Analyzing Sideswipe and Narrow Overlap Pedestrian Collisions - A Critique of SAE 2021-01-0881
Introduction
The accident reconstruction literature contains empirical formulas that relate pedestrian throw distance (the distance from first contact with the pedestrian to the pedestrian’s point of rest) to the collision speed of the striking vehicle. The most appropriate empirical equation for analysis of any particular pedestrian collision depends on the type of interaction the pedestrian has with the struck vehicle. As described in Reference 1, the interaction between a pedestrian and the striking vehicle can often be characterized with one of the following categories: (1) a forward projection trajectory; (2) a wrap trajectory; (3) a roof vault; (4) a fender vault; or (5) a pedestrian carry. To this list, we could perhaps add sideswipe pedestrian collisions.
If there is substantial initial overlap between the front of the vehicle and the pedestrian and the upper leading edge of the vehicle sits higher than the pedestrian’s center of mass, the impact will result in a forward projection trajectory. This trajectory is common with blunt and high-fronted vehicles, such as buses, trucks, and sport utility vehicles, or with shorter pedestrians. A forward projection trajectory results in the pedestrian’s center of mass remaining ahead of the vehicle and a significant portion of the vehicle’s impact velocity being imparted to the pedestrian. A wrap trajectory occurs when there is substantial initial overlap between the front of the striking vehicle and the pedestrian and the pedestrian’s center of mass is higher than the leading edge of the striking vehicle. This type of trajectory is characterized by a movement of the pedestrian onto the hood of the vehicle. This will lead to secondary contacts of the pedestrian’s upper torso and head with the vehicle hood, windshield, or A-pillar. Vehicle deceleration from braking is necessary to generate the separation that then occurs between the pedestrian and the vehicle. The pedestrian will typically separate from the vehicle at a speed less than the impact speed of the vehicle. Wrap trajectories are common when the striking vehicle has a low leading edge (sedans and coupes).
A pedestrian carry starts out similar to a wrap trajectory and can occur when the driver of the striking vehicle is not braking at impact. Because of the absence of braking, the pedestrian and the vehicle maintain contact following the initial collision. The vehicle carries the pedestrian along the vehicle’s path, usually until the vehicle driver brakes and the pedestrian separates from the vehicle. A roof vault occurs when the pedestrian is struck such that the vehicle travels underneath them and they impact the roof and then travel completely over the vehicle. Roof vaults often occur when the striking vehicle is traveling at high speeds, or the driver of the vehicle is not braking during the collision. In a roof vault, the pedestrian will come to rest behind the vehicle. A fender vault is essentially an incomplete wrap trajectory. This type of motion occurs when the pedestrian is struck near one of the corners of the front of the vehicle (narrow overlap). The pedestrian will begin the motion of a wrap trajectory but will be projected forward and sideways relative to the vehicle after striking the rounded front bumper and/or passenger or driver side fender. These trajectories can occur with braked or unbraked vehicles. For a fender vault trajectory, the rest position of the pedestrian will be either behind and to the side or next to the vehicle. Sideswipe collisions with pedestrians are collisions in which the engagement with the pedestrian is not even of sufficient width for a fender vault to develop.
Empirical throw distance equations have been developed for forward projection trajectories and wrap trajectories, but not for roof vaults, fender vaults, pedestrian carries, or sideswipes. In part, the lack of empirical equations for these trajectory types is due to a lack of staged collisions of those type on which to base an equation; but, more significantly, these trajectory types are likely to produce a wide range of throw distances for any particular impact speed. The following factors will influence which trajectory type will occur: (a) the height of the pedestrian’s center of mass compared to the height of the upper leading edge of the striking vehicle; (b) which portion of the vehicle first contacts the pedestrian, and how much overlap there is between the pedestrian and the vehicle; (c) the speed of the vehicle; (d) whether or not the driver of the vehicle is braking at the time of the collision; and (e) the speed of the pedestrian. Even within the class of forward projection and wrap trajectories, variation in these variables produces considerable variability in the throw distance associated with any particular vehicle impact speed - hence the ranges associated with the available empirical equations. For pedestrian trajectories involving narrow initial overlap or pedestrian carry, the variability is likely to far exceed the variability that exists for forward projection and wrap trajectories. Despite the considerable variability, in Reference 2, Neale et al. attempted to develop empirical throw distance equations for sideswipes and fender vaults. These equations will be evaluated in this post.
Evaluation of SAE 2021-01-0881 [2]
Reference 2 attempted to extend throw distance equations to narrow overlap (likely to become fender vaults) and sideswipe pedestrian collisions by adding a multiplier to the throw distance equation for wrap collisions developed by Toor and Araszewski [3]. This equation was as follows:
In this equation, S is the pedestrian throw distance in meters and Vv is the vehicle impact speed in km/h. The ± 5.8 km/h in this equation yields the 15th and 85th percentile values, and therefore 70% of instances would be expected to fall within the range established by this formula. The 5th and 95th percentile values could be established with a ± of 9.2 km/h. This range would be expected to encompass 90% of instances.
The authors of Reference 2 used photogrammetric methods to analyze video of 21 sideswipe and narrow overlap pedestrian collisions. Thirteen of these collisions were sideswipes, and 8 were narrow overlap. The vehicle speeds for the sideswipe collisions varied between 9.5 and 38.9 mph. The vehicle speeds for the minor overlap collisions varied between 7.6 and 36.8 mph. The authors observed that, “in all of the impacts analyzed, the pedestrian never achieved a common velocity with the vehicle, but rather only a portion of the vehicles speed was imparted [to] the pedestrian…” The authors of Reference 2 plotted throw distance and vehicle speed as calculated from their video analysis for the 21 collisions they analyzed. They then used Equation (1) to determine what speed this equation would predict based on the throw distance they had determined from the video analysis. Finally, they calculated a multiplier for Equation (1) that if utilized would make the formulas prediction accurate for each instance. Figure 1 is a graph that is similar to Figure 8 in Reference 1, which plots the throw distance versus vehicle impact speed for the 21 pedestrian collisions along with the middle values that would be calculated by Equation (1). The blue diamonds are the individual pedestrian collisions and the black line is Equation (1).
Figure 1– Throw Distance versus Vehicle Impact Speed for the 21 Pedestrian Collisions Analyzed in Reference 2, Plotted with the Toor and Araszewski Wrap Trajectory Equation (Middle Value)
Based on this comparison, the authors of Reference 2 observed: “The comparison between calculated vehicle impact speeds and speeds from video analysis showed that the actual impact speed can be anywhere from approximately equal…to over five times more than the calculated speed [from Equation (1)]. This discrepancy in calculated and actual vehicle speeds showed the importance of pedestrian impact configuration and trajectory analysis in accident reconstruction, as there are potentially large differences in calculated speed values that would negatively affect a reconstruction of a similar pedestrian collision.” This evaluation is both mundane and problematic since the importance of impact configuration and trajectory analysis has long been recognized in pedestrian accident reconstruction and because the authors did not consider the uncertainty in the empirical model represented by Equation (1). Figure 2 is similar to Figure 1, but in this graph, instead of plotting the middle value produced by Equation (1), the 15th and 85th percentile values from this equation have been plotted (the two dashed black lines). The space between the two black dashed lines is the 15th to 85th percentile range from Equation (1). Plotting this range reveals that 5 of the collisions fall within the range, and another 2 are very close. These two would certainly be contained by the 5th and 95th percentile band of the model.
Figure 2 – Throw Distance versus Vehicle Impact Speed for the 21 Pedestrian Collisions Analyzed in Reference 1, Plotted with the Toor and Araszewski Wrap Trajectory Equation (15th and 85th Percentile Values)
The authors of Reference 2 did not include adequate documentation in their article for an evaluation of the trajectory types involved in each of the collisions they analyzed. Could it be that the 7 collisions adequately captured within the range of Equation (1) fit the assumptions of that model, whereas the other 14 collisions did not? Regardless, no multiplier needs to be applied for Equation (1) to adequately characterize these 7 collisions.
The authors of Reference 2 continued their analysis by characterizing the interaction between the pedestrian and the vehicle in each of the collisions as engagement or non-engagement. The graph in Figure 3 is similar to Figure 2, with the exception that the points for the non-engagement collisions have been removed and the color of the points for the engagement collisions have been changed to orange. From examination of Figure 3, it is apparent that the non-engagement collisions were further from the extents of the Toor and Araszewski wrap trajectory model. This is expected since wrap trajectories are characterized by substantial engagement between the pedestrian and the vehicle. For the remaining points on Figure 3, the 15th and 85th percentile envelope of the Toor and Araszewski model captures about half of the points.
Figure 3 – Throw Distance versus Vehicle Impact Speed for the 13 Pedestrian Collisions with Engagement Analyzed in Reference 1, Plotted with the Toor and Araszewski Wrap Trajectory Equation (15th and 85th Percentile Values)
Before going further into the analysis reported in Reference 2, consider several additional datasets that will illuminate underlying issues with the approach adopted by Reference 2. First, consider the research by Randles et al. in Reference 4. These authors studied real-world pedestrian collisions captured from a camera in a bus station clock tower “overlooking a busy downtown intersection” in Helsinki, Finland. The camera captured 15 vehicle-pedestrian collisions, and Randles et al. analyzed 13 of these using “digitizing motion analysis software to quantify the pre-impact and post-impact trajectories of both the vehicle and the pedestrian for each accident.” These 13 collisions included 4 fender vaults, 7 wrap trajectories, and 2 forward projections. In Figure 4, the four fender vaults from Reference 4 are plotted along with the engagement collisions reported by Reference 2, since these fender vaults are consistent with the category of collisions in Reference 1 that had narrow overlap with good engagement. Figure 4 represents these points with purple circles. These points fall outside the 15th to 85th percentile extents of the Toor and Araszewski wrap trajectory model.
Figure 4 – Additional Collisions Added to Figure 3
Next, consider a 2009 study by Moser et al. [5] published at the joint ITAI-EVU Conference. This study compared a simulation using the PC-Crash pedestrian model to a real-world pedestrian collision and a crash test intended to mimic this collision. This study describes two crash tests, but only reported the speed and throw distance for one of them. That datapoint is also plotted on Figure 4. This datapoint falls outside the 15th and 85th percentile range of the Toor and Araszewski equation.
Finally, consider the 2009 study by Kasanicky and Kohut [6], which presented 9 successful “partial overlap” pedestrian impact tests. These authors reported 13 total tests, but 4 of these were excluded from the analysis by the authors. This dataset for the remaining tests is also plotted on Figure 4. All 9 points fall within the 15th and 85th percentile range of the Toor and Araszewski equation. It is interesting that despite being partial overlap collisions, the Kasanicky and Kohut tests fall fully within the boundaries of the Toor and Araszewski formula. The implies greater velocity transfer to the dummy in these tests from the test vehicle than what would typically occur in a partial overlap impact configuration. We suspect this is the result of the characteristics of the dummy used for these tests. This dummy is shown in Figure 5. This dummy is atypical for pedestrian impact tests in that it is able to stand without support. This indicates joints that are stiff or constrained in a way that the joints of most pedestrian dummies are not, and this is likely to result in more significant velocity transfer to the entire dummy through these joints.
Figure 5 – The Dummy Utilized by Kasanicky and Kohut
Ultimately, the reason that some of the points in Figure 4 fall within the extents of the wrap trajectory model and others do not can be thought of in terms of projection efficiency, which is defined as follows:
In this equation, vproj is the projection speed of the pedestrian, vimpact is the impact speed of the vehicle, and nproj is the projection efficiency. This is a measure of the percentage of the vehicle speed that is imparted to the pedestrian. Searle reported a typical projection efficiency of 0.64 for adults impacted by a low-fronted vehicle, 0.744 for adults impacted by a high-fronted vehicle, 0.727 for children impacted by a low-fronted vehicle, and 0.831 for children impacted by a high-fronted vehicle. Toor and Araszewski [3] reported an average projection efficiency for wrap trajectories of 0.8 and an average projection efficiency for forward projection trajectories of 0.95.
The points that fall within the extents of what Equation (1) would predict are from collisions with projection efficiencies within the range of those characteristic of wrap trajectories. Those that fall outside the extents of Equation (1) have projection efficiencies lower than typical of wrap trajectories and more consistent with fender vaults. Thus, the crux of the issue is not really if the engagement with the pedestrian is narrow or substantial as much as it is how much of the vehicle’s velocity is imparted to the pedestrian. In some instances, a collision with a pedestrian could be with the front-end corner of the vehicle but the collision could still impart significant velocity to the pedestrian. In other instances, the collision could be with the front-end corner and the pedestrian could fall off the side of the vehicle before a substantial portion of the vehicle’s velocity was imparted to them. This could be influenced by the shape of the vehicle, the pedestrian’s velocity, and the gait position of the pedestrian when struck.
In my view, it is not advisable to lump fender vaults and sideswipes with wrap trajectories to try and find an empirical model that will fit both. This is essentially what the authors of Reference 2 were attempting by introducing a multiplier to a wrap trajectory model to make it fit with fender vaults or sideswipe impacts. If one wanted to make such an attempt, one could leave the lower bound of Equation (1) intact and apply a multiplier to the upper bound. For example, Figure 6 shows how the extents of the wrap trajectory model would change if the upper bound were multiplied by 1.7. This would encompass most of the data (excluding the sideswipes) but would produce speed ranges with too much uncertainty to be useful in most cases. Our contention in this paper is that, particularly for fender vaults and sideswipe pedestrian collisions, it would be better to have a method of analysis (namely, multibody simulation, to be covered in a future post) that allows the analyst to consider the specific evidence (throw distance, contact points on the vehicle and pedestrian, injury locations, pedestrian velocity, etc.) and correlate that to the speed of the vehicle.
Similar criticisms could be offered in relationship to Reference 2’s attempt to fit the Toor and Araszewski wrap trajectory model to the non-engagement collisions they studied. Figure 7 shows these points (blue diamonds) plotted in comparison to the 15th and 85th percentile extents of the Toor and Araszewski wrap trajectory model. Why attempt to fit this model to the wrap model, when a simple linear fit appears it would be adequate? There are likely too few collisions represented to say if this pattern would hold up with a larger dataset, but there are more than adequate points to cast doubt on an attempt to morph the wrap trajectory model to fit these points.
Figure 6 – Throw Distance versus Vehicle Impact Speed for the 13 Pedestrian Collisions with Engagement in Reference 1 Plus Additional Tests, Plotted with the Toor and Araszewski Wrap Trajectory Equation (15th and 1.7 x 85th Percentile Values)
Figure 7 – Non-Engagement Collisions from Reference 1 Plotted in Comparison to the Toor and Araszewski Wrap Model and with a Simple Linear Fit
References
Ravani, B., Brougham, D., Mason, R.T., “Pedestrian Post-Impact Kinematics and Injury Patterns,” SAE Technical Paper 811024, doi:10.4271/811024.
Neale, W.T., Danaher, D., Donaldson, A., and Smith, T., “Pedestrian Impact Analysis of Side-Swipe and Minor Overlap Conditions,” SAE Technical Paper 2021-01-0881, 2021, doi:10.4271/2021-01-0881.
Toor, A. and Araszewski, M., “Theoretical vs. Empirical Solutions for Vehicle/Pedestrian Collisions,” SAE Technical Paper 2003-01-0883, 2003, https://doi.org/10.4271/2003-01-0883.
Randles, B., Fugger, T., Eubanks, J., and Pasanen, E., “Investigation and Analysis of Real-Life Pedestrian Collisions,” SAE Technical Paper 2001-01-0171, 2001, doi:10.4271/2001-01-0171.
Moser, A., Steffan, H., Strzeletz, R., “Movement of the Human Body Versus Dummy after the Collision,” Proceedings of the 1st Joint ITAI-EVU Conference, 18th EVU Conference, 9th ITAI Conference, pp. 87-105, 2009.
Kasanicky, G., Kohut, P., “New Partial Overlap Pedestrian Impact Tests,” Proceedings of the 1st Joint ITAI-EVU Conference, 18th EVU Conference, 9th ITAI Conference, pp. 107-126, 2009.
Featured image by Wesley Tingey on Unsplash