to acheve ths, the Germans use only 0.25 meter shoulders (1 0 nch) and requre a 0.5 meter (1.6 feet) separaton between the opposng lanes traffc wth a physcal barrer f possble. Ths s not typcal of the cross-secton generally presented to U.S. drvers on rural roads. t wll probably not only confuse them, but the vrtual lack of shoulders would present a hazard n a stopped vehcle stuaton. The Canadan desgn uses two 1.2 meter ( feet) shoulders whle the Mexcan desgn provdes for a wder shoulder on the opposng lane sde than on the passng lane sde. Ths makes the most sense n that a vehcle breakdown on ether sde of the Super Two secton wll stll leave suffcent room for one unobstructed lane n each drecton. A Mexcan study of truck lanes was publshed n the Transportaton Research Record (Mendoza & Mayoral, 1996) whch ndcated that benefts accrued from ncreased travel speeds as measured by the World Bank method outweghed the constructon costs by as much as fve tmes (Mendoza & Mayoral, 1996). Turkey has consdered a smlar scheme as an opton to leverage scarce constructon dollars whle enhancng safety as that country bulds ts nterstate hghway system. Studes have also been done n Great Brtan (McDonald, et al, 199), Chna (Xng, 199), and Australa (Oppy, 1992) regardng the provson of alternatng passng lanes to both releve congeston and enhance safety on two-lane roads wth a hgh percentage of truck and bus traffc. The Brtsh study s partcularly nterestng n that one does not consder Brtan as country wth a lot of long rural roads. The motvaton n that study was to mnmze rght-of-way acquston cost n a country where avalable rght-of-way s extremely rare and comparatvely costly. Even ths parallels the current envronment n Texas, especally when one consders Super Two as a means to ncrease hghway capacty wthn exstng rght-of-way lmts. Ths project had three major phases. Frst, a bench markng analyss of the lterature, current TxDOT desgn crtera and cross sectons, and assembly of approprate standards for geometrc desgn, sgnng/strpng, and mnmum traffc volumes was conducted. The output of ths ntal effort dentfed potental alternatves for provdng ths capacty that were evaluated n the next phase. t also estmated traffc volume justfcaton crtera (maxmum and mnmum ADT's) whch wll permt ths desgn to be a feasble alternatve to four-lane hghways. The second phase entaled a formal feasblty study to assess the costs and potental benefts of each of the varous Super Two alternatves. Benefts and costs due to delay attrbuted to dfferental speed and headway were estmated usng queung theory (Khasnabs et. al, 190). At the outset, a lmted Monte Carlo smulaton (Khasnabs et. al, 190) was consdered as a way to more accurately estmate delay savngs benefts, but ths was determned to be unnecessary as the ADT's nvolved dd not justfy themselves on a classcally derved warrant bass. t was also found that Super Two could not be justfed on delay savngs alone. Accdent savngs had to be ncluded and make up the majorty share of the savngs. Thus, a determnstc approach to calculatng delay savngs was determned to be adequate. The predcted values were then tested n a lmted feld traffc study on the case study hghway to ensure that the determnstc model matched actual feld observatons. Detals of the traffc study can be found n Appendx B. The fmal phase formalzed the results of the frst two phases by producng the necessary desgn documents to brng the concept to lfe on a test project. The documents nclude engneerng drawngs, sgnng, and strpng plans are contaned n Appendx C. Project Page

15 Applcaton of Queung Theory to Super Two Geometrc Desgn n order to model the traffc flow characterstcs on a two-way, two-lane hghway, queung theory s appled. Queues are observed on that knd of hghways when the opportunty to overtake a slow-movng vehcle s lmted. The two basc components of queung are arrval and servce rate and ther dstrbutons. As traffc ncreases, the number of vehcles n a queue also gets larger because of ncreasng arrval rate and decreasng passng opportuntes. Knowng these parameters, one can compute the average number of vehcles watng to overtake the slowmovng vehcle. Lght to medum traffc condtons on a rural roadway can be modeled usng Posson arrval dstrbuton for the arrval rate. Assumng a negatve exponental servce rate dstrbuton, expected number of vehcles n a queue (E(m)) and average watng tme (E(w)) for a vehcle n a queue can be calculated usng equatons and 2 respectvely. 2 E(m) - _q=--- Q(Q-q) (1) E(w)- q Q(Q-q) (2) Where q s arrval rate and Q s the servce rate, both tenns are expressed as the number of vehcles per unt tme. As can be seen from equaton 1, E(m), ncreases rapdly as the arrval rate ncreases or servce rate decreases. ncreasng ADT values on a roadway causes both the arrval rate to ncrease and servce rate to decrease. n a stuaton where the arrval rate and servce rates are close to each other, the queues tend to be nfnte. Ths behavor of queung theory makes the model applcable to smulate rural roadway traffc condtons. The average number of vehcles n a queue obtaned from queung theory s used for detennnaton of the passng lane length. Average amount of tme spent n a queue s utlzed to calculate the tme savngs that passenger cars wll beneft from the constructon of passng lanes. Arrval and Servce Rate Computaton A major dffculty n the applcaton of the theory on a traffc problem s the dynamc characterstcs of the traffc flow. The computaton of the servce rate (Q) should ncorporate the fact that the truck percentage wll have an nfluence on the servce rate. Therefore, the servce rate, Q, s computed usng equaton (Hghway Capacty Manual, 197) below. Ths equaton gves the maxmum servce volumes (SV), on rural two-lane, two-way hghways under unnterrupted flow condtons. Servce volume s then converted nto servce rate (Q) usng a drectonal factor to fmd the servce rate n one drecton (n the case study a drectonal factor of 0.6 s assumed). Q values are further substtuted nto the equatons 1 and 2. Unlke the servce rate calculaton, arrval rate, (q) s drectly obtaned from ADT values. Therefore, the arrval rate s an adjusted ADT value n one drecton of roadway for a peak hour traffc volume. t s further assumed that the trucks are evenly dstrbuted along the hghway and they are not nvolved n passng maneuvers. Hence, the number of trucks are subtracted from ADT values durng the calculaton of the arrval rate. Project PageS

16 SV = 2000 (vc) WL TL () Where:SV =Servce volume (mxed vehcles per hour, total for both drectons) vc = Volume to capacty rato WL =Adjustment for lane wdth and lateral clearance at a gven level of servce T L = Truck factor at a gven level of servce The truck factor (T L) and adjustment for lane wdth and lateral clearance (WL) are taken from the Hghway Capacty Manual ( 197). Volume to capacty rato values are obtaned from the Hghway Capacty Manual (197). A level of servce ofb s assumed to smulate the md volume rural condtons that are consdered n ths study. The volume to capacty rato (v/c) s a functon of the probablty of a passng sght dstance of 1500 feet (60 meters). Volume to capacty ratos are nterpolated accordng to changng probablty of havng a passng sght dstance of 1500 feet (60 meters). Snce the roadway s on level terran, the probablty of havng a passng ste dstance s 100 %. However, ths probablty wll change accordng to the avalable gap between two vehcles n oncomng traffc. Ths gap wll be a functon of ADT level and the probablty of havng a gap equal or greater than 1500 feet (60 meters) s calculated usng equaton assumng a Posson dstrbuton n oncomng traffc. Gven that the probablty of passng sght dstance s 100%, the probablty value obtaned from equaton can be drectly substtuted nto equaton to determne the servce rate. Where: A.= average number of vehcles n the opposng drecton per unt tme h = tme gap between two consecutve opposng vehcles t = tme gap between two opposng vehcles whch are 1500 feet apart. The average number of vehcles n the opposng drecton per unt tme (A.) s a drect functon of ADT values. Equaton mples that as the traffc volume on a roadway ncreases, probablty of havng a tme gap that wll enable a safe passng opportunty wll decrease. Ths decrease n the probablty wll reduce the servce to capacty rato obtaned from the Hghway Capacty Manual. Lower servce to capacty ratos wll cause a drop n the servce volume or servce rate. Ths theory s then extended to develop a desgn algorthm whch optmzes both passng lane length and the dstance between passng sectons wth respect to ADT and truck percentage. The detals of ths method can be found n Texas Department of Transportaton Research Report TX R (Gransberg et. al, 199) and are detaled n Appendx D. The method assumes that the optmum length of a passng lane s controlled by the tme t takes the average queue to overtake the slow movng vehcle that has caused the queue to form. The optmum dstance between passng sectons s related to the tme t takes for the queue to form behnd the next slow movng vehcle. As a safety factor the desgn uses a length based on the average queue plus one car. As arrval rates are assumed to be modeled by the Posson dstrbuton, ths provdes an effectve length that should permt safe passng for about 5% of the predcted dstrbuton of queue szes () Project Page6

17 Beneft-Cost Analyss To justfy the mplementaton of Super Two desgn on a publc project, the benefts accrued by the desgn geometry must outwegh the cost of mplementaton. Ths s typcally portrayed by dvdng the equvalent annual beneft by the equvalent annual cost to compute the rato of benefts to costs. f the resultant value s greater than unty, the project s economcally feasble and warranted at the constrants mposed on the analyss by ts underlyng assumptons (Newnan, 1996). To complete such an analyss on Super Two hghway desgn, the benefts are defned as the value of savngs due to accdent reducton and the value of tme saved due to decreased delay. These benefts are computed as follows. Accdent cost savngs are obtaned from the model provded by the equaton 5 (Taylor and Jan, 19). The constant 1.6 n equaton 5 s used to convert 19 dollars to 199 dollars. Bacc = (AC)(65)(ARF)(ADT)(l0- )(Lptloo)(1.6) (5) Where Bacc Annual accdent cost savngs provded by a one mle passng lane ($/yr/mle); AC average cost of accdents by severty (value s taken to be $26,70 n 19 dollars); and ARF = average reducton n accdents by severty for dfferent ADT values (value s taken to be 7.7) Tme savngs of the cars s the amount of tme that can be accrued from the applcaton of the desgn methodology. The value shows the amount of tme that s saved by a car avodng any watng tme behnd a truck for a chance to overtake. The average watng tme per car, E(w) that had already been calculated from the queung theory, Equaton 2 s assumed to form the bass of tme savng calculatons. The major assumpton s the elmnaton of ths watng tme wth the applcaton of passng lane sectons. n other words, wth the applcaton of passng lanes the cars are modeled to have an almost unnterrupted desgn speed. Tme savngs per vehcle per 100 klometers (62.5 mles), (Btme) s annualzed by multplyng them by ADT values and number of days n a year, 65 as shown n Equaton 6. Number of trucks s excluded from the total number of vehcles snce they don't beneft from tme savngs. The dfferent tme cost of busness and lesure trps are ncorporated n the calculatons (Taylor and Jan, 19). Where:S10o =tme savng benefts per 100 klometers Sbt =tme value of busness trps Pb,= percentage of busness trps S1, = tme value of lesure trps P1, = the percentage of lesure trps ANp = average number of passengers passenger vehcle Constructon Costs To calculate a correspondng constructon cost per 100 klometers (62.5 mles) of road, a conceptual desgn of the amount of roadway whch must be upgraded to Super Two crosssectonal geometry must be determned. Addtonally, t s assumed that the upgrade wll consst of an average wdenng of 60 centmeters (2 feet). t should be noted that f the specfc project n queston s determned to not requre a small shoulder on the passng lane sde, then the cost of (6) Project Page7

18 mplementng Super Two geometry s merely the cost of new sgnage and strpng. The conceptual desgn begns wth determnng the effectve length of a Super Two passng lane. An effectve length of passng lane s long enough for the drvers of the passenger cars to feel comfortable overtakng the slower movng truck. There should also be enough length provded for the trucks to merge nto the passng lane. Tapered sectons at the begnnng and end of the passng lane would effectvely provde ths space. But the tapered sectons would not be ncluded n the length of the passng lane. The tapered sectons should be equal to the dstance traveled by the truck as t moves nto and out of the passng lane safely clearng the passenger cars n the queue. Lepl = (t ace + f pl )~, (7) Where:Lept = Effectve length of passng lane (meters) tacc = Tme for a passenger car to accelerate (seconds) tp 1 = Tme for platoon n queue to pass (seconds) The dstance from the pont where a car overtakes the frst truck to the pont where t reaches the next truck s consdered as the dstance between two passng lanes, (Dpl) as shown n equaton. Assumng an even dstrbuton of the trucks and trucks wll cause no delay for cars, ths length also ncludes the passng lane secton of the hghway. deally the passng lanes are desgned to be located at the ponts when cars reach the next slow movng truck. t s assumed that the queue wth an average number of cars, E(m) would be formed by the tme the platoon reaches th~ next passng lane. () Where:Dpt =dstance between passng lanes (meters) V tr = truck speed; qtr = truck arrval rate V pc = passenger car speed ~ V pc-tr = dfferental speed between truck and passenger car The calculated values for the length and the separaton of the passng lanes wll be converted nto a representaton per a reference bass. For practcal purposes presentng the values n a per dstance bass s more meanngful. Therefore an nterval of 100 klometers (62.5 mles) s selected to form that bass. Equaton 9 represents the number of passng lanes per 100 klometers (PL10o). Snce, the dstance between passng lanes has already been calculated, the number per 100 klometers s obtaned by dvdng 100 klometers to dstance between passng lanes. t should be kept n mnd that ths dstance ncludes the passng lane length and the result wll drectly gve the number of passng lanes per 100 klometers. Total length of the passng lanes per 100 klometers can also be calculated after the number of passng lanes per 100 klometers (Lpnoo) s shown n Equaton 10. Project Page

19 (9) (10) Constructon cost per 100 klometers of roadway secton, Cpb s found from Equaton 11 by multplyng by two snce the passng lanes n the opposng drecton must be consdered. The length of merge and dverge areas s not a functon of length of passng lane. C = 2 (uc p!lep/loo + UC PL ~ 1000 ~ J 100 (11) Where: UCp 1 = Constructon cost of 1 klometer of passng lane UCcd =Constructon cost of converge and dverge sectons per each passng lane The constructon cost s a one-tme cost that occurs at the begnnng of the project. t should be ncorporated n the economcal analyss n annual bass so that comparson of the cost and beneft values can be done. Equaton 12 annualzes the constructon cost of the passng lanes usng a lfe cycle ofn years and an nterest value. Lfe cycle perod of the project should be estmated accordng to the characterstcs of the roadway. (12) (A \P, %, n) = Captal recovery factor for an nterest value of % and for n years Case Study-Parametrc Calculatons of Tme Savngs A case study usng actual data from Hghway 7 between Dalhart and Texlne n Dallam County, Texas s presented n the followng sectons to exemplfy the proposed equatons. The most crtcal ADT level of 600 vehcles/day s chosen for the example. Each formula presented n the prevous secton wll be calculated based on assumed parameters. Varous calculatons for dfferent ADT and truck percentage levels are presented n ths report. The desgn speeds for the passenger cars and slower movng trucks are decded to 70 mph and 60 mph, respectvely. However, for the sake of metrc unt calculatons ther speeds are taken as 112 k/h and 96 k/h, respectvely. A representatve truck percentage of 10% s chosen for ths specfc case study. The upgrade of the exstng roadway to a -lane pavement wth a passng lane s planned wth a 60 centmeter pavement wdenng as shown n Fgure 2. Snce the structural capacty of the exstng -meter (10 feet) shoulders s the same wth regular lane sectons, shoulders should be kept as they are. The 60 centmeter (2 feet) new constructon s foreseen wth the same structural capablty of present pavement. The exstng and proposed sectons are comprsed of a 0.6 meter (2 feet) flexble subbase, a 0.6 meter (2 feet) fly ash base, and a two course surface treatment Project Page

20 After the pavement s extended 60 centmeters (2 feet), a fnal seal coat applcaton s desgned to cover exstng markngs. Ths prepares for the strpng of new pavement markngs. Another constructon actvty would be the merge and dverge areas or the tapered areas of the passng lanes. The cost of these areas does not depend on the length of the passng lane. The approxmate constructon costs are as follows. A two-course surface treatment wth AC-5, Grade aggregate s needed on the new shoulder. Applcaton rate of bnder s 2 11m 2, and dstrbuton rate of aggregate s 17 m 2 /m t s calculated to be $1,020/0.6m wdth/lklometers length. A one-course seal coat applcaton wth AC-5, Grade aggregate s needed across the entre cross secton. The applcaton rate of bnder s 211m 2, and the dstrbuton rate of aggregate s 17 m 2 /m t s calculated to be $12,0911.0m wdth/lklometers length. Fly ash stablzed base constructon cost s calculated to be $9,000/0.6m wdtb/lklometers length. Flexble subbase constructon cost s calculated to be $6,000/0.6m wdth/1klometers length. Excavaton cost s $1,91/0.6m wdth/lklometers length. Embankment cost s $1,1 05/0.6meters/1klometers length. Cost of dverge and converge areas s $1, meters wdth/passng lane. Total cost excludng sgnng cost s $0,25. The analyss shown n Fgure s performed at a constant truck percentage of 10% and wth varyng ADT levels. The B/C rato ncreases wth ncreasng ADT levels. The Super Two Hghway can be justfed from an ADT level of2500. Ths justfcaton s manly caused by the accdent cost savng benefts. The equaton used n ths calculaton can be further elaborated or examned to conform to the actual accdent cost savng analyss specfcally conducted for a roadway secton. t s evdent that tme savng benefts are not adequate to justfy the constructon of the Super Two Hghway (approxmately 15% of the savngs are contrbuted by the tme savng benefts). However, the constructon cost pertanng to the upgradng of the hghway s prmarly wdenng cost. Many people wth hghway constructon experence agree that wdenng s not a necessty. For the segments of the hghway wth passng lanes, strpng wll be adequate for safe traffc condtons. The cost of strpng s much less than constructon cost. f hghway agences can adopt ths dea, the constructon of passng lanes at gven ntervals wll be a vable soluton to the mprovement of the two-way two-lane rural hghways. Project Page O

21 = <{ 1.00 a:: 0.0 (.) CD ADT Fgure. Super Two Beneft Cost (B/C) Rato versus Average Daly Traffc (ADT). t s evdent that, tme savng benefts are not adequate to justfy the constructon of the Super Two secton (approxmately 15% of the savngs are contrbuted by the tme savng benefts). However, the constructon cost pertanng to the upgradng of the hghway s prmarly wdenng cost. Many people wth hghway constructon experence agree on that wdenng s not a bg necessty and they thnk that for the segments of the hghway wth passng lanes only strpng wll be adequate for safe traffc condtons. The cost of strpng s much less than constructon cost, fhghway agences can adopt ths dea then constructon of passng lanes at gven ntervals wll always be a vable soluton to the mprovement of the two-way two-lane rural hghways. Another outcome of the constant ADT and changng truck percentage analyss s the B/C rato s not senstve to truck percentage. Ths s caused by the structure of the accdent cost beneft equaton. Fgure s plotted for a constant ADT of 600 and varyng truck percentage. An almost constant lne s observed. Ths s because accdent cost savngs ncluded n the numerator and constructon costs ncluded n the denomnator are both functons of the passng lane length, and therefore cancel each other out. Ths leaves a constant B/C wth respect to truck percentage. Project Page 11

22 0 +=> ('(! a::: () -m Truck Percentage Fgure. Super Two Beneft Cost (B/C) Rato versus Truck Percentage Desgnng the Super Two Secton 5 0 The prevous equatons are drawn from a more detaled dervaton contaned n Appendx D. Ths analyss optmzes both the length of passng secton and the number of passng sectons per 100 klometers ( 62.5 mles) of hghway wth respect to cost. For ths analyss, a passng secton s defned as provson of passng lanes for both drectons of travel. t can be seen n Appendx A that there are four basc types of Super Two sectons. n Type B, Separated Passng Sectons, the engneer wll need to be careful to ensure that there s a passng secton developed for both drectons. At ths pont, the desgn methodology s very smple and straghtforward. ts steps are as follows. 1. Determne the ADT and percentage of trucks for the hghway n queston. Ths can be based ether on exstng traffc data adjusted for future growth or from another more approprate method or polcy. 2. Wth ths nput data, enter Tables 1 and 2, and determne the number of passng sectons per 100 klometers (62.5 mles) and the mnmum length of each passng secton.. Takng plan and profle nformaton for the hghway n queston, determne those portons of the road where safe passng sght dstance s not avalable due to horzontal curves, vertcal curves, and other obstructons.. Allocate Super Two passng sectons to roadway sectons where passng ste dstance s unavalable. 5. Dstrbute any remanng passng sectons evenly between the passng sectons already allocated. 6. Takng the average passng secton length from Table 1, adjust as necessary for those sectons wthout adequate passng sght dstance to provde safe passng throughout the length of the sght dstance restrcton. Project Page 12

23 70 17 T\Cl<% AOT a < ~ $ e 7e SO ' , & r r 7 r 7 7 7& 7 75 r e t rt 70 rt 70 rt r0 70 ro 70 ro rn 7& ! e ru 75 rea 75& rea ru so 75 75o t5e < u ree roe 1ee rae ree 7e 7e ree ro11 rea 7 7e 7ee rea nr r11r rea 711 rea 71 ree 100 reo 1eo t t71 7t r72 rr r t us tee tee rae reo tee rea 1ee 7ee rae rae 7&0 7eo 7U 70 tn roo 1oo a t o ros ro ts roe 71 roe roe roe 11r 707 rn 111 ne 7u u 00 oo ao2 ao2 eo eo 110 ao eo 0 ao & ao5 0S eo5 ao eoe ao aoa ao7 aor ao aoo 5oo eo9 110 ooo e12 e eu a1 1 1 & e1e au 1& u au 1111 e ~o &2 e2 2 e2s e2e e2e e r uo ,o ao u1 1 1 n e e11 11 r 7 r 7 11e & so eo a&!l 1150 e5o a&1 11\ e n2 es2 ee 5 U & ass 55 a5e est ae2 ae ee eu see eea see eee ear eee eea ao sao no aro 1111 t1. a12 an an '', ett 77 en a1e 7e e7a no e1o a1o uo eeo ea1 ee ae2 ee ee ee,11 eee ee5 11 see ea7 ae1 see aao a eo au at eos au 505 aoe eoe so1 ao7 07 eoe eoe aoo aoo ooo ooo oo5 oo11 ooe oot ooa oo5 oo e \ f < oe1 01 oe2 0 oe oe oe oe e oar oae oee oeo oto 011 or on ote 010 oeo 91 oe u~ oas 5oo ou oe oeo ooo ooo oo1 eo2 oo2 90 oo 00 oos oo 001 ooe ooo o o1 1ou \02e 1027 \ \ los~ t eo & 10ee \ \07e 107t \Ota e \

24 Truck y, AOT ! ~00 ~ ~ & 6 5 l l 5 l 5 l l, e ' ' u H H l7

25 Case Study Desgn Example Clayton, NM Oklahoma r ~exlne ADT = 200 j ADT= 600 New Mexco Fgure 5: Case Study Map 1727 Dalhart Fgure 5 shows the detals of the case study area. Ths s also the area on whch the traffc study was conducted to valdate the determnstc queung model on whch the desgn methodology s based. The ADT volumes come from the current Amarllo Dstrct traffc map. As ADT ranges from 200 to 600, a Super Two desgn s warranted as mnmum ADT s greater than or equal to 200. For purposes of llustraton only, let us assume that desgn ADT wll equal 600 wth 1 0 percent trucks. Usng Table 1, we fnd that the average length of the passng secton wll be 1061 meters. From Table 2, we fnd that 5 passng secton per 100 klometers are warranted. The dstance s 62 klometers; therefore, the number of sectons must be adjusted as follows. Actual number of sectons= 62 km (5 sec) =.1 => passng sectons lookm Thus, the engneer must dstrbute three Super Two sectons along the road between Dalhart and Texlne. As ths hghway runs between two populaton centers, the frst passng secton wll be a Type A splt wth the westbound half extng Dalhart and the eastbound half extng Texlne. Ths permts those passenger cars that catch the slow movng vehcles n town due to the slower speeds to take advantage of ther faster acceleraton to hghway speed and avod formng queues mmedately outsde of the two towns. That leaves two passng sectons to be dstrbuted between the two towns. The prorty would be to place these at locatons where passng sght dstance s nadequate. To mnmze constructon costs, these remanng sectons would be Type B, Separated Super Two sectons. They would be roughly 20 klometers apart. Fgure 6 s an dealzed depcton of the fnal desgn layout. Project Page 15

26 Texlne 1.06 km TYPE A Texlne Half - 1 km,.,.., km TYPEB Separated Secton 1.06 km -1 km 1.06 km -62 km TYPEB Separated Secton 1.06 km - 1 km -----'.,.., km TYPE A Dalhart Half Fgure 6. Super Two Desgn for US 7 from Dalhart to Texlne. Dalhart Project Page 16

27 Feld Traffc Study of Case Study Area A short traffc study was done on the case study area n July 199 to compare the actual observed effect of Super Two geometry to the effect computed n the determnstc queung model. The observed peak hour volume on July 17, 199 was 52. The average number of vehcles for the same hour s counted as.00 accordng to Traffc Count Summary Sheet (Table E-1). The same parameter can be found from the desgn method as descrbed earler n the Case Study porton of the report. The peak hour corresponds to an ADT of 5 7 by usng a peak hour factor of As a result, the average number of vehcles per queue calculated by the determnstc queung model for the case study s.15 vehcles per queue. Ths result valdates the model and the desgn approach of basng passng lane length and spacng on an average predcted queue plus one. The traffc study also valdated the hypothess that mplementng Super Two would greatly enhance level of servce on low volume rural hghways. From Table E-6, one observes that the average number of vehcles n queues gong towards North at the data collecton pont n Texas s.5. Whereas, the same parameter becomes 2.0 after vehcles cross Clayton where the effect of Super Two passng lane sectons occur. The reducton rate s 2 percent. n the other drecton, the followng numbers are observed. n New Mexco, the average number of vehcles n queue s 1.1 (Table E-) for the vehcles leavng the passng lane where ths number has drect effect of passng lane. The same parameter becomes.7 n Texas (Table E-6). Then, the correspondng reducton rate n the average number of vehcles n queues due to Super Two s 52 percent. Thus mplementng Super Two can be concluded as havng a strong postve mpact on traffc flow. Conclusons A number of nterestng conclusons can be made. Ths methodology can be used to justfy the Super Two Hghway at ADT levels less than 200 vehcles per day. A Super Two secton that requres a 60-centmeter wdenng s economcally feasble at ADT levels greater than 200 vehcles per day. f no wdenng s requred (.e. no shoulder on passng secton sde), then Super Two s economcally justfed at much lower ADT levels. Super Two B/C rato s nsenstve to truck percentage. Typcal queues wll contan less then four vehcles. Desgnng for the number of passng lanes per 100 klometers of road provdes hgh desgn flexblty wthout ntroducng sgnfcant error. f ADT levels exceed 200 vehcles per day, the passng lane desgn should be based on smulatons or other approprate urban desgn methods. t should be noted once agan that 0 to 200 vehcles per day s the ADT range where the feasblty study s applcable. After a certan level of ADT, watng tmes of the passenger car n the queue become very large and then the values drop below zero. Ths drastc change n the values s caused by the characterstc of queung theory. The theory s vald for the arrval rates (q) less than servce rate (Q). However, the research model has ncreasng arrval rates wth ADT, and servce rate decreases as ADT values become larger because of the physcal lmtatons of the hghway. The pont where two values ntersect there s an nfnte queue. Ths s obvously not an approprate stuaton for the rural hghways. The lmtng ADT value for the applcaton of the model s 200. For the upper traffc levels other technques lke smulaton programs may be used to model the real traffc condtons. Ths knd of method, however, s not n the scope of ths research. Project Page 17

28 The combnaton of the traffc study n New Mexco and the results of the determnstc model, valdate the desgn methodology detaled n ths report. The economc justfcaton comes not from delay savngs, but from the savngs accrued by a reducton n accdents. However, when the secton s mplemented, addtonal savngs wll be accrued due to enhanced level of servce. These savngs are not ncluded n the model. Therefore, the model s a conservatve approach to ths ssue. Fnally, t must be remembered that the model developed n ths study assumes a requred wdenng of the standard 1. meter ( feet) cross-secton to 1.6 meters (6 feet). The determnaton of the requrement for a shoulder on the passng lane sde of the road s a judgement call that should reflect actual condtons for each ndvdual project. There are numerous examples of slow movng vehcle passng lanes throughout the State of Texas where no shoulder s provded. f ths can be done, Super Two s economcally justfed at much lower ADT's than those shown n economc analyss of the model. One could argue that f project condtons permt the use of no shoulder, Super Two could be mplemented for the cost of a seal coat, new strpng, and new sgnage. Therefore, the Department could accrue sgnfcant benefts due to ncreased level of servce and decreased accdents at very lttle cost. Recommendatons We have two recommendatons as a result of the above dscussons. Frst, the Department should mplement Super Two as soon as possble. t provdes a means to upgrade level of servce on hghways that cannot justfy an upgrade to a four-lane cross-secton. t also enhances safety for the travelng publc at very lttle ncremental cost. Secondly, the Department should survey ts major rural hghways and dentfy those that could be upgraded to Super Two wthout the requrement for a shoulder. These roads could be systematcally converted to Super Two geometry n conjuncton wth the dstrcts' annual seal coat contracts. The only addtonal expense would be a slght ncrease for strpng and the cost of resgnng the Super Two sectons. Ths s an opportunty to mmedately mplement the results of ths research. Project Page 1

29 APPENDX A: LTERATURE REVEW ntroducton n recent years there has been an ncreasng nterest n the operaton of two-lane rural and suburban roadways. ncrease of traffc volume and reduced fundng levels are some of the prmary reasons behnd t. The recent statutory change of speed lmt causes a sgnfcant mpact on rural two-lane, two-way traffc. The new speed lmts of 70 mph for passenger vehcles, 60 mph for trucks and 50 mph for school buses have changed the flow of traffc through these rural hghways. Trucks are now usng these rural hghways for hgher speed lmt (whch was 55 mph) and shorter travel dstance. Ths ncrease n traffc volume and dfferental speed lmt causes drvers to take potentally unsafe passng maneuvers. The flat terran of West Texas s also workng as a catalyst to that. Now there s a growng need to maxmze capacty, moblty and safety of exstng two-lane hghways. One way to solve the problem s to provde four lane hghways. However, The cost of constructon, $1.0 to 2.0 mllon per mle, s not economcally feasble. That's why the "Super Two" concept comes nto the frame wth a medan to provde passng facltes alternately. The access to ths medan wll be controlled accordng to the flow of traffc. The concept of Super Two s not totally new. There are many roadways that meet super two requrements such as two-lane freeways that have been bult, ether as a frst stage or as a fnal product. These versons of the Super Two usually have been consdered only as nterm steps to full four-lane freeways. Some of the key features of the Super Two are full wdth lanes, full wdth shoulders, frequent passng lane locatons and the extensve use of rght turn lanes, left turn lanes, and contnuous left turn lanes. Therefore the Super Two wll provde facltes of a four-lane hghway wth low constructon cost. Defnton Super Two refers to a freeway or controlled access at-grade roadway wth a sngle through lane per drecton. The dea behnd Super Two s to ncrease the capacty and safety of the exstng two-lane two way hghways. The key elements of a Super Two Hghway are lsted below. 1) Full wdth lanes, paved shoulders and clear zones 2) A center passng lane ) Lmted access, wth turn lanes for all permtted turns ) Horzontal and vertcal curves wth hgh speeds 5) Passng lanes, speed dfferental, and truck lanes 6) Provsons for expanson to freeway or dvded roadway 7) Proper nterchange desgn for a two-lane freeway For a new faclty to be classed Super Two, most gudelnes should be met. For upgradng an exstng roadway, these defnng features can serve as a menu of mprovements for consderaton. Project Page A-1

30 Project Objectve The objectve of ths project s to produce a standard methodology to desgn and to construct a Super Two hghway. Ths means to modfy the exstng two-lane two-way hghways to a Super Two hghway. Ths goal wll be acheved n three phases. n the frst stage, revews of lterature, TxDOT desgn crtera, and cross sectons and standards for sgnngs and strpng have been accomplshed. The result of these revews and studes s the desgn alternatves we set for further dscussons. The next phase wll be the cost-beneft analyss for the dfferent desgn alternatves and ADT's for these roadways. n order to fnd the cost of delay, an analytcal technque nvolvng queung.theory wll be mplemented at ths phase. The possble two or three desgn alternatves wll be decded from the outcome of ths analyss. The thrd and the fnal phase wll be to summarze the results of the above two phases wth necessary desgn documents and drawngs to be mplemented nto a test project. Ths wll be arranged wth engneerng drawngs, cross sectons, passng lane desgn detals, sgnng, and strpng. The documents wll nclude proposed traffc volume crtera, cost estmaton nformaton and a formal constructblty revew for each desgn alternatve. Desgn Phlosophy The phlosophy of Super Two s to provde smooth traffc movement and overtakng maneuvers n the tradtonal two-lane two-way hghways. f constructed as a two-lane freeway, the Super Two wll provde the facltes of a four-lane at-grade roadway. n plannng a regonal road system, the Super Two would be a type of faclty that would typcally be used for mnor arterals and volume prncpal arterals. Desgn Features Two-Lane Rural Hghway lr-- oooc--+~. ;ooo-' ~~ o------J """J ~~ The basc two-lane hghways have two mddle lanes of.7 mn each drecton (as shown n the above fgure) and shoulders of.0 m each. That makes the total wdth of the hghway 1.0 m, and cross slope s 2%. There s no passng lane n t, and shoulders are desgned fully surfaced. Project Page A-2

31 Desgn Speed The Desgn Speed for Super Two should range from 0 to 110 kmlh when an exstng two-lane hghway s upgraded to Super Two. n all new constructon and reconstructon, the Desgn Speed of 100 to 110 kmlh should be used throughout (Mnnesota DOT). n all cases, when upgradng the exstng roadway, the desgner should apply the speed that s greater than or at least equal to the posted speed. Average Daly Traffc The ADT value of 2000 s consdered to be the crtcal ADT between two and four lane hghways. n a study publshed n the Transportaton Research Record (TRR) 10, "Warrants for Passng Lanes", shows that Passng Lanes on rural two-lane hghways have favorable beneft/cost rato at ADT's of 6500 and greater. The length of a passng lane s dependent on the volume of vehcles per hour (vph) for the project. The optmal length of passng lanes to reduce platoonng s 0. to 1.6 km (Mnnesota DOT). A general gudelne for the development of desgn length s as follows. Vehcles per hour (vph) one way Length of passng lane 1.2 to 1.6 km 1.6 to 2.0 km The spacng desgn for a passng lane s dependent on traffc volume. For a vph ofless than 700, ths spacng may vary from 16 to 2 k.m. On the other hand ths spacng may vary from 5 to km or even more frequent for a vph of 700 or more. The three-lane secton conssts of an added lane n the mddle to provde passng facltes n alternate drectons. Ths change of drecton of the mddle lane may be unform or traffc actuated, dependng on stuaton. The center lane added to the two-lane secton s of the same wdth or a bt dfferent than that. The shoulders of a three-lane secton may be narrower than that n the two-lane secton, as beng practced n Germany, Canada, Mexco, Turkey, and some other countres of the world. Bref descrpton of the German, Canadan and the Mexcan cross sectons are as follows. Project Page A-

32 Three Lane Hghway Cross Secton n Canada J \l! 1\ L The desgn conssts of two.7 m lanes and a.6 m lane wth shoulders of 1.2 m each. The drecton of passng wll have a.7 m and a.6 m lane as shown n the above fgure. The total wdth of the hghway remans 1.0 m. Three Lane Hghway Cross Secton n Germany r-m rh r- \ \ \ o ~ ~ n Germany, the hghway s desgned wth two.75 m and one.5 m lanes. The mddle lane of.75 m wdth s provded to facltate passng n alternate drectons shown n fgure. The curbs are of0.25 m each makng the wdth of the hghway as 12.0 m. Ths desgn s sutable for an ADT less than Overtakng s prohbted n the opposng lane. Project Page A-

33 Three Lane Hghway Cross Secton n Mexco Dovbl Poss e Borr er ~ ne V r_je'(' -- ~ ! \ \' Lo L C:. 000 Lo.lOOO l {..'-0 lfco J. 000 ~ ~ Ths desgn alternatve practced n Mexco conssts of three equal lanes of.5 m each wth a central medan of0. m. Here the shoulder n the drecton of passng s lmted to 0. m and that on the reverse drecton s 1.5 m as shown n fgure. Ths change n shoulder wdth may provde some added safety to the drver. Prevous Beneft-Cost Analyses of Super Two Hghways The growng need for the two-lane hghways wth more capacty, moblty, and safety has lead researchers to put emphass on alternatve desgns. On the other hand, lmted fundng and envronmental ssues are bg concerns n openng new corrdors to handle heavy traffc flows. As a result, the Super Two concept has recently started drawng more attenton. There are more than mllon mles of rural hghways n the Unted States; ths fgure represents about 97 percent of the total rural system and 0 percent of all U.S. roadways. t s estmated that about 6 percent of the rural transportaton and 0 percent of all travel n U.S. s done on the rural two-lane system. The major benefts of a passng lane are reductons n delay and accdents. n order to evaluate the effectveness of the passng lanes, the cost savngs of the motorsts over a wde range of traffc volumes and the constructon and mantenance cost of the passng lanes should be compared. The reducton n delay provded by a passng lane results n operatonal cost savngs to the road users. A unt value of tme that s usually expressed n dollars per traveler hour s multpled by the amount of tme saved n order to compute the tme cost savngs. Furthermore, besdes the needs for updatng these values to current prce levels, travel tme value s senstve to trp purpose, travelers' ncome levels, and the amount of tme savngs per trp. Project Page A-5

34 Accordng to AASHTO, the tme savngs s dvded nto three categores and can be expressed as a functon of tme saved n a trp and type of a trp. 1. Low tme savngs (0-5 mn): For work trps and average trps, the values of tme per traveler hour are suggested as $0. (6. percent of average hourly famly ncome) and $0.21(2. percent of average hourly ncome), respectvely. 2. Medum tme savngs (5-15 mn): For work trps and average trps, the values of tme per traveler hour are suggested as $2.0 (2.2 percent of average hourly famly ncome) and $1.0 (2. percent of average hourly famly ncome), respectvely.. Hgh tme savngs (over 15 mnutes): For work trps and average trps, the value of tme per traveler hour s suggested as $.90 (52. percent of average hourly ncome). Accdent Cost Savngs An analyss of accdents on two-lane hghways wth and wthout passng lanes determned the effectveness of a passng lane n reducng accdents. The accdent data was obtaned from the state fle for all two-lane road sectons on rural hghways throughout Mchgan for 5 years, 19 to 197. The accdent cost savngs provded by passng lanes are computed wth the followng equaton. ACS=(AC)(65)(ARF)(ADT) 1 o Where:ACS =annual accdent cost savngs provded by a 1 mle passng lane ($/year/mle) AC = Average cost of accdents by severty ARF = Average reducton n accdents by severty for dfferent ADT values (per 100 mllon vehcle-mles) The equaton above s used to compute the safety benefts of a passng lane on rural two-lane hghways n Mchgan. The values of average cost of an accdent are taken as the total rural accdent cost for fatal, njury, and PDQ accdents. Drect costs are consdered n the equaton. Total benefts of the road users are calculated by addng the delay benefts to accdent cost savngs. Equvalent unform annual cost (EUAC) s calculated based on the passng lane of 1.0 mle long. The lfe ofthe road s taken as n=15 years. For =5 and 10, the values of the captal recovery factor are calculated as and 0.115, respectvely. By usng the analyss above, the warrants for a passng lane are met at a percent grade, 1 0 percent trucks, and average trp type, as the user benefts are greater than constructon costs for a passng lane for all ADT values greater than 6500 for a dscount rate of 5 percent. Smlarly, for the same value of truck percentage, grade, and trp type, the benefts are greater than constructon cost for two passng lanes for ADT values greater than 9000 for a 1 0 percent dscount rate. Project PageA-6

35 Super Two Desgn Alternatves and Classfcatons On two-lane rural roads, passng lanes have two mportant functons. One s to reduce the delay at specfc bottleneck locatons, such as steep upgrades or locatons where trucks frequently travel next to farmland n the rural areas. The second man dea s to mprove the overall traffc operatons on a two-lane hghway by breakng up the traffc platoons and reducng delays caused by nadequate passng opportuntes over substantal lengths of hghway. The desgn alternatves that have been evaluated for Super Two hghways nclude many confguraton of passng lanes. These alternatves can be classfed nto four categores accordng to the passng lane confguratons. These categores are detaled n the followng fgures. ME::;(GE A'(EA DVERGE ACZ'EA Fgure A-1: Type A- Desgn wth Contnuous nteror Alternatng Passng Lane The basc Super Two secton wth alternate passng lanes n the mddle provded n one drecton or another. For that specfc alternatve the man advantage s that there s no added cost of constructng addtonal lane. The exstng pavement wdth can be modfed fulfllng the lane wdth and shoulder requrements. They may not be sutable for a roadway where traffc volume s even n both drecton and where queung occurs frequently n both drectons. Project Page A-7

36 A2.A D TAL- TA.L HEAD HE RLAPP'\!G Fgure B-2: Type B Desgn wth Separated Passng Sectons Type B s the most common desgn used to provde passng facltes for the two-way two-lane rural hghways. Ths s sutable for the hghway sectons havng equal ADTs for both drectons. The separated desgns are often used n pars, one n each drecton at regular ntervals along a two-lane hghway. Where head-to-head or tal-to- tal sectons are used passng by opposng drecton vehcle s prohbted. The cost of constructng extra passng lanes should be consdered Project Page A-

37 before the fnal decson. The head-to-head and tal-to-tal sectons wll handle the platoonng n dfferent manners. The head-to-head confguraton s preferable because the lane drop areas of the opposng passng lanes are not located adjacent to each other. S E BY SDE f Lo'le U'ldvded) Fgure A-: Type C Desgn wth Overlappng Sectons. Type C s probably the least desred secton because of the ncreased cost of constructon due to ts ncreased wdth, and the need for addtonal rght-of-way. t s ncluded n ths dscusson to ensure that hghway desgners have a comprehensve set of alternatves from whch to select the optmum condton for each ndvdual project. Fgure A-: Type D Desgn solated Passng Secton Ths knd of solated passng lane can serve the specfc purpose of reducng delay at a specfc bottleneck. Ther mportance may be perceved n an solated secton of a rural two-lane hghway where passng opportuntes requred n an solated porton of the road, say close to a farmland. A vehcle usng the rural road needs some sort of passng facltes where slow movng vehcles lke a cotton gn mght use the porton of the road frequently. One dsadvantage of ths knd of solated passng lane s they wll be less traveled because of the seasonal varaton of traffc volume. However, from the economc pont of vew ts more cost effectve than constructng passng lanes at regular ntervals for the full length of the roadway. Project Page A-9

38 Concluson After evaluatng hghway characterstcs, Super Two concept s a good approach to the soluton of the problem. Ths type of hghway wth added passng lanes could provde a cost-effectve method for mprovng the level of servce on two-lane hghways. Not only can passng lanes mprove traffc operatons on two-lane roads, but they have also been documented to reduce accdents. However, before the desgn phase, a thorough analyss of the hghway n terms of comparng savngs wth the constructon and mantenance costs s mportant. n order to come up wth a sound analyss, feld data revealng the characterstcs of a partcular hghway should be connected. By takng nto account all.delay and accdent savngs, Super Two should be consdered as a permanent soluton or a temporary constructon between two-lane hghways and four-lane hghways. Project Page A-10

39 APPENDX B: APPLCATON OF QUEUNG THEORY N TWO-WAY-TWO-LANE RURAL DGHWAYS ntroducton The congeston of the traffc on urban hghways especally durng peak hours s a bg concern of the traffc engneers. Ths congeston results n the formaton of queues on expressway on-ramps and off-ramps at sgnalzed and unsgnalzed ntersectons, and on arterals, where movng queues may occur. On the rural hghways the congeston of the traffc s much less frequent than those of the urban hghways. However, the formaton of the queue s stll encountered on the rural hghways. Slow movng vehcles preventng other fast movng vehcles from drvng at ther desred speeds manly cause that event. Ths s the case of a platoon of the passenger vehcles beng lead by a truck. An understandng of the processes that lead to the occurrence of queues and the subsequent delays on hghways s essental for the proper analyss of the effects of queung. The theory of queung comprses the mathematcal algorthms to descrbe the processes that result n the formaton of the queues, so that a detaled analyss of the effects of queues can be performed. These mathematcal algorthms can be used to determne the probablty that an arrval wll be delayed, the expected watng tme for all arrvals, the expected watng tme of an arrval that wats, and so forth. Examples where the theory can be appled nclude vehcles watng to be served at a gasolne staton, passengers or vehcles lned up at a transt termnal, computer jobs awatng for executon or prntng, and so forth. The servce can be provded n a sngle channel or n several channels. Proper analyss of the effects of such a queue can be carred out only f the queue s fully specfed. Ths requres that the followng characterstcs of the queue be gven. (1) The characterstc dstrbuton of arrvals such as unform or Posson (2) The methods of servce such as frst come-frst served, random, and prorty. () The characterstc of the queue length (fnte or nfnte) ( ) The dstrbuton of servce tmes (5) The channel layout (sngle or multple channels and seres or parallel) Some terms used to classfy the queues are gven below. Arrval Dstrbuton: The arrvals can be descrbed as ether a determnstc dstrbuton or a random dstrbuton. A Posson dstrbuton usually descrbes lght-to-medum traffc, and ths s generally used n queung theores related to traffc flow. Servce Method: Queues can also be classfed by the method used n servng the arrvals. These nclude fst come fst served, where unts are served n order of ther arrval, and last n-frst served, where the servce s reversed to the order of arrval. The servce method can also be based on prorty, where arrvals are drected to specfc queues of approprate prorty levels. Queues are then servced n order of ther prorty level. Project Page B- 1

40 Characterstcs of the Queue Length: The maxmum length of the queue, or the maxmum number of unts n the queue, s specfed. n ths case the queue s a fnte or truncated queue, or else there may be no restrcton on the length of the queue. Fnte queues are sometmes necessary when the watng area s lmted. Servce dstrbuton: Ths dstrbuton s also usually consdered as random, and the Posson and negatve exponental dstrbutons have been used. Number of Channels: The number of channels usually corresponds to the number of watng lnes and s therefore used to classfy queues, for example, as a sngle-channel or mult-channel queue. Oversaturated and Undersaturated Queues: Oversaturated queues are those n whch the arrval rate s greater than the servce rate, and undersaturated queues are those n whch the arrval rate s less than the servce rate. The length of an oversaturated queue may vary but wll reach a steady state wth the arrval of unts. However, the length of an oversaturated queue wll never reach a steady state but wll contnue to ncrease wth the arrval of unts. Sngle channel, Undersaturated, nfmte Queues Rate of arrval q Queue Rate of servce Q Fgure B-1. Queue n a sngle channel Fgure B-1 represents a sngle channel queue where servce type s FFO (frst n, frst out) and wth Posson arrvals and exponentally dstrbuted customer servce tmes. The rate of arrval, q (vph), s less than the rate of servce, Q (vph), snce t s an undersaturated system. n the system customers are assumed to be patent, n other words they do not leave the system. Ths system s assumed to have an unlmted holdng capacty, whch means there s no lmt on the number of customers that can be n the watng lne. For an undersaturated queue (q<q), assumng that both the rate of arrval and the rate of servce are random, the followng equatons are developed. (Ncholas J. Garber, Lester A. Hoel, 1997) 1. Probablty of n unts n the system p (n) = 1- ~) ( ~ n Where:n s the number of unts n the system, ncludng the unt beng servced. Project Page B-2

41 2. The expected value (the average number of unts n the system at any tme s) q E(n)=- Q-q. The expected number of unts watng to be served (the mean queue length) n the system E ~'m 1 - _q.;;; ''/ Q(Q-q) 2. Average watng tme n the queue E ~'w 1 - q Q(Q-q) 5. Average watng tme n the system 1 E(v)=- Q-q Mult channel, Undersaturated, nfnte Queues A more complex queung system s a FFO system wth N dentcal servce counters n parallel The average servce rate per counter s q and Q s the arrval rate. The rate of servce rate to the arrval rate s r = q/q. n ths case probablty equaton s as follows. (C.S. Papacostas, P.D. Prevedouros, 99). 1. Forn=O (~ n! J (N -l)!(n-r) N-1 rn rn p(o)= - + [ ] -1 For l:s n :SN rn p(n)=-p(o) n! Forn>N rn p(n) = N!Nn-N p(o) Project Page B-

42 2. The average number of unts n the system [ rn+ ] E(n) = r + (N -1)!(N- r)z p(o). The mean queue length [ rn+ ] E(m) = (N -1)!(N- r)z p(o). The expected tme n the queue E(w) = E(m) q 5. The expected tme n the system E(v) = E(n) q Applcaton of the Theory The major problem that creates the need for two-lane two-way hghways to upgrade to Super Two Hghways s the lack of the passng opportuntes. Ths event results n the tme delay caused by speed dfference between the vehcles. n order to compute the average delay, the queung theory s carred out n ths research. The major components of the theory are rate of arrval and rate of servce. The arrval rate The arrval rate s computed usng ADT fgures taken from Texas traffc map. On ths map a partcular secton s consdered for the calculaton of the delay tme. Ths specfc secton s on hghway 7 at Dalhart n Dallam County (Northeast Texas). The ADT ranges from 200 to 600 vehcles on that road. On rural roads wth average fluctuaton n traffc flow, the 0th hghest hourly volume of the year approxmates 15 percent of ADT. The peak-hour traffc volume s then equal to 15 percent of the ADT. Accordngly, the arrval rates are calculated usng the peakhour traffc volume takng nto account a drectonal dstrbuton coeffcent of 0.60 wth an ncrement of 50 vehcle per hour. The fgure ncludes the number of both cars and trucks travelng on the hghway. On the other hand, queung theory s modeled assumng the trucks are servers and the cars are unts beng served. n order to come up wth a proper value to use n the performng of the queung theory, number of trucks should be extracted from the total number of vehcles. The deducton of 10 percent of trucks gves the number of passenger cars used for calculatng the arrval rate. Project PageB-

43 The servce rate Two dfferent approaches for calculatng the servce rate are taken towards the soluton of ths problem. One s calculatng the servce rate from the servce volume computed drectly from capacty under deal condtons. (Hghway Research Board, 197) SV= 2000 (v/c) WL TL Where:(v/c) =volume to capacty rato W L = adjustment for lane wdth and lateral clearance at any gven level of servce T L = truck factor at gven level of servce A typcal cross secton of the rural hghways conssts of two 12-foot lanes and two 10-foot shoulders makng a -foot cross secton. For our case we assume 10 percent truck traffc. The secton that s consdered has a maxmum ADT of 600 vehcles yeldng a peak-hour traffc of 50 vehcles for both drectons. Ths fgure falls n the proper range ( ) of servce volume for Level of Servce B. Therefore, the servce rate s calculated for LOS B, as a result the servce rate s computed by usng proper adjustment factors for a hghway constructed on level terran. SV = 2000 (0.5) (1.0) (0.7) = 7 vph, total for both drectons. Subsequently, the servce rate s the followng equaton. Q 7 x 0.60 = 70 vph = 7. vehlmn, one drecton The sectons wthout passng lanes are consdered as a sngle channel model. The max arrval rate s the followng equaton. qmax=.6 vehlmn (ADT=600) The servce rate can be consdered wthout truck percentage whch s 10%. Q=7. 05 vehlmn s greater than qmax As a result sngle channel undersaturated queue model s applcable for computng average delays per vehcle on that road. Another way of determnng the servce rate s to fnd the number of cars that can pass the truck for a unt tme. Ths method s useful snce t reflects the real stuaton on the roadway from a physcs standpont. For that case, a physcs problem where the perod tme for a fast movng vehcle (passenger car) overtakes the slow movng car (truck) s solved. The speed lmt of70 mph and 60 mph are the fgures used n calculatng the amount of tme spent for overtakng the slow movng vehcles leadng the platoon. n order to perform a safe passng, for the speed group mph, the dstance traveled whle the passng vehcle occupes the left lane (d 2 ) s 95.5 ft. The average passng speed for the same speed range s Vavg=62. mlhr (.5 ftlsec ). (AASHTO, 199) Project Page B- 5

44 The computatons are shown below. tavg = = 11. seclveh = 0.1 mnlveh By nvertng the average tme for a vehcle to pass the truck we can compute the average servce rate Qavg Qavg = 1 tavg = 5.2 vehlmn Sectons Wth Passng Lane For the sectons of the road wth passng lanes, a multple channel model wth two dentcal channels (N=2) s used. The average delay tme per vehcle, average queue length for sectons wth and wthout passng lanes are computed usng the formulas gven above. The results are gven n spreadsheets 1 and 2. Sample Problem For a Hghway Secton where an ADT of200 vehcles s observed, the truck percentage s 7%. Determne average delay tme per vehcle. Soluton: Peak-hour traffc: 200 x 0.15 x 0.60 = 216 vehlhr (Total traffc for one drecton) x0.7 = 16 vehlhr (Number of cars-unts served) The arrval rate s: q = 2.27 vehlmn The servce rate s: Q = 5.2 vehlmn Average delay: E (w) = 2 27 q x60 =.0sec lveh Q(Q-q) 5.2( ) Note: Consderng a traffc composton wth 7% of trucks, the number of trucks s 0 meanng 0 platoons wll form on the road. Then, the total delay tme of a car to pass all the vehcles wll be Ttot= 0 x. = 672 sec= 11.2 mn. Project Page Bw 6

45 ADT PEAK DRECTONAL ARRVAL Watng Tme - E(w) Watng Tme - E(w) Mean Queue Mean Queue RATE No passng Wth Passng Lane Length Sngle Length Passng Lane( sec) (sec) lane E(m) lane E(m)

46 1~r ~ -1ror ~~ 0. w rn - w ror ~----~ ::E = ~ ror ~~ = <( ~ ~r ,--~ ~ 0~--*=-=-=~~~~~~~~~~~=-~~~~~~~~~~ ~ ~ ~ ~ ~ ~ ~ ~ m ~ w ~ ~ ~ Fgure B-2. Watng Tme vs. ADT (Servce Rate= 5.2 vehlmn) Project Page B-

47 ADT PEAK DRECTONAL ARRVAL Watng Tme - E(w) Watng Tme - E(w) Mean Queue Mean Queue RATE No passng Wth Passng Lane Length Sngle Length Passng Lane( sec) (sec) lane E(m) lane E(m)

48 - - 0 w w : V) 12 j: 10 C) z j: ~ ~ / / ~ ~ /! ADT (VEH DAY) -+-No Passng Lane --Wrth Passng Lane Fgure B-. Watng Tme vs. ADT (Servce Rate= 7.05 vehlmn) Project Page B- 10

49 APPENDX C: GEOMETRC DESGN STANDARDS Studes show that Super-Two sectons can be justfed for rural two-lane hghways wth traffc levels between 1500 and 7000 ADT wth composte grades (Mendoza and Mayoral). For a twolane hghway wthout shoulders and an ADT level below 1500, t s dffcult to justfy the constructon of a Super-Two secton from the economc pont of vew. For ADT greater than 7000 t s more approprate to consder constructon of a four-lane hghway. From the accdent cost standpont Super-Two sectons are justfable for an ADT levels of 2500 or over. Traffc Operaton n a Super-Two Secton When vehcles enter the Super-Two secton, all the vehcles wll be on one lane wth slow movng vehcles at the front of the queue. As they enter the Super-Two secton, slow vehcles wll stay n the rght lane and wll allow the faster movng vehcles to go through. All the faster movng vehcles wll complete passng maneuver usng the passng lane wthn the Super-Two secton. At the end of the Super-Two secton slow vehcles wll merge nto the stream of faster movng vehcles whle yeldng the way. Spacng The Super-Two sectons should be as regularly spaced as possble. Factors to be consdered n the desgn of Super-Two secton are lsted below. (l)adt (2) Truck Percentage () Topography () Local needs (presence of off-road vehcles, School busses etc.) From the case study, for a rural two-lane hghway wth ADT of 600 and 10 percent trucks, the frequency of Super-Two secton was found to be 20.7 km unless other factors such as topography and local needs dctate. Table C-1 shows how the spacng between Super-Two sectons vary for dfferent ADT levels. We can also calculate the total number of Super-Two sectons usng the same table needed for a gven stretch of hghway. Topography of the area s a controllng factor for the placement of Super-Two sectons. Super Two sectons can be consdered at clmbng lanes and at composte grades provded the porton of the hghway has adequate sght dstance. Project Page C- 1

50 Truck% 5 ACT !'"' "t:: ~ ('0 () 1'-)

51 Local features such as a factory or a farm may dctate the mplementaton of Super-Two secton at that pont of the hghway when accompaned wth the approprate levels of traffc. The desgn procedure for the spacng of Super-Two secton s as follows. (a) Determne the ADT of the hghway concerned and the Percentage of Trucks for the hghway. (b) Determne the total number of Super-Two sectons requred usng Table C-1 of Appendx C. (c) dentfy the number of Super-Two sectons needed due to topographcal and local requrements and deduct that number from the total n (b). (d) Dstrbute the remanng number of Super-Two sectons evenly over the hghway whle tryng to mantan the desgn spacng as much as possble. Engneerng judgment should be used n calculatng the postonng and spacng of the Super Two secton. The desgn engneer's experence should be utlzed to determne the local needs of the porton of hghway concerned. Cross Secton The cross secton of two-lane arterals and collectors s shown n fgure C-1. t shows two lanes of.6 m and two shoulders of.0 m each. n Texas these shoulders are often used by trucks to provde passng maneuvers for faster vehcles. Fgure C-2 shows the layout of the proposed Texas Super-Two wth a.6 m lane n one drecton and two.5 m lane n the other. Wdths of shoulders are not the same n ths arrangement. n one drecton the shoulder wdth remans same as.0 m but t s reduced to 0.6 m on the other sde as shown n Fgure C-2. A number of sectons of prmary hghways wth wde paved shoulders n Western Canada (Frost and Moral, 1995) have been retroftted wth passng lane. Also, dfferent shoulder wdths have been used n Mexcan Two-lane roads (Mendoza and Mayoral, 1996). Length, Confguraton and Spacng of Super-Two t s preferable to poston the Super-Two secton where adequate sght dstance s avalable and platoons can dverge easly. Fgure C- shows the proposed confguraton of Texas Super-Two. A bref descrpton of dfferent portons of the Super-Two secton s gven n the followng paragraphs. Lane Dverge Taper The prmary functon of the dverge area s to drect slow movng vehcles to the outsde lane and leave the nsde lane free for passng maneuvers. The length of lane merge taper s calculated as a functon of the length of lane dverge taper gven by equaton 29. (29) Project Page C-

52 Where Ld and Lm are the lengths of lane dverge and lane merge taper respectvely. The value of Lm can be found usng Equaton (2). Table C-2 shows dfferent values oflane dverge tapers for dfferent lane wdth and desgn speed. Passng Lane The lengths of passng lanes for dfferent ADT values can be calculated usng the followng equaton. Lepl = (t ace + (p )v;r (27) Where:Lepl s the effectve length (excludng tapers) of passng lane lace s the tme for acceleraton tp1 s the tme to pass a vehcle n the queue Vtr s the desgn speed of truck (or slow movng vehcle) Here the ndcated length of passng lane s from the end of lane dverge taper to the begnnng of lane merge taper. Table C- shows values of passng lane lengths for dfferent ADT values. From ths chart we can see passng lane length ncreases wth ncreasng ADT and wth ncreasng of percentage of trucks. Lane Merge Taper The functon of a lane merge taper s to allow the fast and slow movng vehcle streams to form nto a sngle stream. The merge taper lengths may vary wth approach speed (So) of the faster vehcle and the wdth of the lane (W). Ths can be calculated by usng the followng equaton. Usng Table C- we can calculate the lengths oflane merge tapers for dfferent desgn speeds and lane wdths. (2) Project Page C-

53 Table C-2. Lengths of Passng lane for varable ADT and Truck Percentage Truck % ~ ~ ' ! A'>d Project Page C- 5

54 Table C-. Lengths of Lane Dverge Taper, Ld wth respect to Desgn Speed and Lane Wdth esgn Speed {km/h) Ld {m) Lane Wdth (m), ll ~ Project Page C- 6

55 Table C-. Lengths of Lane Merge Taper, Lm wth respect to Desgn Speed and Lane Wdth Desgn Speed (km/h) Lm (m) Lane Wdth (m)! = ! Project Page C-

56 Sgnng and Pavement Markng Fgure C- shows the proposed Texas Super-Two secton wth sgnng and pavement markng used Tx.DOT. They can be dvded nto four separate zones as descrbed below. Zone 1 provdes advanced notfcaton of the Super-Two secton Zone 2 ndcates the dverge area Zone provdes advance notfcaton of the end of the passng lane Zone provdes nformaton regardng next Super-Two secton and also warns to traffc movng n the opposng drecton n Zone 1 advance notfcaton s posted at km, 2 km and 1 km n advance of the Super-Two secton. Zone 2 provdes notfcaton of the begnnng of the dverge area and the regulatory sgn 'SLOWER TRAFFC KEEP RGHT'. Zone provdes advance notfcaton of the lane merge. Zone provdes regulatory sgns 'KEEP RGHT' and 'DO NOT CROSS DOUBLE LNE' for the on comng vehcles and nforms about the next Super-Two secton. Double lnes and the dotted lne along the center of the roadway are yellow lnes. Rased pavement marker may be used n between those double yellow lnes to dscourage accdental crossover. The dotted lne markng the passng lane and all other lnes are marked by whte. All pavement markngs should be n agreement wth Texas MUTCD. Case Study Problem US hghway connects Chldress and Hamln and the dstance between them s km (1 0 mles). For the purpose of llustraton t s assumed that the ADT of ths hghway s 500 wth 12 percent truck. t passes through the three towns Paducah, Guthre and Aspermont at dstances of km (0 mle), 9 km (5 mle) and 15 km (95 mle) from Chldress respectvely. Wdth of passng lane s.5 m and the desgn speed s 120 km/h. Calculate the number of Super-Two sectons requred to dmnsh platoonng of vehcles n ths hghway. Soluton: For 500 wth 12 percent of trucks, usng Table C-1 the mnmum number of Super-Two sectons requred per 100 km s found to be 6. Correspondng mnmum number of Super-Two sectons requred for 166 km s 9.96 = 10. The three towns Paducah, Guthre and Aspermont wll provde lmted passng facltes. Therefore, at least 7 addtonal passng sectons are needed along the rural portons of the hghway. One Super-Two secton s provded at the outskrts of each ctes to mnmze Queueng and Platoonng caused by low speed low speed lmts and traffc lghts nsde the cty lmt. Usng Table C-5 the desgn spacng for the Super-Two sectons s found to be 21. km (1. mle). Project Page C- 9

57 '"0... ~ &. - (1> g ~ -...J w \0 ~ V '"tl ~ "Tj 1 1& & ~.0!UO tu H.U HS tuf tl, f..., UY :::: (") '-<! ()> '"t < ~. ~ (D..., r::r n... en :::: (1Q ~ (1) 6..., Q....., ~ '"tl (1) (-1 (1) u... uo Ut u.;:......!a '"..... Ut $).'1 (1Q (1) '"0 ~ (1> (") -0

58 Therefore, Provde Super-Two sectons between Chldress and Peducah. Ths wll provde a spacng of 15 km (9.5 mle). Provde Super-Two sectons n between Peducah and Guthre wth a spacng of 1 km (. 70 mle). Provde Super-Two sectons n between Guthre and Aspermont wth a spacng of 1.50 km (11.50 mle). Provde 1 Super-Two sectons n between Aspermont and Hamln wth a spacng of 1.0 km (.9 mle). Usng Table C-2 for the desgn speed of 120 kmlh and lane wdth of.5 m we can fnd the lengths of Lane Dverge Taper to be 162m. From Table C- for the ADT of 500 and 12% trucks we can fnd lengths of Passng Lane to be 691 m. Usng Table C- for the desgn speed of 120 kmlh and lane wdth of.5 m we can fmd the lengths of Lane Merge Taper to be 29m. Therefore, the total length of Super-Two secton s 1102 m n detaled layout of the Super-Two sectons shown n Fgure C-5. Studes have shown that the ncluson of Super-Two sectons can mprove the level of servce of a standard Two-Lane hghway by ncreasng safety (Frost and Morrall, 1995). From our study t s found that the Super-Two s cost-effectve for an ADT range of200 to 200. Beyond ths range we need to use computer smulaton technque to justfy ts valdty. From our Traffc survey n New Mexco t s found that the Super-Two secton s very effectve n reducng Queues and Platoons. t s shown that the advent of Super-Two sectons reduces Queueng by 55% to 66%. The Super-Two sectons wll be the sutable soluton for Two-Lane roads that need to rase the level of servce for the exstng traffc and the funds avalablty. Project Page C- 11

59 Fgure C-1. Cross Secton of a Rural Two-Lane Hghway n Texas ~ _._ - Project Page( 2

60 Fgure C-2. Cross Secton for Texas Super-Two - Project 951 Page C- 1

61 Fgure C-. Lane Confguraton for Texas Super-Two, " r T T T! D / ~ ! -lr om> ~ act a. a-:::1 -to... rrr -- ;::f:t 0 ::r octet :::1 n :::1:::1:::1 1:!: a NO :::1?> --- oao., a ""m ct a a a ::r a :::1 :::1 ct -5" O.o. "'0 a.?n a- Cl < 0.,.a ""'a 10 ct., 5".,., a cog o::ja a a- < ac'o 0., Cl ::., 5" 0 Project Page C- 1

62 Fgure C-. Sgnng and Pavement Markng for Texas Super-Two [U]-- --ru ~-- \ --~...!! 0 N - -[@] - --m --m Project Page C- 15

63 Fgure C-5. Layout of Super-Two sectons from Chldress to Hamln for the example problem. (Detals of sgnng and pavement markngs are shown n Fgure C-. Project Page C- 16

64 APPENDX D: ECONOMC EVALUATON OF SUPER TWO HGHWAY DESGN GEOMOTERY ntroducton Two-lane, two-way rural roads are of great mportance n the Amercan Hghway System. There are more than mllon mles of two-lane rural hghways n the Unted States, and they comprse about 97% of the total rural system and 0% of all U.S. roadways. t s estmated that 6% of rural travel and 0% of all travel occur on these rural two-lane roads. Fundng s lmted consderng the extensveness of the rural hghway system and the envronmental concerns, and research for ways to mprove the servce of these roadways s essental. Because of the low average daly traffc (ADT) levels carred on these rural hghways, general low-cost mprovements are advantageous over the classcal methods nvolvng major modfcatons such as four-lane sectons and extensve modfcaton of road geometres. The number of trucks usng the rural hghways ncreases the exstng safety and operatonal problems n the desgn of two-lane, two-way hghways. Heavy vehcles create operatonal problems n terms of delay, a reduced level of servce, and an ncrease n passng attempts, aborted passes, and drver frustraton. The Super Two Hghway nvolves the constructon of passng lanes at set ntervals to mprove the level of servce on two-way rural roads. The constructon of passng lanes n rural areas where two-lane, two-way hghways are provded wll result n a beneft to the publc. These benefts prmarly orgnate from the delay tme savngs and preventon of accdents. For the regons such as Texas where the hghways are constructed for the most part on level terran, the savngs that could have been benefted from vehcle operaton are neglgble. These knds of savngs are partcularly of great mportance n the mountanous areas where the average speed of trucks decreases sgnfcantly and passng opportuntes are elmnated. Tme delays are affected by traffc composton, and the presence of the slow-movng vehcles creates traffc platoons consstng of passenger cars followng the trucks. Durng the tme spent n the platoon, passenger cars wll have to drve at a lower speed snce the speed lmt for trucks ( 60 mph) s lower than that of the passenger cars (70 mph). n addton, the platoons may cause the drvers to be more mpatent. Ther attempts to overtake the trucks at mproper locatons or stuatons may cause unsafe maneuvers, whch can result n undesrable crcumstances such as traffc accdents and njures. The man purpose of the research study s to search for adequate reasonng towards the mplementaton of passng lanes on rural two-way, two-lane hghways where passng opportuntes are lmted. An economc study s performed to reveal the beneft/cost (B/C) ratos for dfferent stuatons. As a result of the economc study, t s possble to have the B/C ratos for dfferent ADTs and percentage of trucks. However, the values such as cost data, desgn perod, and nterest rates can be modfed n order to meet the partcular propertes of the project. Project Page D-1

65 Another mportant result of the research s an approprate methodology that wll enable transportaton engneers to desgn the passng lanes. The ssues n the desgn such as the length and ntervals of the passng lanes are based on parametrc computatons. The hghway desgners wll have the flexblty of applyng ther own consderatons or proper fgures n the analyss. n addton to havng a desgn method, the engneers wll have the capablty to evaluate the economc sde of ther desgn. The best decson needs to be made after consderng the economc outcomes of the project. Assumptons The followng s a lst of assumptons drectly related to the constructon of a Super Two Hghway. 1. The number of cars on a two-lane, two-way hghway s modeled wth the applcaton of Queung Theory. Arrval rates of the vehcles on the desgned roadway s modeled by a Posson dstrbuton, but the servce rate provded by the road secton as a whole s modeled wth a negatve exponental dstrbuton. All the formulas used n the calculatons of the average number of cars n the queue and the average watng tmes n the queue are derved from Queung Theory. These assumptons smulate the real traffc flow wth low to medum ADT levels (less than 200 ADT). Hgh ADT levels are not recommended wth these assumptons. These assumptons are not vald for ADTs greater than 200 vehcles per day. (Garbor and Hoel, 1997) 2. The arrval rate s obtaned by consderng the maxmum hour traffc (ADT x 0.15) wth an uneven drectonal dstrbuton of 60% and 0% n each drecton.. The trucks are excluded from the arrval rate value because they are assumed to be relatvely constant.. The servce rate of a roadway secton s calculated from the formula provded by the Hghway Capacty manual. (197) 5. Servce volume capacty (SV) s utlzed to fnd the servce rate of the lane to be used n the queung analyss. 6. Physcal condtons on the rural hghway that s chosen for the case study s assumed to have a 100% passng sght dstance of at least 1500 feet. However, as the ADT value ncreases, the passng sght dstance provded by the opposng traffc wll decrease. The cumulatve probablty of havng a tme gap that would allow a 1500 feet passng sght dstance between consecutve opposng vehcles s calculated. Ths probablty s ncorporated n a servce volume equaton just as the probablty of havng a physcal passng sght dstance of 1500 feet. Ths approach enables the dynamc behavor of servce rate, because servce rate or servce volume decreases wth ncreasng ADT levels. 7. The servce rate obtaned from Equaton (6) gves the total number of vehcles n an hour n both drectons. To fnd the servce rate n the crtcal lane, ths servce s multpled wth Drectonal Factor (DF), whch s taken as 0.6. (HRB Specal Report, 197). To fnd the tme savngs of a Super Two Hghway, the number of trucks that a typcal passenger car would catch s calculated frst. The number of trucks that would be caught wll be a functon of dfferental velocty between car and truck and wll also depend on the average watng tme n the queue. As the watng tme of a car n the platoon ncreases, there would be fewer trucks to catch along a certan length of the roadway because the. average Project PageD- 2

66 velocty of the car would approach the speed of the truck. The average watng tme n each queue per passenger car s then calculated. Tme savng calculatons were based on the assumpton that an deal Super Two Hghway s constructed n such a fashon that would avod any speed reducton due to the presence of trucks. After the frst passng secton, passenger cars would be able to travel wthout reducng ther speeds. Hence, each car wll beneft from travelng wth the desgn speed durng the entre roadway rather than travelng wth some reduced speed nterruptons when they travel the same speed as the truck where there exst platoon formatons. Tme savng due to a unform desgn speed, rather than a reduced speed whle n a platoon and a transton speed durng the acceleraton to the desgn speed are calculated as well 9. The passng lanes are desgned n such a manner that they wll avod any nterrupton of desgn speed of the passenger car. Therefore, trucks are assumed to be travellng wth even dstances among them. The tme requred the frst car to overtake a truck and reach the next truck gves the dstance between passng lanes. 10. Accdent cost reductons and tme savng monetary values are modeled wth the formula provded n the study mplemented by Wllam C. Taylor and Mukesh K. Jan "Warrants for Passng Lanes", Transportaton Research Record. (19) 11. Exstng roadway wll have a standard -foot cross-secton as seen n Fgure D-1. Opposng Lane Truck Lane Shoulder l 1' n r--] Shoulder l.o "' ""... ""... ~ Fgure D-1. Current Two-Lane Rural Hghway Cross-secton Project Page D-

67 12. A super-two cross secton wll requre wdenng 60 centmeters. Ths cross-secton s shovm n detal n Fgure D-2. Shoulder 1 Opposng Lane Passng Lane Truck Lane Shoulder ~ Fgure D-2. Proposed Super-Two Cross-secton Assumptons and 9 are an dealzed condton wth passng sectons located at unform ntervals. n practce, ths wll not be the case. However, the relatvely low volumes of traffc allow ths smplfcaton wthout ntroducng a sgnfcant error. For example, at ADTs below 600 the average queue s less than four cars. Therefore, as the recommended desgn s based on the average queue length plus one, both the length of the passng lane and the dstance between passng sectons should be adequate more than 0% of the tme. Addtonally, ths method does not attempt to compensate for the number of vehcles that are able to pass between passng sectons. Therefore, an adequate safety factor s nherent to the process. Project Page D-

68 Desgn Method The two man components of the queung theory are the servce and arrval concepts. A major dffculty n the applcaton of the queung theory on a traffc problem s the dynamc characterstcs of the traffc flow. The computaton of the servce rate (Q) should ncorporate the fact that the truck percentage wll have an nfluence on the servce rate. Therefore, the servce rate, Q, s computed from the equaton that s publshed n the Hghway Capacty Manual (197). Ths equaton gves the maxmum servce volumes on rural two-lane, two-way hghways under unnterrupted flow condtons. Hghway Capacty Manual Table 10.7 consders the truck factor (TL) adjustment for lane wdth and lateral clearance (WL). A volume capacty rato (v/c), dependng on a passng ste dstance of 1500 ft, s consdered a suffcent dstance to perform a safe passng maneuver. Therefore, a probablstc method consderng the probablty of havng a safe passng dstance n oncomng traffc s ntegrated nto the servce rate calculaton method. A decrease n the safe passng dstance probablty wll gve a lower volume capacty rato (v/c), therefore yeldng a lower servce rate. The equaton for servce volume s gven below and explaned n greater detal n the followng secton. SV=2000 (vc) WL TL On the hghway secton where the ADT values are obtaned, maxmum hourly servce volumes are n the range of a level of servce (LOS) B. Therefore, the factors taken from the table correspond to that LOS. The WL parameter has a value of 1.0 snce the hghway cross secton conssts of 12-foot lanes wth 10-foot shoulders. The probablstc approach for the servce rate, Q, s mplemented n accordance wth the followng formulas. 'A=Vff Where: 'A = the average numbers of vehcles arrvng per second Ths equaton gves the probablty of havng a gap oft seconds or greater n the traffc flow assumng a Posson dstrbuton. The outcome of the equaton s used to determne the servce volume of the hghway by selectng a proper v/c rato accordng to the probablty of havng an adequate passng dstance from Table D-1. V /C ratos n the probablty ranges gven n the table are calculated by nterpolatng ther safe passng sght dstance values. Ths dstance s gven as 1500 ft. The maxmum speed of the vehcles n oncomng traffc s 70 mph. Passng dstance of 1500 ft gves a gap of 1.7 seconds. Then dfferent servce volumes are determned accordng to the oncomng traffc. Project PageD- 5

69 The oncomng traffc s 0% of the total traffc flow assumng a drectonal splt factor of 60/0. An example for the servce volume for a gven ADT s shown below usng actual data from Hghway 7 n Dallam County. P~t)=e '-t A-=216/ 600=0. 06 t=1.7 second P(~1.7)=e x 1 7 = 1.2% Where:ADT=600 vehcles/hour hourly peak traffc= 50 vehcles/hour (15% of ADT) oncomng traffc= 216 vehcles/hour (0% of peak volume) Then, for LOS B, the v/c value s 0. (See Table D-1) TL= 0.7 (10% truck and level terran) WL= 1.0 SV= 2000 x 0. x 0.7 x 1.0 = 592 vehcles/hour (total both drectons) Arrval rates ( q) are values taken from the traffc maps prepared on Hghway 7 n Dallam County, Texas. The ADT values at the varous locatons of the map are converted to hourly peak volumes usng the AASHTO (1990) standards. An ADT range of200 to 600 passenger cars s observed on that map and utlzed n the development of the research study. Hourly peak volume of the road s accepted as ffteen percent of the ADT value. However, another concern s the drectonal splt factor of the roadway, t s known that there wll be more traffc flow n the drecton towards a major cty at certan tmes than away from that cty. Therefore, a drectonal splt factor of sxty percent s used to represent that reasonng. Applcaton of the queung theory s possble after calculatng the servce and arrval rates. The average watng tme n the queue (E (w)) of the roadway used s calculated to predct the delay tme savngs that wll occur after the constructon of the passng lanes. Due to the nature of traffc, the average watng tme s not dle as t can be attrbuted to the example of a customer watng to place an order at a hamburger restaurant. The watng tme n the traffc stuaton s the tme spent n the queue, but snce traffc flow s contnuous, tme delay can only be attrbuted to the amount of tme lost because of the speed dfference between the slow movng trucks and passenger cars. n Texas the truck speed lmt s 60 mph, and passenger car speed lmt s 70 mph. Another result from the applcaton of the queung theory s the average number of passenger cars n the queue (E(m)). Ths value s used to calculate the passng lane length accordng to changng ADT levels. Table D-1 below explans each LOS. Table D-2 descrbes lateral clearance and lane wdth. Table D- explans truck adjustment n terms of terran for each LOS. Project PageD- 6

70 Table D-1. Levels of Servce and Maxmum Servce Volumes on Two-Lane Hghways under Unnterrupted Flow Condtons (Normally Representatve of Rural Operaton) (HRB Specal Report, 197) Level of Traffc Flow Condtons Passng Sght Servce Maxmum Servce Dstance Volume/Capacty Servce Volume Descrpton Operatng >1,500 FT (v/c) Rato Under deal Speed (%) Condtons (Total, (MPH) both drectons, per hour) ~ A Free Flow ~ ~ Stable Flow B (upper speed ~ range) s; c Stable Flow ~ Project Page D-7

71 Adjustment.Factors WLFor Lateral Clearance And Lane Wdth Dstance From Obstructon on One Sde Only Obstructon on Both Sdes Traffc Lane Edge 12 FT Lanes ll FT Larjes 10-FT, 1 Lanes 12-FT Lanes ll FT Lanes 10-FT Lanes 9-FT Lanes To Level Level Level Level Level Level Level Level Level Level Level Level Level Level Level Level Obstructon B E B E B E B E B E B E B E B E ' Q

72 Table D-. Truck Adjustment Factors for Each Level of Servce on Dfferent Terrans Truck adjustment Factor, T L Percentage Level Terran Rollng Terran Mountanous Terran of Trucks, PT Level of Level of Level of Level of Level of Level of Level of Level of Level of Servce Servce Servce Servce Servce Servce Servce Servce Servce A BandC DandE A landc DandE A BandC DandE - ' " The desgn method seeks to reflect real condtons of the traffc flow. All of the man factors nvolved n the dynamc structure of the traffc flow are ncorporated n the methodology. These factors comprse the effect of road geometres, truck percentage, and condtons of oncomng traffc. The probablstc approach that s used to represent the gap acceptance concept provdes a smulaton of the traffc n terms of passng opportuntes. t therefore yelds a servce rate provded by the roadwc> ' on the ablty to perform safe passng maneuvers. Project PageD- 9

73 Parametrc Calculatons of Tme Savngs Ths secton provdes a useful tool to a desgn engneer for applyng the desgn method. nstead of gong through the entre procedure makng all of the calculatons, t s more practcal to follow the steps n the parametrc calculatons. The type of parameters that wll be used should frst be determned. The values of the parameters may be dfferent accordng to dfferent project characterstcs such as the speed lmt of trucks and passenger cars. Consequently, all the parameters appled wth the approprate unts wll result n the desgn components of the roadway that a Super Two Hghway s gong to be bult on. n addton to these desgn components such as the length and nterval of passng lanes, the data that s necessary for the economcal feasblty can be obtaned. The economc feasblty that s explaned n ths research ncludes some assumptons for constructon cost and economcal fgures such as nflaton rate. However, usng an agency's own cost data and project parameters wll result n more realstc analyss. The followng equatons are the desgn parameters explaned n detal n terms of ther use and unts. Arrval rate (g) (vehcles/mnute) (PHF)(DF)(ADT)(l- TP) q = 60 (1) Where PHF= Peak Hour Factor DF= Drectonal Dstrbuton Factor (major drecton) ADT Average Daly Traffc TP = Truck Percentage Probabltv of avalable passng sght dstance of 1500 feet durng peak hour P(h > t) Probablty dstrbuton of opposng traffc s assumed to be Posson dstrbuton. The cumulatve probablty of havng a tme gap that would provde a passng sght dstance of 1500 ft between two oncomng vehcles s found usng Equaton (). Tme gap (t) between two oncomng vehcles 1500 ft (50 m) apart s found usng Equaton (2), and the average number of cars n the opposng drecton (A.) s calculated usng Equaton (). t = (0.5)(600) (2) vpc A.= (ADT)(PHF)(l- DF) 600 () () Where h =tme gap between two consecutve opposng vehcles (seconds) t =tme gap between two opposng vehcles 1500 ft apart (seconds) A.= average number of cars n the opposng drecton (vehcles/second) Servce Volume CSV) (vehcles/hour) Project PageD-10

74 Servce volume s a functon of P(h ;;;::: t) and assumes the total mxed vehcles per hour n both drectons (HRB Specal Report, 197). Correspondng v/c rato n the followng equaton s found accordng to probabltes of havng a passng sght dstance of 50 m. Use Table D-1 for approprate probablty values. SV = 2000 (vc) WL Tr (5) Where v/c= Volume to capacty rato (a functon of P(h;;;::: t)) WL= Adjustment for lane wdth and lateral clearance at gven level of servce T L = Truck factor at gven level of servce Servce Rate (Q) (vehcles/mnute) Servce value s derved from SV by convertng to vehcles/mnute and multplyng by Drectonal Factor (DF). Q == (SV)(DF) 60 (6) Average watng tme n queue (E(w)) (mnute/vehcle) Queung theory wth the assumpton of Posson arrval dstrbuton and exponental servce rate dstrbuton would gve the average tme each car spends n the queue watng to ntate overtakng the slow-movng truck. t should be kept n mnd that the average watng tme n a queue does not nclude the overtakng duraton (5). E(w)- q (7) Q(Q-q) Tme savngs (S) (mnute/vehcle/truck) Ths parameter shows the amount of tme n seconds that can be accrued from the applcaton of the desgn methodology. The value shows the amount of tme that s saved by a passenger car approachng behnd a slow movng truck and watng for a chance to overtake. The average watng tme (E(w)) should be converted to seconds by dvdng by 60. The tme spent watng n the queue s not lost completely because tme savngs consders the fact that a passenger car can travel at a reduced speed whle behnd a truck. The tme spent overtakng the truck s part of the tme savngs as well. Equatons () and (9) are used to determne tme savngs. v S:::: E(w)- E(w)!!_+ dtpass () vpc _6 T pass = fot- vottot V pc Where LlTpass = tme saved by not overtakng the truck (seconds) Vat average speed of passenger car whle overtakng the truck tot= tme requred to overtake the truck by a passenger car (seconds) (9) Project 7-95 PageD-

75 Average Speed on the road CVm) (klometers/hour) The parameter ndcates the average speed devates from the speed lmt of a passenger car. Ths s due to the presence of the slow-movng trucks'on the roadway. Ths parameter s the average speed that a passenger car travels before the constructon of passng lanes. Equaton (1 0) assumes an average speed equal to the speed lmt wth the absence of slow movng trucks n the traffc. (10) qtr= (ADT)(PHF)(DF)(J'P) (11) Where qtr= truck arrval rate (vehcles/hour) Number of trucks a passenger car would catch n 1 hour at V D::g constructed CNtr) before passng lanes are The denomnator of Equaton (12) s the amount oftme t takes a passenger car to reach the next slow movng truck after overtakng one truck. Ths s done at an average speed per hour (600 seconds.). N = 600 lr E(w)+Tpass +((V')( 600 )J q lr fl. Vr- pc (12) Converson Factor to convert per 1 00 klometers/vehcle (F J.QQ} The prevous parameter s an hourly value of the number of trucks that a passenger car can catch. For practcal purposes, presentng the values on the bass of dstance s more meanngful. Therefore, an nterval of 100 klometers s selected to form that bass. The prevous parameter can be converted to a 100 klometers bass usng a Ftoo parameter. 100 F;oo = Vavg (1) Project Page D l2

76 Number of trucks a passenger car would catch n per 100 klometers before passng lanes are constructed (Ntrtool Ths parameter s a result of the two prevous calculatons. t shows the number of trucks that are caught n a dstance of 100 klometers by modfyng the hourly value n Equaton (12). (1) Dstance between Passng Lanes (Dru) (klometers) The dstance from the pont where a passenger car overtakes the frst truck to the pont where t reaches the next truck s the dstance between two passng lanes. The dstance between the passng lanes assumes an even dstrbuton of the trucks and the trucks do not cause a delay for the passenger cars. Ths length also ncludes the passng lane secton of the hghway. 1 -~r D = qtr V (15) pt Ll.V pc pc-tr Number of Passng Lanes (PS) per 100 klometers (PL.LQQ} deally the passng lanes are desgned to be at the pont when passenger cars reach the next slow movng truck. t s assumed that the queue wth an average number of passenger cars E(m) would be formed by the tme the platoon reaches the next passng lane. P~oo = 100 (16) DP, Tme Savngs for 100 klometers of Roadway for Passenger Cars (Stool Tme savngs results from the constructon of passng lanes. t s calculated from the number of trucks that a passenger car encounters n a 100 klometers secton of hghway. Tme savngs (S) s the amount of tme that a drver n a passenger car wll save from the constructon of the passng lanes, and t s expressed n seconds. (17) Summary Tme savngs that wll be ganed from the applcaton of a Super Two secton s explaned n parametrc terms wth the number of passng lanes per 100 klometers. t s assumed that all watng tmes are elmnated by the constructon of passng lanes. ntally, the average tme, E(w), spent n a queue s found from queung theory. The number of queues n a 100 klometer stretch of roadway and the tmes savngs for the passenger cars n a 100 klometer stretch of roadway s essental to constructng a Super Two Hghway. The total tme savngs per year that a Super Two Hghway can brng s also mportant and should be calculated. The number of passng lanes s found usng the dstance a passenger car wll travel n order to reach the next truck on the hghway. The parameter refers to the number of passng lanes that Project PageD-1

77 should be constructed n a 1 00-klometer secton of the hghway n order to avod the tme loss caused by slow movng trucks. t s assumed that the trucks are evenly dstrbuted and the dstance between the trucks s a result of the hghway's ADT value. The number of passng lanes s an deal fgure that wll reflect the objectves of the study on the feld. Ths parameter's value should be rounded to closest nteger as an approxmaton. As a result, ths number can be used n fndng the number of addtonal passng lanes that should be constructed after the constructon of the necessary ones because of lmtatons on the hghway such as curves and hlls. Parametrc Calculatons of Passng Lane Length Ths secton prmarly shows the parametrc calculatons of the roadway geometres and economc consderatons that are assocated wth a Super Two Hghway. Queung theory s used n computng the number of cars n queues, and those queues wll be elmnated after the mplementaton of a passng lane. Equaton (19) s a conservatve approach to the number of cars n the desgn. Average Queue Length E(m) Ths parameter s a result of the queung theory to obtan a smulaton of the traffc pattern that occurs on a hghway wth a determned ADT. The ADT wll yeld the arrval (q) and servce rates (Q) as explaned n the prevous secton. The average queue length s the number of passenger cars behnd a slow-movng truck. 2 E(m)- q (1) Q(Q-q) Probablty of more than N Vehcles n the Queue P(n>N) (5) The number of vehcles n the queue s the expected value of the number of passenger cars n the platoon. Hence, the probablty of havng a longer queue should be nvestgated. The probablty of havng more than N cars n the platoon s obtaned usng Equaton (19). Snce the length of the passng lane s drectly effected by the number of watng cars n the queue, the desgn of the passng lane should be based on a queue level that s more crtcal than the average number of cars n the queue. n ths analyss the average number of cars n the queue s ncreased by one to obtan a more crtcal desgn parameter. Probablty of observng a hgher number of cars n the queue s calculated below wth a comparatve bass between E(m) and E(m)+ 1 stuatons (Equaton 20). The effect of ths operaton wll not be the same at dfferent levels of ADT. At low ADT levels, the mean number of cars at the queue wll be lower when compared to hgh ADT levels. Therefore the relatve effect of addng one to the mean number wll be much hgher. f the confdence level needs to be hgh (the desgn queue length s based on consderably low probablty levels of P(n > N)), the desgn of the passng lane should be over conservatve because t has been desgned for Peak Hourly Volume of ADT. N+l P(n>N) = ( ~ J (19) Project PageD- 1

78 Average Queue Length plus one Vehcle E (m)+ 1 (number of passenger cars n queue) The average queue length plus one vehcle s smply a conservatve determnaton of the average queue length. Ths parameter s expandng from Equaton (1). 2 E(m)+1= q +1 (20) Q(Q-q) Platoon Length Ll?..(m) The passenger cars that form the platoon behnd a slow movng truck are assumed to be 20 ft n length. The headway between the two followng cars s assumed to be 0ft, and the truck length s assumed to be 55ft. (HRB Specal Report, 197). The platoon length can then be obtaned by multplyng the number of cars n the platoon by the length of the car plus headway dstance. These lengths are approxmately 1m and 16.5 m, respectvely. LP =(E(m)+1) (21) Whle the truck travels n the passng lane, the last passenger car n the platoon should be able to pass the truck. The length of the passng lane s desgned n such a way that, the when the passng lane ends, the last car would have just passed the slower movng truck. The movement of the passenger cars s assumed to be n two phases. The frst phase begns as soon as the truck pulls nto the passng lane, and the platoon accelerates as a whole. The second phase s the platoon overtakng the slower movng truck. The passenger cars travel at the maxmum desgn speed durng ths phase, and ths phase s over when the passng lane ends. Therefore, the total tme that the truck should spend n the passng lane should be the sum of face and fpt Equaton (22) shows the dstance the last car n the platoon must travel to pass the slower movng truck. Ths dstance should be equal to the sum of the platoon length, Lp, and the dstance traveled by the truck n the passng lane, Lepl. Ths dstance s the effectve passng lane length. Equatons (22) and (2) represent the physcal equlbrum that should exst between the dstance traveled by a passenger car and the platoon length and effectve passng lane length. Equaton (2) wll gve the amount of tme the passenger car spends n the passng lane, fpt, rather than acceleraton tme, face dpc = Lp + Lepl (22) Where: dpc= dstance traveled by the passenger car whle the truck s n the passng lane tp1 + tacc =the tme spent by the truck n the passng lane (seconds) tacc = acceleraton tme of passenger car (seconds) ape= acceleraton of a passenger car whle overtakng a truck. (2.lkm/hour/second) (0.67m/sec 2 ) (AASHTO, 1990) (2) (2) Project PageD- 15

79 Acceleraton of the vehcle (agj (meters/second 2 ) The acceleraton phase takes place when a passenger car overtakes the slower movng truck after the truck pulls nto the passng lane. The tme requred (At) for a passenger car to accelerate to a speed to pass the truck (deally from 60mph to 70 mph) s gven as.5 seconds (AASHTO, 1990). Equaton (25) converts the speed nput n klometers/hour to an acceleraton value n m per square meter. AV Vpc- ~r 1000 a pc = -!::.!- = :.!::.! 600 (25) Acceleraton tme of the vehcle Ctacc) (seconds) f an acceleraton value of the passenger car s used other than.5 seconds, the acceleraton tme of the passenger car should be determned usng Equaton (26). (26) Effectve Length of Passng Lane (Le_) (meters) An effectve length of the passng lane s long enough for the drvers of the passenger cars to feel comfortable overtakng the slower movng truck. There should also be enough provded space for the trucks to ease nto the passng lane. Tapered sectons at the begnnng and end of the passng lane would effectvely provde ths space. But the tapered sectons would not be ncluded n the length of the passng lane. The tapered sectons should be equal to the dstance traveled by the truck as t moves nto and out of the passng lane safely clearng the passenger cars n the queue. (27) Effectve length of Passng Lanes per 100 klometers CLenoo) (klometers) The effectve length of the passng lanes should be studed over a 1 00 klometer secton of the hghway to establsh a better comparson bass. Ths parameter expands from Equaton (27). (2) Project PageD- 16

80 Constructon Cost per 1 OOk:m of road secton (CruL.Cll The constructon cost of a passng lane s found by multplyng by 2 snce the passng lane n the opposte drecton must also be consdered. Snce the length of converge and dverge areas s not a functon of the length of a passng lane, the number of passng lanes rather than the length of the passng lane affects the constructon cost per 100 klometer roadway. C = 2 pl eplloo + UC P L ( uc L J p 1000 cd 100 (29) Where: UCpz = Constructon cost of 1 klometer of passng lane UCcd = Constructon cost of converge and dverge sectons per each passng lane Annual Constructon Cost per 1 OOk:m of road secton (AC~ The constructon cost s a one-tme cost that occms at the begnnng of the project. t should be ncorporated nto the economcal analyss n annual bass so that cost and beneft values can be compared. Equaton (0) annualzes the constructon cost of the passng lanes usng a lfe cycle of n years and an nterest value,. The lfe cycle perod of the project should be estmated accordng to the characterstcs of the roadway. (0) Where (A \P, %, n) = the captal recovery factor for an nterest value of % and for n years Annual Tme Savng Benefts fftme) ($) Annual tme savng benefts must be multpled by 65 to ncorporate the entre year. The dfferent tme costs of busness and lesme trps are ncorporated nto the calculatons. (1) Where:S 100 =Tme savng benefts per 100k:m (seconds) Sbt =Tme value of busness trps ($/passenger/second) Pbt= Percentage of busness trps Szt = Tme value of lesme trps ($/passenger/second) Pzt = Percentage of lesure trps ANp = Average number of passengers passenger vehcle Project PageD- 17

81 Accdent Reducton Beneft (B~ ($/1 OOkm/yr) Accdent cost reductons and tme savngs n terms of monetary values are modeled usng Equaton (2). B = _( A_C_)_(_65_)_(A_RF_)(_A_D_T_)(_1 o_- _)(_L, pn_oo_)(_._6_) ~ 1~ () Where: Bacc = the annual accdent cost savngs provded by a 1-m passng lane AC =the average cost of accdents by severty ARF= average reducton n accdents by severty for dfferent ADT values (assumed value of7.7) The constant 1.6 n Equaton (1) s used to convert 19 dollars to 199 dollars. The equato s further dvded by 1.6 to fmd the cost reducton per klometer. The equaton orgnally gave the cost reducton per mle. Total Beneft (TB) ($) The monetary beneft s the total of tme savngs that passenger cars wll experence and accdent reducton beneft on a hghway due to the upgradng t to a Super Two Hghway. () Beneft Cost Rato (B/C) The result of the economcal analyss s to have a meanngful parameter that wll ndcate whether the constructon of the Super Two Hghway s vable or not. Values greater than or equal to 1 prove the applcaton of the project economcally feasble. B 1 C = TotalBenefts Total Costs () Taper Lengths CLm1J!:.-g) (m) (Mendoza and Mayoral, 1996) The tapered sectons at the begnnng and end of a passng lane are calculated usng the followng equatons. Equatons (27) and (2) must frst be used to calculate effectve passng lane lengths. Lm = (0.62)(SJ(W) Ld = (0.65)(Lm) (5) (6) Where:Lm =taper length at the merge area Ld = taper length at the dverge area So = operatng speed after nstallng the extra lane n the gven subsegment (klometers/hour) W= normal lane wdth (m) Project PageD- 1

82 Total Passng Lane Length bl(m} The total passng lane length s the effectve passng lane length and the length of the tapered sectons of the passng lanes. (7) Summary Followng the parametrc calculatons n the prevous sectons s a practcal way to obtan the characterstcs of a roadway that s beng consdered as a Super Two Hghway. The second part of the parametrc calculatons provdes the equatons that are useful for determnng the length of passng lanes. The equatons necessary to obtan a beneft/cost rato wll help make a decson whle takng nto account the economc concerns. Constructon costs are the costs related to the wdenng of the exstng roadway, and desgners are recommended to use ther own cost data to obtan a more approprate economc analyss. Alternatves wthout wdenng the road should also be consdered. Case Study-Parametrc Calculatons of Tme Savngs A case study usng actual data from Hghway 7 between Dalhart and Texlne n Dallam County, Texas s presented n the followng two sectons to exemplfy the proposed equatons. The most crtcal ADT level of 600 vehcles/day s chosen for the example. Each formula presented n the prevous secton wll be calculated based on assumed parameters. Varous calculatons for dfferent ADT and truck percentage levels are presented n ths report. The desgn speeds for the passenger cars and slower movng trucks are decded to 70 mph and 60 mph, respectvely. However, for the sake of metrc unt calculatons ther speeds are taken as 112 km/h and 96 km/h, respectvely. A representatve truck percentage of 10% s chosen for ths specfc case study. Arrval rate {g) (vehcles/mnute) (PHF)(DF)(ADT)(l- TP) q= 60 (0.15)(0.6)(600)(1-0.1) q= 60 q =.6 (1) Where:PHF Peak Hour Factor DF= Drectonal Dstrbuton Factor ADT = Annual Daly Traffc TP = Truck Percentage Project PageD- 19

83 Probablty of avalable passng sght dstance of 1500 ft durng peak hour P{h>t) (0.5)(600) t =..;....::...; :;... vpc t = 1.5sec A= (ADT)(PHF)(l- DF) 600 A= A= 0.06 P(h :2:: t)= e-).j P(h :2:: 1.5)= e-o.06x 15 P(h :2:: 1.5) = 0.2 (2) () () Where:h =tme gap between two consecutve opposng vehcles (seconds) t = tme gap between two opposng vehcles 1500 ft apart (seconds) A= average number of cars n the opposng drecton (vehcles/second) Servce Volume CSV) (vehcles/hour) (HRB Specal Report, 197) SV = 2000 (vc) WL TL SV= 2000 (0.2) (1) (0.7) SV = 59 vehcles/hour (5) Where:SV= Servce volume (mxed vehcles per hour, total for both drectons) v/c= Volume to capacty rato (a functon of P(h :2:: t)) W L = Adjustment for lane wdth and lateral clearance at gven level of servce T L =Truck factor at gven level of servce Servce Rate fqj (vehcles/mnute) Q= (SV)(DF) 60 Q = (59)(0.6) 60 Q =5.9 (6) Project 7~951 Page 0~20

84 Average watng tme n queue (E(w)) (mnute/vehcle) E(w)- q Q(Q-q) E(w) =.6 5.9(5.9-.6) E(w) = 0.72mn Tme savngs (S) (mnute/vehcle/truck) v vpc (7) () s = (0.72)(60)- (0.72)(60)( 96 ) Ll T pass = 1 ot S = 7.5sec V ot tot v pc ATpass = 1. seconds ( 62 )( 11. ) /:::,. T pass = Where:ATpass= tme saved by not overtakng the truck (seconds) Vat= average speed of passenger car whle overtakng the truck tme requred to overtake the truck by a passenger car (seconds) t 01 S = E(w)-E(w)- 1 ' + f:l.tpass Average Speed on the road VavrCklometerslhour) E(w)Vtr+Tp<SSVp<SS+ Vtr 600 J Vpc [ q" AVtr-pc V~= ~~--~~- E(w)+Tp<SS +[V" 600 J qtr AVtr-pc (10) (.2)(96) + (11.)(1 00) + ((96)(600))112 v = (2.)(16) avg (~x 600 ) V~::::lll

85 qrr= (ADT)(PHF)(DF)(FP) qt,.= (600)(0.15)(0.6)(0.1) qt,.= 2. (11) Where qrr= truck arrval rate (vehcles/hour) Number of trucks a passenger car would catch n 1 hour at V (!l!g before passng lanes are constructed (Ng} N = 600 tr E(w)+Tpass +((v;')( 600 )J N = 600 qtr ~v;r-pc tr ((~)(600)) Ntr =.99 (12) Converson Factor to convert per 100 klometers/vehcle (F!!!!l). 100 ~oo=- VOl'g (1) F, = ~00 = 0.9 Number of trucks a passenger car would catch per 1 OOkm before passng lanes are constructed NtrlOO = Ntr~OO (1) N 1,. 100 =.99x0.9 NtrlOO =.50 Project Page D-22

86 Dstance between Passng Lanes CDru) (klometers) 1 -v;, D = qtr V p AV pc L.l. pc-tr (15) 1 --x96 D = 2. xl12 p 16 Dp 1 = 20.7km Number of Passng Lanes (PS) per 100 klometers (PLQQ} PL Dpl (16) =JQQ_ PL PLlOO =.2 Tme Savngs per 100 klometers for Passenger Cars (SQQ} Swo = (S)NtrOO s1oo = (7.50)(.50) SlOO =.seconds (17) Case Study-Parametrc Calculatons of Passng Lane Length Average Queue Length E(m) (passenger cars) 2 E(m)- _q=-- Q(Q-q) (1) E(m) = (5.9-.6) E(m) =.52 Project Page D-2

87 Probablty of more than N Vehcles n the Queue (P(n>N)) P(n>N)=(~f (19) P(n >.52) = (.6) P(n >.52) = 0.9 P(n >.52) = (.6) P(n >.52) = 0.2 Average Queue Length plus one Vehcle (E(m)+ 1) (passenger cars) 2 E(m)+1= q +l Q(Q-q) (20) E(m)+1=.52+1 E(m)+l=.52 Platoon Length (b).(m) LP =(E(m)+l).l+16.5 LP =(.52)(1)+16.5 LP =97.6m (21) dpc = Lp + Lepl (22) Project PageD- 2

88 (2) Where:dpc dstance traveled by car whle truck travels n the passng lane (m) fpt +face= tme spent by the truck n the passng lane (seconds) face= acceleraton tme of passenger car (seconds) ape = acceleraton of a passenger car whle overtakng a truck. LP - (0.5)a pct 2 ace t p = --" ':; - Vpc-V:r (0.5)(0.9)(.5) t =---;..._..:;...:;..;;...;.._~ p (2) tp 1 = 19.76seconds Acceleraton of the vehcle (agj (m/sec 2 ) lv V pc - V:r 1000 a =-=--'--- pc lt M 600 (25) a = lv = (112)- (96) 1000 = 0. 9 m/sec2 pc lt Acceleraton tme ofthe vehcle Ctacc) (seconds) - ~v - vpc - v;r face -----=---- a pc (0.9).(.6) t =---- ace (0.9)(.6) (26) face =.5 seconds Effectve Length of Passng Lane (L~ll.(m} Lepl =(face + f p )v;r L _ ( )(96) epl -.6 Lepl = 6m (27) Effectve Length of Passng Lanes per 100 klometers CLenlloo) (klometers) LeplOO LeptPLJOo LeplOO = (1.061)(.2) Leplloo =5.11 klometers (2) Project Page D-25

89 Constructon Cost of Passng Lane Sectons per 100km (Cnl.ll C pt = 2 ( UC pt L ept UC cd PL 1oo ) 1000 cpl = 2((025)(5.11)+(1222)(.2)) c p = $26,12 (29) Where: UCpt Constructon cost of 1 klometer of passng lane UCpt = $0,25 UCcd = Constructon cost of converge and dverge sectons per each passng lane UCcd = $1,222 Annual Constructon Cost per 1 OOkm of road secton (A Crull$). ACP 1 = CP 1 (A \ P,%,n) AC pt = (26,11)(0.1295) AC p = $2,22 (0) Where: (A \P, %, n) = Captal recovery factor for an nterest value of % and for n years. (A\P, 5% 10) = Annual tme Savng Benefts fftme) ($) (1- TP)<ADT)(S 100 )(65)(~tSbr + ~rsu )ANP Btme = 600 B. = (1- o.(x600)(.)(65)((0.2)(0.)(1.6) + (0.)(0.21)(1.6))(2) ttme 600 Btme = $7,956 (1) Where S 100 =Tme savng benefts per 100km (seconds) S10o =. seconds Sbt =Tme value of busness trps ($/passenger/hour) Sb 1 = $0. /passenger/hour (Taylor, Muckesh, 19) Pb,= Percentage of busness trps Pb,= 20% s,,= Tme value of lesure trps ($/passenger/hour) S 11 = $0.21 /passenger/hour (Taylor, Muckesh, 19) P 11 = Percentage of lesure trps Pt 1= 0% ANP = Average number of passengers n a vehcle AN. =2 p Project PageD- 26

90 Accdent Reducton Beneft (B~($/lOOkm/yr) (Taylor. Muckesh. 19) B = (AC)(65)(ARF)(ADT)(10- )(LP 1100 )(1.6) ace 1. 6 B = (26,70)(65)(7.7)(600)(10- )(5.11)(1.6) ace 1. 6 Bacc = $57,622 (2) Where:Bacc =Annual accdent cost savngs provded by a 1-m passng lane ($/yr/mle) AC =Average cost of accdents by severty (value s taken to be $26,70 n 19 dollars) ARF= Average reducton n accdents by severty for dfferent ADT values (value s taken to be 7.7) Total Beneft CTB) ($) TB = B ace + Btme TB = 57, ,956 TB = $65,57 () Beneft Cost Rato CB/C) B 1 C = Tot a/benefts Tota!Costs BC = 65,57 2,22 BC = 1.55 () Taper Lengths (61_(1~) (m) (Mendoza. Mayoral, 1996) Lm = (0.62)(So)(W) Lm = (0.62)(112)(.6)= 250m Ld = (0.65)(Lm) Ld = (0.65)(250) = 16 m (5) (6) Where Lm =taper length at the merge area Ld = taper length at the dverge area So = operatng speed after nstallng the extra lane n the gven subsegment (klometers/hour) So = 112 klometers/hour W= normal lane wdth (m) W=.6m Project PageD- 27

91 Total Passng Lane Length b!_(m) LP, = Lepl +Lm +Ld LP 1 = = 106lm (7) Constructon Costs The upgrade of the exstng roadway to a -lane pavement wth a passng lane s planned wth a 60cm pavement wdenng as shown n Fgure D-2. Snce the structural capacty of the exstng 1Oft shoulders s the same wth regular lane sectons, shoulders should be kept as they are. The 60 em new constructon s foreseen wth the same structural capablty of present pavement. The exstng and proposed sectons are comprsed of the followng layers. 0.6m Calche subbase 0.6m fly ash base 2 course surface treatment After the pavement s extended 60 em, a fnal seal coat applcaton s desgned to cover exstng markngs. Ths prepares for the strpng of new pavement markngs. Another constructon actvty would be the merge and dverge areas, or the tapered areas of the passng lanes. The cost of these areas does not depend on the length of the passng lane. Ths s reflected n cost Equaton (2). The approxmate constructon costs are as follows. Analyss A two-course surface treatment wth AC-5, Grade aggregate s needed. Applcaton rate of bnder s 211m 2, and dstrbuton rate of aggregate s 17 m 2 /m. t s calculated to be $1,020/0.6m wdth/lkm length. A one-course seal coat applcaton wth AC-5, Grade aggregate s needed. The applcaton rate of bnder s 211m 2, and the dstrbuton rate of aggregate s 1 7 m 2 /m t s calculated to be $12,09/1.0m wdth/lkm length. Fly ash stablzed base constructon cost s calculated to be $9,000/0.6m wdth/lkm length. Calche sub-base constructon cost s calculated to be $6,000/0.6m wdth/lkm length Excavaton cost s $1,91!0.6m wdth/lkm length. Embankment cost s $1,105/0.6m/lkm length. Cost of dverge and converge areas s $1, m wdth/passng lane. Total cost excludng sgnng cost s $0,25. Varous fgures obtaned from the applcaton of the desgn methodology show the outcomes of the study for the two-lane two-way rural hghways, or Super Two Hghway. These fgures are the results of applyng the desgn parameters and cost values that are explaned prevously n the report. They wll gve a general understandng of the desgn logc and modfcatons of the parameter values wll show the correspondng study results. Project PageD- 2

92 The fgures show the varance of the most necessary parameters such as ADT, beneft cost rato, and the length of passng lanes as other varables change. Therefore, a desgn engneer can evaluate dfferent aspects of the project and decde on tradeoffs. Beneft-Cost Rato vs. ADT The analyss shown n Fgure D- s performed at a constant truck percentage of 10% and wth varyng ADT levels. The B/C rato ncreases wth ncreasng ADT levels. The Super Two Hghway can be justfed from an ADT level of Ths justfcaton s manly caused by the accdent cost savng benefts. The equaton used n ths calculaton can be further elaborated or examned to conform to the actual accdent cost savng analyss specfcally conducted for a roadway secton. t s evdent that tme savng benefts are not adequate to justfy the constructon of the Super Two Hghway (approxmately 15% of the savngs are contrbuted by the tme savng benefts). However, the constructon cost pertanng to the upgradng of the hghway s prmarly wdenng cost. Many people wth hghway constructon experence agree that wdenng s not a necessty. For the segments of the hghway wth passng lanes, strpng wll be adequate for safe traffc condtons. The cost of strpng s much less than constructon cost. f hghway agences can adopt ths dea, the constructon of passng lanes at gven ntervals wll be a vable soluton to the mprovement of the two-way two-lane rural hghways <C 0::: (..) -aj ADT Fgure D-. B/C Rato to ADT Levels Beneft-Cost Rato vs. Truck Percentage Another outcome of the constant ADT and changng truck percentage analyss s the B/C rato s not senstve to truck percentage. Ths s caused by the structure of the accdent cost beneft equaton. Fgure D- s plotted for a constant ADT of 600 and varyng truck percentage. An almost constant lne s observed. Ths s because accdent cost savngs ncluded n the numerator and constructon costs ncluded n the denomnator are both functons of the passng lane length, and therefore cancel each other out. Ths leaves a constant B/C wth respect to Truck Percentage. Project Page D-29

93 :;:::; 1.2 ll 0:: ~ Truck Percentage Fgure D-. B/C Rato to Truck Percentage Mean Queue Length vs. ADT The average number of passenger cars n a platoon changes exponentally accordng to the Posson dstrbuton. The number of cars n the queue s low, but ths s realstc because of the low rural hghway traffc volumes. The average number of cars n the platoon for ADT s approxmately vehcles. These values wll be compared to the actual values that wll come from a traffc count on the Hghway where the ADT values orgnated. Consequently, ths comparson wll be a measure of how realstc the outputs of the study are. Fgure D-5 shows the relatonshp between the mean queue length and ADT. ~! Q) :::J Q) :::J 0 c: ll ~ ll (,.) z ~ / ~ ~... ~ / / ADT Fgure D-5. Number of Cars n Queue at Dfferent ADT Levels (mean queue length) E(m) Project PageD- 0

94 Passng Lane Frequency Fgure D-6 shows the passng lane frequency of passng lanes per 1 00 klometers and the ntervals of the passng lanes as the ADT values change. There wll be certan ponts of the hghway where constructon of passng lanes wll be requred regardless of the nterval values determned by the desgn method. The necessary passng lanes may occur where nadequate road geometry mpars traffc condtons. Examples of such locatons are places wth low sght dstances, turns and hlls. Fgure D- can be used n establshng a bass for the selecton of the passng lane locatons. Accordng to the length of a partcular hghway, the total number of passng lanes wll be known. After selectng the segments of roadway that necesstate the constructon of passng lanes, the other passng lanes can be dstrbuted at equal ntervals. E..:.:.: o.oo 'E..:.:.: Q. 0 c: "'" -..J Cl) Cl) -No. ofpl n 100km !..J Cl) Q..c -t-dstance... Between f o.oo - B PL (km) 0 c: z ca 1/) l ADT Fgure D-6. Passng Lane Frequency Senstvty ofb/c Rato to Busness Trps A senstvty analyss s performed n order to show the effects of busness trp percentages on the beneft cost rato. f the ADT remans at a constant level of 600 and all other varables are constant, the busness-trp percentage ncreases from 10 percent to 50 percent n ncrements of 10 percent. The busness trps are more crtcal over the lesure trps because dollar value of busness trps per hour s hgher than that of lesure trps. Therefore, t s more sgnfcant to see the effects of a changng volume of vehcles that are usng the roadway for busness purposes. Fgure D-7 shows an upward trend n B/C rato wth ncreasng busness trp percentages n the traffc volume as delay savngs ncreases more rapdly. Project PageD- 1

95 ! ~ 1.5-0::: 1. (.) m % of Busness Trps Fgure D-7. Senstvty ofb/c Rato (ADT = 600) Passng Lane Length! 00 klometers vs. ADT Fgure D- shows passng lane lengths and the number of passng lanes wth respect to ADT values. n addton, the product of these two numbers gves the total length of passng lanes n 100 klometers. These values can be used n estmatng the constructon or strpng costs of the hghway to be upgraded. The number of passng lanes and the passng lane lengths ncrease wth ADT to meet the assumptons of preventng platoon formng on the hghway. Because of the queung theory's nature, the ncrease of total passng lane length has an exponental pattern. 6,000 Cl) - 5,000 c E ~ e,ooo...- en.:.:: c ; g,000 /)'"" cue en cu c - Cl) ~..J 1, ~ ADT Fgure D-. Passng Lane Lengths en c.00 1/).:.:: ; E... cuo C..o Cl) Cl) c 2.00 ~ ~ : 1.00 z Total Passng Lane Length/100km -+-Passng lane length(m) -Number of Passng Lane/1 00 km Project Page D-2

96 Passng Lane Length and Nwnber of Passng Lane for Dfferent ADT and Truck Percentage Values Table D- shows passng lane length for varous ADT and truck percentage combnatons. Ths table s obtaned from the case study performed on a rural two-way two-lane hghway at Dalhart n Dallam County (Northwest Texas). t s observed that passng lane lengths slghtly ncrease wth ncreasng ADT values. The overrdng factor s the level of ADT where passng lane lengths ncrease sgnfcantly. Table D-5 s a chart where one can see the nwnber of passng lanes per 100 klometers of roadway wth varyng ADT and truck percentage. Ths chart may be used as a reference before startng the upgradng process of the roadways. The percentage of trucks, rather than the ADT levels determne the nwnber of passng lanes. Project PageD-

97 Truck% AOT SO " 70 7< <0 7<0 7< < H < 7< 7 7 7< < GO < & oe GB oo ~ 1~ & ! !2 U o o &7 7 1' o aa5 7 &7 9 9 oo ls oeo oea oo oe1 9 oe us Ott \

98 Truck'' ADT U ~ e e e e 6 e e e 9 9 e e e e e e e ' e e e ' '

99 Conclusons and Recommendatons The followng conclusons and recommendatons can be made. Ths methodology can be used to justfy the Super Two Hghway at ADT levels less than 200 vehcles per day. A Super Two secton that requres a 60-centmeter wdenng s economcally feasble at ADT levels greater than 200 vehcles per day. f no wdenng s requred (.e. no shoulder on passng secton sde), then Super Two s economcally justfed at much lower ADT levels. Super Two B/C rato s nsenstve to truck percentage. Typcal queues wll contan less then four vehcles. Desgnng for the number of passng lanes per 100 klometers of road provdes hgh desgn flexblty wthout ntroducng sgnfcant error. f ADT levels exceed 200 vehcles per day, the passng lane desgn should be based on smulatons or other approprate urban desgn methods. A crtcal ssue that we should make comments on s the ADT range where the feasblty study s applcable. After a certan level of ADT, watng tmes of the passenger car n the queue become very large and then the values drop below zero. Ths drastc change n the values s caused by the characterstc of the Queung theory, the theory s vald for the arrval rates (q) less than servce rate (Q). However, the research model has ncreasng arrval rates wth ADT, and servce rate decreases as ADT values become larger because of the physcal lmtatons of the hghway. The pont where two values ntersect there s an nfnte queue, ths s obvously not an approprate stuaton for the rural hghways. The lmtng ADT value for the applcaton of the model s 200. For the upper traffc levels other technques lke smulaton programs may be used to model the real traffc condtons. Ths knd of methods, however, s not n the scope of that research. Project PageD- 6

100 Lst of Varables AC ACp1 ADT ANp (AlP, %, n) ARF B/C Bacc Btme Cp1 DF Average Cost of Accdents by Severty Annual Constructon Cost per 100 klometers of Roadway ($) Average Daly Traffc Average Number of Passengers per Passenger Vehcle The Captal Recovery Factor for an nterest Value of% and for n Years. Acceleraton of the Vehcle (meters/second 2 ) Average Reducton n Accdents by Severty for dfferent ADT values Beneft Cost Rato Annual Accdent Cost Savngs provded by a one-mle Lane Annual Tme Savng Benefts ($) Constructon Cost per 100 klometers of Roadway ($) Drectonal Dstrbuton Factor (major drecton) Dstance Traveled by the Passenger Car whle the Truck s n the Passng Lane Dstance Between Passng Lanes (klometers) Passng Tme Saved (seconds) E(m) E(m) + 1 E(w) F10o h Lepl LepllOO Lm Lp Lp1 Ntr Ntr!OO Average Queue Length Average Queue Length plus one Average Watng Tme n Queue (mnute/vehcle) Converson Factor to Convert per 100 klometers/vehcle Tme Gap between Two Consecutve Opposng Vehcles (seconds) Taper Length at the Dverge Secton of the Passng Lane Effectve Length of Passng Lane (meters) Effectve Length of Passng Lanes per 100 klometers (klometers) Taper Length at the Merge Secton of the Passng Lane Platoon Length (meters) Total Passng Lane Length (meters) Number of Trucks a Passenger Car would catch n One Hour at Vavg before Passng Lanes are Constructed Number of Trucks a Passenger would Catch per 100 klometers before Passng Lanes are Constructed Project PageD- 7

101 P(h~ t) Probablty of Avalable Passng Sght Dstance of 1500 feet durng Peak Hour Percentage of Busness Trps PHF Peak Hour Factor Number of Passng Lanes per 100 klometers Percentage of Lesure Trps A. q Q s Average Number of Cars n the Opposng Drecton (vehcles/second) Arrval Rate (vehcles/mnute) Servce Rate (vehcle/mnute) Truck Arrval Rate (vehcles/hour) Tme Savngs (mnute/vehcle/truck) Tme Savngs for 100 klometers of roadway for Passenger Cars Tme Value of Busness Trps ($/passenger/second) Tme Value of Lesure Trps ($/passenger/second) sv t tacc TB Operatng Speed after nstallng the Extra Lane n the Gven Subsegment (klometers/hour) Servce Volume (vehcles/hour) Tme Gap between Two Opposng Vehcles 1500 feet apart (seconds) Acceleraton Tme of the Vehcle (seconds) Total Beneft ($) Truck Factor at a gven Level of Servce Tme Requred to overtake the Truck by a Passenger Car (seconds) TP tpl UCcd UCpt v/c Vavg Vot w Truck Percentage Amount of Tme a Passenger Car spends n the Passng Lane (seconds) Constructon Cost of Converge and Dverge Sectons for each Passng Lane ($) Constructon Cost of one klometer of Roadway ($) Volume to Capacty Rato (a functon ofp(h~t)) Average Speed on the Road (klometers/hour) Average Speed of Passenger Car whle overtakng the Truck Normal Lane Wdth (meters) Adjustment for Lane Wdth and Lateral Clearance at a gven Level of Servce Project PageD-

102 APPENDX E: TRAFFC STUDY The goal of ths study s to evaluate the effect of a Super-Two secton n an exstng hghway. The traffc study was made on US 7 hghway. The porton of the hghway (for ths study) starts from Dalhart to a few mles north of Clayton close to the border of Texas and New Mexco. The selectons of the hghway sectons were made to get the best set of data that wll depct the Super-Two effect. Analyss based on these data was made to show the sgnfcance of a Super Two secton n reducng queung. Data Collecton Process Traffc data was accwnulated for two days, from 6 a.m. to 6 p.m. evenng, n two dfferent sectons of Hghway 7. Two teams were nvolved n collectng data and they were engaged on those two dfferent sectons alternately to mnmze the error. Each team conssted of two people to count traffc n both drectons. Both of them counted traffc sttng on both sdes of a partcular pont of the hghway. The dfferent aspects of traffc count focused were: Nwnber of vehcles Nwnber of queues Nwnber of vehcles n a queue and Nwnber oftrucks (or slow vehcles) Detaled data accwnulated s attached n Appendx F. Factors nvolved n Data Collecton n general a truck or any slow movng vehcle followed by at least one passenger car was consdered as the defnton of a queue. The maxmwn dstance between a fast and a slow movng vehcle to be consdered n a queue was taken as m (0ft). Speed of the vehcles nvolved n a queue wasn't consdered to be a decdng factor n queue formaton. n general any bg truck, a pckup or any passenger car drven slowly was consdered to be a slow movng vehcle. Traffc was counted usng human eye. Subjectve judgment used by the people collectng the data was an mportant factor n ths study. Synopss of Traffc Data The traffc data was collected on an hourly bass startng from 6 a.m. to 6 p.m. Data was collected on separate sheets for dfferent hours, drectons and dates. The followng s a synopss of the accwnulated data: Project Page E- 1

103 Reducton n Number of Queues Due To Passng Lanes The sketch of the area where traffc data s collected s shown below: Southbound "'"' (Raton) Clayton... ~------~~ ~ " :~~::::::::::::::::::::~:::~~:::::::::~~::~:~:... us.6... (-- )~ ? ~ ntersecton 7 & > Northbound (Dalhart) NM TX Clayton s a small town wth a populaton around The locatons of the data collecton ponts are at both sdes of Clayton. One s on the south drecton at the ntersecton of US 7 and 179, the other s on the opposte drecton and just before frst passng lane secton. The passng lanes are constructed on the northern part of Clayton towards Raton. On the frrst day of traffc count (07/17/9 Frday) on US 6 and towards Clayton, the number of queues n traffc after the frst passng lane s 16. Ths number has the effect of Super 2 n t because certan number of queues s elmnated because of the passng opportuntes provded by passng lane. At the opposte drecton towards Dalhart, there s no passng lanes provded, the road s only a two-way two-lane rural road and the effect of the Super 2 can no longer be seen. The number of queues then becomes 2. There s a 62 percent reducton n number of queues. The number of vehcles n the queue s 57 after frrst passng lane whereas the same number s 796 at the other data collecton pont. As a result there s a 55 percent reducton n the number of vehcles per queue. Another way to measure the effect of Super-Two s to count traffc n between two Super-Two sectons. n ths way we can measure the queues developed between passng sectons and the effect of the secton to elmnate queues. Ths s left for future study. Traffc Count and Desgn Method One result of the traffc study s to determne how good the real traffc condtons match the dealzed traffc condtons. The key terms n understandng and revealng the consstency between the real and computed traffc characterstcs are the parameters. The parameter that we can compare s the average number of vehcles on the Hghway. t should be noted that the traffc count s a very long and vgorous job that nvolved a substantal amount of personal judgement n determnng the queue formaton and number of vehcles per queue. n addton, to reflect the dynamc characterstcs of the traffc, the desgn methodology that s used for Super- Project Page E- 2

104 Two sectons was based on probablstc approach. Therefore, the parameters that are found at the end of the study are the average or expected numbers, havng the most probablty to occur. t s never possble to fmd the exact numbers n a traffc count study. Nor, s t possble to observe the same traffc condtons on another day. The desgn methodology utlzes ADT values only as a way to calculate the hourly peak volume, the desgn and the other computatons such as those that are nvolved n beneft/cost analyss are based on ths hourly traffc volume. Therefore, a comparson can be possble snce the traffc count also has the hourly traffc volumes. The maxmum traffc volume n the Summary sheet for both drectons s selected as the peak hour volume for comparson purpose. Snce the desgn method only computes the average number of vehcles per queue before the constructon of passng lanes, we should compare the traffc volumes on the drecton where there s no effect of Super-Two passng lanes. Because of the nherent lmtatons due to the Queung theory when the arrval and servce rates come closer, the desgn method s applcable up to a certan traffc levels. The traffc count shows that these traffc levels are exceeded for the data collected on Saturdays. As a result of ths ncrease n traffc n weekend, the comparson s done accordng to Frday's data collecton. The observed peak hour volume on 07/17/9 s 52, the average number of vehcles for the same hour s counted as.00 accordng to Traffc Count Summary Sheet (Table 1). The same parameter can be found from the desgn method as descrbed earler n the Case Study porton of the report. The peak hour corresponds to an ADT of 57 by usng a peak hour factor of As a result, the average number of vehcles per queue calculated n the case study s.15 vehcles per queue. The observed feld values and computed analytc values show sgnfcant consstency. t s also mportant to remember that for safety reasons, the number of average vehcles per queue s ncreased by one. Reducton n the number of vehcles n the queue s man objectve of the study. n order to understand the benefts of the Super-Two, t s also possble to examne how the Super-Two sectons affect the platoonng of passenger cars. For nstance, the tables that provde nformaton on the queung formaton wll be useful to determne the change n average number of vehcles n queues caused by passng lanes. On Frday, 07/17/9 the average number of vehcles n queues northbound Texas (Data Collecton pont s ntersecton at US 7 and FM 179) s 2.55 (Taken from Table 2). From ths pont the vehcles go towards north and they enter Clayton, a small town wth a populaton of2500. Ths small town has a man avenue of about 1 mle wth fourlanes, and a few traffc lghts. Ths man avenue serves as a passng lane, because the passenger cars wll have enough opportuntes to overtake the slow movng vehcles at traffc lghts, as well as on four-lane man avenue. Therefore, the town tself s consdered as passng lane secton. After leavng the town, the vehcles wll pass through the other data collecton pont n New Mexco. The average number of vehcles n queues s then observed 2.25 (Taken from Table ). The reducton rate n the average number of vehcles n queue s 12 percent. Project Page E-

105 On the other hand, the traffc condtons change durng weekends, the total nwnber of vehcles that travel ncrease sgnfcantly compared to weekdays. Therefore, n our traffc count study also, there s an ncrease n traffc due to weekend. The total nwnber of vehcles observed durng 12 hours s 761 for Frday and 556 for Saturday. Ths numbers are the average of the total traffc volwnes comng from the data collected n two dfferent collecton ponts n the same day as presented n Tables 1,,5, 7. The fact that there s a town between the two data collecton ponts s the major reason of the dfference between the two numbers. The ncrease n the traffc volume on Saturday compared to Frday s calculated as 2 percent. The ncrease n the traffc volumes on weekends has also effect n the reducton of the average number of vehcles n queues. On Saturday, from Table 6, t s notced that the average number of vehcles n queues gong towards North at the data collecton pont n Texas s.5. Whereas, the same parameter becomes 2.0 after vehcles cross Clayton where the effects of passng lane sectons occur. The reducton rate s 2 percent. n the other drecton, the followng numbers are observed. n New Mexco, the average nwnber of vehcles n queue s 1.1 (Taken from Table ) for the vehcles leavng the passng lane where ths number has drect effect of passng lane. The same parameter becomes.7 (Taken from Table 6). Then, the correspondng reducton rate n the average nwnber of vehcles n queues s 52 percent. As a result of comparng the reducton rates for Frday and Saturdays, the reducton rates are much hgher for Saturday than they are for Frday. We can conclude that the Super Two sectons are more effectve n the weekends when there s more traffc usng the roadway. More mportant pont to make s that Super Two Hghways are successful n reducng the queues and provdng a hgher level of servce for two-way two-lane rural hghways. Project Page E-

106 Table E-1. Traffc Count Summary Sheet on 07/17/9 Frday- ntersecton at US 7 & 179 (TX) Hourly Tme Number of Cars Number of Trucks Total Number of Vehcles Volume (2 Drectons) Northbound Southbound Northbound Southbound Northbound Southbound 6:00-7: :00-: :00-9: :00-10: :00-11 : :00-12: :00-1: :00-1: :00-15: :00-16: ~ 16:00-17: ~ :00-1: Total Table E-2. Summary of Queue Formaton on 07117/9 Frday- ntersecton at US 7 & 179 (TX) Number of Tme Number of Queues queues per Vehcles Queue Hour Northbound Southbound Average# of Vehcles n Queue Northbound Southbound Northbound Southbound 6:00-7: :00-: :00-9: :00-10: :00-11: :00-12: :00-1: :00-1: :00-15: :00-16: :00-17: :00-1: Total Project Page E- 5

107 Table E-. Traffc Count Summary Sheet on 07/17/9 Frday US 6 Before 1st Passng Lane (NM) Hourly Tme Number of Cars Number of Trucks Total Number of Vehcles Volume (2 Drectons) South bound North bound South bound North bound South bound North bound 6:00..7: :00..: :00..9: :00..10: :00-11: :00-12: :00-1: :0()..1: :00-15: ~ :00..16: :00-17: :00-1: Total Table E-. Summary of Queue Formaton on 07117/9 Frday -US 6 Before st Passng Lane (NM) Number of Average # of Vehcles n Tme Number of Queues queues per Vehcles Queue Queue Hour South bound North bound So h bound South bound North bound 6:00-7: :00-: :00-9: E 9:00..10: :00-11: :00-12: :00-1: :00-1: :00-15: :00-16: ~ Total Project Page E-6

108 Table E-5. Traffc Count Summary Sheet on 07/1/9 Saturday- ntersecton at US 7 & 179 (TX) Hourly Tme Number of Cars Number of Trucks Total Number of Vehcles Volume (2 Drectons) North bound South bound North bound South bound North bound South bo 6:00-7: :00-: :00-9: :00-10: :00-11 : :00-12: :00-1: :00-1: :00-15: :00-16: :00-17: :00-1: Total Table E-6. Summary of Queue Formaton on 07/1/9 Saturday- ntersecton at US 7 & 179 (TX) Number of Tme Number of Queues queues per Vehcles Queue Hour North bound South bound Average #of Vehcles n Queue North bound South bound North bound South bound 6:00-7: :00-: :00-9: :00-10: :00-11 : :00-12: :00-1:00 E :00-1: :00-15: :00-16: :00-17: :00-1: Total= Project Page E-7

109 Table E-7. Traffc Count Summary Sheet on 07/1/9 Saturday- US 6 Before 1st Passng Lane (NM) Hourly Tme Number of Cars Number of Trucks Total Number of Vehcles Volume (2 Drectons) Southbound Northbound Southbound Northbound Southbound Northbound 6:00-7: :00-: :00-9: :00-10: :00-11: :00-12: :00-1: :00-1: :00-15: :00-16: :00-17: :00-1~ Total Table E-. Summary of Queue Formaton on 07/1/9 Saturday US 6 Before 1st Passng Lane (NM) Number of Tme Number of Queues queues per Vehcles Queue Hour Average # of Vehcles n Queue Southbound Northbound Southbound Northbound Southbound Northbound 6:00-7: :00-: :00-9: :00-10: :00-11 : s 11:00-12: :00-1: :00-1: :00-15: :00-16: ~ 16:00-17: :00-1: Total Project PageE-