EI Consultants (formerly The Engineering Institute) has been studying solid rear axle tramp for well over a decade, and contributed several publications to the literature outlining recommended test methods and their results. Throughout the history of EI’s research, sustained tramp inputs have been achieved by use of a tire featuring affixed lumps of rubber to induce wheel hop at one end of the axle. The principal methodological guide for studying the vehicle response to this input has been the test methods and data analysis recommendations of test standard SAE J266: Steady-State Directional Control Characteristics for Passenger Cars and Light Trucks. More specifically, past testing has been patterned almost exclusively on the circle test (constant-radius/slowly-increasing-speed) method discussed in J266. Historically, the J266 recommendation for data analysis and presentation, i.e. understeer/oversteer gradients derived from a wheel angle versus lateral acceleration plot, were principally used. Recent research, along with fresh analysis of previous testing results, revealed limitations of the circle test and the J266 recommended manner of data analysis in the context of tramp resonance testing. During a constant-radius/slowly-increasing-speed test, a single control variable (speed) has the effect of changing both the lateral acceleration and the tramp input frequency simultaneously. This effect results in a non-steady-state test event where only a narrow portion of each test run expresses the resonant axle tramp phenomenon that is the intended object of the observation. To provide a wider view of vehicle response characteristics during sustained axle tramp, EI Consultants selected and evaluated expanded test methods in a recent testing project. These methods included performing circle tests at multiple radii, performing continuous tests modeled after the J266 constant-speed/variable-radius method, and performing path-following tests modeled after the slowly increasing steer method. Expanded data analysis and presentation methods were developed to quantify and understand the vehicle oversteer response in more effective ways than those recommended by J266. Due to the abrupt discontinuity in the vehicle’s response upon reaching the resonant tramp frequency, novel methods of data presentation were shown to be more useful in assessing vehicle characteristics during resonant tramp. Of particular value was examining the steering input delta in the vehicle speed and tramp input frequency domains during the phase of resonant axle response; and examining the difference between the actual yaw rate and the theoretical Ackerman yaw rate derived from the measured steer angle. This paper will detail the data analysis techniques that were developed to overcome the limitations of the J266 standard’s steer gradient methodology, and thus introduce a more useful approach to evaluating understeer/oversteer characteristics during non-steady-state test events. This paper is the first of two companion papers presenting theory and results from EI Consultants’ most recent axle tramp testing. This paper focuses on new understandings of test data analysis theory, while the second paper will summarize the results of numerous tests and their application to various suspension design strategies for improving solid rear axle tramp control, with a motivation for enhancing vehicle controllability and highway safety.

EI Consultants (formerly The Engineering Institute) has, for over a decade, researched and tested methods of mitigating the controllability effects of solid rear axle tramp by optimizing rear axle rotational damping. This optimization has explored the balance between increasing the damping forces of the shock absorbers and increasing the distance between the shock absorbers positioned along the axle. Axle tramp is detrimental to vehicle handling and stability, since the reduction in normal force at the rear tires can lead to a total loss of control situation. On solid rear axles such as those common on SUVs and light trucks, underdamped tramp motion will result in an oversteer characteristic of the vehicle as the rear lateral capacity is compromised due to the tires alternately bouncing out of firm contact with the road surface. In severe cases of axle tramp, the alternating normal forces at both the input tire and the opposite tire will go to zero when each tire fully leaves contact with the ground. EI Consultants has tested numerous SUVs and light trucks and their responses to axle tramp. In order to excite the tramp mode in a sustained fashion for close study of suspension design alternatives, the test methodology utilizes one rear tire with three vulcanized rubber lumps, placed equidistant about the circumference of the tire. Throughout this research, increased effective rotational damping has been repeatedly demonstrated to have a direct relationship to increased controllability.The most recent testing included maneuvers modeled after those recommended in test standard SAE J266: Steady-State Directional Control Characteristics for Passenger Cars and Light Trucks. This testing included multiple shock absorber configurations, and the data was analyzed in multiple domains to provide insight on the effectiveness of various shock absorber design strategies.Several shock absorber design variables were evaluated, with the most significant of these being the lateral distance between the shock mounts along the axle. Other variables that were able to be observed and evaluated in the latest testing included the balance between shock absorber rebound and compression forces, and the relative effect of "staggered" shocks in side-view angle, where one shock is positioned with a rearward angle, and the other shock is positioned with a forward angle. The effectiveness of placing shocks further apart along the length of the axle was unmatched.This paper is the second of two companion papers presenting theory and results on EI Consultants' most recent axle tramp testing. Where the first paper focused on new understandings of test data analysis theory, this paper will summarize the results of numerous tests and their application to various design strategies for improving solid rear axle tramp damping, with a motivation for enhancing vehicle controllability and highway safety.

This paper documents experimental research determining the belt forces required to create visible and distinct markings on plastic automobile D-rings. The “D-Ring” is the loop through which the shoulder belt feeds before reaching the retractor. In the experimental configuration, ballast is attached to the belt webbing and dropped from a predetermined elevation. By varying the drop height the belt loading characteristics were also changed. Photographs document the resulting loading marks. A Mathematical Dynamic Modeler was used to calculate the Rigid Body Dynamic models to determine occupant belt loads from 5th and 50th percentile Hybrid III anthropomorphic test devices under various crash pulse conditions. These values were correlated to the experimental research. Conclusions are made relating D-ring markings to the delta-V of an automotive accident.

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FORMULAE and curves arc given for the derivatives lρ and lξ for three types of wing; elliptic, straight tapered and trapezoidal, based on a modified form of the Schrenk distribution of lift. Comparison with experimental curves for the derivatives shows that the method gives good agreement and enables reasonably accurate estimation of the rolling performance of an aircraft to be made.