of Pedestrian Impact Collisions with Virtual CRASH 3 and Comparisons with IPTM Staged Tests

Tony Becker, ACTAR, Mike Reade, Bob Scurlock, Ph.D., ACTAR

Introduction and dummy systems as point-like particles. From the dummy was used rather than the puck. Again we see work- theorem [3], we expect a change in kinetic excellent agreement between the analytic solution and In this article, we present results from a series of Virtual energy to be associated with dissipative frictional forces. , with only some slight deviation at high CRASH-based pedestrian impact simulations. We That is: friction values. This is due to the dummy’s body compare the results of these Virtual CRASH pedestrian rotating toward the end of its motion at high speeds. impact simulations to data from pedestrian impact 푓 ̅ collisions staged at the Institute of Police Technology 푊 = ∫ 퐹 ∙ 푑푟̅ = ∆퐾퐸 Figure 3 illustrates the sliding distance and speed versus and Management. 푖 for the puck and dummy, where each is given an 1 2 1 2 = 푚푣푓 − 푚푣푖 (1) initial speed of 30 mph, and a ground contact 2 2 1 Staged Pedestrian Impact Experiments coefficient-of-friction of 0.6 is used in the simulations. where the mass is displaced from point i to point f along We see very good agreement in the behaviors of the Each year the Institute of Police Technology and some path. In the one-dimensional constant frictional puck and dummy. Indeed, focusing on the Management (IPTM) stages a series of pedestrian force approximation, we have: versus time behavior of the two systems in Figure 4, impact experiments as a part of its Pedestrian and first-order polynomial fits are performed to both sets of Bicycle Crash Investigation courses. These experiments 퐹̅ = −휇푚푔푥̂ data. With a simulated ground contact coefficient-of- offer a unique opportunity for participants to gain friction value of 0.6, the puck’s average deceleration hands-on experience setting up controlled experiments, and rate is within 0.3% of the expected value, and the gathering data and evidence, and performing full dummy’s average deceleration rate is within 0.7% of analyses of the collision events using standard 푑푟̅ = 푑푥̅ the expected value. reconstruction approaches in the accident reconstruction community. These analyses can then where 푥̂ points along the direction of . Airborne Trajectory Simulation compared to direct measurements obtained during the Assuming the mass comes to rest at point f, we can write experiments. an expression relating the total sliding distance to the Virtual CRASH is a fully three-dimensional simulation environment; therefore, collision forces can project pre-slide velocity at point i, 푣푖. This is given by: The Virtual CRASH Simulator objects vertically, causing them to go airborne for some 1 time. Indeed, the user can run simulations specifying an Virtual CRASH 3 is a general-purpose fully three- −휇푚푔∆푥 = − 푚푣2 arbitrary initial velocity vector orientation at the start of 2 푖 dimensional accident reconstruction software package simulation, allowing objects to go airborne independent developed by Virtual CRASH, s.r.o., a company based or more familiarly: of collision events. out of Slovakia. Virtual CRASH is a simulation package that uses rigid-body dynamics to simulate 푣2 For clarity, let the x-direction point along the forward collisions between vehicle objects within its ∆푥 = 푖 (2) direction. Let the z-direction point upward vertically, environment; Virtual CRASH simulates multibody 2푔휇 antiparallel to the gravitation direction. In collisions in a manner similar to packages such as the following, we will neglect restitution effects, and so MADYMO [1] or Articulated Total Body [2]. The where ∆푥 = 푥푓 − 푥푖. We conducted a series of assume that the projectiles either come to rest upon impact dynamics are also determined by pre-impact experiments in Virtual CRASH, testing the distance landing or slide to rest at some time after initial ground geometry and specification of the coefficients-of - required to stop a mass as a function of pre-slide speed. contact. From basic kinematics, for a point-mass object friction and -restitution, as well as the inertial properties The puck and dummy objects started at ground height with initial height at ground level, launched at a velocity and were given an initial horizontal velocity. of the objects, which are all specified in the user of magnitude, |푣푖̅ |, at an angle 휃 with respect to the x- interface. Virtual CRASH offers a unique, fast, and Rearranging (2), one expects the simulation to yield axis, we expect the z-position as a function of time to visually appealing way to simulate pedestrian impacts. results consistent with the relation: be given by:

2 Sanity Checks 푣푖 = 휇 ∙ (2푔∆푥) (3) 1 2 푧(푡) = 푣푧,푖푡 − 푔푡 2 2 Simulation of Dissipative Forces Figure 1 illustrates the square of the initial velocity, 푣푖 , 1 = |푣̅ |sin(휃)푡 − 푔푡2 (4) plotted as a function of the quantity (2푔∆푥). In the 푖 2 To better understand how Virtual CRASH performs simulations, the puck was given an initial velocity compared to our expectations from classical physics, we between 10 to 50 mph. The coefficient-of-friction was The total time, 푡푎, in which the object is airborne can be conducted a series of ground slide and projectile motion varied from 0.1 to 1.0 and the total sliding distance was solved for by obtaining the solution to the quadratic: experiments for a cylindrical “puck” and a dummy noted. As indicated by equation (3), the slope of a first- model. The puck was given the same mass as the default order polynomial fit to each set of points should yield 1 푧(푡 ) = |푣̅ |sin(휃)푡 − 푔푡2 = 0 (5) pedestrian model. the coefficient-of-friction used in the corresponding 푎 푖 푎 2 푎 simulations. Excellent agreement is observed between First, we evaluated the distances required for the puck the analytic solution and the simulation as indicated by which yields: and dummy systems to slide to a stop via frictional the slopes of the fits, which serve as estimates of . forces as they traveled along level flat terrain. In our Figure 2 illustrates the corresponding results for the treatment below, we mathematically model the puck same experiments, where the Virtual CRASH default

1 See video online at: https://youtu.be/htIwFYLG_W8 2|푣̅ |sin(휃) Therefore, from (9), (10), and (11) we have: 훥푣 = −(1 + 휀) ∙ 푣 (22) 푡 = 푖 (6) 푛 푅푒푙푛,푖 푎 푔 ∆푣푡 = 휇 · ∆푣푛 (12) Figure 5 shows the total airborne time for simulated 30 훥푣푡 = −휇(1 + 휀) ∙ 푣푅푒푙푛,푖 (23) mph launches of the puck and dummy systems as a The sign of the impulse ratio is determined by the function of sin(휃).2 First-order polynomial fits to these relative velocity vector component tangent to the Let us assume the ground is a flat level surface such 푛̂ = data points yield slopes that estimate the quantity contact surface at the moment of contact. The impulse 푧̂ and 푡̂ = 푥̂ . Let object 1 be an object undergoing ratio is typically associated with the inter-object surface 2|푣푖̅ |/g. Excellent agreement is observed between our projectile motion, and let object 2 be the infinitely analytic solution and simulation to the 1/100% level for contact coefficient-of-friction, whose average behavior massive ground plane. In the no-restitution limit, we is often referred to as the drag factor. In this paper, we both systems. have at time 푡푎 + ∆푡: use the terms interchangeably since we neglect any time-dependent behavior of 휇. Since the object undergoes uniform motion along the Δ푣푧 = |푣푧(푡푎)| (24) horizontal direction (neglecting air resistance), we can solve for the total horizontal airborne distance by: The coefficient-of-restitution is given by the ratio of and normal components of the final to initial relative at the point-of-contact. Δ푣 = −휇 ∙ |푣 (푡 )| (25) 퐷 = 푣 푡 = |푣̅ |cos(휃)푡 푥 푧 푎 푎 푥,푖 푎 푖 푎 2 푣푅푒푙푛,푓 2|푣̅푖| sin(휃) ∙ cos(휃) 휀 = − (13) where the collision pulse width, ∆푡, can be taken as = (7) 푣 푔 푅푒푙푛,푖 vanishingly small. Figure 7 illustrates the relation between the simulated horizontal changes-in-velocity Equation (7), of course, is the famous range equation where the relative velocity is defined as the difference from and vertical changes-in-velocity for the puck and from classical physics. between the velocity vectors of the two interacting dummy systems at the moment just after ground impact, objects at the point-of-contact: after the downward vertical velocity has been arrested. Figure 6 illustrates the total airborne distance as a The plots in this figure were created using 30 mph 푣̅ = 푣̅ − 푣̅ (14) function of the quantity (푠in(휃) ∙ cos(휃)) for 30 mph 푅푒푙 1 2 launch speeds at increasing launch angles between 5

degrees (lowest Δ푣푧) to 85 degrees (largest Δ푣푧) from launches of the puck and dummy systems. First-order The normal and tangent projections of this are given by: polynomial fits to the data serve to estimate the quantity horizontal. There are a few interesting features of note

(2|푣̅ |2/푔). Again, excellent agreement between the in this figure. First, from equation (25), we expect a 푖 푣 = 푣̅ ∙ 푛̂ (15) simulations and the analytic solution is observed to 푅푒푙푛 푅푒푙 first-order polynomial fit to yield a slope equal to the and better than a fraction of a percent. ground contact coefficient-of-friction used in the

simulations. This is indeed the case to within 0.4% for 푣 = 푣̅ ∙ 푡̂ (16) Ground Contact 푅푒푙푡 푅푒푙 the puck system and 6% for the dummy model. We also

note in the dummy model simulations, when Finally, we can rewrite the normal change-in-velocity During the landing phase of projectile motion, the test Δ푣푧exceeds 15 mph (30 degrees), Δ푣푥 deviates from its as: mass interacts with the ground such that a contact-force initial linear behavior. For Δ푣푧 > 25 mph we see a is imparted to the mass, 퐹̅(푡), over a time ∆푡, which dramatic drop in Δ푣푥 for the puck system. Δ푣 = 푣 − 푣 arrests the vertical motion of the mass and 푅푒푙푛 푅푒푙푛,푓 푅푒푙푛,푖 simultaneously retards its horizontal velocity. The = −휀 ∙ 푣푅푒푙푛,푖 − 푣푅푒푙푛,푖 For the dummy system, there are two effects that impulse imparted to the test mass is given by [4]: or explain the non-linear behavior. First, as the launch angle increases, thereby increasing Δ푣푧 , the torque ∆푡 훥푣푅푒푙푛 = −(1 + 휀) ∙ 푣푅푒푙푛,푖 (17) imparted to the dummy’s body increases, causing an 퐽̅ = ∫ 푑푡 ∙ 퐹̅ = 푚∆푣̅ increase in rotational rather than a 0 decrease in linear kinetic energy. Therefore, we see a ∆푡 ∆푡 and slight reduction in the expected horizontal change-in- = ∫ 푑푡 ∙ 퐹푛푛̂ + ∫ 푑푡 ∙ 퐹푡푡̂ (8) 0 0 훥푣푅푒푙푡 = −휇(1 + 휀) ∙ 푣푅푒푙푛,푖 (18) velocity. In the second region, Δ푣푧 > 25 mph, we see the same sharp reduction in Δ푣푥 as in the puck system. This where 푛̂ is the unit vector pointing along the direction Again, we treat the objects as point-like masses for our is related to the reduction in the maximum possible normal to the surface of contact (ground), and 푡̂ points simplified mathematical model. For two objects horizontal impulse that can be delivered to the objects, in the direction orthogonal to 푛̂ . Along the normal- undergoing a collision, the change-in-relative-velocity which is naturally bounded such that the maximum direction we have: is related to the change-in-velocity at the center-of- horizontal change-in-velocity cannot exceed the initial gravity of object 1 is given by the relation [4]: horizontal launch speed. This is further discussed below. ∆푡 퐽푛 = ∫ 푑푡 ∙ 퐹푛 = 푚∆푣푛 (9) 푚̅ Post-Ground Contact 0 ∆푣1̅ = ( ) ∆푣푅푒푙̅ (19) 푚1 and along the tangent direction, we have: The vertical velocity component at first ground contact Here, the system’s reduced mass is given by: is given by: ∆푡 퐽 = ∫ 푑푡 ∙ 퐹 = 푚∆푣 푚1 ∙ 푚2 푣 = 푣 − 푔푡 푡 푡 푡 (10) 푚̅ = (20) 푧,푓 푧,푖 푎 0 푚 + 푚 2|푣̅ |sin(휃) 1 2 = |푣̅ |sin(휃) − 푔 ∙ 푖 (26) 푖 푔 where ∆푣 and ∆푣 are the normal and tangent axis 푛 푡 In the limit where the mass of object 2 becomes infinite projections of change-in-velocity vector ∆푣̅ (such in a ground impact), we have the following: which simplifies to: respectively. The “impulse ratio” is given by:

(21) ∆푣1̅ = ∆푣푅푒푙̅ 푣푧,푓 = −|푣푖̅ |sin(휃) (27) 퐽푡 휇 = (11) 퐽푛

2 A video of the 30 mph 40 degree launch is online at: https://youtu.be/3aSFtCC6y4c With this and equation (25), we can now solve for the To simplify the above expression, let: This implies the condition: final ground speed after landing. This is given by: 푥̃ cos(휃) − 휇 ∙ sin(휃) ≥ 0 (46) cos(휃) = (37) 푣푥,푓 = 푣푥,푖 + Δ푣푥 √푥̃2 + 푦̃2 There are two equivalent ways to interpret this = |푣푖̅ |cos(휃) − 휇|푣̅푖|sin(휃) and condition. First, we can solve for the angle, which gives = |푣푖̅ | ∙ (cos(휃) − 휇 ∙ sin(휃)) (28) 푦̃ the solution to cos(휃) − 휇 ∙ sin(휃) = 0. This gives us a Assuming kinetic energy is dissipated through ground- sin(휃) = (38) boundary angle: √푥̃2 + 푦̃2 contact frictional forces, we can use equation (2) to 1 solve for the total slide distance. −1 Therefore, using (37) and (38), we have: 휃̃ = tan ( ) (47) 휇

푣2 푥,푓 푥̃ + 휇푦̃ 퐷푆푙푖푑푒 = cos(휃) + 휇 ∙ sin(휃) = (39) Therefore, when the launch angle satisfies the condition 2푔휇 2 2 2 √푥̃ + 푦̃ 휃 < 휃̃, equation (32) holds. Otherwise, if the condition |푣̅ | 2 = 푖 ∙ (cos(휃) − 휇 ∙ sin(휃)) (29) is violated, the total distance is simply given by the 2푔휇 The extremum condition above is now given by: range equation (7), where no sliding is expected. Thus, we have: The total projectile travel distance is given by the sum −푥̃′ + 휇 ∙ 푦̃′ = 0 (40) 2 of the sliding distance and the airborne travel distance; |푣̅ |2 ∙ (cos(휃) + 휇 ∙ sin(휃)) 푖 , 휃 < 휃̃ that is: or, 2푔휇 퐷푇표푡푎푙 = (48) 2|푣̅ |2sin(휃) ∙ cos(휃) 푖 , 휃 ≥ 휃̃ 퐷푇표푡푎푙 = 퐷푎 + 퐷푆푙푖푑푒 (30) cos(휃′) + 휇 ∙ sin(휃′) = { 푔 or Figure 9 shows the total throw distance as function of 푥̃′ ∙ (1 + 휇2) = √1 + 휇2 (41) launch angle for 30 mph launches with 휇 =0.6 for both 2|푣̅ |2sin(휃) ∙ cos(휃) 푥̃′√1 + 휇2 puck and dummy systems. We see the simulated results 퐷 = 푖 푇표푡푎푙 푔 track very closely to our analytic solutions. We also see 2 Therefore, using (41), the total throw distance at angle beyond the calculated boundary angle at 59 degrees, the |푣̅ |2 ∙ (cos(휃) − 휇 ∙ sin(휃)) 푖 휃′, is given by: simulated behavior switches from following the Searle + (31) 2푔휇 equation to the Range equation. Table 1 shows the |푣̅ |2 2 difference between the analytic solution and simulated 푖 2 which simplifies to: 퐷푇표푡푎푙(휃′) = ∙ (√1 + 휇 ) 2푔휇 results. The simulated puck system shows better than | |2 0.4% agreement and the dummy system shows better 2 푣푖̅ 2 |푣푖̅ | 2 = ∙ (1 + 휇 ) (42) than 4% agreement with the analytic solution given by 퐷 = ∙ (cos(휃) + 휇 ∙ sin(휃)) (32) 2푔휇 푇표푡푎푙 equation (48), each with much lower averages. This is 2푔휇 shown in Table 1. Checking the concavity at 휃′ , we apply the second Figure 8 illustrates the total throw distance as a function derivative: 2 ̃ of the quantity (cos(휃) + 휇 ∙ sin(휃)) for the puck and We note here that the equation for 휃 has a dependence dummy systems with 30 mph launch speeds and 휇 =0.6. 휕2퐷 푣2 on restitution that has been neglected in this treatment 푇표푡푎푙 = 푖 × {(−sin(휃′) + 휇 ∙ cos(휃′)) and therefore will have different behavior when The slope of a first-order polynomial fit yields estimates 휕2휃 푔휇 2 generalized to account for this effect. This will be the of the quantity(|푣̅ | /2푔휇). This estimate is within × (−sin(휃′) + 휇 ∙ cos(휃′)) 푖 topic of a future article. 0.05% of the expected value for the puck and within +(cos(휃′) + 휇 ∙ sin(휃′))

0.6% for the dummy. Again, we see the deviation from +(cos(휃′) + 휇 ∙ sin(휃′)) The second way to interpret equation (46), is as an upper the linear behavior for higher angles that is associated × (−cos(휃′) − 휇 ∙ sin(휃′))} (43) limit on the impulse ratio. with the expected reduction of horizontal impulse at large launch angles. This is explored below. which simplifies to: 휇(휃) ≤ 1/tan(휃) (49)

Here we note that solving the above expression for |푣̅ | 2 2 푖 휕 퐷푇표푡푎푙 |푣푖̅ | yields the familiar Searle Equation: (휃′) = − < 0 (44) That is, when using the Searle equation, one could use 휕2휃 2 푔휇√1 + 휇 the following form for the coefficient-of-friction:

√2푔휇퐷푇표푡푎푙 1 |푣̅푖| = (33) Thus, the second derivative is negative definite, cos(휃) + 휇 ∙ sin(휃) 휇 = min (푓푑, ) (50) implying that our function 퐷푇표푡푎푙(휃) at 휃′ is indeed a tan(휃) maximum value. Returning to equation (32) above, taking the first where 푓푑 is the measured or typical ground contact drag derivative gives: Limit on Horizontal Impulse factor for the subject case. Let us suppose we know the launch angle is sufficiently large such that we must use 휕퐷 |푣̅ |2 푇표푡푎푙 = 푖 ∙ (cos(휃) + 휇 ∙ sin(휃)) Let us now focus on the particular behavior of our test 휕휃 푔휇 mass just after ground impact. We know a retarding 휇(휃) = 1/tan(휃) (51) × (−sin(휃) + 휇 ∙ cos(휃)) impulse is imparted to our mass upon ground impact; (34) this is given by equation (10). This tangent impulse will Substituting (51) into equation (32) gives: Solving for the extremum values requires the following only be applied so long as there is relative motion along 2 relation to hold: the tangent axis direction between the interacting |푣푖̅ | objects at the point of contact. Once the relative motion 퐷푇표푡푎푙 = 2푔(1/tan(휃)) −sin(휃′) + 휇 ∙ cos(휃′) = 0 (35) vanishes, this impulse component no longer acts on the 2 mass. Therefore, the following relation must hold true × (cos(휃) + (1/tan(휃)) ∙ sin(휃)) for our expression for 퐷 (휃) given by equation (32) 2 whose solution is given by: 푇표푡푎푙 2|푣푖̅ | sin(휃) ∙ cos(휃) to remain valid: = (52) 푔

tan(휃′) = 휇 (36) 푣푥,푓 = |푣푖̅ | ∙ (cos(휃) − 휇 ∙ sin(휃)) ≥ 0 (45) which is simply equation (7), thereby indicating that The impact location along the Ford’s front bumper was simulated behavior is in good agreement with the when the condition of no post-impact ground speed set to either 0.5 ft or 1.5 ft away from the center line, as observed behavior during staged tests. occurs, the total throw distance is simply given by the this was not a well-controlled parameter during the classical range equation, as expected. staged IPTM tests. The simulated dummy’s pre-impact Conclusions orientation was set to either 0 degrees (impact to rear of Figure 10 shows the launch speed as a function of total dummy) or 90 degrees (impact to left side of dummy). We have tested Virtual CRASH for use in modeling throw distance for simulated launches between 10 and Figure 15 depicts the moment-of-impact for two of the pedestrian impacts. The simulator faithfully reproduces 50 mph, held at 20 degree launch angles. The simulated scenarios. It was found that there were no the expected behavior of projectiles during both the coefficient-of-friction is set to 0.6. The corresponding significant differences in the throw distances for airborne and ground sliding phases of their trajectories. Searle curve from equation (33) is shown as well. The impacts to the simulated dummy’s left side compared to The throw distances as a function of impact speed Searle minimum and maximum curves are also drawn. right side. behavior of the simulated dummy model does a good Good agreement is evident between the Searle equation job reproducing the behavior observed during staged and the simulated behavior as shown in Table 2. Note From (48), we expect that the simulation should yield impact experiments as well as that which was observed there is no deviation from Searle behavior, as the 20 the following relation: in prior experiments. degree launch angle is well below the 59 degree boundary angle given by equation (47). |푣푖̅ | ∝ √ 퐷푇표푡푎푙 (53) About the Authors

Staged Collisions at IPTM Figure 16 illustrates the dependence of impact speed as Tony Becker has conducted extensive research in pedestrian and cyclist traffic crash investigation and a function of √ 퐷 . First-order polynomial fits are On August 12, 2015, a series of staged impacts were 푇표푡푎푙 published several articles and books that are widely shown as well. Indeed, we see linear behavior over the conducted at the Institute of Police Technology and used in the field. He is an ACTAR certified accident ensemble of the test runs for each given test scenario. Management at the University of North Florida. These reconstructionist and trainer in Florida. He can be Detailed summaries of the results are shown in Table 5 impacts were conducted as a part of the IPTM course on contacted at [email protected]. and Table 6. To quantify how well Virtual CRASH Pedestrian and Bicycle Crash Investigation. An aerial simulates the dummy behavior observed in the IPTM view of the test site can be seen in Figure 11. During Mike Reade, CD is the owner of Forensic staged tests, we calculate the differences (residuals) these experiments, a plastic anthropomorphic dummy Reconstruction Specialists Inc., a collision between first-order polynomial fits to the Virtual was impacted by a 2005 Ford Crown Victoria. The reconstruction consulting firm located in Moncton, New CRASH results and the test data. A plot of the residuals dummy was 49 lbs in weight and measured 5.83 feet in Brunswick Canada. He is also an Adjunct Instructor is shown in Figure 17. Here we see that the best match height. Prior to impact, the dummy was suspended in an with the Institute of Police Technology and to set of IPTM data is given by Scenario 3, where the upright position, using high-strength fishing line Management – University of North Florida (IPTM- maximum deviation of the predicted impact speed attached to a boom (Figure 12). The boom was mounted UNF) based out of Jacksonville, Florida. He can be based on total throw distance using Virtual CRASH to the rear of a truck offset from the collision path. reached at [email protected]. simulations is less than 3 mph when compared to the Upon impact, the fishing line broke free of the boom, IPTM dataset. allowing the dummy to effectively interact with the Bob Scurlock, Ph.D., ACTAR, is the owner Scurlock vehicle structure, unimpeded. High-speed video footage Scientific Services, LLC, an accident reconstruction was captured of each collision event. Measurements of Figure 18 depicts data from Scenarios 1 and 3, as well consulting firm based out of Gainesville, Florida, USA. the post-impact travel distance were recorded after each as the Searle Minimum curve. The IPTM dataset is He is also a Research Associate at the University of impact, as well as the average deceleration rate of the shown. We also show the best fit to data for wrap Florida, Department of Physics. His website can be 2005 Ford Crown Victoria, which was made to hard trajectory impacts aggregated in the meta-analysis found at www.ScurlockPhD.com. He can be reached at brake upon impact. The point of the dummy’s first presented by Happer et al., along with the [email protected]. ground contact was also carefully recorded (Figure 13). corresponding 85% prediction interval [5]. Here we see The impact speed was also recorded for each test. A excellent agreement between Virtual CRASH simulated References summary of the test data is given in Table 3 and Figure impacts, IPTM data, and expectations from prior studies. 14. Participants of the 40 hour program conducted an [1] “The Pedestrian Model in PC-Crash – The accident reconstruction analysis of each impact, based Simulating Gross Behavior of Test Dummy Introduction of a Multi-Body System and its on the total throw distance of the dummy. Validation”, A. Moser, H. Steffan, and G. Kasanicky. Reconstructed pre-impact vehicle speed estimates were In addition to simulating the total throw versus impact SAE 1999-01-0445. compared to known values recorded during each speed behavior of the test data, we wanted to see if we collision. could simulate the overall behavior of the test dummy’s [2] “Articulated Total Body Model Enhancements, motion using Virtual CRASH. The height and weight of Volume 2: User’s Guide”, L. Obergelfell et al. Report Comparison of Staged Collision Data with Virtual the dummy were both input into Virtual No. AAMRL-TR-88-043 (NTIS No. A203-566). CRASH Dummy Behavior CRASH. The joint stiffness properties of the Virtual CRASH simulated dummy can be adjusted such that the [3] “Classical Dynamics of Particles and Systems”, J. A series of simulations were run in the Virtual CRASH user can tune the dummy’s overall rigidity. This can be Marion and S. Thornton, Harcourt College Publishers, 3 software environment. The simulated dummy’s height done separately for each joint if needed. We chose to New York, New York, 1995. and weight were set to match that of the IPTM test focus on adjusting three of the dummy parameters to get dummy described above. The simulated Crown Victoria reasonable agreement between behavior observed in the [4] “Rigorous Derivations of the Planar Impact passenger vehicle weight was set equal to that of the staged collision 4 video and the Virtual CRASH output: Dynamics Equations in the Center-of-Mass Frame”, B. IPTM test vehicle weight plus driver weight. The these parameters were the overall coefficient-of- Scurlock and J. Ipser, Cornell University Library simulated ground-contact coefficient-of-friction value restitution, coefficient-of-friction, and joint stiffness. arXiv:1404.0250. was set to the average measured at the scene (0.511), as These values were tuned until overall gross behavior was the vehicle-contact coefficient-of-friction (0.5). A was observed to match that of the staged experimental [5] “Comprehensive Analysis Method for coefficient-of-restitution of 0 was used for both ground dummy. The sequence can be seen in Figure 19 for Vehicle/Pedestrian Collisions”, A. Happer et al. SAE 3 and vehicle contact. Table 4 gives a summary of IPTM crash test 4. As expected, we found that one can 2000-01-0846. parameters used for the Virtual CRASH simulation runs. optimize the Virtual CRASH settings until the overall

3A video of this simulation and staged collision footage can be seen online at: https://youtu.be/FM9W9SCteYc

Figure 1: Results from puck slide-to-stop experiments in Virtual CRASH.

Figure 2: Results from dummy slide-to-stop experiments in Virtual CRASH.

Figure 3: Total slide distance versus time (top) and velocity versus time (bottom) for puck and dummy Virtual CRASH simulations. The results for the puck are shown in black. Results for the dummy are in red.

Figure 4: Velocity versus time for Puck (top) and Dummy (bottom) versus time. First-order polynomial fits yield the decelerations rates for the simulation.

Figure 5: Total airborne time for puck (top) and dummy (bottom). First-order polynomial fits are shown.

Figure 6: Total airborne horizontal displacement for puck (top) and dummy (bottom) as a function of (풔퐢퐧(휽) ∙ 퐜퐨퐬(휽)).

Figure 7: 횫풗풙versus 횫풗풛 for the puck (top) and dummy (bottom) systems. First-order polynomial fits are performed to the linear region (open circles).

Figure 8: Total throw distance for puck (top) and dummy (bottom). First-order polynomial fits are performed to the linear region (open circles).

Figure 9: Total throw distance as a function of launch angle for puck and dummy systems.

Table 1: Difference between analytic solution and simulation for the puck (top) and dummy (bottom) systems.

Figure 10: Launch speed estimates as a function total throw distance. Results from puck and dummy simulations are shown for a 20 degree launch.

Table 2: Differences between analytic solution of estimated launch speed and simulations of puck and dummy systems for a 20 degree launch.

Figure 11: Aerial view of test site at IPTM.

Figure 12: Anthrophonic test dummy pre-impact configuration.

Figure 13: Dummy post-impact position.

Table 3: Summary of staged collision data.

Figure 14: Plot depicting impact speed versus total throw distance for staged impacts.

Table 4: Summary of simulation input parameter settings used in Virtual CRASH 3.0.

Figure 15: Moment-of-impact depicted for Scenario 1 (left) and Scenario 4 (right).

Figure 16: Plots depicting relationship between Impact Speed and the square root of the total throw distance. Plots are shown for the four simulated scenarios. The IPTM test data is plotted as well.

Table 5: Summary of results for simulation Scenarios 1 (top) and 2 (bottom).

Table 6: Summary of results for simulation Scenarios 3 (top) and 4 (bottom).

Figure 17: Plot of residuals as a function of simulation fit values for all four Scenarios.

Figure 18: Plot depicting impact speed versus square root of total throw distance for Scenarios 1 and 3.

Figure 19: Comparing simulation of Test #4 of IPTM staged impact.