1、_SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising theref
2、rom, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments andsuggestions.Copyright 2017 SAE InternationalAll rights reserved. No part of this public
3、ation may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE.TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada)Tel: +1 724-776-4970 (outs
4、ide USA)Fax: 724-776-0790Email: CustomerServicesae.orgSAE WEB ADDRESS: http:/www.sae.orgSAE values your input. To provide feedback on thisTechnical Report, please visithttp:/standards.sae.org/J2969_201701SURFACE VEHICLERECOMMENDED PRACTICEJ2969 JAN2017Issued 2017-01Use of the Critical Speed FormulaR
5、ATIONALEThis SAE Recommended Practice was developed to provide a guideline for the recommended use of the critical speed formula. The basic procedures and techniques for data collection and use of the method shown in this document are not to be considered all inclusive.TABLE OF CONTENTS1. SCOPE 22.
6、REFERENCES 22.1 Applicable Publications . 22.1.1 SAE Publications. 22.1.2 Related Publications . 23. DEFINITIONS . 44. THEORY . 54.1 Critical Speed Formula 55. RECOMMENDED METHOD. 65.1 Vehicle Considerations . 65.2 Roadway Documentation 65.3 Tire Mark Evaluation . 65.4 Calculation 85.5 Accuracy . 86
7、. SPECIAL CONSIDERATIONS . 97. NOTES 97.1 Revision Indicator 9FIGURE 1 FREE BODY DIAGRAM OF A CAR TRAVELING ON A BANKED, CURVED ROAD WITH SUPERELEVATION . 5FIGURE 2 TIRE MARK SHOWING DIAGONAL STRIATIONS THAT TURN TO PARALLEL STRIATIONS WHEN THE TIRE BEGINS TO SKID. 7FIGURE 3 EXAMPLES OF METHODS 1 AN
8、D 2 MEASUREMENT TECHNIQUES . 8TABLE 1 EXAMPLE OF ERROR ASSOCIATED WITH POSSIBLE 1 INCH UNCERTAINTY IN MEASURING THE MIDDLE ORDINATE 9SAE INTERNATIONAL J2969 JAN2017 Page 2 of 91. SCOPEThis SAE Recommended Practice provides guidelines for procedures and practices used to obtain and record measurement
9、s and to analyze the results of the critical speed method. It is for use at accident sites using manual or electronic measurements. The method allows for many unique factors and the recommended procedure will permit a consistent use of the method in order to reduce errors and uncertainty in the resu
10、lts. The results from the critical speed formula should always, when possible, be compared to other accident reconstruction methodologies. When different accident reconstruction methods are used, the uncertainty of each method should be analyzed and presented.2. REFERENCES2.1 Applicable Publications
11、The following publications form a part of this specification to the extent specified herein. Unless otherwise indicated, the latest issue of SAE publications shall apply.2.1.1 SAE PublicationsAvailable from SAE International, 400 Commonwealth Drive, Warrendale, PA, 15096-0001, Tel: 877-606-7323 (ins
12、ide USA and Canada) or +1 724-776-4970 (outside USA), www.sae.org.SAE J670 Vehicle Dynamics TerminologySAE J2505 Measurement of Vehicle-Roadway Frictional Drag2.1.2 Related PublicationsMore than 20 years of critical speed research has been evaluated in order to prepare this recommended practice. The
13、 majority of the historical research supports the critical speed method, although there are a few publications listed below that criticize the method. The SAE Critical Speed Task Force has evaluated these reports and has determined the method to be valid within its limits of uncertainty when used co
14、rrectly, which further supports the need for a recommended practice to ensure the method is used correctly. The following publications were evaluated to prepare this recommended practice:Amirault, G. and MacInnis, S., “Variability of Yaw Calculations from Field Testing,“ SAE Technical Paper 2009-01-
15、0103, 2009, doi:10.4271/2009-01-0103.Asay, A. and Woolley, R., “Rollover Testing of Sport Utility Vehicles (SUVs) on an Actual Highway,“ SAE Technical Paper 2010-01-0521, 2010, doi:10.4271/2010-01-0521.Bartlett, W., Wright, W., Masory, O., Brach, R. et al., “Evaluating the Uncertainty in Various Mea
16、surement Tasks Common to Accident Reconstruction,“ SAE Technical Paper 2002-01-0546, 2002, doi:10.4271/2002-01-0546.Bartlett, W. and Wright, W., “Summary of 56 recent critical speed yaw analysis tests, including ABS and electronic stability control on pavement, gravel, and grass: corrected,” Acciden
17、t Reconstruction Journal, May/June, pp. 29-32, 2008.Bellion, P., “Project Y.A.M. (Yaw Analysis Methodology) Vehicle Testing and Findings - Victoria Police, Accident Investigation Section,“ SAE Technical Paper 970955, 1997, doi:10.4271/970955.Bohan, T. and Keierleber, J., “Speed from “Skuffs” on a Gr
18、assy Field: A Case for Dr. Daubert?” Proceedings of the American Academy of Forensic Sciences, Annual Meeting, Atlanta, GA, Feb. 11-16, 2002.Brach, R., “An Analytical Assessment of the Critical Speed Formula,“ SAE Technical Paper 970957, 1997, doi:10.4271/970957.SAE INTERNATIONAL J2969 JAN2017 Page
19、3 of 9Brach, R.M. and Brach, M., “Vehicle Accident Analysis and Reconstruction Methods,” (Warrendale, Society of Automotive Engineers, Inc., 2005), ISBN 978-0-7680-0776-3.Cannon, J., “A Study of Errors in Yaw-Based Speed Estimates Due to Effective Braking,“ SAE Technical Paper 2003-01-0888, 2003, do
20、i:10.4271/2003-01-0888.Cliff, W., Lawrence, J., Heinrichs, B., and Fricker, T., “Yaw Testing of an Instrumented Vehicle with and without Braking,“ SAE Technical Paper 2004-01-1187, 2004, doi:10.4271/2004-01-1187.Daily, J., Shigemura, N., and Daily, J., “Fundamentals of Traffic Crash Reconstruction V
21、olume 2 of the Traffic Crash Reconstruction Series,” Institute of Police Technology and Management, University of North Florida, 2006.Dickerson, C., Arndt, M., Arndt, S., and Mowry, G., “Evaluation of Vehicle Velocity Predictions Using the Critical Speed Formula,“ SAE Technical Paper 950137, 1995, d
22、oi:10.4271/950137.Fischer, G., “Rebuttal to criticism of critical speed formula,” Proceedings of the American Academy of Forensic Sciences, Annual Meeting, Seattle, WA, Feb. 19-24, 2001.Fischer, W., “Challenging the Critical Speed Formula In Light Of the Daubert Decision,“ SAE Technical Paper 2005-0
23、1-3141, 2005, doi:10.4271/2005-01-3141.Fricke, L., “Traffic Accident Reconstruction, Volume 2 of the Traffic Accident Investigation Manual,” Northwestern University, 1990, ISBN 0-912642-07-6.Hague, D., Lambourn, R., and Turner, D., “Critical speed studies I: The accuracy of speeds calculated from cr
24、itical curve marks, and their striations,” The Institute of Traffic Accident Investigators, Proceedings of the 3rd National Conference, Telford, 14-16 November 1997.Hague, D., Turner, D., and Williams, A., “Critical speed studies II: The generation of tyre marks by cornering vehicles,” The Institute
25、 of Traffic Accident Investigators, Proceedings of the 3rd National Conference, Telford, 14-16 November 1997.Lambourn, R., “The calculation of motor car speeds from curved tyre marks,” Journal of Forensic Science Society, 1989, 29(6):371-386.Lambourn, R., “Braking and Cornering Effects with and with
26、out Anti-Lock Brakes,“ SAE Technical Paper 940723, 1994, doi:10.4271/940723.Manning, L. and Bentson, L., “Highway Speed vs. Sideslip (Critical Speed in a Curve),” Journal of the National Academy of Forensic Engineers, Vol. 1, No. 2, October, 1984.Manning, L., “Critical Speed: A False Doctrine,” Proc
27、eedings of the American Academy of Forensic Sciences, Annual Meeting, Reno, NV, Feb. 21-26, 2000.Masory, O., Delmas, S., Wright, B., and Bartlett, W., “Validation of the Circular Trajectory Assumption in Critical Speed,“ SAE Technical Paper 2005-01-1189, 2005, doi:10.4271/2005-01-1189.Reveley, M., B
28、rown, D., and Guenther, D., “A Comparison Study of Skid and Yaw Marks,“ SAE Technical Paper 890635, 1989, doi:10.4271/890635.Sledge, N. and Marshek, K., “Vehicle Critical Speed Formula - Values for the Coefficient of Friction - A Review,“ SAE Technical Paper 971148, 1997, doi:10.4271/971148.Yamazaki
29、, S. and Akasaka, T., “Buckling behavior in contact area of radial tire structure and skid marks left by tires,” JSAE Review, Vol. 9, No. 3, pp. 51-55, 1988.Yamazaki, S., “Friction coefficients of tires and skid marks left by tires,” Proceedings of the International Workshop on Traffic Accident Reco
30、nstruction, Organized by National Research Institute of Police Science, Japan, Nov. 12-13, 1998.SAE INTERNATIONAL J2969 JAN2017 Page 4 of 93. DEFINITIONSThe following terms and acronyms are defined for use herein:ABS DECELERATION VALUE: Average deceleration value over the entire stopping test conduc
31、ted with ABS activated.ACCELERATION: Rate of change of velocity with respect to time.CHORD: A straight line distance between two points on an arc.COEFFICIENT OF FRICTION: A number representing the resistance to sliding of two flat surfaces in contact defined as the ratio of the resistance force to t
32、he normal force between the surfaces.CENTRIPETAL ACCELERATION: The scalar value of the component of vehicle acceleration in the direction of the horizontal normal to the horizontal velocity vector SAE J670.CRITICAL SPEED: The maximum speed at which a vehicle can traverse a path with a specific radiu
33、s of curvature without loss of directional control; the speed of a vehicle undergoing a turn maneuver at which the tires leave visible sideslip marks. The speed when the centripetal acceleration is limited by roadway friction. f = n m, where f is the drag factor, is the coefficient of friction, n is
34、 the percentage of braking, and m is the slope. This is valid for slopes less than 10q.CRITICAL SPEED FORMULA: A formula that calculates the speed of a vehicle from the radius of curvature of its tires critical speed scuff marks, taking into account roadway grade, superelevation and frictional drag
35、coefficient.CRITICAL SPEED SCUFF MARK: A tire yaw mark caused by a sidesliping tire often showing a diagonal striped pattern called striations.EQUIVALENT ROAD FRICTION: The average locked-wheel frictional drag coefficient which includes road grade.FRICTIONAL DRAG COEFFICIENT: The ratio of the fricti
36、onal drag force to the vehicles weight at a given speed, position or instant in time SAE J2505.FRICTIONAL DRAG FACTOR: The frictional drag force averaged over a fully braked stop as used in the stopping distance formula in SAE J2505.INERTIA: A physical property of a body that represents its resistan
37、ce to acceleration.MIDDLE ORDINATE: A distance measurement from the chord to the curve that is perpendicular to the chord and measured at the mid-point of the chord.RADIUS OF CURVATURE: The measured or calculated radius of a critical speed scuff mark at the point of measurement used in the critical
38、speed formula.SEALED SURFACE: A roadway with a hard-sealed surface of bitumen, tar, or concrete.SIDESLIP: Lateral/transverse translation of a vehicle perpendicular to its heading.SIDESLIP ANGLE: The angle between the vehicles heading and the velocity vector of its center of mass.STRIATIONS: Periodic
39、 stripes that appear diagonal to the tire marks from a vehicle traveling at its critical speed.SUPERELEVATION: The slope of the surface perpendicular to the critical speed scuff mark.UNSEALED SURFACE: A roadway not sealed with bitumen, tar, or concrete (for instance a loose gravel or dirt roadway).S
40、AE INTERNATIONAL J2969 JAN2017 Page 5 of 94. THEORY4.1 Critical Speed FormulaThe derivation of the critical speed formula is available in many references, such as Brach and Brach (2005) and Daily et al. (2006). The formula assumes a vehicle is traveling along a surface that is possibly banked (super
41、elevation) and uphill or downhill (road grade) during the time that the critical speed scuff marks are being generated. During this time, the center of mass of the vehicle traces out a near circular arc with the center of the arc located on a horizontal plane at distance r inside of the turn. It is
42、also assumed that there are no aerodynamic loads and that the force from friction is proportional to the normal force on the road. It is assumed that the vehicle is a point mass, traveling at an instantaneous constant speed, is in a steady state maneuver, and traveling in uniform circular motion.Fig
43、ure 1 - Free body diagram of a car traveling on a banked, curved road with superelevationFigure 1 shows a vehicle in a turn. When a vehicle is trying to turn, the frictional force is lateral to the vehicles motion. If this vehicle is in a critical speed yaw, then the maximum amount of lateral fricti
44、onal force is being generated by the tires.When the maximum amount of frictional force is being generated the tires are saturated and evidence of such usually manifests itself as a critical speed scuff mark on the pavement. The critical speed formula is:)1()(eegrveqeqPP (Eq. 1)where:g = acceleration
45、 due to gravityr = radiuse = superelevation of the road in percenteq = equivalent road frictionThis is the general form of the critical speed formula and is valid for any unit system. However, there are restrictions on the admissible values of eq and e. There are two mathematical requirements for e
46、andeq:SAE INTERNATIONAL J2969 JAN2017 Page 6 of 94.1.1 The product of eq and e must be less than 1 (i.e.,eqe 0). The physical significance is the fact that if the slope is negative (i.e., the curve slopes away) by an amount greater than the coefficient of friction, then the vehicle will simply slide
47、 off the road regardless of its speed. This would require either a very steep bank or a very slick surface.For nearly level surfaces, Equation 1 simplifies to:Peqgrv (Eq. 2)5. RECOMMENDED METHOD5.1 Vehicle ConsiderationsThe method as outlined here does not apply to articulated trucks and has not bee
48、n tested on other non-standard vehicles like motorcycles and trikes.It is recommended to document the vehicles tires make and model, as well as the tires DOT number. Do not use the critical speed formula when significantly dissimilar tires are installed like a donut spare on the loaded side of the t
49、urning vehicle.5.2 Roadway DocumentationMeasure the vehicle-to-roadway frictional drag factor in accordance with SAE Recommended Practice J2505. Althoughthe tire generates lateral friction during a critical speed maneuver, the method has been correlated through research using the average longitudinal frictional drag factor and therefore, this value should be used.Measure the road superelevation to be us
