DOCSLIB.ORG

Study of Heavy Commercial Vehicle Crash Reconstruction

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Study of Heavy Commercial Vehicle Crash Reconstruction STUDY OF HEAVY COMMERCIAL VEHICLE CRASH RECONSTRUCTION WITH COMPARATIVE ANALYSIS OF PASSENGER VEHICLES A Thesis Presented to the faculty of the Department of Mechanical Engineering California State University, Sacramento Submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in Mechanical Engineering by Dhanashri Patel SPRING 2020 © 2020 Dhanashri Patel ALL RIGHTS RESERVED ii STUDY OF HEAVY COMMERCIAL VEHICLE CRASH RECONSTRUCTION WITH COMPARATIVE ANALYSIS OF PASSENGER VEHICLES A Thesis by Dhanashri Patel Approved by: __________________________________, Committee Chair Jose Granda __________________________________, Second Reader Troy D. Topping ____________________________ Date iii Student: Dhanashri Patel I certify that this student has met the requirements for format contained in the University format manual, and that this thesis is suitable for electronic submission to the Library, and credit is to be awarded for the thesis. _________________, Graduate Coordinator ___________________ Troy D. Topping Date Department of Mechanical Engineering iv Abstract of STUDY OF HEAVY COMMERCIAL VEHICLE CRASH RECONSTRUCTION WITH COMPARATIVE ANALYSIS OF PASSENGER VEHICLES by Dhanashri Patel Commercial motor vehicles crash investigation and reconstruction technology is a great interest to vehicle design engineers. It is of interest to identify the cause behind heavy vehicle crashes for safer designs. Regulatory agencies like the Commercial Vehicle Safety Alliance (CVSA) is concerned with the public safety. To this aim, this thesis seeks to research this area using state of the art technology and analysis methods based on experimental results and applicable to commercial vehicle crashes for reconstruction purposes. Northwestern University Public Safety department has been a leader in developing the theory in vehicle crashes for passenger cars and the field of heavy vehicles. Heavy vehicles field is still in need of further development. Also, The National Highway Transportation Safety Administration, NHTSA, a government agency has been conducting tests of vehicles of several manufacturers and models to determine crash factors and determine heavy commercial vehicle behavior under collisions. CVSA (Commercial Vehicle Safety Alliance) is another entity, which is a non-profit organization. It is establishing safety v standards for motor vehicles, drivers by providing necessary education and training programs. For this reason, already existing methods and data allows a base structure for developing new methods. Important factors for reconstruction of heavy commercial vehicles have been identified and studied. With the use of already available data, a detailed approach of analysis for important crash factors has been developed. _______________________, Committee Chair Jose Granda _______________________ Date vi ACKNOWLEDGMENTS I would like to thank Professor Jose Granda for his interest in the topic I selected for this thesis. I would also like to express my sincere gratitude to him for his continuous support during my time at California State University, Sacramento. Next, I would like to thank Professor Troy Topping for his guidance. Finally, I would like to thank my husband and parents, whose support and understanding have made me what I am today. vii TABLE OF CONTENTS Page Acknowledgments............................................................................................................. vii List of Tables ..................................................................................................................... xi List of Figures ................................................................................................................... xii Chapter 1. INTRODUCTION ......................................................................................................... 1 1.1 Purpose .............................................................................................................. 1 1.2 Problem Statement ............................................................................................ 2 2. HEAVY-DUTY VEHICLE LAYOUT AND CLASSIFICATION ............................... 3 2.1 Heavy-Duty Vehicle layouts ............................................................................. 3 2.2 Vehicle Classification ....................................................................................... 6 3. BRAKE SYSTEM ....................................................................................................... 10 3.1 Hydraulic Barking System .............................................................................. 10 3.2 Air Braking System......................................................................................... 10 3.3 Reason to Use Air Braking System in Heavy-Duty Vehicles......................... 11 3.4 Brake System in Heavy-Duty Vehicles .......................................................... 11 4. POST-CRASH INSPECTION ..................................................................................... 17 4.1 Commercial Vehicle Safety Alliance .............................................................. 18 4.2 Brake System .................................................................................................. 20 4.2.1 Brake Adjustment Limits ................................................................. 21 viii 4.3 Measure Applied Push-Rod Stroke ................................................................. 24 4.4 Axle Weight Measurement ............................................................................. 26 4.4.1. Dimensional Measurement ............................................................. 28 5. CENTER OF MASS LOCATION ............................................................................... 30 5.1 Center of Mass Lateral Location..................................................................... 34 5.2 Center of Mass Vertical Location ................................................................... 35 6. BRAKING DISTANCE AND SPEED ........................................................................ 37 6.1 Single Adjusted Drag Factor Method ............................................................. 38 6.2 Resultant Drag Factor Method ........................................................................ 39 7. ENERGY ANALYSIS FOR COMMERCIAL VEHICLES ....................................... 45 7.1 Law of Conservation of Energy ...................................................................... 45 7.2 Conservation of Energy in Vehicles ............................................................... 45 8. GENERAL ANALYSIS FOR CONSERVATION OF MOMENTUM ...................... 48 8.1 Momentum ...................................................................................................... 48 8.2 PDOF and ∆ .................................................................................................. 52 9. MOMENTUM ANALYSIS FOR COMMERCIAL VEHICLE .................................. 58 9.1 Velocity/ Speed Factor for Commercial Vehicles .......................................... 58 9.2 PDOF Factor for Commercial Vehicles .......................................................... 59 9.3 Case Study ...................................................................................................... 61 9.3.1 Rear End Collision Case 1 ............................................................... 61 9.3.2 Rear End Collision Case 2 ............................................................... 67 ix 9.3.3 Rear End Collision Case 3 ............................................................... 71 9.3.4 Side Collision Case 4 ....................................................................... 76 9.3.5 Side Collision Case 5 ....................................................................... 81 9.3.6 Side Collision Case 6 ....................................................................... 86 10. CONCLUSIONS......................................................................................................... 92 References ......................................................................................................................... 93 x LIST OF TABLES Tables Page 1. Types of Articulated Vehicles ................................................................................ 5 2. Vehicle Classification System as Per Weight Rating Value ................................... 7 3. Vehicle Classification System as Per Number of Axles ......................................... 9 4. Brake Adjustment Limits for Clamp Type Brake Chamber ................................. 23 5. ECM Report from Freightliner Truck Tractor ...................................................... 62 xi LIST OF FIGURES Figures Page 1. Heavy Duty Truck Tractor with Semitrailer ........................................................... 2 2. Single Unit Truck .................................................................................................... 3 3. Conventional Truck Tractor .................................................................................... 3 4. Cab-Over- Engine Truck Tractor ............................................................................ 4 5. Single Axle Dolly Converter .................................................................................. 6 6. Typical Truck Tractor Semitrailer Braking System.............................................. 12 7. Typical Truck Tractor Air Supply System...........................................................
Load more

Recommended publications
  • TRAFFIC ACCIDENT INVESTIGATION J (----- ( July 1993 )
    If you have issues viewing or accessing this file contact us at NCJRS.gov. , ------ l' ,J .,~ " \; .c I, ~.. 2t . · I '~i t ". ,tt:1~ •. - I I I BASIC COU·RSE INSTRUCTOR j "· I " j • 1 UNI'T GUIDE I i ~----------------------~ i : h).~ J r: .... I ( 29 ) I \1 i TRAFFIC ACCIDENT INVESTIGATION J (----- ( July 1993 ) 144216 U.S. Department of Justice National Institute of Justice This document has been reproduced exactly as received from the • person or organization originating it. Points of view or opinions stated in this doc~ment ~re those o,f t,he authors and do not necessarily represent the official position or poliCies of the National Institute of Justice, Permission to reproduce this copyrighted material has been granted by California Commission on Peace Officer Standards and Training to the National Criminal Justice Reference Service (NCJRS), Further reproduction outside of the NCJRS system requires permission of the copyright owner, /\ THiS COMMDSSiON . .' ~':) • 'ON PIEACIE OfFICER STANDARDS AND> lRAt£\H~.G .: • This unit of instruction is designed as a guideline for performance objective-based law enforcement basic training. It is part of the POST Basic Course guidelines system developed by California law enforcement trainers and criminal justice educators for the California Commission on Peace Officer Standards and Training. This guide is designed to assist the instructor in developing an appropriate lesson plan to cover the performance objectives which are required as minimum content of the Basic Course. • • • II UNIT GUIDE 29 II TABLE OF CONTENTS u.ming Poruin 21 Tratfie Accident InvestigaIJon Page Exercises 9.14.1 Traffic Collision Investigation .........................
    [Show full text]
  • Pavement Skid-Resistance Measurements and Analysis in The
    Pavement Skid Resistance Measurement and Analysis in the Forensic Context C.C.O.Marks Pavement Skid Resistance Measurement and Analysis in the Forensic Context Christopher C. O’N. Marks Managing Director, Marks and Associates Limited ABSTRACT Skid resistance measurement and analysis is now a routine procedure in motor vehicle crash analysis. In fact it was one of the earliest investigative and analytical tools used for this work. Many different measurement methods are in common use, including: visual estimation assisted by friction tables; various dragged devices with friction force measurement and instrumented vehicle skid-to-rest testing, the last having become the preferred alternative for many investigators over the past decade or so. The skid resistance measurement devices at present commonly used by traffic engineers for pavement condition monitoring and maintenance intervention, such as SCRIM, ROAR, Griptester and the British Pendulum, are only rarely used for forensic purposes in New Zealand although in some other countries these may be applied as a routine procedure during crash-scene investigations. The interpretation and analysis of the results obtained by skid resistance measurement in the forensic context may seem to be an obvious process but it is not always straightforward. Uncertainties exist and there is considerable scope for fundamental error. The latter is of significant concern, given the potential adverse consequences of an analyst presenting flawed expert testimony in Court. This paper examines the most common skid resistance measuring methods used for forensic purposes and discusses the interpretation and analysis of the results obtained, the uncertainties involved and the expression of expert opinion in Court.
    [Show full text]
  • Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach
    Journal of the Brazilian Society of Mechanical Sciences and Engineering manuscript No. (will be inserted by the editor) Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach Alexandre M. Ribeiro · Alexandra Moutinho · Andr´eR. Fioravanti · Ely C. de Paiva Received: date / Accepted: date Abstract The performance of vehicle active safety sys- different road surfaces and driving maneuvers to verify tems is dependent on the friction force arising from the effectiveness of the proposed estimation method. the contact of tires and the road surface. Therefore, an The results are compared with a classical approach, a adequate knowledge of the tire-road friction coefficient model-based method modeled as a nonlinear regression. is of great importance to achieve a good performance Keywords Road friction estimation Artificial neural of different vehicle control systems. This paper deals · networks Recursive least squares Vehicle safety with the tire-road friction coefficient estimation prob- · · · Road vehicles lem through the knowledge of lateral tire force. A time delay neural network (TDNN) is adopted for the pro- posed estimation design. The TDNN aims at detecting 1 Introduction road friction coefficient under lateral force excitations avoiding the use of standard mathematical tire models, One of the primary challenges of vehicle control is that which may provide a more efficient method with robust the source of force generation is strongly limited by the results. Moreover, the approach is able to estimate the available friction between the tire tread elements and road friction at each wheel independently, instead of the road. In order to better understand vehicle handling using lumped axle models simplifications.
    [Show full text]
  • The Braking Force
    association adilca www.adilca.com THE BRAKING FORCE From the point of view of driving, emergency braking is probably the most difficult skill to perform. Yet it is an essential skill because, according to the Highway Code, only braking allows the driver to remain in control of one’s car. What does physics teach us about braking? What should be measured? What can be calculated? What about the braking force, this particular force without which nothing would be possible? What do we know about it? Here are some answers. Braking tests If you want to explore the secrets of braking, tests involving a driver, a modern car and a test track are necessary. The few measures will then be used for various calculations. This kind of test is regularly organized by automotive testers, and the obtained results have much to teach us. But to guarantee reliable measures, how is it necessary to proceed? And what do we have to measure? Choose the right track! At first, what track to choose? It must obey the some characteristics: a flat road, a long straight line without slope or banking, stocked with uniform cover, an asphalt of last generation if you wish to measure maximal performance of braking. The car must be recent, in good mechanical condition and entrusted to a driver able to brake efficiently (not so frequent it seems!). A passenger is required to balance the masses. Let’s go! A classic method: the decametre! The more traditional method is to measure the initial speed of the car and the braking distance.
    [Show full text]
  • Speed and Space Management
    T OOLBOXTOPICS.COM C AUTION CAUTION CAUTION C AUTION C AUTION Location Trainer Date SPEED AND SPACE MANAGEMENT Proper speed management means operating at the appropriate speed for all road conditions. Proper space management means maintaining enough space around your vehicle to operate safely. This article focuses on the importance of managing vehicle speed and space in order to deal with the ever- changing conditions on the road. Speed & Stopping Distance There are four factors involved in stopping a vehicle — perception distance, reaction distance, brake lag distance, and braking distance. Perception Distance — Perception distance is the distance a vehicle travels from the time you see a hazard until your brain recognizes it. The perception time for an alert driver is approximately ¾ of a second. At 55 mph a vehicle travels about 60 feet in ¾ of a second. Reaction Distance — Reaction distance is the distance a vehicle travels from the time your brain tells your foot to move from the accelerator until your foot hits the brake pedal. The average driver has a reaction time of ¾ of a second. At 55 mph that accounts for another ¾ of a second and another 60 feet traveled. Brake Lag Distance — When operating a vehicle with air brakes, it takes about ½ of a second for the mechanical operation to take place. Braking Distance — Braking distance is the distance it takes a vehicle to stop once the brakes are applied. Braking distance is affected by weight, length, and speed of the vehicle as well as road condition. A heavy vehicle's components (brakes, tires, springs, etc.) are designed to work best when a vehicle is fully loaded.
    [Show full text]
  • The Crime Scene
    11/18/2013 Got Cars? Demonstrative Evidence & Visual Trial Theory Investigation & Prosecution of Vehicular Homicides Warren Diepraam Montgomery County District Attorney’s Office Vehicular Crimes Cases The Crime Scene • High Profile • Highly Emotional • Location? • Highly Likeable Defendants • Move Along? • High Degree of Expertise • Cleared Scene? • Highly Complicated • Police Attitudes? Question? • Evidence? What Evidence? No, Really! What Evidence? • Photos • 911 Calls • Maps • Medical Records • Photos • Diagrams • Autopsy • Charts • Insurance Records • Measurements • Reconstruction • Receipts • Cars • SFSTs • GPS Data • Phones • Blood Evidence • Dispatch Recordings • OnStar / AAA Roadside • Blood • Videos • Civil Documents • Cell Phones • Social Media • Internet Posting • Social Media • Statements • Doctor’s Records 1 11/18/2013 Got the Evidence –Now What? Learning Types • Demonstrative Evidence vs. Exhibits • Kinetic Learners = 5% • Predicates • Auditory Learners = 30% • Rules of Evidence • Visual Learners = 65% Kinetic • Publishing & Presenting 5% –Trial Fusion (www.trialfusion.net) Auditory –PowerPoint 30% Visual 65% • Consider . Visual Learners Introduction ‐ Visual Facts You MUST Make It Visual! Sounds Fun, But . • We Don’t Have the Equipment. – Forfeiture Funds? – Grants? – MADD or Other Organizations – Beg, Borrow, or Buy Your Own – Go “old school” and blow it up! = WINNING! 2 11/18/2013 When You Can –Bring It In! Photos –Key Points • Quantity? • Quality? • Get there Fast! • All the Evidence. • Think Outside the Box. • Consider the Defenses. Good Photo of Damage Better Photo of Damage Good Photo of Scene Good Photo of Scene 3 11/18/2013 Better Photo of Scene Better Photo of Scene Some Beer… Wine Cooler… 4 11/18/2013 Still Cold… Here’s Why DNA On the driver’s seat . and the wheel.
    [Show full text]
  • HVE Data Inputs Based on Testing for a Wet Pavement Accident Involving an Intercity Bus and an SUV
    WP#2005-1 HVE Data Inputs Based on Testing for a Wet Pavement Accident Involving an Intercity Bus and an SUV Lawrence E. Jackson, PE, MS, ACTAR, David Rayburn, Dan Walsh, PE, Jennifer Russert, National Transportation Safety Board and David Gents, George A. Tapia, Vincent M. Paolini General Dynamics Tire Research Facility ABSTRACT speeds, and with different water depths. The surface used on the TIRF was This paper will discuss the technique validated with the ASTM ribbed and used to simulate a wet pavement smooth tires. The results of these tire accident. It will discuss the weather tests are presented. Finally, the data data, the environment data and the inputs for the surface friction factors and surface friction inputs and the bus tire the tire in-use factors will be discussed. friction inputs used for an HVE SIMON(1)1 loss-of-control simulation on INTRODUCTION wet pavement. By knowing the rain intensity, texture, drainage path length In 2002, the National Highway Traffic and cross slope of the pavement, it could Safety Administration (NHTSA) be determined that the surface was reported that there were 2,981 fatal flooded. The surface was documented crashes, 207,000 injury crashes, and with an ASTM skid trailer using a 479,000 property damage only (pdo) treaded and a smooth tire. This data crashes when rain was reported(2). This showed that for smooth tires the friction represents 7.8% of the fatal crashes, changed both longitudinally every 0.1- 10.7% of the injury crashes and 11.0% mile and laterally between wheel paths, of the pdo crashes.
    [Show full text]
  • Tire-Pavement Friction Coefficients
    d........Tehia eot ... IEPVMN RCINCEFCET IX% r. .... Api.17 K 7 TechnicalAVAReotTR-AEMIENT FRICIONER COMCIN Sprored by h ~ ,~NAVLFACLTENIERINGCOMMAN 1 or fHFeder alnifor&enial Information Springfield, Va. 22151 This document ha been approved for public release and sia; its distribution is unlimited. TIRE-PAVEMENT FRICTION COEFFICIENTS Technical Report R-672 Y-F01 5-20-01-012 by Hisao Tomita A ABSTRACT An investigation consisting mainly of a literature review and a review of current research done outside NCEL was conducted to determine the and Marine o methods needed to provide safe, skid-resistant surfaces on Navy Corps airfield pavements. Much of the information reported herein serves to update the information contained in NCEL Technical Report R-303. or example, new information is included on friction-measuring methods, corre- lation of the measuring methods, factors affecting friction coefficients, minimum requirements for skid resistance, and methods of improving the skid resistance Gf slippery pavements. However, some new topics which are of recent interest are also discussed in detail. These topics include hydro- planing, the mechanism of rubber friction, the friction associated with various operating modes of aircraft tires, the relationship of friction coefficients to pavement surface texture and to surface drainage of water, and the effects of pavement grooving on hydroplaning and on friction coefficients. All the information from the investigation is summarized, and recommendations are given for research and development efforts needed to provide safe, skid-resistant surfaces for airfield pavements. ........................... ... .............\ ...................his document has been appro.-,d for public release and sale; its distribution is unlimited. ............ Vi - Ctopies availiable at the Clearinghouse for Federal Scientific & Technicalti.
    [Show full text]
  • Highway Design Distances.Backup
    Introduction to Transportation Engineering Discussion of Stopping and Passing Distances Dr. Antonio A. Trani Professor of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Fall, Spring 2009 Virginia Tech 1 Introductory Remarks • The presentation of the materials that follow are taken from the American Association of State and Highway Officials (AASHTO): • “A Policy on Geometric Design of Highways and Streets - 2004” • This text is the standard material used by transportation engineering to design highways and streets Virginia Tech 2 Driver Performance • The human-machine system • The driver • Perception and reaction • Vehicle kinematic equations • Acceleration and deceleration problems • Stopping distance criteria • Passing sight distance criteria • Examples Virginia Tech 3 Human Machine Systems • Complex human-machine behavior in transportation engineering • Some examples: • Air traffic controllers interacting with pilots who in turn control aircraft • Highway drivers maneuvering at high speeds in moderate congestion and bad weather • A train engineer following train control signals at a busy train depot Virginia Tech 4 Sample Problem • Driving behavioral models are perhaps the easiest to understand Driver Strategy: control, guidance, and navigation Virginia Tech 5 The Driver • Transportation engineers deal with large numbers of drivers Elderly Middle age Young Handicapped, etc. • Design standards cannot be predicated on the basis of the “average driver” • In-class discussion • Example of reaction time study Virginia Tech 6 Anecdotal Experience About Drivers • Drivers do not like more than 0.3 g of lateral acceleration at low speeds (< 30 m.p.h.) • No more than 0.1 g at 60 m.p.h. • Human factor issues in highway design: a) As speed increases so does visual concentration b) As speed increases, the focus of visual concentration changes (600 ft.
    [Show full text]
  • BAYESIAN RECONSTRUCTION of TRAFFIC ACCIDENTS 71 at the Start of the Skid As 17·8 Meters/Sec
    Law, Probability and Risk (2003) 2, 69–89 Bayesian reconstruction of traffic accidents GARY A. DAV I S† Department of Civil Engineering, University of Minnesota, 122 CivE, 500 Pillsbury Drive SE, Minneapolis, MN 55455, USA [Received on 20 January 2003; revised on 17 April 2003; accepted on 9 May 2003] Traffic accident reconstruction has been defined as the effort to determine, from whatever evidence is available, how an accident happened. Traffic accident reconstruction can be treated as a problem in uncertain reasoning about a particular event, and developments in modeling uncertain reasoning for artificial intelligence can be applied to this problem. Physical principles can usually be used to develop a structural model of the accident and this model, together with an expert assessment of prior uncertainty regarding the accident’s initial conditions, can be represented as a Bayesian network. Posterior probabilities for the accident’s initial conditions, given evidence collected at the accident scene, can then be computed by updating the Bayesian network. Using a possible worlds semantics, truth conditions for counterfactual claims about the accident can be defined and used to rigorously implement a ‘but for’ test of whether or not a speed limit violation could be considered a cause of an accident. The logic of this approach is illustrated for a simplified version of a vehicle/pedestrian accident, and then the approach is applied to four actual accidents. Keywords: possible worlds; accident reconstruction; Bayes networks; Markov chain Monte Carlo; forensic inference. Limited creatures that we are, we often find ourselves having to base decisions on less than complete information.
    [Show full text]
  • SECTION 5 Negative Acceleration: Braking Your Automobile
    Chapter 1 Driving the Roads SECTION 5 Negative Acceleration: Braking Your Automobile Section Overview speed or acceleration is the change in the speed of an object in a given time period. Acceleration, This section addresses the distance traveled avt=Δ Δ (Δv represents the change in velocity that during negative acceleration as a function of the is measured by recording velocity at two different initial speed. Students continue the cart-stopping periods). The initial velocity is often indicated as v1 investigation by analyzing the problem of “slowing and fi nal velocity as v2. In this section, the students down” a cart. Students collect data by setting up will be solving for the distance required to stop, an experiment in which a toy cart is rolled down a while traveling at different velocities. ramp. The initial speed of the cart versus its braking distance is plotted on a graph. The change in speed Plotting speed vs. time, results in a straight line, of the cart as it comes to a stop is explained by with the slope of that line indicating acceleration. using the term negative acceleration. The effect of increasing the initial speed is recorded as data and then plotted on a speed versus time graph. Students study the similarities and differences in their data to ) fi nd the relationship of initial speed to the braking v distance. Braking distance is fi nally defi ned and determined to be proportional to the initial velocity speed ( squared. time (t) Background Information avt=Δ Δ The physics of stopping a cart involves reaction time while moving with constant or uniform motion, and The unit for v is m/s and for t is s.
    [Show full text]
  • Tyre Dynamics, Tyre As a Vehicle Component Part 1.: Tyre Handling Performance
    1 Tyre dynamics, tyre as a vehicle component Part 1.: Tyre handling performance Virtual Education in Rubber Technology (VERT), FI-04-B-F-PP-160531 Joop P. Pauwelussen, Wouter Dalhuijsen, Menno Merts HAN University October 16, 2007 2 Table of contents 1. General 1.1 Effect of tyre ply design 1.2 Tyre variables and tyre performance 1.3 Road surface parameters 1.4 Tyre input and output quantities. 1.4.1 The effective rolling radius 2. The rolling tyre. 3. The tyre under braking or driving conditions. 3.1 Practical brakeslip 3.2 Longitudinal slip characteristics. 3.3 Road conditions and brakeslip. 3.3.1 Wet road conditions. 3.3.2 Road conditions, wear, tyre load and speed 3.4 Tyre models for longitudinal slip behaviour 3.5 The pure slip longitudinal Magic Formula description 4. The tyre under cornering conditions 4.1 Vehicle cornering performance 4.2 Lateral slip characteristics 4.3 Side force coefficient for different textures and speeds 4.4 Cornering stiffness versus tyre load 4.5 Pneumatic trail and aligning torque 4.6 The empirical Magic Formula 4.7 Camber 4.8 The Gough plot 5 Combined braking and cornering 5.1 Polar diagrams, Fx vs. Fy and Fx vs. Mz 5.2 The Magic Formula for combined slip. 5.3 Physical tyre models, requirements 5.4 Performance of different physical tyre models 5.5 The Brush model 5.5.1 Displacements in terms of slip and position. 5.5.2 Adhesion and sliding 5.5.3 Shear forces 5.5.4 Aligning torque and pneumatic trail 5.5.5 Tyre characteristics according to the brush mode 5.5.6 Brush model including carcass compliance 5.6 The brush string model 6.
    [Show full text]