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Several sources report simple equations for calculating the lean angle required for a motorcycle and rider to traverse a curved path at a particular speed. These equations utilize several assumptions that reconstructionists using them should consider. First, they assume that the motorcycle is traveling a steady speed. Second, they assume that the motorcycle and its rider lean to the same lean angle. Finally, they assume that the motorcycle tires have no width, such that the portion of the tires contacting the roadway does not change or move as the motorcycle and rider lean. This study reports physical testing that the authors conducted with motorcycles traversing curved paths to examine the net effect of these assumptions on the accuracy of the basic formulas for motorcycle lean angle. We concluded that the basic lean angle formulas consistently underestimate the lean angle of the motorcycle as it traverses a particular curved path.

This paper explores the accuracy of a planar, impulse-momentum impact model in representing the dynamics of three vehicle-to-ground impacts that occurred during a SAE J2114 dolly rollover test. The impacts were analyzed, first, using video analysis techniques to obtain the actual velocity conditions, accelerations, impact force components and the energy loss for each of the impacts. Next, these same impacts were analyzed using the known initial velocity conditions and the subject impact model. The equations of this impact model yielded calculated values for the velocity changes and energy loss for each impact. These calculated results were then compared to the actual dynamics data from the video analysis of the impacts to determine the accuracy of the impact model results. For all three vehicle-to-ground impacts considered in this study, the impact model results for the velocity changes and energy loss showed excellent agreement with the video analysis results for these parameters.

This paper explores the dynamics of rollover crashes and examines factors that influence the severity of the roof-to-ground impacts that occur during these crashes. The paper first reports analysis of 12 real-world rollover accidents that were captured on video. Roll rate time histories for the vehicles in these accidents are reported and the characteristics of these curves are analyzed. Next, the paper uses analytical modeling to explore the influence that the trip phase characteristics may have on the severity of roof-to-ground impacts that occur during the roll phase. Finally, the principle of impulse and momentum is used to derive an analytical impact model for examining the mechanics of a roof-to-ground impact. This modeling is used to identify the influence of various impact conditions on the severity of a roof-to-ground impact.

This paper explores the influence of the impact conditions on the dynamics and the severity of rollover crashes. Causal connections are sought between the impact conditions and the crash attributes to which they lead. The paper begins by extending previously presented equations that describe the dynamics of an idealized vehicle-to-ground impact. It then considers the behavior of these equations under a variety of impact conditions that occur during real-world rollovers. Specifically, the equations of this impact model are used to explore the ways in which and the extent to which rollover dynamics and severity are influenced by the following factors: (1) the vehicle's shape and its orientation at impact, (2) its weight, center-of-mass location, and roll moment of inertia, (3) its translational speed, (4) its downward velocity, and (5) its roll velocity. Throughout this discussion, data from real-world and staged rollover crashes is used to give the parameter study an empirical basis.

This paper evaluates the use of PC-Crash simulation software for modeling the dynamics of a dolly rollover crash test. The specific test used for this research utilized a Ford sport utility vehicle and was run in accordance with SAE J2114. Scratches, gouges, tire marks and paint deposited on the test surface by the test vehicle were documented photographically and by digital survey and a diagram containing the layout of these items was created. The authors reviewed the test video to determine which part of the vehicle deposited each of these pieces of evidence. Position and orientation data for the vehicle in the test were then obtained using video analysis techniques. This data was then analyzed to determine the vehicle’s translational and rotational velocities throughout the test. Next, the test was modeled using PC-Crash.

This paper examines the validity of the effective mass concept used in the CRASH 3 damage analysis equations. In this study, the effective mass concept is described, the simplifying assumptions that it entails are detailed, and the accuracy of the concept is tested by comparing ΔVs calculated from the CRASH 3 equations to results of numerical simulations with a non-central impact model. This non-central impact model allowed the effective mass concept to be tested in isolation from other assumptions of the CRASH 3 program. The results of this research have shown that the effective mass concept accurately models the effects of collision force offset when certain conditions are met. These conditions are discussed, along with their implications for damage interpretation. This paper also presents an analytic expression that relates damage energy to closing speed (initial relative velocity) for the general case of non-central collisions.

Calculating the speed of a yawing and braked vehicle often requires an estimate of the vehicle deceleration. During a steering induced yaw, the rotational velocity of the vehicle will typically be small enough that it will not make up a significant portion of the vehicle’s energy. However, when a yaw is impact induced and the resulting yaw velocity is high, the rotational component of the vehicle’s kinetic energy can be significant relative to the translational component. In such cases, the rotational velocity can have a meaningful effect on the deceleration, since there is additional energy that needs dissipated and since the vehicle tires can travel a substantially different distance than the vehicle center of gravity. In addition to the effects of rotational energy on the deceleration, high yaw velocities can also cause steering angles to develop at the front tires. This too can affect the deceleration since it will influence the slip angles at the front tires.

This paper clarifies the relationship between the absorbed crush energy and the dissipated crush energy and explores the use of each in crush and conservation of energy analysis. There is inconsistency and confusion in the literature of accident reconstruction regarding when crush analysis and conservation of energy analysis should use the absorbed crush energy and when it should use the dissipated crush energy. It is demonstrated in this paper that crush analysis calls for the absorbed energy, while conservation of energy analysis calls for the dissipated energy. However, this paper also shows that the equations of crush analysis and conservation of energy analysis can be written in terms of either the absorbed or the dissipated crush energies, since the absorbed and dissipated energies are related through the coefficient of restitution (when friction-type energy losses are assumed negligible). The assumptions of crush analysis are explored in order to develop a consistent approach.

This paper reports a method for analyzing data from a DriveCam unit to determine impact speeds and velocity changes in vehicle-to-vehicle impacts. A DriveCam unit is an aftermarket, in-vehicle, event-triggered video and data recorder. When the unit senses accelerations over a preset threshold, an event is triggered and the unit records video from two camera views, accelerations along three directions, and the vehicle speed with a GPS sensor. In conducting the research reported in this paper, the authors ran four front-to-rear crash tests with two DriveCam equipped vehicles. For each test, the front of the bullet vehicle impacted the rear of the stationary target vehicle. Each of the test vehicles was impacted in the rear twice - once at a speed of around 10 mph and again at a speed around 25 mph. The accuracy of the DriveCam acceleration data was assessed by comparing it to the data from other in-vehicle instrumentation.

Accurately reconstructing the speed of a yawing and braking vehicle requires an estimate of the varying rates at which the vehicle decelerated. This paper explores the accuracy of several approaches to making this calculation. The first approach uses the Bakker-Nyborg-Pacejka (BNP) tire force model in conjunction with the Nicolas-Comstock-Brach (NCB) combined tire force equations to calculate a yawing and braking vehicle's deceleration rate. Application of this model in a crash reconstruction context will typically require the use of generic tire model parameters, and so, the research in this paper explored the accuracy of using such generic parameters. The paper then examines a simpler equation for calculating a yawing and braking vehicle's deceleration rate which was proposed by Martinez and Schlueter in a 1996 paper. It is demonstrated that this equation exhibits physically unrealistic behavior that precludes it from being used to accurately determine a vehicle's deceleration rate.

In a 2012 paper, Brach, Brach, and Louderback (BBL) investigated the uncertainty that arises in calculating the change in velocity and crush energy with the use of the CRASH3 equations (2012-01-0608). They concluded that the uncertainty in these values caused by variations in the stiffness coefficients significantly outweighed the uncertainty caused by variations in the crush measurements. This paper presents a revised analysis of the data that BBL analyzed and further assesses the level of uncertainty that arises in CRASH3 calculations. While the findings of this study do not invalidate BBL's ultimate conclusion, the methodology utilized in this paper incorporated two changes to BBL's methodology. First, in analyzing the crash test data for several vehicles, a systematic error that is sometimes present in the reported crush measurements was accounted for and corrected.

PC-Crash™, a widely used crash analysis software package, incorporates the capability for modeling non-constant vehicle acceleration, where the acceleration rate varies with speed, weight, engine power, the degree of throttle application, and the roadway slope. The research reported here offers a validation of this capability, demonstrating that PC-Crash can be used to realistically model the build-up of a vehicle's speed under maximal acceleration. In the research reported here, PC-Crash 9.0 was used to model the full-throttle acceleration capabilities of three vehicles with automatic transmissions - a 2006 Ford Crown Victoria Police Interceptor (CVPI), a 2000 Cadillac DeVille DTS, and a 2003 Ford F150. For each vehicle, geometric dimensions, inertial properties, and engine/drivetrain parameters were obtained from a combination of manufacturer specifications, calculations, inspections of exemplar vehicles and full-scale vehicle testing.

Previous studies have reported and validated equations for calculating the lean angle required for a motorcycle and rider to traverse a curved path at a particular speed. In 2015, Carter, Rose, and Pentecost reported physical testing with motorcycles traversing curved paths on an oval track on a pre-marked range in a relatively level parking lot. Several trends emerged in this study. First, while theoretical lean angle equations prescribe a single lean angle for a given lateral acceleration, there was considerable scatter in the real-world lean angles employed by motorcyclists for any given lateral acceleration level. Second, the actual lean angle was nearly always greater than the theoretical lean angle. This prior study was limited in that it only examined the motorcycle lean angle at the apex of the curves. The research reported here extends the previous study by examining the accuracy of the lean angle formulas throughout the curves.

When reconstructing vehicle accidents, it is often important to record the accident scene roadway geometry. Survey techniques such as the plane surveying method1 and the coordinate and triangulation method2, have been the most widely used recording methods and are generally accepted in the industry. This paper proposes to introduce video tracking photogrammetry as a new tool in gathering accident scene and roadway data. The video tracking photogrammetry technique makes it possible to use accident scene video to record the accident scene geometry by incorporating photogrammetry principles. This paper will also report on the accuracy of the video tracking photogrammetry technique and discuss its strengths and limitations.

This paper details a method for obtaining the coefficient of restitution from a vehicle-to-vehicle crash test and for quantifying the uncertainty in the resulting value. The coefficient of restitution is determined by analyzing accelerometer data to obtain the post-impact velocity conditions for the test and, by then, using the method of least squares to fit an impulse-momentum solution to the results of the accelerometer data analysis. Uncertainties that affect the accelerometer data analysis include uncertainties associated with the acceleration readings and the accelerometer locations within the vehicle-fixed coordinate system. Uncertainties that affect the fit between the impulse-momentum solution and the post-impact velocity conditions include uncertainty associated with the vehicle weights and moments of inertia and uncertainty associated with the placement of the impact center.

This paper presents equations that relate the orientation and spacing of yaw mark striations to the vehicle braking and steering levels present at the time the striations were deposited. These equations, thus, provide a link between physical evidence deposited on a roadway during a crash (the tire mark striations) and actions taken by the driver during that crash (steering and braking inputs). This paper also presents physical yaw tests during which striated yaw marks were deposited. Analysis of these tests is conducted to address the degree to which the presented equations can be used to determine a driver’s actual steering and braking inputs. As a result of this testing and analysis, it was concluded that striated tire marks can offer a meaningful glimpse into the steering and braking behavior of the driver of a yawing vehicle. It was also found that consideration of yaw striations allows for the reconstruction of a vehicle’s post-impact yaw motion from a single tire mark.

Improvements in computer image processing and identification capability have led to programs that can rapidly perform calculations and model the three-dimensional spatial characteristics of objects simply from photographs or video frames. This process, known as structure-from-motion or image based scanning, is a photogrammetric technique that analyzes features of photographs or video frames from multiple angles to create dense surface models or point clouds. Concurrently, unmanned aircraft systems have gained widespread popularity due to their reliability, low-cost, and relative ease of use. These aircraft systems allow for the capture of video or still photographic footage of subjects from unique perspectives. This paper explores the efficacy of using a point cloud created from unmanned aerial vehicle video footage with traditional single-image photogrammetry methods to recreate physical evidence at a crash scene.

This paper examines the use of camera-matching video analysis techniques to quantify the vehicle dynamics and deformation for a dolly rollover test run in accordance with the SAE Recommended Practice J2114. The method presented enables vehicle motion data and deformation measurements to be obtained without the use of the automated target tracking employed by existing motion tracking systems. Since it does not rely on this automated target tracking, the method can be used to analyze video from rollover tests which were not setup in accordance with the requirements of these automated motion tracking systems. The method also provides a straightforward technique for relating the motion of points on the test vehicle to the motion of the vehicle's center-of-mass. This paper, first, describes the specific rollover test that was utilized. Then, the camera-matching method that was used to obtain the vehicle motion data and deformation measurements is described.

This paper describes, demonstrates and validates a method for incorporating the effects of restitution into crush analysis. The paper first defines the impact coefficient of restitution in a manner consistent with the assumptions of crush analysis. Second, modified equations of crush analysis are presented that incorporate this coefficient of restitution. Next, the paper develops equations that model restitution response on a vehicle-specific basis. These equations utilize physically meaningful empirical constants and thus improve on restitution modeling equations already in the literature of accident reconstruction. Finally, the paper presents analysis of four vehicle-to-vehicle crash tests, demonstrating that the application of the restitution model derived in this paper results in crush analysis yielding more accurate ΔV calculations.