# SAE J695V002

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 entirelyvoluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.QUESTIONS REGARDING THIS DOCUMENT: (724) 772-8512 FAX: (724) 776-0243TO PLACE A DOCUMENT ORDER: (724) 776-4970 FAX: (724) 776-0790SAE WEB ADDRESS http://www.sae.orgCopyright 1998 Society of Automotive Engineers, Inc.All rights reserved. Printed in U.S.A.SURFACEVEHICLE400 Commonwealth Drive, Warrendale, PA 15096-0001RECOMMENDEDPRACTICESubmitted for recognition as an American National StandardJ695REAF.DEC1998Issued 1954-10Reaffirmed 1998-12Superseding J695 DEC89Turning Ability and Off Tracking—Motor VehiclesForeword—This reaffirmed document has been changed only to comply with the new SAE Technical StandardsBoard Format. References were added as Section 2. Definitions changed to Section 3. All other section numbershave changed accordingly.1. Scope—This SAE Recommended Practice sets forth a method by which the turning ability and off tracking ofmotor vehicles can be determined.2. References2.1 Applicable Publication—The following publication forms a part of this specification to the extent specifiedherein. Unless otherwise indicated, the latest version of SAE publications shall apply.2.1.1 SAE PUBLICATION—Available from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001.SAE SP-374—The Truck Steering System from Hand Wheel to Road Wheel3. Definitions3.1 Turning Center—That point about which all parts of a vehicle or combination of vehicles revolve in describinga turn of constant radius. For ideal steering, free of tire scrubbing, the extended axis of all wheel spindlespasses through this center. In the case of two-axled bogies or tandems in which the axles are constrained toparallelism, the turning center is assumed to fall on a line parallel to and midway between these axlecenterlines (see Figure 1).3.2 Turning Radius—The distance from the turning center to the center of tire contact with the road of the wheeldescribing the largest circle, while the vehicle is executing its sharpest practicable turn (usually to the outsidefront wheel) (see Figure 1).3.3 Turning Diameter—Twice the turning radius (see Figure 1).3.4 Turning Diameter—Wall-to-Wall—The diameter of the smallest circle, which will enclose the outermostpoints of projection of the vehicle while executing its sharpest practicable turn. This is equal to the minimumturning diameter plus twice the radial overhang beyond the turning radius (see Figure 1).SAE J695 Reaffirmed DEC1998-2-3.5 Turning Diameter—Curb-To-Curb—The diameter of the smallest circle within which the vehicle will clear acurb 150 mm high, while the vehicle is executing its sharpest practicable turn. This is equal to the turningdiameter plus twice the horizontal distance from the center of tire contact with the road to the arc subtended bya chord drawn between the points of intersection of the outermost projection of the tire shoulder on a horizontalplane 150 mm above the surface on which the tire rests (see Figure 1).FIGURE 1—4. Determinations—The following determinations, based on Ackerman steering geometry (see Figures 2 and 3),may be made mathematically as explained in detail as follows:FIGURE 2—DIAGRAM ILLUSTRATING FACTORS OF FRONT AXLE CONFIGURATIONSAE J695 Reaffirmed DEC1998-3-FIGURE 3—DIAGRAM ILLUSTRATING EFFECT OF WHEELBASE ON TURNING RADIUSWITH A GIVEN FRONT AXLE CONFIGURATION4.1 Turning diameter1 with a given wheelbase2 and front axle configuration.4.2 Configuration required to provide a given turning diameter1.1. At the maximum turning angle, there is normally Ackerman geometry error between the front wheels that can be described as shown in the equation in 6.2.2 or 6.2.3. This error will result in tire scrub of both front tires. If equal slippage of both front wheels is assumed, the theoreti-cal turning center will lie midway between the intersections of the turning angle lines of outside and inside front wheels with the centerline of the rear axle. Due to the centrifugal force, the greater pressure on the outer wheel due to this centrifugal force, and other influences, the true turning center will actually lie closer to the outer intersection than to the inner.2. To determine the turning ability of a three-axled vehicle, it is customary to measure the wheelbase from the front axle center to a point midway between the two rear axles and to consider a transverse line through this point as the equivalent of the center of the rear axle of a two-axled vehicle. Since these rear axles are constrained to parallelism, a moment is created during a turn that must be overcome by the front tires. This moment increases the front tire slip angle or tire scrub, and results in a larger turning diameter or a turning diameter equivalent to a vehi-cle with a longer wheelbase. Tests have shown that the true location of the turning center is somewhat further to the rear than midway between the axles. The actual location of the turning center depends on whether the tire equipment is single or dual, whether the tires are radial or biased ply construction, the load distribution between the two rear axles, the load on the front axle, and the Ackerman error in the tie-rod linkage. Calculations to accurately predict the effects of these various factors would be quite complex.SAE J695 Reaffirmed DEC1998-4-4.3 Curb clearance increment (see Figure 4).FIGURE 4—CURB CLEARANCE DIAGRAM5. Factors of Front Axle ConfigurationTR - Turning radius (see Figure 1)TD - Turning diameterT - Track of tires at ground (see Figure 2)PC - Distance between knuckle pivot centers at groundOS - Offset, pivot center to track of tire at groundCa - Camber angle of wheel, loadedKI - Kingpin inclination from verticalKS - Kingpin spacingTW - Tire widthWB - Wheelbase2LL - Cross steering lever lengthLP - Cross steering lever positionLA - Cross steering lever angle from axle centerline (true)RR - Rolling radius of tireITa - Inside wheel turning angle (see Figure 3)OTa - Outside wheel turning angle (see Figure 3)H - Height of center of kingpin from ground (loaded)R - Radius to pivot center for correct wheelbase (see Figure 3)RS - Radius to pivot center for shorter than correct wheelbase (see Figure 3)RL - Radius to pivot center for longer than correct wheelbase (see Figure 3)C - Curb contact length (see Figure 4)CR - Curb clearance radius (see Figure 4)CI - Curb clearance increment (see Figure 4)TOS - Tire offset measured along spindle centerlineSAE J695 Reaffirmed DEC1998-5-6. Formulas6.1 Several of the following formulas use the term pivot centers, the distance between knuckle pivot centersmeasured at the ground. Pivot centers can be calculated from given axle dimensions as follows:(Eq. 1)For small measures of camber angle of wheel, loaded, the formula for pivot centers can be simplified with littleloss of accuracy to:(Eq. 2)6.2 To determine turning diameter3 with a given wheelbase4 and front axle configuration (see Figure 3):6.2.1 With correct wheelbase4:(Eq. 3)6.2.2 With wheelbase shorter than correct (SWB):(Eq. 4)6.2.3 With wheelbase longer than correct (LWB):(Eq. 5)6.3 To determine configuration required to provide a given turning diameter (see Figure 3):6.3.1 Given pivot centers, offset, and wheelbase4, to find the turning angle necessary to front wheels:(Eq. 6)6.3.2 Given offset and turning angle of outside front wheel, to find the necessary wheelbase (see Figure 3):(Eq. 7)6.4 To determine curb clearance increment to turning radius (see Figure 4):(Eq. 8)3. See Footnote 1.4. See Footnote 2.PCKS2 (RR CaTOS Ca)sin+cosKItan×+=PCKS2 RRKItan×+=TD2 WBOTasin-------------------- OS +=TD4SWB2 SWBOTatan--------------------- PCSWBITatan------------------22OS++++=TD4LWB2 LWBOTatan--------------------- PCLWBITatan------------------22OS++++=OTaarc WBTD2------- OS–-----------------------ITaarc OTaPCWB---------–cotcot=sin=WBTD2------- OS– sin OTa=CITRTW2---------+2 C2----2 TR–+=SAE J695 Reaffirmed DEC1998-6-6.5 To determine correct cross steering lever configuration for a given wheelbase5 and pivot centers (see Figure 3).The conventional tie-rod linkage cannot provide perfect Ackerman geometry for all turn angles. In addition, it isoften necessary to use one linkage configuration for several different wheelbases. The solution is, therefore,not a simple answer to a set of equations. It is a cut and try iterative process of examining various alternativeswith respect to all wheelbases. Most engineering organizations use computer programs to compare theproposed design to perfect Ackerman geometry and then choose the best available design.A detailed graphical method may be found in Appendix 1 of SAE publication SP-374, The Truck SteeringSystem from Hand Wheel to Road Wheel.7. Field Test Procedure7.1 Check steering geometry alignment and correct, if necessary.7.2 Check the front wheel cut angles to manufacturers recommendations. Wheel stops should be so set that theminimum clearance between the tire and the nearest point of interference is 20 mm; or, so that with the wheelstops in contact, a margin of a quarter turn of the steering wheel is left before the maximum travel of thesteering gear is reached. In some cases, tire interference will be the limiting factor and in others, the steeringgear travel will limit the maximum cut angle.7.3 Load the vehicle to the maximum recommended gross weight.7.4 Run the vehicle on a dry, flat apron, making turns in both directions in low gear at engine idle speed. Thewheels should be turned to the maximum cut angle. At least two complete circles should be made beforemaking measurements. The path of the outside wheel is marked on the pavement by pouring water on the tirewhile making the complete circle.7.5 To determine the turning diameter, measure from the midpoint of tire contact trace on the pavement to a similarpoint across the diameter of the trace. Turning radius will be half this distance, and the turning center will be atthe midpoint of the diameter.7.6 To determine the curb clearance increment, place a straight edge horizontally across the outside face of thetire at an elevation of 150 mm above the pavement surface, and with a plumb line, locate the point on thepavement directly beneath the foremost point of contact between the straight edge and the tire shoulder. Thedistance from this point to the turning center is the curb clearance radius, and the difference between it and theturning radius is the curb clearance increment.7.7 To determine the turning diameter, wall-to-wall, drop a plumb line from the extreme outside radial extension ofthe vehicle and locate the point on the pavement directly beneath it. The distance thence to the turning centeris the vehicle clearance radius, twice which is the turning diameter, wall-to-wall.8. Graphical Determination—Alternative to the mathematical formulas and field test procedures above,determinations may be made by the graphical or draftman s method in accordance with the followingprocedures. Results secured by this method, like those by the mathematical method, are theoretical and maybe somewhat less exact. The following graphical method is somewhat easier and more rapid:In Figure 5, dimensions are defined and the sequence of operations indicated by the circled numerals:5. See Footnote 2.SAE J695 Reaffirmed DEC1998-7-FIGURE 5—GRAPHICAL PROCEDURE FOR DETERMINATION OF TURNING RADIUSGiven pivot centers, offset, outside wheel turning angle, and wheelbase:8.1 Draw a horizontal line representing the longitudinal centerline of the chassis.8.2 Draw a second line perpendicular to the first line, representing the centerline of the front axle.8.3 Locate a point on the second line a distance above the chassis centerline equal to half the distance betweenpivot centers.8.4 Through this point, draw a line at an angle to the front axle centerline equal to the outside front wheel turningangle.8.5 Locate a point on this line a distance above the pivot center equal to the offset of the center of the tire trackfrom the pivot center. This is the front wheel track.8.6 At a point on the chassis centerline, a distance from its intersection with the front axle centerline equal to thewheelbase, drop a perpendicular line intersecting the diagonal line from the pivot center. This is the turningcenter.8.7 Measure the distance from this center to the point on the diagonal representing the front wheel track. This isthe turning radius.9. Definitions—(See Section 3.9.1 A typical off tracking situation for a tractor semitrailer, including definitions, is shown in Figure 6.9.2 Off tracking is the difference in radii from the turning center to the vehicle centerline at the foremost andrearmost axles of a vehicle or combination and represents the increase beyond the tangent track occasionedby a turn (see Figure 6).SAE J695 Reaffirmed DEC1998-8-FIGURE 6—TYPICAL OFF TRACKING SITUATION9.3 Turning track is the radial width between centers of road contact of the outermost and innermost tires of avehicle or combination of vehicles in negotiating a turn. In the case of dual tires, center of road contact is takento be that midway between those of individual tires (see Figure 6).9.4 General—In addition to physical trial, there are two methods by which the amount of off tracking may bedetermined, namely, mathematically and graphically. These two methods were published in SAE J695approved October 1954 and reaffirmed without change in June 1963. Since these methods required a verygood knowledge of mathematics and graphics, many fleet operators and others found these methods toocumbersome and complicated to use. In recent years, data have been developed, which are accurate enoughto use for all practical purposes. Therefore, the old mathematical and graphic methods have been deleted fromthis publication. The new method was developed by the Western Highway Institute and a detailed discussion ispresented in Research Committee Report No. 3, “Off Tracking Characteristics of Trucks and TruckCombinations.“ An equation in the calculation of maximum off tracking was used as the basis for off trackingdistances when the radius of curve is known and the squares of the component wheelbases of a combinationhave been totalled. Thus, the method has become known as the “sum of the squares.“ It is this method, easyto calculate and simple to apply, which is recommended as a general practice.SAE J695 Reaffirmed DEC1998-9-10. Factors of Off Tracking10.1 Amount of Off