INTRO TRANSPORTATION ENG
INTRO TRANSPORTATION ENG CIVL 2030
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W 7 ciik7 2030 Introduction to 7 7 W rtation Engineering Satish Ukkusuri PhD Assistant Professor JEC 4032 Email ukkussmiedu Web httpwwwrpieduukkuss Today s Outline st About Me st About This Class st Class Objectives Why Transportation Engineering st GradingAdministrivia st Introduction st Finally About You Rensselaer I airman l l l clS El39f M 030 PhD in Transportation Systems from UT Austin 00 MS in Civil Engineering from Univ of Illinois ego BTech from IIT Madras 030 Research Interests Transportation Network Optimization for Planning and Operations Transportation Security Transportation Safety 220 Hobbies Music Mathematics and Reading Rensselaer E Eil t lm Course Syllabus and Overview Ransselasr I zzrxzzsac About the Teaching Assistants Cora Torres second year graduate student in transportation engineering MS st Robyn Marquis Undergraduate TA expected to complete BS in May 09 Renssdaer I airman 020 Understand critical elements of HighwayTransportation Engineering gt30Understand the basic definitions tools and methods to plan operate and design transportation systems 00 Provide the required skills to pass the FE and PE exam transportation component 030 Develop a critical insightful thought process 020 Skills to make big bucks in the transportation industry Rensselaer E Eil t lm Class Overview st Meeting Times MondayThursday Noon 150 st Office Hours Please try to use them Course HomePage htt wwwr iedu ukkuss classes CIVL2030 I will try to post lecture notes before class st Chapter dates are somewhat tentative Ransselaer I mean fir x is ll c 00 Informal 00 Learning is better if you participate Iwill call on you during class 0 30 Nonanalytical lectures using multimedia q oAnalytical lectures using overhead slides 030 No question is stupid Rensselaer I E t lm Philosophy of the class Theory without practice is an alienation Practice without theory is empirismquot B Pascal Rousselaer I E Zil t lm 0 Homework and Lab grades are a function of Z Correctness of the solution approach ZoQuality of the analysis 03 Clarity and neatness of written section 0 Late Assignments Will only be accepted under extraordinary circumstances 00 Exam grades are a function of Z Correctness Z Quality of analysis Rensselaer I E Ell t lm Class handouts available at course website httpwww mi du CIVL2030 of Other references ll iqlm39dl Garber and Hoel Traffic and V nqin 39ririnq Highway Engineering Highway Capacity Manual HCM Manual on Uniform Traffic Control Devices MUTCD A Policy on Geometric Design of lt Highways and Streets AASHTO Green Book Rensselaer maze Great Expectations 61 am expected to Teach Be at my office hours Give you feedback on how you are doing in a timely fashion You are expected to Learn Attend lectures and participate Do the problem sets Not be rude if possible sleeping cell phones using laptops for chatting email etc Rensselaer airman Chapter 1 Introduction Ransselasr I zzrxzzstc Outline Transportation and traffic engineering sthe profession in general Transportation and US history st Institutional system and professional organizations Transportation modes st Key transportation statistics Ransselaer airman n2nfyws m np 15 l l lgil magi ll lcl oonraffic The actual movement of vehicles or pedestrians on a facilityquot ogoTransportation engineering The application of technological and scientific principles to the planning functional design operation and management of facilities for any mode of transportationquot Rensselaer E Eil t lm o oTraffic engineering The phase of Transportation Engineering dealing with the planning geometric design and traffic operations of roads street and highways their networks terminals abutting lands and relationships with other modes of transportation 030 the science of measuring traffic and travel the study of the basic laws relating to traffic flow and generation and the application of knowledge to the professional practice of planning designing and operating traffic systems to achieve safe and efficient movement of persons and goodsquot Rensselaer E Eil t lm The profession of transportation engineering Specialties in transportation zsPlanning stesign Construction and maintenance straffic Operations Renssdaer airman 7Hill llquotlg Select projects for design and construction not necessary Planning involves 00 Forecast the impact of the project upon the system eg transportation environment 020 Setting up the specifications of the project 030 Determining benefits and costs 00 Interact with the decision makers to achieve final decisions Rensselaer E Eil t lm Planning 5 w m m m mm rm mm x New mmm mm mm LR nsselaer mime Involves the specification of all the features of the project so that it can be built q ogeometric design horizontal and vertical 00 pavement design ozodetermination of right of way drainage structures fencing etc taking into consideration the users of the system 020 part of the design process is the production of construction plans eg plans profiles details Rensselaer E Eil t lm Its objectives are related to using the facility in the most efficient way It involves 030the use of analytical models to determine the most efficient way to operate the facility some use of monitoring devices to determine actual conditions and level of service 030 the use of devices to implement control strategies Rensselaer E Eil t lm Traffin Operations amp Safely Issues Pines Boulevard at Flamingo Road Projett Develnpmem and Environmem Study R nsselaer 25mm Future Transportation Trends 00 More smart highways and driverless trains Rapid res mminuns m i mgmammanm slemcanqultkly detect and resvond to Incidents and Deep mm Inning smuotmy A mm closed cm mar mmwmm mu m Mm m A m um lane comm signals m quotw virizh a sage y bands Rensselaer I 2NtZe Importance of transportation Rousselaer zzmzsn Importance of transportation a necessary condition for economic growth though not sufficient b interacts with land use determining location and character of cities and regions c national security Rensselaer airman Forecasting is no easy task The road system as a matter of national importance is a thing of the past The system of internal water routes is a thing of the present in more senses than one A Hadley Instructor of Political Sciences Yale College In Railroad Transportation 1896 Renssdaer zzmzsri Components of the transportation system Renssdaer I 3323t m a f A x r C l or II uni u m r q i d 59 030 Physical facilities streets highways ports railroads etc 00 Fleets of vehicles trucks passenger cars vessels oZoOperating bases and facilities maintenance facilities offices o oOrganizations ozo Facility oriented those involved in planning design construction maintaining and operating fixed facilities Z Operating organizations carriers railroads airlines shipping companies private individuals ltgt3 Operating strategies routing scheduling traffic control mom or ncmzaxmc 333934 3 m m I v r r r N quot V r F are 477 was 5 3911 a aquot 7 3W x 4 fa 7 ll l l italAlli Mtgll l l 6 l ls1i lacl as transportation mode is a specific way to travel usually defined by either the physical system being used by the technology used or the organizational characteristics 3ltTransportation modes include 030 walking tail 1 by Dir 02 AUtO s ogging rm q v r Damian 60 Tra nst 12 39 in Famemxao O lt 39 1 O 0 1n a o 9 Water 7 g Lm ua ms 139 00 quot 39i g V xquot quot 19mm H O ver 00 Ra II 3535 Rensselaer I 2amp23ile Highways Z Over 625 million km 39 million miles 210 million vehicles travel more than 41 trillion vehkm 25 trillionmiles 0 Key issues traffic congestion state of the infrastructure urban sprawl 0 Urban Transit zIncludes buses and rail systems eg subways light rail Z New York City accounts for 13 of USA transit demand other American cities unable to effectively generate demand for transit 03 Key issues funding land use 0 090 Hensselaer I attest OAir ZGeneral aviation represents 62 billion vehkm 38 billion vehmi ZAir freight is less than 1 of total freight though it is high valued cargo ego Key issue airport expansion more high speed rail is needed 030 Rail ozoMuch of infrastructure removed in past 50 years Amtrak Passenger rail other railroad companies freight 020 Key issues Amtrakother railroads financials R nssdaer 323 Rc 030 Water ZIncludes ocean shipping and barge lines inland waterways 9242000 km 26000 mi of navigable waterways 00 Key issues Z The Jones Act requires that all vessels used for water domestic transportation be built in the US Since US ships are more expensive there are few entrants to coastal shipping About 250 million or more for one ship 00 Pipelines Z Mostly for transportation of liquid bulk cargoes R nssdaer E a l lm Think Why is private auto use high in the US as compared to other countries Percent The transportation system is hierarchical st For instance Interstate highways provide the backbone for long distance travel State highways provide connectivity at the State level Local streets provide access to local destinations Our job as transportation engineers is to put together these hierarchies Rensselaer airman v39uU a4iquot 39Rensselaer I 22325 mg Introductions Ransselasr I zzrxzzsac The institutional setting is also important Rousselaer zzmzsri US Department nsporta39tlon Federal Highway Administration National Highway Traffic Safety Ad ministration Urban Mass Transportation Ad ministration Federal Aviation Administration Federal Railroad Administration Maritime Administration Coast Guard Local level 20 State Department of Transportations eg NYSDOT Caltrans 00 Municipal Planning Organizations also known as Metropolitan Planning Organizations MPO s eg NYMTC 03 Special purpose agencies eg NYS Thruway Authority Port Authority of New York and New Jersey Rensselaer E z t lm 4 oZoTraffic congestion is one of the major issues facing New York City planners not only on a traffic engineering level but also on a much more macro scale eg politicians economists 00 Latest proposal from Mayor Michael Bloomberg is to Implement a congestion pricing plan o oWhile congestion pricing could solve many or all of the traffic engineering issues political social and economic concerns present major obstacles 03 Proposal Overview 8 for cars 21 for trucks to enter Manhattan below 86th Street Rensselaer I E Eil t lm quot My quotWM m I lt5 LU i ll lt800000 vehicles currently enter Manhattan below 60th Street on weekdays pricing scheme would lead to approximately a 10 reduction note Transportation Planners for MPO s andor consultants typically make these projections 00 Most transportation professionals recognize that seemingly small 10 reduction in vehicles would eliminate most congestion issues in New York City again part of the transportation planning process Rensselaer E Eil t lm 020 Political Issues oz Proposal requires state support in form of funding or state application for federal funding cooperation required from politicians at both the state and regional NYC level oz Request for state support occurred during the largest political squabble in New York State in decades Governor Spitzer vs Senator Bruno vs Aty Gen Cuomo o2 Democratic Governor and Republican Senate Majority Leader supported plan but were stymied by Democratic Assembly Leader who wanted to tradeoff support for other issues Rensselaer I E Ell t lm quot My quotWM m I lt5 LU i ll 020 Neighborhoods surrounding the congestion zonequot concerned that they will become parking lots for users of mass transit egoOne major goal of the plan is to reduce incidences of asthma especially in children ltgtfgtoOpponents feel that the plan helps the wealthy Manhattanites at the expense of the lowerclass Bronx neighborhoods Rensselaer E Eil t lm 020 Even a seemingly flawless engineering scheme is not always easily implemented 030 Politics and social issues are often mitigating factors that derail even the soundest of engineering plans ltgt3 Coordination between decisionmakers ie politicians government officials and plannersengineers is essential 030 Plannersengineers must be effective at conveying ideas to politicians Rensselaer I E Eil t lm Where to get more information 4 Next Time Chapter 1 Highway Engineering and Traffic Analysis Introduction Rensselaer I were 76PM S IGHT DST chE i3 SLOPE op THE cable 116090 3 Ito 60 s GNEQOBO Introduction to rtation Engineering Satish Ukkusuri PhD Assistant Professor JEC 4032 Email ukkussmiedu Web httpwwwrpieduukkuss Outline Introduction Tractive Effort and Resistance Aerodynamic Resistance Rolling Resistance Grade Resistance Available Tractive Effort 2 Maximum Tractive Effort 2 Engine Generate Tractive Effort Vehicle Acceleration Fuel Efficiency Rousselaer zzmzsrm Outline st Principles of Braking Braking Forces Braking Force Ratio and Efficiency Antilock Braking Systems Theoretical Stopping Distance Practical Stopping Distance Distance Traveled during Driver PerceptionReaction Rousselaer zzmzsrm Introduction stighway design and traffic analysis is based on performance of road vehicles st Examples Length of freeway Highway grades Stopping sight distance Passing sight distance Vehicles performance is also utilize for design of traffic control devices and the timing of traffic signal control systems Rensselaer airman u x l 10 7 1 r H z w L Roads with vertical or horizontal curves have more strict speed limits While straight roads have more freedom of movement therefore having higher speed limits Rensselaer I 252ampE Ra Ii 39lf ll oonhe objective of this chapter is to explain basic principles of vehicle performance egoWhy study vehicle performance 92 Provides insight for highway design and traffic operations so Provides a basis to create more advanced vehicle technologies ozoWhy is this important 2Advances in vehicle technology requires updates based on highway design guidelines Z Better understanding of vehicle performance Rensselaer E Eil t lm Tractive Effort and Resistance st This are the two primary forces when determining the straight line performance of vehicles st Definitions Tractive Effort force available at roadway surface which is able to create work on a vehicle Units Newtons N Resistance force that impedes vehicle motion Units Newtons N Renssdaer armrest 02 There are 3 major sources of vehicle resistance gt20 Aerodynamic Resistance 0 Rolling Resistance 00 Gravitational Resistance 8 Chapter 2 Road Vehicle Performance Page 8 ofclass book Figure 21 Fortes acting on a road vehicle iRensselaer 25mm 020 Figure 21 Forces acting on a road vehicle oioRa aerodynamic resistance in lb N s rolling resistance of the front tires in lb N 2 rolling resistance of the rear tires in lb N 633 available tractive effort of the front tires in lb N 2F available tractive effort of the rear tires in lb N 4 W total vehicle weight in lb N 4 8g angle of the grade in degrees z m vehicle mass in slugs kg and oza acceleration in fts2 msZ Ransselaer I E Ell t lm lt oAdding forces at longitudinal axis F Ff F and R Rf R 21 FmaRaRrRg 22 Rg grade resistance W sin 89 8 Chapter 2 Road Vehicle Performance Figure 2 Fumes acting on a road vehicle Rensselaer I 22mm Future of Tractive Effort Technologies httpWWWyoutubecomwatchveT8nNFg 234W 1 Renssdaer 23mm 020 Can have significant impact on vehicle performance 020 Sources 2 Turbulence around the body 85 Z Air friction 12 Z Air ow through components 3 030 Basic Formula Rensselaer E Eii t im 0 Basic Formula Aerodynamic Resistance Ra aerodynamic resistance in lb N sop air density in slugsft3 kgm3 oiocp coefficient of drag and is unit less Z A frontal area of the vehicle projected area of the vehicle in the direction of travel in ft2 m2 and 0EN speed of the vehicle in fts ms For more accurate results V can be used as the speed of the vehicle relative to the prevailing wind speed Rensselaer E Ell t lm 10 Chapter 2 Road Vehicle Perfoxmance Table 2l Typical Values ofAir Dans under Speci ed Atmospheric Condiliuns Altitude Temperature 39F O 590 150 5000 1500 39 l 10000 3000 Tables 21 and 22 page 10 of Chapter 2 Air density slugsfr J kgm3 78 12256 0002045 10567 0001755 09096 I e 22 Ranues39 of Drag C ml39 ci ms for Typical anl Vclmlcs Drug coef cient CD Automobile us TraderTrailer Motorcycle SCHOOL OF ENGINEERING Rensselaer Aerodynamic Resistance Table 23 Drag Coef cients of Selected Automobiles Vehicle Drag coef cient C D 1967 Chevrolet Corvette 1967 Volkswagen Beetle 1977 Triumph TR7 1977 Jaguar XJS 1987 Acura Inlegra 993 Pm Ranger lruck I907 Lexus L540 1997 ln nii 045 2000 l lonrlu nsiglu hth id 2002 Acuru ISX 2002 Lexus 13431 2003 Dodge Carinm1 minivan 2003 Ford Explorer SUV 003 Dodge Ram truck 2004 Mercedes Benz C240 Rensselaer rzrzzsn Drag Coefficient 00 Recent vehicles have lower coefficients 00 Large personal vehicles have higher coefficients Figure 22 page 11 Even minor factors as opening a window can have a signi cant effect on drag coefficients and therefore affecting total aerodynamic resistance Rensselaer I 223th jgiy39wearr uig Power required to overcome air resistance US Customary Metric Ransselaer earnest Aerodynamic Resistance Where zshpka horsepower required to overcome aerodynamic resistance 1 horsepower equals 550 ftIbs st Pkg power required to overcome aerodynamic resistance in Nms watts and Other terms as defined previously Rousselaer airman 030 Resistance generated from vehicle s mechanical components and pneumatics as they generate friction by interacting with road surface 030 Sources 2 Tire deformation 90 Z Pavement penetration 4 o Friction other sources 6 Factors influencing sources Z Tire inflation temperature speed I SCHOOL or ENGINEERING 020 It can be approximated as the product of friction terms and the weight of the vehicle acting as a normal force on the road surface US Customary fr 0011 L 147 Metric Where ozof coefficient of rolling resistance and has no units and Z V vehicle speed in fts ms 361185613610 ENGINEERING For most highway applications the angle of grades eg is very small the assumption of cos eg 1 can be used Therefore R f W 26 0 US Customary Z Metric 24 PR frl I Rensselaer I E Eil t lm Where 00 hpRr horsepower required to overcome rolling resistance 1 horsepower equals 550 ft Ibs 00 PM power required to overcome rolling resistance in Nms watts and gt30 W tota vehicle weight in lb N 8 Chapter 2 Road Vehicle Performance Figure 21 Fumes acting on a road vehicle Rensselaer 221am Example 21 A 2500lb 111kN car is driven at sea level p 0002378 slugsft3 or 12256 kgm3 on a level paved surface The car has Cd 038 and 20 ft2 186 ml of frontal area and It is known that a maximum speed 50 hp 373 kW is being expended to overcome rolling and aerodynamic resistance Determine the car s maximum speed Rensselaer I 2321231 Grade Resistance st Gravitational force acting on a vehicle RgWsineg 28 st Highway grades are usually very small so sin 89 tan 89 RgWtanegWG 29 st Grades are expressed as percentages G 005 9g 286 0 Not to scale Rensselaer zzmzsri 14 l in 1 w 9 4 030 Force available to overcome resistance and accelerate a vehicle There are two ways to achieve this gtZ Vehicle s engine ozoMaximum value that will be a function of the vehicle s weight distribution and the characteristics of the road surface 11quot quot39 blah I 39 v i i Sign indicating that vehicle should hit breaks since it is approaching a downhill WWWZirdinccom I SCHOOL or ENGINEERING 1 Mil l l39TEilCClVT if No matter how much force a vehicle s engine produces there is a point beyond where this force does not overcome resistance or accelerates the vehicle Figure 23 Vehicle forces and momenbgenerating di c Ransselaer I signers Wlaxlrl ltil39n Tr 020 Figure 23 Vehicle forces and momentgenerating distances F available tractive effort of the front tires in lb N ZF available tractive effort of the rear tires in lb N Z W total vehicle weight in lb N Z ll weight of the vehicle on the front axle in lb N 20 W weight of the vehicle on the rear axle in lb N Z 89 angle of the grade in degrees o2m vehicle mass in slugs kg ozoa rate of acceleration in fts2 msZ 0M length of wheelbase Ransselaer arrests Maximum Tractive Effort 4 Cont Figure 23 7 height of the center of gravity above the roadway surface distance from the front axle to the center of gravity and distance from the rear axle to the center of gravity Adding moments to determine maximum tractive effort WRahWlfcosegmahiWhsineg W h sin 69 is positive for upward slopes and negative for downward slopes igt irrgtirruurn Trz 00 Rearranging terms and using basic physics the maximum tractive effort will be the normal force multiplied by the coefficient of road adhesion 22 For Rear wheel drive max u coefficient of road adhesion Rensselaer E Eil t lm J 39 1 30 L g i a p 030 Typical Values of Coefficients of Road Adhesion 28 Chapter 2 Road Vehicle Performance Table 24 Typical Values ofCeef eiems of In some instances the Road Adhesion c0eff1c1ent of roads adhesion values can exceed the value of 1 Coef cient of mad adhesion Pavement mien of road adhesion values the and 0f Section 27 SCHOOL OF ENGWEERING Example 23 A 2500lb 111 kN car is designed with a 120inch 3048m wheelbase The center of gravity is located 22 inches 559 mm above the pavement and 40 inches 112 m behind the front axle If the coefficient of road adhesion is 06 what is the maximum tractive effort that can be developed if the car is a frontwheel drive and b rear wheel drive Rensselaer I 2321231 or no F39li39i ort 030 The two most ommonly used measures for engine output are 20 Torque work generated by the engine ftlb or Nm 2 Power rate of engine work expressed in horsepower hp or kW Power is related to torque by the following equations 216 Rensselaer E Eil t lm 229Where 06 h enginegenerated horsepower 1 horsepower equals 550 ftlbs 00 P6 enginegenerated power in kW osze engine torque in ftlb Nm and ozone engine speed in revolutions per second the speed of the crankshaft Figure 24 Typical torquepower 4 curves for a gasoline powered automobile engine Rensselaer I 2amp Es i trsicz Fffort 00 Gear reduction provides the mechanical advantage necessary for acceptable vehicle acceleration 030 There are two factors that determine the amount of tractive effort reaching the drive wheels ZMechanical efficiency of the driveline nd 075 to 095 2 Overall gear reduction ratio 217 Engine Generated Tractive Effort Rensselaer I Zil hc Engine Generated Tractive Effort Where Fe enginegenerated tractive effort reaching the driving wheels in lb N r radius of the drive wheels in ft m Me engine torque in ftlb Nm Eo overall gear reduction ratio and m mechanical efficiency of the driveline075 to 095 Rousselaer 2mm 020 Relationship between vehicle speed and engine speed is 2mmg 1 i n 0 0 Where 2 V vehicle speed in fts ms ozo ne crankshaft revolutions per second do i slippage of the driveline generally taken as 2 to 5 i 002 to 005 for passenger cars and z Other terms as defined previously Rousselaer attest l raljir lo 521 ic3rrlol Trag39tiwitj Fifior39t Example 24 It is known that an experimental engine has a torque curve of the form Me ane bneZ where Me is engine torque in ftlb n8 is engine speed in revolutions per second and aand bare unknown parameters If the engine develops a maximum torque of 92 ftlb 12475 Nm at 3200 revmin what is the engine s maximum power Rensselaer E Eil t lm u f ant oonhere is a relationship between traction resistance and forces available to accelerate 00 Basic equation F Z R 7mm 219 o refers to force available to accelerate z is the mass factor rotational inertia Z This is approximated as 7 10400025 QioThis is an adaptation of equation 22 taking note that the vehicle s rotating parts provide an inertia which must be overcome for acceleration Rensselaer I E Eil t lm oonhe force required to accelerate is Fug F ZR ozoIf Em 0 the vehicle is already at maximum speed ZIf Em gt 0 the vehicle is traveling at less than maximum oonhe two measures of vehicle acceleration that we study in depth are time and distance to accelerate Z For the case of the equation can differential form as Rensselaer I E Eil t lm ltgt oAs Fnet is a function of vehicle speed Fm f39V ltgt3ltgtThis relationship is used to integrate Fnet 221 Rensselaer I zznzsn Example 25 A car is traveling at 10 mih 161 kmh on a roadway covered with hardpacked snow coefficient of road adhesion of 02 The car has Cd 03 Af 20 ft2 186 m2 and W 3000 lb 1334kN The wheelbase is 120 inches 3048 m and the center of gravity is 20 inches 508 mm above the roadway surface and 50 inches 127 m behind the front axel The air density is 0002045 slugsft3 1054 kgm3 The car s engine is producing 95 ft lb 1288 Nm of torque and is in a gear that gives an overall gear reduction ratio of 45 to 1 the wheel radius is 14 inches 356 mm and the mechanical efficiency of the driveline is 80 If the driver needs to accelerate quickly to avoid an accident what would the acceleration be if the car is a frontwheel drive and b rear wheel drive Rensselaer I 232113 020 Several factors influence a vehicle s fuel efficiency ZEngine design 2Driveline slippage ZDriveline efficiency Z Aerodynamics 2 Frontal area Z Weight 2Tire design httpwww Lhcmldxum c omuploads lclicf cicmy gf Rensselaer I 23232236 Principles of Braking t In order to understand braking principles first we consider the force and momentgenerating diagram Hml1Fomes 39 vehicle l i Imm mammamm nsselaer I ESEf ESic 020 Figure 27 Forces acting on a vehicle during braking with driveline resistance ignored ozoRa aerodynamic resistance in lb N Zle rolling resistance of the front tires in lb N Zerr rolling resistance of the rear tires in lb N o be braking force on the front tires in lb N ozoFbr braking force on the rear tires in lb N ZW total vehicle weight in lb N Wf weight of the vehicle on the front axle in lb N Z Wr weight of the vehicle on the rear axle in lb N Ransselaer E Ell t lm Principles of Braking st Figure 27 continued m vehicle mass in slugs kg a acceleration in fts2 msZ L length of wheelbase h height of the center of gravity from the road surface lf distance from the front axle to the center of gravity lr distance from the rear axle to the center of gravity eg angle of the grade in degrees Ranssdaer I zzmzsn ozoWhen a vehicle brakes there is a load transfer from the rear to the front axle ogoThe normal loads experienced by the front and rear axles can be expressed by summing the moments about contact points between the tires and road Front W M 11nm RQ rW sin a W W 11nm RQ rW sin a Rensselaer I E Eil t lm oonhe normal force equations can be rewritten by summing the forces along the vehicle s longitudinal Fl frW 2 ma Ra iW Sin oz From equation 26 we know that ZWe also have the relationship of F Fl oXoThe above equations are substituted in 223 224 226 g Front Wf W1r 1Fb f w 9 Rear WT Wlf hm f W 227 Rensselaer attest oonhe maximum vehicle braking force Fb max is related to the vehicle s weight and coefficient of road adhesion u 4quot Front Ezfman 1Wf and by substitution J quot Lu T 6 Rear and by substitution z z1 f L mu L f H 1 1le fu Rensselaer zzmzsn ltgtiEgtThe tires should be at a point of impending slide in order for maximum braking forces to develop Braking forces will decline when the wheels are locked which results from reduced road adhesion The extent of this reduction depends on the pavement and weather conditions Table 24 MM TypicaanluesofCoc ciemsof RoadAdhesion Coe icientofmadadlesion E hmmmmmtofmndadhesimvdm canexceed 10Seediacmionudleendof8ec on23 S39owoe S G 11H 13 lad H K Blown m l a I SI I 139 39 C I rm lgr AglRB 39 SCHOOL OF ml 91 3056 1981 I ENGiNEERING oonhe maximum attainable vehicle deceleration from the vehicle s braking system is equal to ug where u is the coefficient of road adhesion and g is the gravitational constant oZoVehicle braking systems must distribute the braking forces between the front and rear brakes which is typically done through hydraulic pressures lt oThe frontrear proportioning of these braking forces will be optimal when it is the same proportion as the ratio of maximum braking forces on the front and rear axles SCHOOL or ENGINEERING 020 Maximum braking forces will be developed when the brake force ratio is BFR r Ihzfl Ir11tfl oie39BFRfr max the brake force ratio allocated by the vehicle s braking system that results in maximum optimal braking forces oonhe percentages of braking force that should be allocated to the axles are as follows ZFront 231 ozo Rear 232 Rensselaer E Eil t lm f ril icip Example 26 A car has a wheelbase of 100 inches 254 m and a center of gravity that is 40 inches 1016 m behind the front axle at a height of 24 inches 609 mm If the car is traveling at 80 mih 1287 kmh on a road with poor pavement that is wet determine the percentages of braking force that should be allocated to the front and rear brakes to ensure that maximum braking forces are developed Rensselaer I 2321231 oonhe optimal brake force proportions will be altered with the addition of passengers and cargo as there is now additional loading This shifts the weight distribution and height of the center of gravity oZoTrue optimal brake force proportioning is rarely achieved in nonantilock braking systems so a braking efficiency term is defined m 2 ozonb braking efficiency Zgmax maximum deceleration in g units Zu coefficient of road adhesion a O max u SCHOOL or ENGINEERING Figure 28 highlights the effects of various vehicle loadings on the distribution of braking forces Liam Truck Pnssenger Cll Loaded Loaded 3200 lb 142 km front 2850 lb 127 km from 6800 lb 302 km rear 3015 lb 134 kN rear Mottled Un 3500 lb 156 RN fmnt 2275 lb 101 RN mm 2500 lb 111 W may 2080 lb 93 W mr Road adhesion coefficient 085 Road adhesion coefficient 085 3 E 5 E 2 20 40 60 80 100 39 20 40 60 80 100 Front braking tometotal braking force Front braking forcetotal braking force a b Hunts E ectofbtakefaoepropm oningmthehakingpafamofa gmmkanda passenger car Wbypemimiono heSociayofAmom ve gim mDJ Diem316 lhnley Lidn39lhld rewoan IMMEe sm n ngPufumquotSAE m m Vol 83 m74ll371914 lRenss elaor I 020 In order to prevent the wheels from locking during a braking application many cars are now equipped with antilock braking systems ABS Z ABS prevents the coefficient of road adhesion from dropping to slide values ZThey also have the potential to raise braking efficiency to 100 ozoABS vs nonABS Rensselaer E Eil t lm oonhe relationship between the stopping distance braking force vehicle mass and vehicle speed is Zvb mass factor accounting for moments of inertia during braking which is 104 for automobiles q oWe must integrate to find the stopping distance Rensselaer E Eil t lm 020 By substituting resistances in equation 235 236 b E Ra f W W sin 49 V1 initial vehicle speed in fts ms ozovz nal vehicle speed in fts ms 2frW rolling resistance Wsineg grade resistance for uphill for downhill Rensselaer E Ell t lm 020 By making some assumptions and integrating equation 236 we get S 747w 1n uW Kai12 1 er r W sin 49 2 gKa uW 19V2 f V r W sin 49 I Z We assume that the effect of speed on frl is constant and can be approximated using the average velocity o2 We also let m Wg and Fb pW ZThe equation also utilizes the simplification K zgcpAquot Rensselaer E Ell t lm 0 50 If braking efficienc is considered the actual braking force is m 241 oXoTherefore the theoretical stopping distance is S LWIII 1 ZgKa 030 Equation 235 can also be integrated to give an alternative equation for theoretical stopping distance S 2glll fr isin Z Note aerodynamic resistance is ignored Rensselaer E Eil t lm f ril icip Example 27 A new experimental 2500lb 1112 kN car with Cd 025 and Af 18 ft2 167 ml is traveling at 90 mih 1448 Kmh down a 10 grade The coefficient of road adhesion is 07 and the air density is 00024 slugsft3 124 kgm3 The car has an advanced antilock braking system that gives it a braking efficiency of 100 Determine the theoretical minimum stopping distance for the case where aerodynamic resistance is considered and the case where aerodynamic resistance is ignored Rensselaer I 2321231 oThe previous discussion on vehicle theoretical stopping distances did not take into account the driver s reaction time among other factors olt ltgtThe basic physics equation of serves as the basis for practical stopping distance ZThe equation is rearranged to f 3 3 245 then the equation becomes 1 VI2 246 7 2d AASHTO recommends a deceleration rate a of 112 fts2 32 msZ Rensselaer attest modified to account for the effect Vf 247 00 By assuming that the vehicle comes to a complete stop that sin 69 tan 69 G for small grades and that vb and frl can be ignored we have 5 V1 248 Rensselaer E Eii t im 020 In order to ensure that there is sufficient sight distance for a driver to safely stop the distance traveled during driver perce tion reaction must be taken into consideration h 249 Z V1 initial vehicle speed in fts ms Zt time required to perceivereact to the need to stop oXoThe perceptionreaction time is influenced by several factors such as driver s age and emotional state so AASHTO recommends a conservative estimate of 25 seconds for calculation purposes Rensselaer attest ozoWe can now see that the overall required stopping distance is a combination of theoretical and practical braking distances as well as the distance traveled during perceptionreaction oZoThis is summed up as 250 Zds total stopping distance in ft m Zd distance traveled during braking in ft m viodr distance traveled during perceptionreaction in ft m SCHOOL or ENGINEERING f ril icip Example 210 Two drivers each have a reaction time of 25 seconds One is obeying a 55mih 885kmh speed limit and the other is traveling illegally at 70 mih 1126 kmh How much distance will each of the drivers cover while perceivingreacting to the need to stop and what will the total stopping distance be for each driver using practical stopping distance assuming G 25 Rensselaer I 2321231 a l Lgauem Zn New Ewib gem WWW Note Titl a Q i b 39 a4 O jec39rVE s n c1541 our v5 2 35111 R f giGE EEQULLMEE J21 Cam2a 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Equot V 0 VI VL I VI A Ni quot i n 39M v 4V Vb 139 39 v 1 VI J M 7 Va A 2quotquot L Y 9 f v u gt l m J a vm v F r W 14 Va L I I 2 I I U FM 1 v ILE j QLLL 2 U kquot 7 JV V L V39 V v V V I 3 I Q an KW 1 7 y 6 a womabnoluml a 4 I on K3 9 o ul14l393 mIPZJQrVgtI q A 2amp1 as N 5 quotI 5 3 45 3 Cr 60 0 13 nc I r A 225 n A e 5 A1 f Aeg 9mm c Q IHTM CE I o 10 3 3 K gm L quot 39 t 32 52 l L R39C r nuce i D IN Evy39 1 7L 39 to x 5amp8 EG 2 360ro M 4 A A Ju H 9 L J 39v D D 5 1 Edamg a v MATGD 7mm 7 3 393 24 51 K 03 x 9 amp 1 rdm Nm V I f rn M mu 3535 u t wmm 5 2 r cc 9 3 V Swirmm CV3 II 0330 cN XQoS 06 okaooQM Xu 3 china ll F AhQ rLUL l FinL 9 Z C3foo X56 139 JGRT 39l l 39 39 I we on I all 3 49776 I min1192 79219 I 139 I v 1 qquotI lt9 c O Nm al Nth l TS mesa r wva u N l 50 4 o wkm oo 639 quot ad s 2 51641ch M 69614 I V quot PU quot J e as gt08 39 r n e 4 gas 4quot AM d v c l In b39v W P Q 1 Qb e U30 1 I39 It WAR 39139 l 1 1 r r 392 A 1 A M kc I u ExAM l Kodac VUP v I U A A I mr Hw III35f A IGXT 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AWAUmJ E0 KA 39e 7Q AT 6 12 74M Dem 7 4mc A LUMES g 0 L05 2 NUMge 0t Lma CAFA IT7 INPlov u vors O F TtAFFIc NO 0 Adina I s Vole w DDHV IKIBXDYAADT 3 DDHVa 635 fo 471M Nfovxff oaoxo2x xi 059 774312 61 PHD 92 pHFKKlX fn39foa OSUXZX 1 Lose 71mm 6D 0 PM I291 Losc 010ka x 7l ZqFPIc aNTZoL AND ANAL ysu J 7 Introduction to rtation Engineering Satish Ukkusuri PhD Assistant Professor JEC 4032 Email ukkussmiedu Web httpwwwrpieduukkuss Today s Outline st Introduction st Traffic Stream Parameters 2 Traffic Flow Speed Density Basic Traffic Stream Models 2 Speed density model 2 Flow Density Model 2 Speed Flow Model Models of Traffic Flow 2 Poisson Model 2 Limitations of the Poisson Model Rensselaer I airman Today s Outline szueuing Theory and Traffic Flow Analysis 2 Dimensions of Queuing Models 2 DD1 Queuing 2 MD1 Queuing 2 MM1 Queuing 2 MMN Queuing straffic Analysis at Highway Bottlenecks R nsselaer airman Ii 39lf ll ltgt 0Analysis of vehicle traffic provides the basis for measuring the operating performance of highways ogoAspects that are addressed on traffic analysis ZVehicles per unit of time 2 Vehicle type Z Vehicle speed ZVariation of traffic flow 020 In light of this analysis of traffic flow and queuing provides groundwork for quantifying measures of performance Rensselaer E Eil t lm 030 Two types Uninterrupted Flow traffic stream that operates free from the influence of such traffic control devices as signals and stop signs ZInterrupted Flow traf c streams that operate under the in uence of signals and stop signs 020 Environmental conditions can also affect the flow of traffic y 397 I gquot 4 17 rat I Night Driving Rensselaer l u 2quot t u Um 4 0 50 Traffic Flow 030 Where q traffic flow in vehicles per unit time n number of vehicles passing some designated roadway point during time 1 duration of time interval Units are Vehh even though the analysis flow rate is usually based on the peak 15 minute flow Rensselaer E Eil t lm 03 Headway time between the passage of the front bumpers of successive vehicles at some highway point 020 Time headways are related to t as de ned in Eq 51 by 020 Where t duration of time interval 7 time headway of the ith vehicle the time that has transpired between the arrival of vehicle i and H n number of measured vehicle time headways at some designated roadway point Rensselaer E Eil t lm iiaffic i iciw TEFiiz39vci 39 Substituting Eq 52 into Eq 51 gives 1 or 6 53 and 54 030Where is the average time headway in unit time per vehicle Rensselaer I attest lt Average traffic speed is defined in two waysquot Z Time mean speed lt 0Where timemean speed in unit distance per unit time u spot speed the speed of the vehicle at the designated point on the highway of the ith vehicle n number of measured vehicle spot speeds Rensselaer I airman 020Where space mean speed in unit distance per unit time length of roadway used for travel time measurements of vehicles 1 time necessary for vehicle i to travel a roadway section of length l n number of measured vehicle travel m es Rousselaer I E a l lm Example ogoYou own two cars they are both driven an equal distance and one gets 20 mpg the other 50mpg Is the average mpg 35 50202 Z Nosay they are each driven 100 miles The 50mpg car consumes 2 gallons the 20mpg car 5 gallons This gives 7 gallons for 200 miles or 2875mpg not 35 mpg average Illpg Rensselaer mesa 020 Traffic Density 510 oWhere k traffic density in vehicles per unit distance n number of vehicles occupying some length of roadway at some specified time length of roadway 00 Density can also be expressed as the inverse of the average spacing between vehicles Rensselaer E Eil t lm oonhe simple identity provides the basic relationship among traffic flow speed spacemean speed and density is 514 q uk oXoWhere q flow typically in units of vehicles per hour vehh speed space mean speed typically in units of mih kmh density typically in units of vehmi veh km Rgnsselaer mile Basic Traffic Stream Models st Models that provide understanding of the interaction of the individual macroscopic measures in order to fully analyze the operational performance of traffic stream Renssdaer nurture Speed Density Model Rensselaer I zzrxzzsac r n e 4 gas 4quot AM d v c l In b39v W P Q 1 Qb e U30 1 I39 It WAR 39139 l 1 1 r r 392 A 1 A M kc I u ExAM l Kodac VUP v I U A A I mr Hw III35f A IGXT I lquotNDAT G WARNva MHLAZE Snobv m ll N I life Park Came do rm I 7 1 gt Lbl Carrwaxqal r25 314 f EL gt 2 E udIIr ahIV Avantunmuk I7 I gts55 L S 330 v 358 7 15 a TELer anmgzsmm SA UH 11 TNTEU 961039 m h w Harm m 0 PTIM Hz 5 I mAL I MM 635 lt I VM W v quot 7 739 Awm1m3QE L dencg 39 r 07A 1 U KLA39T IL D TK1T gt m A elv b CVMLW 3p Hutu 114 m Aw 11 M ml U H U uw 7 r I QYIschm um H CM C 24300 V 1 1quot d2 0 U A 8 M W A Ava Mol aim43 avrrwi quot g I 01 MUM 7 A 39 39 quot Ihw h K y i hie all f m 1mquot L 1045 quot39 n I Law 41quot 173 5L4Lwn 39 x W I v bx A1quot 5 I 391 gt rm V Uuumm 10 w gammv wl Au 1 quotrquot f I I I 4 J WM39V 0 Que WWW 39 Z n W494 lN 3 V A r 4 gt4 1 r 0001 W39JH c3vl o um N 3 E 4 wJo n m m O G 39 O J L r 9 5 3 09 6 5396 3 JJ 83 lt 5 3 K I om x 03 I la Q r a l b E K 7 u C u Smo l lt quot 0 N v a 0 370 2L aw L an awaHl IJ 39 I v Lane 377 U Q gtD Sm 230 N 39 19 rvwacim 7 7 222 ltm m 33 so Tl s LI Rh F Jc5lt 1 AW M33 5 J J 7 DEC 9 7513 5234 I gt s u vco F lhl 4F3Yenz A I v m YJR A L 1 7 A as 7 1953 L 39 7 A DQIIC39Y L E15 017741157 U L o o 39T YSB I 6 L OIS8g1 tlmulg A 39L 1 00iiS o YEQ M1043 WY ov f H L Squot WE2 3 lawf Can Rec NxAR rWFZSx 5375 75 472 VF gt Vw Huoranmv L m atv 9l a r l Jim mEEEk f wgm l W A x J 4 H 3 Exam I f 4 LIV v z c3 gt L T 6 Piakg OPQ M7700 Pgmgi PHA39JEZ PHA39JL v 4 lt 591 Maw LOST T39ME Mo PLWEJ 7 mom Lew Tum PWE quot VOLUME Dewy Qupum v gt I QOOIQ 341on J qco ql gt cum qlD 39 Pam mi 00005 1 3M1 ago minim quot39 3 1 WMJQ Y 393me WILL 97 do 1 7 de VD Ianmamly 39wa39e y LwaamV fo0N 63353 9HML alm1vwd 9 ng 1H3 P39 Jr W U V335 700 20 27550 Wb uhg l l gt Wquot quot i r ggn 3tsooo J k 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