If you missed Part I of this article, here is a link: Link to Part I. I'll likely end up putting out this article in 6 or 7 parts.
Prior Studies – Planar Motion and Collisions
Studies Describing the Conceptual Models: The PC-Crash technical manual describes the theoretical models utilized by the software, and users should consult that manual for information related to the latest versions of the models. Beyond that, Steffan and Moser  described the collision and trajectory models used by PC-Crash. The trajectorymodel utilizes the tire and suspension force models and can also account for trailer coupling forces. The collision model utilizes the principle of impulse and momentum, which utilizes a coefficient of restitution and a friction coefficient, or impulse ratio, that influences sliding and relative velocity along the inter-vehicular contact surface. This model assumes the impact force is applied instantaneously to each vehicle and at a single point. The collision model has the capability of incorporating a vertical component. This impact model is similar to the impact model described by Brach and Brach in their accident reconstruction text , though PC-Crash has implemented this model in three dimensions. PC-Crash currently offers two tire models – the linear tire model and the TM-Easy tire model. At the time of Steffan and Moser’s publication, only the linear tire model was available.
In relationship to the PC-Crash tire models, it should be noted that the PC-Crash trajectory model can operate in a three-dimensional context, and so, it can account for the transfer of weight between tires that occurs during a vehicle yaw. However, neither tire model accounts for the change in tire model parameters that occur under varying normal loads. Thus, while the PC-Crash trajectory model has been shown to be adequate for speed analysis purposes, it is unlikely to be adequate for modeling the handling properties and responses of any particular vehicle.
In 1998, Moser and Steffan described the implementation and use of automatic optimization (the “collision optimizer”) within PC-Crash to achieve a reasonable match between the simulation and the actual post-impact trajectory of the vehicles (as defined by physical evidence) and their rest positions. They defined a quality function that would give an objective measure of how closely the simulation matches the evidence. Moser and Steffan stated that the “quality function defines the target of the optimization process. The assumption has been made, that the lower the difference between simulation results and real accident data…the closer the simulation is to the real case.” PC-Crash currently offers three optimization routines – a linear algorithm, a genetic algorithm, and a monte carlo algorithm. The 1998 study by Moser and Steffan demonstrated the use of the linear and genetic algorithms. Moser demonstrated the use of the Monte Carlo algorithm in a 2003 study.
Steffan and Moser  also published an article describing the trailer simulation model of PC-Crash. This model enabled PC-Crash to consider the additional external forces (coupling forces) that would act on the towing and towed vehicles during driving maneuvers and collisions. Steffan and Moser illustrated the use of this model with several example implementations, including one simulation of a crash test involving a vehicle with a trailer.
In a book published in 2012, Wach described the physical models and assumptions used by PC-Crash, including the coordinate systems, the tire models, the antilock brake model, the electronic stability program (ESP) model, the trailer coupling force model, the impact model, the stiffness-based impact model, the mesh-based impact model, the soft-soil model, and the multi-body model. Wach also reports historical information about PC-Crash, noting that “PC-Crash is a program for raod accident simulation. It’s first version was created at the Institute of Mechanics of the University of Graz, Austria, in the early 1990’s. The author of the original idea and basic physical model is Professor Hermann Steffan, in close cooperation with Wolfgang Neubauer and Dr. Andreas Moser. The program development is supported by Dr. Steffan Datentechnick in Linz. The program, a unique world-wide standard in road accident reconstruction, is available in twenty-two language versions.”
Operational Validation Studies: Cliff and Montgomery published a study of the collision and trajectory models of PC-Crash Version 4.1 in 1996. Their stated purpose was “to evaluate PC-Crash in terms of accuracy, based on staged collisions for which speed and trajectory information is known…the staged collisions were reconstructed using PC-Crash and the trajectories were compared to actual measurments of the skid marks and rest positions. Vehicle speeds were compared to the PC-Crash predicted values.” Before analyzing the collisions, Cliff and Montgomery also compared PC-Crash results to hand calculations for simple slide-to-stop and roll-out trajectories. They found that “the simulations and hand calculations produced identical acceleration values for vehicles in locked wheel skids, for vehicle decelerating with partially-braked wheels, and for vehicle in various steering maneuvers.”
Cliff and Montgomery used seven staged collisions reported by Ishikawa [1985, 1993, 1994], which were run at the Japan Automobile Research Institute (JARI), and the twelve staged collisions often referred to as the RICSAC tests (Research Input for Computer Simulation of Automobile Collisions) [McHenry, 1978; Shoemaker, 1978; Jones, 1978; Brach, 1983]. They also used an additional test reported by McHenry in 1973, bringing the total number of collisions they considered to twenty. Cliff and Montgomery noted some inaccuracies in the original test reports for these collisions, including errors related to the degree to which various wheels were impeded following the collisions. They attempted to correct these inaccuracies by examining photographs and sensor data. They also noted that “the vehicle pre-impact speeds were measured, while the post-impact speeds were calculated from accelerometer traces or photographs.”
Cliff and Montgomery noted: “Our evaluation of PC-Crash was conducted in two stages. The first stage was to assess the trajectory model by reconstructing only the post-impact phase of the collisions. The second stage was to assess PC-Crash's ability to model the entire event from initial contact to rest.” The first of these stages would isolate the tire and suspension models in PC-Crash and the second would combine these with the impact model.
In simulating the collisions, Cliff and Montgomery assumed a center of gravity height of 0.5 meters for every vehicle in the study and PC-Crash default suspension values were used on the “medium” setting (now called “normal”). For the first phase (post-impact trajectory only), “Each vehicle was placed in an initial post-impact position on its tire marks…as close to the impact as possible, but where it had likely separated from the other vehicle. Vehicle post-impact velocities and rotational speeds were then varied until the tire traces from the PC-Crash trajectory model matched the tire marks on the [evidence diagram from each test] as closely as possible…Based on the post-impact speeds determined with PC-Crash and the reported pre-impact directions of the vehicles, a linear momentum calculation was done to determine the vehicle pre-impact speeds.”
Cliff and Montgomery concluded that “PC-Crash simulation [predicted] speeds were found to be in good agreement with real world results. For the staged collisions, errors larger than about ±5 km/h could be attributed to inaccuracies in reported wheel brake factors, the inclusion of cases unsuitable for this type of analysis, or tire losses between the initial contact point and where the post-impact simulation was started.”
Other studies agreed with Cliff and Montgomery that there were errors in the RICSAC reports that made up 12 of the collision in their 20 collision dataset. In 1997, McHenry published a reevaluation of the RICSAC collisions, stating that while “the RICSAC tests contain the most comprehensive collection of full-scale test results available to date…some interpretation of the reported results is required, for example, to obtain speed-change (Delta-V) and separation velocities from the accelerometer data. Also some evaluations are required for the approximate extent of wheel drag and steer angles.” McHenry reported analysis to correct some of the reported values for impact-speed changes and separation velocities. McHenry developed “generalized analytical techniques to transform the speed-change information from arbitrary accelerometer locations to the center of gravity. A secondary task was to use the calculated CG speed-change information to calculate the separation velocities…” McHenry presented updated velocity changes and separation velocities (post-impact speeds) for the twelve RICSAC collisions.
In 2002, Brach published another reevaluation of the RICSAC collisions, noting that “some of the collisions lead to a loss in total system momentum, as expected. [Based on the reported information,] some show a gain in system momentum which is not physically possible…it can be concluded that the variations in the change of system momentum are random and due to factors that were not under control in the experimental collisions.”
Cliff and Montgomery also observed that “while conducting simulations in PC-Crash it was found that in cases with significant post-impact vehicle rotation, an adequate estimate of the post-impact velocities could be made by matching the vehicle tire marks during the initial portion of the post-impact spinout. It was not necessary to match the entire trajectory exactly in order to get a good estimate for the velocity.” A 1998 study by Cliff and Bowler, titled “The Measured Rolling Resistance of Vehicles for Accident Reconstruction” confirmed this finding. In that study, Cliff and Bowler found that when there was post-impact rotation of a vehicle, that rotation provided enough evidence to reasonably constrain the vehicle speeds in the simulation. It was not critical to know the level of post-impact braking (or longitudinal resistance) at each wheel. In instances where there was not significant post-impact rotation, they noted that the simulation and the calculated speeds would be more sensitive to the brake factors.
In 2000, Bailey used PC-Crash 5.1 to simulate five staged collisions, the results of which were also reported in his paper. In describing the use of PC-Crash to reconstruct a collision, he observed that “if the simulated post-impact path and rest position match the actual ones, then the investigator can have some confidence in the accuracy of the pre-impact vectors used as input. How accurate the the estimates are still depends on the validity of the particular collision and trajectory models, and on input parameters for the vehicles and terrain.” In describing his results, Bailey concluded that “there was agreement between measured and simulated collision dynamics…the error in calculated pre-impact speeds of the ten vehicles ranged from -3.3 to +4.1 km/h. Vehicle speeds were determined based on post-impact rotation and paths, without detailed information on the braking from each wheel or the actual collision coefficient of restitution.”
Bailey noted that the “five staged collisions were simulated by an engineer not directly involved in the staging of the collisions. Information on wheel-lockups and brake application time were not given to the analyst.” He also noted that “the optimization was usually based only on intermediate positions for each vehicle, rather than rest positions or rest and intermediate positions. The main reason for this is that the braking level of the vehicles was unknown, due to the fact that the brakes could have been applied by the remote vehicle operator at any time near the end of the vehicles’ trajectories.” Given that there was available data related to the collisions which was not provided to the analyst, the results of Bailey’s study tested the operational validity of PC-Crash along with the user’s skill.
Bailey concluded that “the results of the reconstructions suggest that for most cases, where the scene coefficient of friction and vehicle impact and rest positions are known, and at least photographs of the damaged vehicles are available, pre-impact speeds can be estimated within ±5 km/h [3.1 mph] using PC-Crash. Steering and braking values do not need to be known initially, as they can be determined from a certain amount of trial and error work. The ability of the reconstructionist to compare predicted and actual tire paths is a valuable tool available in the simulation approach.”
In 2001, Cliff and Moser reexamined the 20 collisions that Cliff and Montgomery had analyzed in 1996. This time, the collision optimizer was used in PC-Crash Version 5.1. Cliff and Moser stated that “the goal was to let the program determine pre-impact speeds and other impact parameters based on a minimization of the error between the actual and the simulation vehicles’ post-impact trajectories and rest positions…The user still has to enter steering angles, wheel brake factors and some other parameters for the simulation since the optimizer does not vary them. If these parameters are not assumed correctly the collision optimizer may not find an acceptable solution, such that there is poor agreement between the simulation results and the actual collision. In this case the weighted total error will be high, which tells the user that some entered values are likely wrong.”
Cliff and Moser reported that “comparison of the PC-Crash optimizer-determined impact speeds with the actual speeds” resulted in calculated errors “in pre-impact speed ranged from -11.8 to +3.4 km/h, with an average of –1.9 km/h.” In examining Cliff and Moser’s results, it becomes evident that the one case that resulted in an 11.8 km/h speed error was an outlier. For 19 of the 20 cases, the error in pre-impact speed was between -6.3 km/h and +3.4 km/h (-3.9 to 2.1 mph). The error in the vehicle velocity changes for these same 19 cases ranged from -6.7 to +3.5 km/h (-4.2 to +2.2 mph). These results were obtained with optimizer errors ranging from about 1.5% to 10.5%.
In 2012, Heinrichs reexamined the same 20 staged collisions that Cliff and Moser had examined in 2001. Whereas Cliff and Moser had not varied any vehicle parameters or the roadway coefficient of friction in their analysis, Heinrichs examined the sensitivity of the simulation results to such factors. Specifically, he varied the coefficient of friction, the vehicle center of gravity positions, the moments of inertia, the suspension stiffness and damping, the tire model parameters, the wheel braking and steering levels, the intervehicular friction coefficient for the impact, and the coefficient of secondary impacts. Heinrichs concluded that the simulation results were most sensitive to the roadway coefficient of friction. He also showed that when the coefficient of friction was varied, a range of calculated impact speeds would be associated with a single optimizer error level. In other words, the optimizer error is an indicator of simulation quality (how well the simulation matches the optimizer vehicle positions), but not necessarily of simulation accuracy. If the analyst used the “correct” coefficient of friction or considered a range of friction coefficients, then the range of speeds obtained with a low optimizer error would be more accurate than those obtained with a high optimizer error.
Heinrichs did not report actually examining the visual output of a series of simulations that all had the same optimizer error level. This would potentially be a helpful exercise because it is possible that a human analyst would be able to see differences in the simulations that would lead them to reject one of two simulations with the same optimizer error. For instance, one simulation could match tire mark evidence more closely than another and this might not be evident from the calculated optimizer error. At the time of Heinrich’s study, the optimizer error only indicated how well the simulation matched positions input by the user. The most recent version of PC-Crash allows the user to also optimize on tire paths. It would be useful to know the degree to which adding the tire mark paths as a part of the quality function would make the optimizer error an indication of simulation quality, and also, simulation accuracy. The issue of simulation quality versus accuracy will be taken up later in this study.
A 2004 study by Cliff examined two methods for calculating speed from curved tire marks – the critical speed formula and PC-Crash simulation (Version 6.2). Cliff reported 22 yaw tests run with a 1991 Honda Accord EX-R at speeds between 70 and 120 km/h. He indicated that for half the tests, about 30% braking was applied. In its as-manufactured state, the test vehicle had anti-lock brakes, but the ABS system was bypassed and a non-ABS braking system was installed.
In running PC-Crash simulations of these 22 tests, Cliff used the linear tire model. Cliff concluded that “using the measured sliding coefficient of friction, both the critical speed formula and the computer simulations under-predicted the actual speed of the vehicle. Using the measured peak coefficient of friction, both methods over-estimated the actual speed. There was less variance in the computer simulation results.” With the sliding coefficient of friction, the simulations under-predicted the initial speed by an average of 9.0 km/h. With the peak coefficient of friction, the simulations over-predicted the initial speeds by an average of 2.3 km/h. An important observation made by Cliff is that “since the simulation program also takes the change in vehicle path radius into account over a longer distance, it enables the user to easily determine if braking is taking place.”
Zebala  examined the anti-lock braking (ABS) model used in PC-Crash Version 8.2 and compared it to the results of extreme braking tests run with ABS equipped vehicles on a split-µ surface. Zebala notes that, “The accuracy of simulated vehicle movement in the phase of extreme braking is greatly affected by the ABS model. However, it is not practical to include the actual, individual algorithms used in different cars. This is why in [PC-Crash] universal algorithms are used whose task is to meet general criteria of ABS operation in order to solve the majority of typical problems that appear in road accident analysis.” The PC-Crash ABS model controls the level of braking on a wheel-by-wheel basis in order to ensure that each individual wheel does not lock-up. For some real-world ABS systems, the braking level for the rear wheels will be adjusted together and will be limited to the braking level appropriate for the tire on the lower coefficient of friction surface. Zebala refers to this as the “select-low principle” and he notes that the PC-Crash ABS model does not contain this logic. He reported good agreement between PC-Crash and the extreme braking tests on the split-µ surface when this logic was taken into account by manually reducing the braking level on the rear wheel that was on the high-µ surface.
Combination Validation/Calibration Studies: Zebala  used PC-Crash Version 9.2 in conjunction with the linear tire model to analyze lane change maneuvers involving vehicles with reduced tire pressure. Zebala stated, “The authors have made an attempt at parameterization of a tire model in PC-Crash program, based on the results of experimental research into vehicle motion. Attention was focused on one program and one, so-called bilinear tire model, which was selected because of its extreme simplicity from the point of view of an average user. The program validation process enabled first the tuning of the lateral force characteristics of undamaged tires, and next of tires of lowered pressure. Although good compatibility between the simulated and real results was reached, it should be emphasized that the selected maximum slipangles (describing tire lateral force characteristics) have to be treated with the maximum uncertainty of ±33% taken into account. This range also covers the influence of elements neglected in the modeling of the whole vehicle.” Ultimately, Zabala’s study sought reasonable inputs to obtain the best match with his test data, and so while in part a validation study, this study should also be categorized as part calibration study.
Rose  used the “real acceleration” model within PC-Crash 9.0 to model the full-throttle acceleration capabilities of three vehicles with automatic transmissions, as determined from physical testing of those vehicles. This model within PC-Crash yields non-constant vehicle acceleration that depends on speed, weight, engine power, the degree of throttle application, and the roadway slope. Rose reported that “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. In each case, the full-throttle acceleration of the vehicles modeled in PC-Crash showed good agreement with the acceleration of the real vehicles in our road tests.”
Studies that Assume the Validity of PC-Crash: Rose  used PC-Crash to explore the effects of high rates of yaw rotation and steering on the deceleration rates experienced by spinning vehicles. Rose noted that PC-Crash simulation is an efficient and effective manner in which to deal with these effects that are more difficult to incorporate analytically. He stated: “These software packages [HVE and PC-Crash] account for the actual tire travel distances and the effects of rotational kinetic energy using a vector mechanics approach and numerical integration.”
Bailey, M., Lawrence, J., Fowler, S., Williamson, P. et al., "Data from Five Staged Car to Car Collisions and Comparison with Simulations," SAE Technical Paper 2000-01-0849, 2000, doi:10.4271/2000-01-0849.
Brach, R., “Impact Analysis of Two-Vehicle Collisions,” SAE Technical Paper 830468, 1983, doi:10.4271/830468.
Brach, Raymond M., Smith, Russell A., “Re-Analysis of the RICSAC Car Crash Accelerometer Data,” SAE Technical Paper 2002-01-1305, 2002, doi:10.4271/2002-01-1305.
Brach, Raymond M., R. Matthew Brach, Vehicle Accident Analysis and Reconstruction Methods, SAE International, ISBN 0768007763, 2005.
Cliff, W. and Montgomery, D., "Validation of PC-Crash - A Momentum-Based Accident Reconstruction Program," SAE Technical Paper 960885, 1996, doi:10.4271/960885.
Cliff, W. and Bowler, J., "The Measured Rolling Resistance of Vehicles for Accident Reconstruction," SAE Technical Paper 980368, 1998, doi:10.4271/980368.
Cliff, William E., Moser, Andreas, “Reconstruction of Twenty Staged Collisions with PC-Crash’s Optimizer,” SAE Technical Paper 2001-01-0507, 2001, doi:10.4271/2001-01-0507.
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.
Heinrichs, B., Mac Giolla Ri, B., and Hunter, R., "Sensitivity of Collision Simulation Results to Initial Assumptions," SAE Int. J. Passeng. Cars - Mech. Syst. 5(2):807-832, 2012, doi:10.4271/2012-01-0604.
Ishikawa, H., “Computer Simulation of Automobile Collision – Reconstruction of Accidents,” SAE Technical Paper 851729, 1985, doi:10.4271/851729.
Ishikawa, H., “Impact Model for Accident Reconstruction - Normal and Tangential Restitution Coefficients,” SAE Technical Paper 930654, 1993, doi:10.4271/930654.
Ishikawa, H., “Impact Center and Restitution Coefficients for Accident Reconstruction,” SAE Technical Paper 940564, 1994, doi:10.4271/940564.
Jones, I. S., et al., “Research Input for Computer Simulation of Automobile Collisions, Volume IV: Staged Collision Reconstructions,” DOT HS 805 040, December 1978.
McHenry, R., "Computer Program for Reconstruction of Highway Accidents," SAE Technical Paper 730980, 1973, doi:10.4271/730980.
McHenry, Raymond R., et al., “Research Input for Computer Simulation of Automobile Collisions, Volume I: Development of Data Bank,” DOT HS-7-01511, December 1978.
McHenry, Brian G., McHenry, Raymond R., “RICSAC-97: A Reevaluation of the Reference Set of Full Scale Crash Tests,” SAE Technical Paper 970961, 1997, doi:10.4271/970961.
Moser, Andreas, Steffan, Hermann, “Automatic Optimization of Pre-Impact Parameters Using Post-Impact Trajectories and Rest Positions,” SAE Technical Paper 980373, 1998, doi:10.4271/980373.P
Rose, Nathan A., Carter, Neal, Pentecost, David, “Vehicle Acceleration Modeling in PC-Crash,” SAE Technical Paper 2014-01-0464, 2014, doi:10.4271/2014-01-0464.
Rose, Nathan A., Carter, Neal, Beauchamp, Gray, “Post-Impact Dynamics for Vehicles with a High Yaw Velocity,” SAE Technical Paper 2016-01-1470, 2016, doi:10.4271/2016-01-1470.
Shoemaker, Norris E., “Research Input for Computer Simulation of Automobile Collisions, Volume III: Staged Collisions Tests No. 6 through No. 12,” DOT HS-805 039, December 1978.
Steffan, H. and Moser, A., "The Collision and Trajectory Models of PC-CRASH," SAE Technical Paper 960886, 1996, doi:10.4271/960886.
Steffan, Hermann, Moser, Andreas, “The Trailer Simulation Model of PC-CRASH,” SAE Technical Paper 980372, 1998, doi:10.4271/980372.
Wach, Wojciech, Simulation of Vehicle Accidents using PC-Crash, Institute of Forensic Research Publishers, October 23, 2012.
Zebala, J., Wach, W., Ciepka, P., Janczur, R. et al., “Verification of ABS Models Applied in Programs for Road Accident Simulation,” SAE Int. J. Passeng. Cars – Mech. Syst. 3(1):72-99, 2010, doi:10.4271/2010-01-0070.
Zebala, J. and Wach, W., “Lane Change Maneuver Driving a Car with Reduced Tire Pressure,” SAE Technical Paper 2014-01-0466, 2014, doi:10.4271/2014-01-0466.
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