Volume 15, Issue 1

ollision C

Volume 15 Issue 1

The International Compendium for Crash Research

Comparison of Occupant Stress in Frontal Collisions with varying degrees of seat belt use

Crash-Induced Yaw Motion on Airbag Control Module Delta-V

Legal Challenges

Regarding EDR Data In Testimony includes “Mock Deposition”

Corrections to Off-axis Delta-V Measurements from Event Data Recorders

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Contents

Volume 15 Issue 1

inside

6

4

Letter From the Editor (Survey Results)

5

Collision Magazine Info and Advertiser Index

features 6

Corrections to Off-Axis Delta-V Measurements from Event Data Recorders

40

by Bob Scurlock, Andrew Rich, and Kyle Poe

40

Aftermarket ECU’s for Crash Reconstruction in a Growing UTV Market

by David Carr

46

An Overview of the Subaru Eyesight Advanced Driver Assistance System

by Shawn Harrington

56

82

Crashology: Validation of Ford SG3v1 Speeds Acquired and Derived with Berla iVe

by Wesley Vandiver and Robert Anderson

60

Legal Challenges Regarding EDR Data in Testimony

by James Norris and David A. Chapman

82

94

Crash-Induced Yaw Motion Effects on Airbag Control Module Delta-V

by Micky Marine and Steve Werner

94

Comparison of Occupant Stress in Frontal Collisions with Varying Degrees of Seat Belt Use

by Annika Kortmann

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Letter from the editor Not long ago we circulated a poll to see how subscribers felt about Collision moving to an all-digital format. We were expecting a definitive response one way or another; however, it ended up being almost a draw with a slight edge to Collision staying a hard copy print format publication. By a small margin, subscribers want us to stay with a printed format so, at least for the foreseeable future, that's the plan.

That doesn't mean we're not exploring other ways to make Collision or parts of Collision available digitally. As we run out of back issue hard copies, for example, we will continue to make those available digitally.

Another positive outcome of the survey were the requests for comments. One question was: "What do you like the most about Collision Magazine? " The answers also varied widely although the overwhelming majority were positive.

Overall, the comments reflected a widely held view that Collision contained pertinent, timely and fresh/original articles which were seen as wide ranging and, at the same time, perceived as marginally biased toward EDR data topics. However, the overall satisfaction with Collision rated 4.47 on a scale of 1-5. In short, we are open to pretty much every aspect or topic related to crash analysis. However, EDR technology related topics may be viewed by many as the future of this profession; therefore, there is a greater number of EDR research articles coming in at this time.

published in Collision at the $99 subscription rate (that's only about $5.50 per article) which doesn't count the access to EDR Summit presentations and crash test data.

On the flip side, there were great suggestions about valueadd components of the subscription which we're looking into. And other ways to make Collision more useful to subscribers. We'll be looking for ways to implement some of the suggestions as we go forward. More hands-on kinds of case problems, articles on specific topics - newly emerging and those with long-standing higher levels of interest - are all on our "radar" now and, as I noted, we're looking for ways to adopt the many valuable suggestions we got from the survey.

Although we were unable to host an EDR Summit this past year due to COVID-19, we were able to catch up on some of the articles from past Summits and add new and interesting information from other authors to this issue. We're also hoping that we'll be able to return to hosting an EDR Summit in 2022 and are actively looking for a (more) suitable venue and time slot for that event. Ideally, we'd like to be able to announce the date and location in the next issue of Collision but, like so much these days, some things are out of our hands.

On that note, the staff at ColThe other question was: "We'd like to hear more from you lision would like to acknowlabout ways to improve Collision Magazine. If you have edge the untimely passing something more to add, maybe something we didn't ask of another of our long time or a comment or suggestion, feel free to include that." This associates, James "Doug" generated a number of clearly, well thought out responses English. Doug passed retouching on a number of topics and subjects and gave us cently after a valiant struggle some great guidance in terms of future article focus and se- with cancer. Until his retirement from the San Diego lection criteria.

Police department as an AcThere were a couple comments that focused on the cost of cident Investigation Bureau Collision if it were to go digital versus stay in a print for- Sergeant in 2013 Doug had mat; which seems to have exposed a lack of information or served the community in SWAT, Air Support, and the Trafunderstanding of the cost to host a digital copy of the maga- fic division since 1981. For several years, leading to and afzine. Using a secure, digital source to host and distribute an ter his retirement from the PD, Doug was an integral part electronic version of Collision is marginally less expensive of our the ARC-CSI Crash Conference and a leader for the than the current printed version. Many respondants replied Crash Team Boot Camp for more than 4 years. Doug is they would expect the cost of a subscription to decrease survived by his wife, Debbie, 6 children and 6 grandchilsignificantly if moved to a digital format. From a busniess dren. His daughter, Amanda, developed an interest in crash standpoint, we simple can't offer Collision at a lower price investigation and for the last few years has been teaching the and continue to deliver a quality publication; print or digi- CDR Technician class with Doug; she carries on his legacy tally. Consider, for example, that one SAE paper delivered in that regard today. digitally - at the member rate - is about $27. Over the last Scott Baker 15 Volumes of Collision, we average about 9 articles per isManaging Editor sue, twice a year. That equates to roughly 18 original articles 4 Collision Magazine - Volum 15 Issue 1

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ADVERTISER INDEX 4N6XPRT Systems

Inside Back

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SUBMIT AN ARTICLE If you would like to submit an article to be published in Collision please use the following link:

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All rights reserved, © 2021 Crash Data Group Inc. The opinions and conclusions expressed in this publication and any associated data and throughout the articles attributed to specific authors are the opinions and conclusions of the authors noted and not necessarily the editorial staff or anyone else for that matter. While some articles have been reviewed for content, the accuracy of reprinted models or equations cannot be fully guaranteed. It is the responsibility of the reader to apply critical thinking to an individual review of the content and make their own personal judgements as to its value to them, individually.

At the end of the day, facts belong to everybody, any other opinions to us. The distinction is yours to draw...otherwise, the opinions expressed herein are not necessarily those of any employer, not necessarily ours and probably not necessary.

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Corrections to Off-Axis Delta-V Measurements from Event Data Recorders Bob Scurlock, Ph.D., ACTAR

I

ntroduction

Andrew Rich, BSME, ACTAR

In this article, we derive a mathematical transformation which corrects ∆v measurements from event data recorders at arbitrary positions in a vehicle to the equivalent values at the center-of-gravity. The method is illustrated using staged collision data. We also demonstrate the method’s consistency with simulation.

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Kyle Poe

Use of EDR Data It has become increasingly common for event data recorders (EDRs) to play a central role in accident reconstruction analyses. Both pre-crash speed data as well as acceleration and change-in-velocity (CG) data can provide extremely valuable constraints for the analyst’s calculations and corresponding opinions. Though it is common for event data

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recorders to be located very near a vehicle’s CG, this is not always the case. The analyst must be aware of how an EDR’s distance from a vehicle’s CG can cause inaccuracies to be introduced into an analysis if not properly corrected for. 1,2 Even when near or at the center-of-gravity, it is important for the analyst to be aware of how EDR-based results may be affected by issues such as large rotational velocities. Below, we develop a mathematical transformation to correct for EDR displacement from the CG.

Position of Points in a Moving Reference Frame

Mathematical Development of Transformation Equations

where is the position vector of the moving reference is the frame’s origin with respect to the inertial frame, position of point P with respect to the moving reference frame, and is the position of point P with respect to the inertial frame (Figure 1).

We begin with a rigorous derivation of the equations needed for our inverse transformation from EDR measured at the center-of-gravity based on classical to equivalent mechanics. For a thorough review of classical mechanics, we refer the reader to reference. 3

The position of an arbitrary point, P, can be specified with respect to an inertial frame (Earth frame), O, as the vector sum of P’s position with respect to a moving reference frame, O', and the position of the moving reference frame’s origin with respect to the inertial frame. That is,

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Velocity of Points in a Moving Reference Frame Taking the time derivative of the previous equation, we can calculate the linear velocity of point P in the inertial frame. This is given by: � 𝑅𝑅�� � � 𝑣𝑣̅ �,� � 𝑉𝑉� � � 𝑟𝑟̅� �

(1)

where 𝑣𝑣𝑣�,� indicates the linear velocity of point P evaluated in the inertial reference frame 𝑂𝑂, and the linear velocity of frame 𝑂𝑂𝑂 with respect to frame 𝑂𝑂 � � is given by 𝑉𝑉� � � 𝑅𝑅�� � . �

Suppose we know the position of point P with respect to frame 𝑂𝑂𝑂, given by 𝑟𝑟𝑟 .

That is, we can write:

�

𝑟𝑟̅ � � 𝑟𝑟��� 𝑥𝑥� � � 𝑟𝑟��� 𝑦𝑦� � � 𝑟𝑟��� 𝑧𝑧𝑧 �

�

(2)

� � 𝜆𝜆̅ 𝜆𝜆� ̅ � 𝜔𝜔

The components of 𝑟𝑟𝑟 � in frame 𝑂𝑂𝑂 can be related to the components in frame 𝑂𝑂 by a 3�3 rotation matrix M: 𝑟𝑟��� 𝑟𝑟�� � � �𝑟𝑟� � � � ∙ �𝑟𝑟�� � � 𝑟𝑟� 𝑟𝑟���

Taking the derivative of both sides of (2) with respect to time, and applying the product rule, we have:

� , a vector of For an infinitesimal rotation in frame O about an arbitrary axis 𝛿𝛿𝛿 fixed magnitude, 𝜆𝜆̅, is transformed to:

This implies:

� � 𝜆𝜆̅ 𝛿𝛿𝛿𝛿̅ � 𝛿𝛿𝛿 � 𝛿𝛿𝛿𝛿̅ 𝛿𝛿𝛿 � � 𝜆𝜆̅ 𝛿𝛿𝛿𝛿 𝛿𝛿𝛿𝛿

8 Collision Magazine - Volum 15 Issue 1

We can now rewrite (3) as:

� 𝑟𝑟̅� � � 𝑣𝑣̅ �,� � 𝜔𝜔 � � 𝑟𝑟̅ �

�

(4)

(5)

(10)

Here 𝑣𝑣𝑣�,� is the linear velocity of point P whose components are evaluated in the moving reference frame, 𝑂𝑂� : �

�

�

𝑣𝑣̅ �,� � 𝑉𝑉� � � 𝑣𝑣̅ �,� � 𝜔𝜔 � � 𝑟𝑟̅ �

(11)

(12)

Acceleration of Points in a Moving Reference Frame Taking the time derivative of (12), we can now find an expression for the acceleration of point P. This is given by: � � 𝑎𝑎��,� � 𝑣𝑣̅� �,� � 𝑉𝑉�� � � 𝑣𝑣̅� �,� 𝑑𝑑 � �𝜔𝜔 � � 𝑟𝑟̅ � � 𝑑𝑑𝑑𝑑

(13)

The first term is simply the linear acceleration of the moving reference frame 𝑂𝑂� with respect to the inertial frame 𝑂𝑂: � � 𝑉𝑉�� � � 𝑎𝑎� �

(3)

where the term in the first set of parentheses represents the contribution to the time rate of change of vector 𝑟𝑟𝑟 � due to time-dependent components evaluated with respect to frame 𝑂𝑂𝑂, and the second term represents the contribution due to the frame 𝑂𝑂𝑂 time-dependent orientation with respect to frame 𝑂𝑂.

where,

(9)

Thus,

�

𝑧𝑧̂ � ∙ 𝑥𝑥� 𝑧𝑧̂ � ∙ 𝑦𝑦�� 𝑧𝑧𝑧 � ∙ 𝑧𝑧̂

𝜆𝜆̅ → 𝜆𝜆̅ � 𝛿𝛿𝜆𝜆̅

𝑟𝑟��� 𝑥𝑥�� � � 𝑟𝑟��� 𝑦𝑦�� � � 𝑟𝑟��� 𝑧𝑧𝑧� � � � � �𝑟𝑟��� 𝑥𝑥� � � 𝑟𝑟��� 𝑦𝑦� � � 𝑟𝑟��� 𝑧𝑧𝑧 � � 𝜔𝜔

where 𝜔𝜔 � is the instantaneous angular velocity vector of the reference frame 𝑂𝑂� as measured in frame 𝑂𝑂.

Finally, combining (1) and (10), we have our final expression for the linear velocity vector of point P with respect to the inertial frame 𝑂𝑂:

Here 𝑥𝑥�, 𝑦𝑦�, and 𝑧𝑧𝑧 are the ortho-normal basis vectors for the inertial frame 𝑂𝑂, whose orientations we take as fixed (time-independent), and 𝑟𝑟�� , 𝑟𝑟�� , and 𝑟𝑟�� are the time-dependent components along those basis vectors. The rotation matrix is given by the direction cosines:

𝑟𝑟̅� � � �𝑟𝑟���� 𝑥𝑥� � � 𝑟𝑟���� 𝑦𝑦� � � 𝑟𝑟���� 𝑧𝑧𝑧 � � �� 𝑟𝑟��� 𝑥𝑥�� � � 𝑟𝑟��� 𝑦𝑦�� � � 𝑟𝑟��� 𝑧𝑧𝑧� � �

(8)

�

𝑟𝑟̅ � � 𝑟𝑟�� 𝑥𝑥� � 𝑟𝑟�� 𝑦𝑦� � 𝑟𝑟�� 𝑧𝑧𝑧

𝑦𝑦� � ∙ 𝑥𝑥� 𝑦𝑦� � ∙ 𝑦𝑦� 𝑦𝑦� � ∙ 𝑧𝑧̂

𝑥𝑥�� � � 𝜔𝜔 � � 𝑥𝑥� � 𝑦𝑦�� � � 𝜔𝜔 � � 𝑦𝑦� � �𝑧𝑧𝑧 � � 𝜔𝜔 � � 𝑧𝑧̂ �

𝑣𝑣̅ �,� � 𝑟𝑟��� 𝑥𝑥� � � 𝑟𝑟���� 𝑦𝑦� � � 𝑟𝑟�� � 𝑧𝑧𝑧 �

where 𝑟𝑟𝑟 � can be expressed with respect to frame 𝑂𝑂 as:

𝑥𝑥� � ∙ 𝑥𝑥� � � �𝑥𝑥� � ∙ 𝑦𝑦� 𝑥𝑥� � ∙ 𝑧𝑧𝑧

(7)

With (7), we can now evaluate the time derivatives of the frame 𝑂𝑂� basis vectors:

�

where 𝑥𝑥� , 𝑦𝑦� , and 𝑧𝑧𝑧 are the ortho-normal basis vectors for the moving frame 𝑂𝑂𝑂, whose orientations can change with time with respect to frame 𝑂𝑂, and 𝑟𝑟��� , 𝑟𝑟��� , and 𝑟𝑟��� are the time-dependent components along those basis vectors.

Volume 15 Issue 1.indd 8

or in the limit, 𝛿𝛿𝛿𝛿 𝛿 0,

(14)

For the second term, we have:

𝑑𝑑 � � �𝑟𝑟� � 𝑥𝑥� � 𝑟𝑟���� 𝑦𝑦� � � 𝑟𝑟���� 𝑧𝑧𝑧 � � 𝑑𝑑𝑑𝑑 � � 𝑟𝑟���� 𝑥𝑥� � � 𝑟𝑟���� 𝑦𝑦� � � 𝑟𝑟���� 𝑧𝑧𝑧 � � 𝑟𝑟� �� 𝑥𝑥�� � � 𝑟𝑟� �� 𝑦𝑦�� � � 𝑟𝑟� �� 𝑧𝑧𝑧� �

� 𝑣𝑣̅� �,� �

�

�

�

(15)

where 𝑟𝑟���� 𝑥𝑥� � � 𝑟𝑟���� 𝑦𝑦� � � 𝑟𝑟���� 𝑧𝑧𝑧 � is the linear acceleration of point P in frame 𝑂𝑂� , �

which we denote 𝑎𝑎��,� . Using (8), the second term in (15) becomes 𝑟𝑟���� 𝑥𝑥�� � � 𝑟𝑟���� 𝑦𝑦�� � � 𝑟𝑟���� 𝑧𝑧𝑧� � � 𝜔𝜔 � � �𝑟𝑟���� 𝑥𝑥� � � 𝑟𝑟���� 𝑦𝑦� � � 𝑟𝑟���� 𝑧𝑧𝑧 � � � � 𝑣𝑣̅ �,� � 𝜔𝜔

�

(16)

We can thus rewrite (15) as: (6)

� � � 𝑣𝑣̅� �,� � 𝑎𝑎��,� � 𝜔𝜔 � � 𝑣𝑣̅ �,�

(17)

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The final term in (13) is: 𝑑𝑑 �𝜔𝜔 � � 𝑟𝑟̅ � � � 𝜔𝜔 �� � 𝑟𝑟̅ � � 𝜔𝜔 � � 𝑟𝑟̅� � 𝑑𝑑𝑡𝑡

Using (10), we can rewrite the second term in (18) as: �

�

(19)

(20)

Let us now suppose we have two vehicles undergoing a collision. We can assign to each vehicle its own moving reference frame 𝑂𝑂�� , where 𝑘𝑘 is an index used to label the vehicle, and each vehicle frame origin is placed at the CG. Let us also suppose, at a given point P, vehicle k has an accelerometer. Let’s now denote the accelerometer’s position with the superscript A. Suppose that the accelerometer is sufficiently far away from the volume of crush damage, that we can regard its position as fixed and stationary with respect to the vehicle’s reference frame. That is, we have: (21)

�� in cylindrical coordinates by: We can re-express the vectors 𝑟𝑟𝑟�� and 𝜔𝜔 and

(23)

�� �𝑡𝑡� � |𝜔𝜔 �� �𝑡𝑡�| ∙ 𝜔𝜔 ��𝑡𝑡� 𝜔𝜔

(24)

where we define an instantaneous right-handed cylindrical coordinate system whose axes are centered at the accelerometer, where the unit vector 𝑟𝑟�𝑟 � �𝑡𝑡� points from the CG to accelerometer position, 𝜔𝜔 ��𝑡𝑡� defines the axis of rotation, and 𝜃𝜃��� �𝑡𝑡� points in the direction of rotation (Figure 2).

(25)

(26)

Let’s now examine the special case where (1) rotation occurs only about the inertial frame’s 𝑧𝑧𝑧 axis and (2) 𝑟𝑟𝑟�� lies on the �� � � �� � plane, thereby reducing our model to two dimensions (Figure 3). Note, (1) ensures 𝜔𝜔 ��� �𝑡𝑡� and 𝜔𝜔 �� �𝑡𝑡� are � ii both aligned with the 𝑧𝑧𝑧 axis and (2) ensures 𝑟𝑟𝑟�,∥ � 0. With these simplifying assumptions, we have:

�� �𝑡𝑡� � �𝜔𝜔 �� �𝑡𝑡� � 𝑟𝑟̅�� � 𝜔𝜔 � �� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ �𝑧𝑧𝑧 � 𝜃𝜃��� �𝑡𝑡�� � |𝜔𝜔 � �|𝜔𝜔 �� �𝑡𝑡�|� ∙ |𝑟𝑟̅�� | ∙ 𝑟𝑟̂�� �𝑡𝑡� 𝑎𝑎��� �𝑡𝑡� � 𝑎𝑎���� �𝑡𝑡� ��� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ 𝜃𝜃��� �𝑡𝑡� �|𝜔𝜔 �� �𝑡𝑡�|� ∙ |𝑟𝑟̅�� | ∙ 𝑟𝑟̂�� �𝑡𝑡� �|𝜔𝜔

(32)

(33)

With this, we can now relate the acceleration at the CG to the measured acceleration at the accelerometer position. ∆𝒗𝒗 in Continuous Time

Let us now take the dot-product of (33) with an arbitrary unit-vector, 𝑐𝑐𝑐 , which we define as time-independent in the inertial frame, and calculate the time integral of both sides from the start of the crash pulse at time = 0 to the end of the crash pulse at time = ∆𝑡𝑡: ∆�

� 𝑑𝑑𝑡𝑡 ∙ 𝑎𝑎��� �𝑡𝑡� ∙ 𝑐𝑐̂ �

∆�

� � 𝑑𝑑𝑡𝑡 ∙ 𝑎𝑎���� �𝑡𝑡� ∙ 𝑐𝑐̂ � ∆�

� � 𝑑𝑑𝑡𝑡 ∙ |𝜔𝜔 ��� �𝑡𝑡�| ∙ |𝑟𝑟𝑟�� | ∙ 𝜃𝜃��� �𝑡𝑡� ∙ 𝑐𝑐̂ � ∆�

� � 𝑑𝑑𝑡𝑡 𝑡 |𝜔𝜔 �� �𝑡𝑡�|� ∙ |𝑟𝑟̅�� | ∙ 𝑟𝑟̂�� �𝑡𝑡� ∙ 𝑐𝑐̂ �

(34)

We first want to evaluate the second integral using integration by parts:

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(31)

Note, the projections of 𝑎𝑎��� �𝑡𝑡�, 𝑎𝑎���� �𝑡𝑡�, 𝜃𝜃��� �𝑡𝑡�, and 𝑟𝑟�𝑟 � �𝑡𝑡� along the 𝑐𝑐𝑐 axis are all changing as a function of time, and therefore the dot-products cannot simply be factored outside of the time-integrals. Let’s now simplify (34).

This of course implies:

� �𝑡𝑡� 𝜔𝜔 ��𝑡𝑡� � 𝑟𝑟̂�� �𝑡𝑡� � 𝜔𝜔 ��𝑡𝑡� � 𝑟𝑟̂�,�

�� �𝑡𝑡� � 𝑟𝑟̅�� 𝜔𝜔 � |𝜔𝜔 �� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ �𝑧𝑧̂ � 𝑟𝑟̂�� �𝑡𝑡�� �� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ 𝜃𝜃��� �𝑡𝑡� � |𝜔𝜔

The second cross-product in (22) is therefore:

Next, let’s redefine 𝑟𝑟𝑟�� in terms of its components parallel and perpendicular to the unit vector 𝜔𝜔 ��𝑡𝑡� (Figure 2). That is, � � �𝑡𝑡� � � ∙ 𝑟𝑟̂�,� � ∙ 𝜔𝜔 ��𝑡𝑡� � �𝑟𝑟̅�,∥ 𝑟𝑟̅�� � �𝑟𝑟̅�,�

(30)

We can now write (22) as:

(22)

𝑟𝑟̅�� � |𝑟𝑟̅�� | ∙ 𝑟𝑟̂�� �𝑡𝑡�

��� �𝑡𝑡� � 𝑟𝑟̅�� �𝑡𝑡� 𝜔𝜔 ��� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ �𝑧𝑧̂ � 𝑟𝑟̂�� �𝑡𝑡�� � |𝜔𝜔 ��� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ 𝜃𝜃��� �𝑡𝑡� � |𝜔𝜔

We can re-express �𝜔𝜔 �� �𝑡𝑡� � 𝑟𝑟̅�� � by:

Using (20), we can now write an expression for the expected linear acceleration at the accelerometer position as a function of time, in the inertial frame 𝑂𝑂: ��� �𝑡𝑡� � 𝑟𝑟̅�� 𝑎𝑎��� �𝑡𝑡� � 𝑎𝑎���� �𝑡𝑡� � 𝜔𝜔 �𝜔𝜔 �� �𝑡𝑡� � �𝜔𝜔 �� �𝑡𝑡� � 𝑟𝑟̅�� �

(29)

We can now re-express the first cross-product in (22):

Acceleration of Accelerometers in a Moving Reference Frame

�

(28)

Our cross products are thus given by:

�

𝑎𝑎� �,� � 0 � 𝑣𝑣̅ �,� � 0

��� �𝑡𝑡� � |𝜔𝜔 ��� �𝑡𝑡�| ∙ 𝑧𝑧̂ 𝜔𝜔

� � 𝑟𝑟̂�� �𝑡𝑡� � 𝑧𝑧̂ � 𝑟𝑟̂�� �𝑡𝑡� � 𝜃𝜃��� �𝑡𝑡� 𝜔𝜔 � � 𝜃𝜃��� �𝑡𝑡� � 𝑧𝑧̂ � 𝑟𝑟̂�� �𝑡𝑡� 𝜃𝜃��� �𝑡𝑡� � 𝜔𝜔 � � � 𝑧𝑧̂ 𝑟𝑟�𝑟 �𝑡𝑡� � 𝜃𝜃��� �𝑡𝑡� � 𝜔𝜔

Putting this together, we can rewrite (13) asi: 𝑎𝑎��,� � 𝑎𝑎�� � 𝑎𝑎��,� � 𝜔𝜔 �� � 𝑟𝑟̅ � � 𝜔𝜔 � � �𝜔𝜔 � � 𝑟𝑟̅ � � � � � 𝑣𝑣̅ �,� �2𝜔𝜔

(27)

and the angular acceleration becomes:

(18)

where 𝜔𝜔 �� is the angular acceleration of reference 𝑂𝑂� frame as measured in 𝑂𝑂. � � 𝑟𝑟̅� � � 𝜔𝜔 � � �𝑣𝑣̅ �,� � 𝜔𝜔 � � 𝑟𝑟̅ � � 𝜔𝜔 �,�� � 𝜔𝜔 � � 𝑣𝑣̅ � 𝜔𝜔 � � �𝜔𝜔 � � 𝑟𝑟̅ � �

�� �𝑡𝑡� � |𝜔𝜔 �� �𝑡𝑡�| ∙ 𝑧𝑧̂ 𝜔𝜔

∆�

� 𝑑𝑑𝑡𝑡 ∙ |𝜔𝜔 ��� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ 𝜃𝜃��� �𝑡𝑡� ∙ 𝑐𝑐̂ �

(35)

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Figure 1: Illustration of point P position vector in inertial and moving frames.

Figure 2: Illustration of instantaneous cylindrical coordinate unit vectors at accelerometer position A.

Figure 3: Illustration of instantaneous cylindrical coordinate unit vectors at accelerometer position A in simplified model.

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Let us define the function 𝑑𝑑�𝑡𝑡� by:

𝑑𝑑�𝑡𝑡� � |𝑟𝑟̅�� | ∙ 𝜃𝜃��� �𝑡𝑡� ∙ 𝑐𝑐̂

(36)

𝑑𝑑𝑑𝑑 � 𝑑𝑑𝑑𝑑 ∙ |𝑟𝑟𝑟��| ∙ 𝜃𝜃��� ��𝑡𝑡� ∙ 𝑐𝑐𝑐

(37)

We can thus express 𝑑𝑑𝑑𝑑 as:

∆�

�

∆�

�� ∆𝑣𝑣̅�,� � � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑���� �𝑡𝑡� ∙ 𝑥𝑥� � ∆�

(38)

� � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑥𝑥� �

� � ��𝜔𝜔 ��,� � 𝑟𝑟𝑟�,� � 𝜔𝜔 ��,� � 𝑟𝑟𝑟�,� � ∙ 𝑥𝑥�

and (39)

�� �𝑡𝑡�| ∙ 𝑟𝑟̂�� �𝑡𝑡� ∙ 𝑐𝑐̂ 𝑑𝑑𝑑𝑑 � �𝑑𝑑𝑡𝑡 ∙ |𝑟𝑟̅�� | ∙ |𝜔𝜔

(40)

�� �𝑡𝑡�| 𝑑𝑑�𝑡𝑡� � |𝜔𝜔

(41)

��� �𝑡𝑡�| 𝑑𝑑𝑑𝑑 � 𝑑𝑑𝑡𝑡 ∙ |𝜔𝜔

(42)

∆�

� ∆�

� � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑦𝑦� �

� � ��𝜔𝜔 ��,� � 𝑟𝑟̅�,� � 𝜔𝜔 ��,� � 𝑟𝑟̅�,� � ∙ 𝑦𝑦�

Let us now define the function

∆�

∆�

∆�

� � 𝑑𝑑�𝑢𝑢�𝑡𝑡� ∙ 𝑑𝑑�𝑡𝑡�� � � 𝑑𝑑�𝑡𝑡�𝑑𝑑𝑑𝑑 �

�

(43)

∆𝒗𝒗 in the Instantaneous Limit

Using the above, we can rewrite (35) as:

Let us now approximate the collision as occurring instantly in time, thus in the limit ∆𝑡𝑡 𝑡 0. With this, our integrals become:

∆�

� 𝑑𝑑𝑡𝑡 ∙ |𝜔𝜔 ��� �𝑡𝑡�| ∙ |𝑟𝑟̅�� | ∙ 𝜃𝜃��� �𝑡𝑡� ∙ 𝑐𝑐̂ �

∆�

� � 𝑑𝑑�|𝑟𝑟�𝑟 � | ∙ |𝜔𝜔 �� �𝑡𝑡�| ∙ 𝜃𝜃��� �𝑡𝑡� ∙ 𝑐𝑐̂ � � ∆�

�� �𝑡𝑡�|� ∙ 𝑟𝑟̂�� �𝑡𝑡� ∙ 𝑐𝑐̂ � � 𝑑𝑑𝑡𝑡 ∙ |𝑟𝑟̅�� | ∙ |𝜔𝜔 �

(44)

and

Here we see the last term in (44) is equal and opposite to the last term in (34).

(34) therefore simplifies to:

�

or

�� �𝑡𝑡�| ∙ 𝜃𝜃��� �𝑡𝑡� ∙ 𝑐𝑐̂ � � � 𝑑𝑑�|𝑟𝑟̅�� | ∙ |𝜔𝜔 �

�

∆�

�

(45)

�

� � ��,� � 𝑟𝑟̅�,� � 𝜔𝜔 ��,� � 𝑟𝑟̅�,� � ∙ 𝑐𝑐̂ �𝜔𝜔 � �∆𝜔𝜔 �� � 𝑟𝑟̅�� � ∙ 𝑐𝑐̂

(52)

We can therefore rewrite (51) as:

�

� ∆𝑣𝑣̅��� ∙ 𝑐𝑐̂ � �∆𝜔𝜔 �� � 𝑟𝑟̅�� � ∙ 𝑐𝑐̂

(53)

�� � 𝑟𝑟̅�� � ∆𝑣𝑣̅�� � ∆𝑣𝑣̅��� � �∆𝜔𝜔

(54)

Because there is no rotation in the instantaneous limit, we can now factor out our dot-product, and simplify (51) by: (46)

Using (31), (46) can also be written in the equivalent form:

Note, because we are assuming ∆𝑡𝑡 𝑡 0 (the instantaneous collision condition), this will result in some inaccuracies because this approximation assumes there

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(51)

�

∆�

∆�

��|𝜔𝜔 �� �∆𝑡𝑡�| ∙ 𝜃𝜃��� �∆𝑡𝑡� ∙ 𝑐𝑐̂ ∙ |𝑟𝑟̅�� | �� �0�| ∙ 𝜃𝜃��� �0� ∙ 𝑐𝑐̂ ∙ |𝑟𝑟̅�� |� � |𝜔𝜔

∆�

� 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑐𝑐̂ → ∆𝑣𝑣̅�� ∙ 𝑐𝑐̂

𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑐𝑐̂

� � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑���� �𝑡𝑡� ∙ 𝑐𝑐̂

(50)

�

� 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑐𝑐̂ � ∆𝑣𝑣̅�� ∙ 𝑐𝑐̂

∆�

� ∆�

∆�

� 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑���� �𝑡𝑡� ∙ 𝑐𝑐̂ � ∆𝑣𝑣̅��� ∙ 𝑐𝑐̂

Our cross-products become:

∆�

� 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑐𝑐̂

� � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑���� �𝑡𝑡� ∙ 𝑐𝑐̂

∆�

products in the time integrals �� 𝑑𝑑𝑑𝑑𝑑 𝑑𝑑��� �𝑡𝑡� ∙ 𝑥𝑥� and �� 𝑑𝑑𝑑𝑑𝑑 𝑑𝑑��� �𝑡𝑡� ∙ 𝑦𝑦� must be evaluated time-step by time-step as the acceleration vector at the accelerometer position, 𝑑𝑑��� �𝑡𝑡�, will likely rotate as the collision unfolds. Also, recall 𝑑𝑑��� �𝑡𝑡� is the acceleration measured at the accelerometer position in the vehicle. 𝑑𝑑��� �𝑡𝑡� itself is, of course, the acceleration at the accelerometer position, evaluated in the inertial frame. This means to properly evaluate (48) and (49), one must first transform the acceleration vector components, typically given in the moving vehicle frame of reference, to the Earth-fixed inertial frame. This transformation typically requires vehicle yaw angle versus time data which defines the vehicle frame 𝑥𝑥� � �𝑡𝑡� and 𝑦𝑦� � �𝑡𝑡� behavior with respect to the inertial frame.

∆�

�

(49)

where the i and f subscripts denote initial and final values. Note, the dot

Using integration by parts, we have: � 𝑑𝑑�𝑡𝑡�𝑑𝑑𝑑𝑑

(48)

�� � � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑���� �𝑡𝑡� ∙ 𝑦𝑦� ∆𝑣𝑣̅�,�

With this, we can rewrite (37):

and its differential:

(47)

With (47), we can now write our equations to estimate ∆𝑣𝑣̅��� components in the inertial frame. These are given by:

Using (29), (38) becomes:

��𝑡𝑡� � 𝜃𝜃��� �𝑡𝑡� 𝜃𝜃���� �𝑡𝑡� � 𝜔𝜔 � �|𝜔𝜔 �� �𝑡𝑡�| ∙ 𝑟𝑟̂�� �𝑡𝑡�

�

�� �∆𝑡𝑡� � 𝑟𝑟̅�� �∆𝑡𝑡� ��𝜔𝜔 �� �0� � 𝑟𝑟̅�� �0�� ∙ 𝑐𝑐̂ � 𝜔𝜔

Using (7), we know:

𝜃𝜃���� �𝑡𝑡� � 𝜔𝜔 ��𝑡𝑡� � 𝜃𝜃��� �𝑡𝑡� � � 𝜃𝜃��� �𝑡𝑡�� � |𝜔𝜔 �� �𝑡𝑡�| ∙ �𝜔𝜔

∆�

� 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑��� �𝑡𝑡� ∙ 𝑐𝑐̂ � � 𝑑𝑑𝑡𝑡 ∙ 𝑑𝑑���� �𝑡𝑡� ∙ 𝑐𝑐̂

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is no component rotation in ���� during vehicle contact. For collision events in which there are large rotations as forces are being exchanged, this assumption may lead to large inaccuracies.

Equation (54) gives us a convenient way to transform between ∆𝑣𝑣̅�� and ∆𝑣𝑣̅��� ; however, this transformation requires knowledge of ∆𝜔𝜔 �� . One can model expected ∆𝜔𝜔 �� with the aid of computer simulation, but this isn’t necessary.

Below we complete the development of our mathematical transformation between ∆𝑣𝑣̅�� and ∆𝑣𝑣̅��� that is independent of ∆𝜔𝜔 �� through the use of a closed-form impulse-based collision model.

where we express the yaw moment of inertia in terms of vehicle k’s radius of gyration 𝐼𝐼� � 𝑚𝑚� 𝑘𝑘��.

Solving for ∆𝒗𝒗 at the CG

Let’s write our accelerometer position in Earth-fixed inertial frame coordinates:

We can thus write our cross-product by: 𝑥𝑥� �� � 𝑟𝑟̅�� � � 0 ∆𝜔𝜔 � 𝑟𝑟�,�

Impulse Let us define the total impulse imparted to vehicle k by: ∆�

𝐽𝐽�̅ � � 𝑑𝑑𝑡𝑡 ∙ 𝐹𝐹�� �

Torque

(56)

�

Taking the time integral of the total torque over interaction duration ∆𝑡𝑡, we have: ∆�

� 𝑑𝑑𝑡𝑡 ∙ Γ�� � � 𝑑𝑑𝑡𝑡 ∙ �𝐼𝐼� 𝛼𝛼�� � �

(58)

Therefore, the torque delivered over time ∆𝑡𝑡 is associated with a change in angular momentum Δ𝐿𝐿� , where the angular momentum is given by 𝐿𝐿�� � 𝐼𝐼� 𝜔𝜔 �� .

Therefore using (57) and (58), we have:

∆�

�

� 𝑟𝑟̅� � 𝐽𝐽�̅ � 𝑚𝑚� ∙ �𝑟𝑟̅� � ∆𝑣𝑣̅� �

(59)

Change in Angular Velocity Using (59), we can now write an expression for ∆𝜔𝜔 �� in terms of ∆𝑣𝑣̅� : ∆𝜔𝜔 �� �

�𝑟𝑟̅� � ∆𝑣𝑣̅� � 𝑟𝑟̅� � 𝐽𝐽�̅ � 𝐼𝐼� 𝑘𝑘��

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𝑥𝑥� 𝑦𝑦� 𝑧𝑧̂ 𝑟𝑟�,� 0� 𝑟𝑟̅� � ∆𝑣𝑣̅��� � � 𝑟𝑟�,� �� �� ∆𝑣𝑣�,� ∆𝑣𝑣�,� 0 �� �� � 𝑧𝑧̂�𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� �

(65)

We can now rewrite (60) by: �� � ∆𝜔𝜔

�� �� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � �𝑟𝑟�,� ∙ ∆𝑣𝑣�,� 𝑧𝑧𝑧 𝑘𝑘��

�� �� �𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � � ∙ 𝑟𝑟�,� ⎞ 𝑘𝑘�� �� �� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � �⎟ �𝑟𝑟�,� ∙ ∆𝑣𝑣�,� �� ∆𝑣𝑣�,� � ∙ 𝑟𝑟�,� � 𝑘𝑘� ⎠ ⎝

� ∆𝑣𝑣�,� ⎛ � � ��⎜ ∆𝑣𝑣�,�

or

�� ∆𝑣𝑣�,� �

� ∆𝑣𝑣�,� � � � ∆𝑣𝑣�,�

� � 𝑟𝑟�,� ∙ 𝑟𝑟�,� �𝑟𝑟�,� ∙ 𝑟𝑟�,� �� � � ∆𝑣𝑣�,� ∙� � 𝑘𝑘�� 𝑘𝑘�� ⎞ � � ⎟ �𝑟𝑟 ∙ 𝑟𝑟 𝑟𝑟 ∙ 𝑟𝑟 �,� �,� �,� �,� �� �� ∙� � � ∆𝑣𝑣 ∙ �1 � � ∆𝑣𝑣�,� �,� 𝑘𝑘�� 𝑘𝑘�� ⎠ ⎝

∆�

�

(64)

With this, we can evaluate the cross-product in (60):

⎛ �⎜

𝛥𝛥𝛥𝛥�� � 𝐼𝐼� ∆𝜔𝜔 �� � � 𝑑𝑑𝑡𝑡 ∙ �𝑟𝑟̅� � 𝐹𝐹�� � � 𝑟𝑟̅� � � 𝑑𝑑𝑡𝑡 ∙ 𝐹𝐹��

(63)

(66)

Using (66), (63) becomes:

� ∆�

𝑑𝑑𝑑𝑑 �� � � � 𝑑𝑑𝑡𝑡 ∙ �𝐼𝐼� 𝑑𝑑𝑑𝑑 � � � 𝐼𝐼� ∆𝜔𝜔 �� � 𝛥𝛥𝐿𝐿�

�� � � � ∆𝜔𝜔� ∙ 𝑟𝑟�,� ∆𝑣𝑣�,� ∆𝑣𝑣�,� � � �� �� � � ∆𝑣𝑣�,� ∆𝑣𝑣�,� � ∆𝜔𝜔� ∙ 𝑟𝑟�,�

𝑟𝑟̅� � 𝑟𝑟�,� 𝑥𝑥� � 𝑟𝑟�,� 𝑦𝑦�

(57)

where 𝛼𝛼�� � 𝑑𝑑𝜔𝜔 �� /𝑑𝑑𝑑𝑑 is the angular acceleration about the center-of-gravity of object k, and 𝑟𝑟�𝑟 is the lever-arm extending from the CG to the point of contact, and 𝐼𝐼� is the moment-of-inertia for rotation about the Γ�� axis.

∆�

(62)

Let’s now express the impulse centroid position in the Earth-fixed inertial frame:

We can write an expression for the total torque on vehicle k caused by the application of force 𝐹𝐹�� : 𝛤𝛤�� � 𝐼𝐼� 𝛼𝛼�� � 𝑟𝑟̅� � 𝐹𝐹��

𝑧𝑧̂ ∆𝜔𝜔� � 0

With this, (54) becomes:

∆�

𝑑𝑑 𝐽𝐽�̅ � � 𝑑𝑑𝑡𝑡 ∙ � �𝑚𝑚� 𝑣𝑣̅� �� 𝑑𝑑𝑑𝑑 � � 𝑚𝑚� ∙ ∆𝑣𝑣̅� � ∆�̅�

𝑦𝑦� 0 � 𝑟𝑟�,�

� � � 𝑥𝑥���𝑟𝑟�,� ∙ ∆𝜔𝜔� � � 𝑦𝑦���𝑟𝑟�,� ∙ ∆𝜔𝜔� � � � � ∆𝜔𝜔� ∙ ��𝑟𝑟�,� 𝑥𝑥� � 𝑟𝑟�,� 𝑦𝑦��

(55)

where 𝐹𝐹�� is the total force versus time acting on vehicle k during the duration ∆𝑡𝑡. Using Newton’s 2nd Law, we can rewrite (55) as:

(61)

� � 𝑥𝑥� � 𝑟𝑟�,� 𝑦𝑦� 𝑟𝑟̅�� � 𝑟𝑟�,�

�� ∆𝑣𝑣�,� ∙ �1 �

(67)

(68)

(68) can be re-expressed as an equation that takes vector ∆𝑣𝑣̅��� and rotates it to obtain ∆𝑣𝑣̅�� : � � 𝑟𝑟�,� ∙ 𝑟𝑟�,� �𝑟𝑟�,� ∙ 𝑟𝑟�,� � � � �� 𝑘𝑘�� 𝑘𝑘�� ⎞ ∆𝑣𝑣�,� �� � � � ⎟� ∆𝑣𝑣�,� �𝑟𝑟�,� ∙ 𝑟𝑟�,� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � � �1 � � 𝑘𝑘�� 𝑘𝑘�� ⎝ ⎠

� ∆𝑣𝑣�,� ⎛ � � ��⎜ ∆𝑣𝑣�,�

�1 �

(69)

(60)

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PDOF

Where our rotation matrix, 𝐑𝐑, is given by:

� � 𝑟𝑟�,� ∙ 𝑟𝑟�,� �𝑟𝑟�,� ∙ 𝑟𝑟�,� �1 � � � � ⎛ ⎞ 𝑘𝑘�� 𝑘𝑘�� 𝐑𝐑 � ⎜ � � ⎟ �𝑟𝑟�,� ∙ 𝑟𝑟�,� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � � �1 � � 𝑘𝑘�� 𝑘𝑘�� ⎝ ⎠

With (56), we know by obtaining an estimate of ∆𝑣𝑣��� , we also obtain an estimate of 𝐽𝐽�̅ – that is, the principal direction of force:

(70)

𝑚𝑚� � � ∙ �𝑑𝑑 ∙ ∆𝑣𝑣�,� � 𝑏𝑏 ∙ ∆𝑣𝑣�,� � 𝐽𝐽�,� � |𝑹𝑹| 𝑚𝑚� � � ∙ ��𝑐𝑐 ∙ ∆𝑣𝑣�,� � 𝑎𝑎 ∙ ∆𝑣𝑣�,� � 𝐽𝐽�,� � |𝑹𝑹|

Rewriting (69), we have:

∆𝑣𝑣̅�� � 𝐑𝐑 ∙ ∆𝑣𝑣̅���

(71)

where the direction of the impulse is given by: �𝟏𝟏

So long as 𝐑𝐑 is not singular, we can find its inverse, 𝐑𝐑 , such that we can obtain ∆𝑣𝑣̅��� by: ∆𝑣𝑣̅��� � 𝐑𝐑�𝟏𝟏 ∙ ∆𝑣𝑣̅��

(72)

The Lever-Arm

Next, we define four new variables, 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, and 𝑑𝑑 given by: 𝑎𝑎 � 1 � 𝑏𝑏 � 𝑐𝑐 �

𝑘𝑘2𝑘𝑘

�𝑟𝑟𝑘𝑘,𝑦𝑦 ∙ 𝑟𝑟𝐴𝐴𝑘𝑘,𝑥𝑥

𝑑𝑑 � 1 �

ℎ� �

𝑘𝑘2𝑘𝑘

With this, (71) becomes:

𝑎𝑎 � 𝑑𝑑

The inverse, 𝐑𝐑�𝟏𝟏 , is given by: 𝐑𝐑�𝟏𝟏 �

𝟏𝟏 � � |𝐑𝐑| ��

Where the determinate, |𝐑𝐑|, is: |𝐑𝐑| � 𝑎𝑎𝑑𝑑 � 𝑏𝑏𝑐𝑐 �1�

𝑟𝑟𝑘𝑘,𝑦𝑦 ∙ 𝑟𝑟𝐴𝐴𝑘𝑘,𝑦𝑦 𝑘𝑘2𝑘𝑘

�

With (77), (72) now becomes:

�� � �

� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � 𝑘𝑘�

�� � ∆𝑣𝑣�,� ∆𝑣𝑣�,� 1 𝑑𝑑 �𝑏𝑏 � �∙� � � � �� � � |𝑹𝑹| �𝑐𝑐 𝑎𝑎 ∆𝑣𝑣�,� ∆𝑣𝑣�,� � � � 𝑏𝑏 ∙ ∆𝑣𝑣�,� 𝑑𝑑 𝑑𝑑𝑑𝑑�,� 1 � ∙� � � � |𝑹𝑹| �𝑐𝑐 ∙ ∆𝑣𝑣�,� � 𝑎𝑎 ∙ ∆𝑣𝑣�,�

Using (79), we obtain our final form for ∆𝑣𝑣̅��� : 1 � � ∙ �𝑑𝑑 ∙ ∆𝑣𝑣�,� � 𝑏𝑏 ∙ ∆𝑣𝑣�,� � |𝑹𝑹| 1 �� � � ∆𝑣𝑣�,� � ∙ ��𝑐𝑐 ∙ ∆𝑣𝑣�,� � 𝑎𝑎 ∙ ∆𝑣𝑣�,� � |𝑹𝑹| �� � ∆𝑣𝑣�,�

(85)

From (54), we know the velocity change at point P, fixed within the vehicle k frame, can be written as: �� � 𝑟𝑟̅�� � ∆𝑣𝑣̅�� � ∆𝑣𝑣̅��� � �∆𝜔𝜔

(75) (76)

(86)

Using (60), we can write this as: ∆𝑣𝑣̅�� � ∆𝑣𝑣̅��� �

(77)

1 ��𝑟𝑟̅ � � ∆𝑣𝑣̅��� � � 𝑟𝑟̅�� � 𝑘𝑘�� �

Taking the dot-product of

�

���

(87)

��𝑟𝑟𝑟�� � ∆𝑣𝑣̅��� � � 𝑟𝑟𝑟�� � with ∆𝑣𝑣���� , and using the

scalar triple product, and (84), we have:

��𝑟𝑟̅�� � ∆𝑣𝑣̅��� � � 𝑟𝑟̅�� � ∙ ∆𝑣𝑣���� � �𝑟𝑟̅�� � ∆𝑣𝑣���� � ∙ �𝑟𝑟̅�� � ∆𝑣𝑣̅��� � � |∆𝑣𝑣̅��� | ∙ |𝑟𝑟̅�� � ∆𝑣𝑣���� |� � |∆𝑣𝑣̅��� | ∙ ℎ��

(78)

(88)

Thus, taking the dot-product of (87) with ∆𝑣𝑣���� , we have: �𝐶𝐶𝐶𝐶 ∆𝑣𝑣̅�� ∙ ∆𝑣𝑣���� � �∆𝑣𝑣̅��� � � �∆𝑣𝑣 𝑘𝑘 � ∙ � �∆𝑣𝑣̅��� � ∙ �1 �

(79)

2

ℎ𝑘𝑘 𝑘𝑘��

�

2

ℎ𝑘𝑘 𝑘𝑘��

(89)

With (89), we now have a way to express the change-in-velocity component along the impulse direction, at the point of contact.

(80)

Let’s now look at the difference in value for two vehicles:

(81)

� � , 𝑟𝑟�,� , 𝑟𝑟�,� are all signed values, it is possible to obtain Note, because 𝑟𝑟�,� , 𝑟𝑟�,� some combinations of these values which makes 𝐑𝐑 singular (|𝐑𝐑| � 0). From basic linear algebra, we know there is a unique solution for ∆𝑣𝑣̅��� if and only if R is non-singular. We will explore the implications of this further below.

�∆𝑣𝑣̅�� � ∆𝑣𝑣̅�� � ∙ ∆𝑣𝑣���� � �∆𝑣𝑣̅��� � ∙ �1 �

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�� �� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � �𝑟𝑟�,� ∙ ∆𝑣𝑣�,� �� |∆𝑣𝑣̅� |

The Closing-Velocity at the Point-of-Contact (74)

�� �� � ∆𝑣𝑣�,� � 𝑎𝑎 ∙ ∆𝑣𝑣�,� � 𝑏𝑏 ∙ ∆𝑣𝑣�,� �� �� � ∆𝑣𝑣�,� � 𝑐𝑐 ∙ ∆𝑣𝑣�,� � 𝑑𝑑 ∙ ∆𝑣𝑣�,�

(84)

Using (65), this becomes:

𝑘𝑘2𝑘𝑘 𝑟𝑟𝑘𝑘,𝑥𝑥 ∙ 𝑟𝑟𝐴𝐴𝑘𝑘,𝑥𝑥

𝑎𝑎 𝑐𝑐

(83)

ℎ� � �𝑟𝑟̅� � 𝐽𝐽�� � � |𝑟𝑟̅� � ∆𝑣𝑣�� |

(73)

With (73), we can rewrite our rotation matrix: 𝐑𝐑 � �

𝐽𝐽�,� 𝑥𝑥� � 𝐽𝐽�,� 𝑦𝑦� 𝐽𝐽�� � � � � 𝐽𝐽�,� �𝐽𝐽�,�

The lever-arm, ℎ� , is given by the component of the vector 𝑟𝑟�𝑟 perpendicular to the impulse direction 𝐽𝐽�� , and is given by:

𝑟𝑟𝑘𝑘,𝑦𝑦 ∙ 𝑟𝑟𝐴𝐴𝑘𝑘,𝑦𝑦

𝑘𝑘2𝑘𝑘 �𝑟𝑟𝑘𝑘,𝑥𝑥 ∙ 𝑟𝑟𝐴𝐴𝑘𝑘,𝑦𝑦

(82)

��∆𝑣𝑣̅��� � ∙ �1 �

2

ℎ1

� 𝑘𝑘�� 2

ℎ2

��

(90)

𝑘𝑘�

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Note ∆𝑣𝑣̅�� ∙ ∆𝑣𝑣���� is negative since ∆𝑣𝑣̅�� is exactly antiparallel with ∆𝑣𝑣���� from Newton’s 3rd Law; therefore, we know: �∆𝑣𝑣̅�� � ∆𝑣𝑣̅�� � ∙ ∆𝑣𝑣���� � 0

𝛾𝛾� �

𝑘𝑘��

2

𝑘𝑘�� � ℎ𝑘𝑘

(91)

�∆𝑣𝑣̅��� � �∆𝑣𝑣̅��� � � 𝛾𝛾� 𝛾𝛾�

(92)

Let’s now write out the difference:

�∆𝑣𝑣̅�� � ∆𝑣𝑣̅�� � ∙ ∆𝑣𝑣���� �

� � � � � 𝑣𝑣̅�,� � 𝑣𝑣̅�,� ��𝑣𝑣̅�,� � � �𝑣𝑣̅�,� �� ∙ ∆𝑣𝑣���� � � � � � � 𝑣𝑣̅�,� � 𝑣𝑣̅�,� ��𝑣𝑣̅�,� � � �𝑣𝑣̅�,� �� ∙ ∆𝑣𝑣����

(93)

(94)

(95)

With the relative velocities defined, we can rewrite (93): (96)

Let’s define the coefficient-of-restitution byiii: � ∙ ∆𝑣𝑣���� 𝑣𝑣̅���,� � 𝑣𝑣̅���,� ∙ ∆𝑣𝑣����

(97)

Thus, the differences in final and initial relative velocity can be re-expressed by: � � � 𝑣𝑣̅���,� �𝑣𝑣̅���,� � ∙ ∆𝑣𝑣���� � � � 𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� � 𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� � � � �� ∙ 𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� � 𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� � � ��1 � �� ∙ �𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� �

�∆𝑣𝑣̅��� � �∆𝑣𝑣̅��� � � 𝛾𝛾� 𝛾𝛾�

With Knowledge of Only One ∆𝒗𝒗

(99)

(100)

From Newton’s 3rd Law, we know (again, neglecting any external forces):

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� ∙ ∆𝑣𝑣���� � �𝑣𝑣̅���,� 1 1 1 � ∙ �𝑚𝑚� ∙ �∆𝑣𝑣̅��� � ∙ � � �� 1�� 𝛾𝛾� 𝑚𝑚� 𝛾𝛾� 𝑚𝑚�

(104)

With our mathematical formalism on firm footing, we now demonstrate the method using staged collision data.

Above, we derived the corrections needed to transform ∆𝑣𝑣̅ estimates based on data from accelerometers positioned away from the CG, to the equivalent values at the CG. Ideally, this method is tested using staged collisions where the test vehicles are instrumented with perfectly accurate accelerometers distributed at various locations within the test vehicles. In what follows below, we present the results of applying our transformation to EDR-based ∆𝑣𝑣̅ estimates from four EDRs distributed throughout a test vehicle subjected to a staged collision event.

Though the soundness of the transformation method is demonstrated, using EDR data for this purpose comes with its own challenges related to potential errors in the EDR-based ∆𝑣𝑣𝑣 values themselves. The tangential but important issue of accounting for potential EDR-based ∆𝑣𝑣𝑣 errors when such transformations are applied is also discussed below.

A crash test was performed on May 21, 2018 in Orlando, Florida. The crash test was crash test number 3 from IPTM’s Symposium on Traffic Safety. The crash configuration was of the T-bone type. The bullet vehicle struck the target vehicle behind the rear axle.

We can thus solve for the magnitude of the closing-velocity vector component parallel with the PDOF axis byiv: 1 �∆𝑣𝑣̅��� � �∆𝑣𝑣̅��� � ∙� � � 1�� 𝛾𝛾� 𝛾𝛾�

(103)

Experimental Set-up

(98)

� � Note, because we defined the closing velocity vector as 𝑣𝑣𝑣�,� � 𝑣𝑣̅�,� , we expect � � �� �� 𝑣𝑣𝑣���,� ∙ ∆𝑣𝑣�� � 0, and therefore ��1 � �� ∙ �𝑣𝑣̅���,� ∙ ∆𝑣𝑣�� � � 0.

� ∙ ∆𝑣𝑣���� � � �𝑣𝑣̅���,�

(102)

2018 IPTM Crash Test 3

With (92), (96), and (98), we finally have: � ��1 � �� ∙ �𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� � �

2

Demonstration of Method

is simply the final relative velocity of vehicle 1 with respect to vehicle 2 at the moment just after impact (the “separation-velocity”).

���

2

𝑚𝑚� ℎ2 �∆𝑣𝑣̅��� � ∙ �1 � � � 𝑚𝑚� 𝑘𝑘�

We can thus solve for the magnitude of the closing-velocity vector component parallel with the PDOF axis by:

The difference

� � �∆𝑣𝑣̅�� � ∆𝑣𝑣̅��� ∙ ∆ 𝑣𝑣���� � �𝑣𝑣̅ ���,� � 𝑣𝑣̅���,� � ∙ ∆ 𝑣𝑣����

�

� ��1 � �� ∙ �𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� � 1 1 �� � 𝑚𝑚� ∙ �∆𝑣𝑣̅� � ∙ � � � 𝛾𝛾� 𝑚𝑚� 𝛾𝛾� 𝑚𝑚�

is simply the initial relative velocity of vehicle 1 with respect to vehicle 2 at the moment just prior to impact (the “closing-velocity”).

� � � 𝑣𝑣̅���,� � 𝑣𝑣̅�,� � 𝑣𝑣̅�,�

2

ℎ1

𝑘𝑘��

Using (96) and (98), this becomes:

The difference

� � � 𝑣𝑣̅���,� � 𝑣𝑣̅�,� � 𝑣𝑣̅�,�

�

2

ℎ1

𝑚𝑚� ℎ2 �� ∙ �1 � � �� 𝑚𝑚� 𝑘𝑘�� 𝑘𝑘� 1 𝑚𝑚� 1 �� � �∆𝑣𝑣̅� � ∙ � � ∙ � 𝛾𝛾� 𝑚𝑚� 𝛾𝛾� 1 1 � � 𝑚𝑚� ∙ �∆𝑣𝑣̅��� � ∙ � � 𝛾𝛾� 𝑚𝑚� 𝛾𝛾� 𝑚𝑚�

� �∆𝑣𝑣̅��� � ∙ ��1 �

(90) can therefore be rewritten: �∆𝑣𝑣̅�� � ∆𝑣𝑣̅�� � ∙ ∆𝑣𝑣���� �

Therefore, (90) can be written:

�∆𝑣𝑣̅�� � ∆𝑣𝑣̅�� � ∙ ∆𝑣𝑣���� � �∆𝑣𝑣̅��� � ∙ �1 �

Let’s define a new parameter:

(101)

𝑚𝑚� ∙ ∆𝑣𝑣̅��� � �𝑚𝑚� ∙ ∆𝑣𝑣̅���

The target vehicle was a 1998 Chevrolet Malibu LS 4-door bearing VIN 1G1NE52M3W6XXXXXX (see Figure 4). Note, we will use the index “1”, “vehicle 1”, “Chevy”, and “target vehicle” interchangeably below. The Chevy was stationary at impact. Its weight was obtained with Rebco 1200-pound scales.

The weight on the front axle was 1806 pounds and the weight on the rear axle was 1026 pounds, for a total weight of 2832 pounds.

The bullet vehicle was a 2002 Buick LeSabre Custom 4-door bearing VIN 1G4HP54K72UXXXXXX (see Figure 5). Note, we will use the index “2”, “vehicle 2”, Buick, and “bullet vehicle” interchangeably below. The bullet was driven into impact at 27 MPH by a volunteer driver. The impact speed was obtained with a VBox Sport. The Vbox Sport measures speed with a 20 Hz GPS engine. The Buick and its driver were weighed with Rebco 1200-pound

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scales. The The weight on the front axle was scales. was 2334 2334 pounds pounds and and the theweight weighton onthe the rear axle axle was was 1421 1421 pounds pounds for rear for aa total total weight weight for for the the vehicle vehicleand anddriver driverofof3755 3755 pounds. The The impact impact configuration configuration isis shown pounds. shown in in Figure Figure6.

6.

The Chevy Chevy was was instrumented instrumented with The with 22 laboratory-grade laboratory-grade +/-250G +/-250Gaccelerometers accelerometers and 11 laboratory-grade laboratory-grade +/-600 and +/-600 deg/sec deg/sec rate rate gyro. gyro. The The rate rate gyro gyrowas wasaaSummit Summit Instruments model model 31206B 31206B and Instruments and the the two two accelerometers accelerometers were were Measurement Measurement Specialties model model 34208A 34208A (see Specialties (see Figures Figures 77 and and 8).

8). One One accelerometer accelerometer was was mounted at at the the CG CG and mounted and the the rate rate gyro gyro was was mounted mounted just just behind behind the the accelerometer mounted mounted at accelerometer at the the CG. CG. The The second second accelerometer accelerometerwas wasmounted mountedon on the firewall, firewall, inside inside the the engine the engine compartment. compartment. The The measured measured locations locations ofofthe the accelerometers are are documented documented in accelerometers in Table Table 1.

1. The The position position of of the therate rategyro gyrowas was not documented documented because because angular not angular rate rate isis constant constant within withinaarigid rigidbody. body.

The data acquisition equipment used for the laboratory-grade equipment were The data acquisition equipment used for the laboratory-grade equipment were two Vericom Computers VC4000DAQs. The VC4000s were set to sample data two Vericom Computers VC4000DAQs. The VC4000s were set to sample data at 1000 Hz. One of the VC4000s was used to record longitudinal and lateral at 1000 Hz. One of the VC4000s was used to record longitudinal and lateral acceleration data at the CG as well as the yaw rate. The other VC4000 recorded acceleration data at the CG as well as the yaw rate. The other VC4000 recorded longitudinal and lateral acceleration at the firewall. Acceleration along the z-axis longitudinal and lateral acceleration at the firewall. Acceleration along the z-axis was not recorded. All data was stored as voltage, which was later post-processed was not recorded. All data was stored as voltage, which was later post-processed in ROOT [4] into accelerations and yaw rate. in ROOT [4] into accelerations and yaw rate.

Seven “ride-along” EDRs were installed in the Chevy (see Figure 7). A rideSeven “ride-along” EDRs were installed in the Chevy (see Figure 7). A ridealong EDR is an airbag control module that is attached to the structure of a along EDR is an airbag control module that is attached to the structure of a vehicle for capturing the crash pulse. The EDRs used in this crash test were GM vehicle for capturing the crash pulse. The EDRs used in this crash test were GM sensing and diagnostic modules (SDM) that were used in the 2005 to 2009 sensing andTrailblazer diagnosticand modules (SDM)(Bosch that were in the 2005 toEDRs 2009 Chevrolet GMC Envoys cableused 3293).

Ride-along Chevrolet Trailblazertoand Envoys (Bosch 3293).

Ride-along EDRsbe are not connected theGMC vehicle’s CAN bus,cable so no pre-crash data may are not connected to the EDRs vehicle’s bus,bysoa no pre-crash maypack. be obtained.

The ride-along are CAN powered small externaldata battery obtained.

The ride-along EDRs by a small external battery In the subject collision, four of are the powered seven ride-along EDRs recorded an back. event.

In theofsubject of were the seven ride-along EDRsofrecorded an close event.to Two the fourcollision, ride-alongfour EDRs installed in the trunk the Chevy, Two of the four ride-along EDRs were installed in the the Chevy, the impulse-centroid.

One EDR was installed ontrunk the of center tunnelclose just to the impulse-centroid.

Oneand EDR the front centerpassenger tunnel just behind the center-of-gravity, two was wereinstalled installed on on the floor behind twocenter-of-gravity. were installed onThe the front passenger floor pan, tothe thecenter-of-gravity, right and ahead and of the two ride-along EDRs pan, the right aheadwith of the twowith ride-along EDRsyin thetotrunk wereand installed theircenter-of-gravity. longitudinal axesThe aligned the negative in theoftrunk installed withride-along their longitudinal axes with compartment the negative axis the were Chevy.

The two EDRs in thealigned passenger y-axis of the Chevy.

The longitudinal two ride-along in with the passenger compartment were installed with their axesEDRs aligned the positive y-axis of the were installed with their locations longitudinal axesride-along aligned with the positive y-axis of the Chevy.

The measured of the EDRs are documented in Chevy.

Table 1. The measured locations of the ride-along EDRs are documented in Table 1.

The crash test was documented with several video cameras including one highThe test was documented withand several cameras including highspeedcrash camera running at 240 fps one video unmanned aerial systemone (UAS). speed camerawere running and one unmanned system Photographs takenatof240 bothfpsvehicles before and afteraerial the crash test.(UAS).

The Photographs were taken after of both vehicles anddocumented after the crash The scene was photographed the test and itbefore was also withtest. a Riegl scene was photographed afterrest the positions test and itofwas alsovehicles documented with a Riegl 3-D laser scanner. The final both were documented 3-D The final rest as positions both vehicles with laser handscanner. measurements, as well the Rieglofscanner and thewere UAS.documented with hand measurements, as well as the Riegl scanner and the UAS. Accelerometer Measurements Accelerometer Measurements Table 1 shows the location and the cumulative ∆𝑣𝑣 from the instruments and the ride-along Locations with respect to the xy using SAE Table 1 shows EDRs. the location and are thegiven cumulative ∆𝑣𝑣 from the CG instruments and conventions. instrumentation-grade were in the ride-alongThe EDRs. Locations are givenaccelerometers with respect to thepost-processed CGxy using SAE ROOT from The voltage to acceleration and then integrated were to getpost-processed cumulative ∆𝑣𝑣.in conventions. instrumentation-grade accelerometers Figure 9from shows the longitudinal, lateral and yaw rate graphs from ROOT voltage to acceleration andacceleration, then integrated to get cumulative ∆𝑣𝑣. the laboratory-grade instruments.lateral The black lines show acceleration values Figure 9 shows the longitudinal, acceleration, andtheyaw rate graphs from withlaboratory-grade a 60 CFC Butterworth filterThe applied the acceleration data. Figure 10 the instruments. blacktolines show the acceleration values showsa 60 the CFC corresponding longitudinal andtolateral ∆𝑣𝑣 graphs, data. as well as the with Butterworth filter applied the acceleration Figure 10 change-in-yaw, which were obtainedandbylateral numerically integrating shows the corresponding longitudinal ∆𝑣𝑣 graphs, as well as the the accelerometer and rate gyro From by this numerically data, we estimate that the change-in-yaw, which were data. obtained integrating the �� � �1.04 mph, �6.30 for that vehicle cumulative local ∆𝑣𝑣̅����� accelerometer and rate gyro data.

From thismph�. data, Correcting we estimate the �� (see “∆𝒗𝒗 in Continuous Time” section above) using coordinate axis � �1.04 mph, �6.30 mph�. Correcting for vehicle cumulative localrotation ∆𝑣𝑣̅����� � � yaw versus time, (see the “∆𝒗𝒗 global frame Time” values section are above) ∆𝑣𝑣̅ ������ coordinate axis rotation in Continuous using �� �1.31 mph, �6.14 mph�.

Note, the analyst will typically need global frame� yaw versus time, the global frame values are ∆𝑣𝑣̅����� � and �6.14 therefore global frame , for will various calculations; however, ∆𝑣𝑣̅�� ,mph, �1.31 mph�.

Note, the∆𝑣𝑣̅ analyst typically need global frame because yaw rate data often isn’t available �� � in EDR data, the analyst will not be ∆𝑣𝑣̅ , and therefore global frame ∆𝑣𝑣̅ , �for various calculations; however, since data, the exact yaw versus timebe able to yaw precisely calculate frame ∆𝑣𝑣̅in EDR because rate data oftenglobal isn’t available the analyst will not

able to precisely calculate global frame ∆𝑣𝑣̅ � since the exact yaw versus time

��� behavior values behaviorisisunknown. unknown.InInthe theresults resultsthat thatfollow followbelow, below,the thetrue true∆𝑣𝑣𝑣 ∆𝑣𝑣̅����� ����� values from from our our accelerometer accelerometer atat the the CG CG are are obtained obtained by by applying applying rotational rotational �� corrections �𝑡𝑡�. We correctionstotothe thecomponents componentsofof 𝑎𝑎�𝑎𝑎����𝑡𝑡�.

We make make no no attempts attempts toto apply apply �� ���� similar corrections to ∆𝑣𝑣𝑣 in order to approximate the real-world ����� similar corrections to ∆𝑣𝑣̅����� in order to approximate the real-worldscenario scenario encountered encounteredbybymany manyanalysts. analysts.

Note, firewall diddid notnot record a crash Note,the the250 250GGaccelerometers accelerometersmounted mountedat atthethe firewall record a crash pulse. pulse.

Rate RateGyro GyroMeasurement Measurement The Therate rategyro gyroshowed showedananaverage averagepeak peakrate rateofof204.5 204.5deg/sec deg/secand andaarotation rotationofof 12.3° 12.3°during duringthe the~100 ~100ms mscrash crashpulse. pulse.The Theintegrated integratedtotal totalrotation rotationfrom fromimpact impact to final rest was 134.6° (see Figure 11). Hand measurements determined that to final rest was 134.6° (see Figure 11). Hand measurements determined that the total rotation was 135° and that the Chevy’s CG translated 15.3 feet to final the total rotation was 135° and that the Chevy’s CG translated 15.3 feet to final rest. rest.

EDR Measurements EDR Measurements Figure 12 depicts the location of the four EDRs used in this analysis.

Figure 12 depicts the location of the four EDRs used in this analysis.

EDR A was placed in the trunk, toward the rear, at position (-7.8 ft, -1.5 ft) in EDR A was placed in the trunk, toward the rear, at position (-7.8 ft, -1.5 ft) in the Chevy’s reference frame. The data obtained from EDR A is shown in Figure the Chevy’s reference frame. The data � obtained from EDR A is shown in Figure � �5.09 mph, �24.19 mph�.

13. From this data, we estimate ∆𝑣𝑣𝑣 ����� � ���� � �5.09 mph, �24.19 mph�.

13. From this data, we estimate ∆𝑣𝑣̅����� �

EDR B was placed in the trunk, toward the front, at position (-6.98 ft, -1.5 ft) was placed in theframe. trunk,The toward front, atfrom position ft, -1.5in ft) inEDR the B Chevy’s reference datathe obtained EDR(-6.98 B is shown in the14.

Chevy’s frame.

The ∆𝑣𝑣𝑣 data from EDR B is shown in � �obtained � Figure From reference this data, we estimate � �5.09 mph, �21.01 mph�. ���� � ���� � �5.09 mph, �21.01 mph�.

Figure 14. From this data, we estimate ∆𝑣𝑣̅����� EDR C was placed in the occupant cabin, behind the center-of-gravity, at EDR C was placed in the occupant cabin, behind the center-of-gravity, at position (-0.67 ft, 0.0 ft) in the Chevy’s reference frame. The data obtained position (-0.67 ft, 0.0 ft) in the Chevy’s reference frame. The data obtained � from EDR C is shown in Figure 15. From this data, we estimate ∆𝑣𝑣𝑣 ����� �� ���� � from mph, EDR �6.37 C is shown �0.64 mph�.in Figure 15. From this data, we estimate ∆𝑣𝑣̅����� � �0.64 mph, �6.37 mph�.

EDR D was placed in the occupant cabin, in front of the center-of-gravity, at EDR D was placed in the occupant cabin, in front of the center-of-gravity, at position (0.3 ft, 0.73 ft) in the Chevy’s reference frame. The data obtained from position (0.3 ft, 0.73 ft) in the Chevy’s reference frame. The data obtained� from EDR D is shown in Figure 16. From this data, we estimate ∆𝑣𝑣𝑣 ����� �� ���� � ����� � EDR D �5.73 is shown in Figure 16. From this data, we estimate ∆𝑣𝑣̅ �0.0 mph, mph�. �0.0 mph, �5.73 mph�.

Crush Damage Crush Damage

The damage profile of the Chevy was documented by hand measurements as Theasdamage profile the Chevy documented by hand measurements well a Carlson totalofstation.

Twowas separate sets of measurements were takenas as aOne Carlson total station. Twoincluded separatethe setsinduced of measurements were bywell hand. set of measurements damage, and onetaken set hand. One setincluded of measurements includeddamage. the induced damage, and one set ofbymeasurements only the contact The hand measurements of shown measurements only the contact damage.the The hand measurements are in Tableincluded 2. In the analysis that follows, impulse centroid was are shown Table 2. In the analysis the impulse was taken at the in point of maximum crush onthat the follows, direct contact damagecentroid only crush taken of at the the Chevy. point of maximum crush on the direct contact damage only crush profile profile of the Chevy.

∆𝑣𝑣� and ∆𝑣𝑣� Estimates ∆𝑣𝑣� and ∆𝑣𝑣� Estimates Using equations (80) and (81), the transformed ∆𝑣𝑣𝑣 ����� values were obtained. � �� values wereweobtained.

Using equations (80) and ∆𝑣𝑣̅�the Because all parameters were(81), not the welltransformed controlled in experiment, used a ����� Because all parameters were not well in the experiment, weasused Monte Carlo analysis script written for controlled ROOT to obtain best-estimates, wella analysis script obtain best-estimates, as well asMonte upper Carlo and lower limits for written our ∆𝑣𝑣𝑣 �for values.to The inputs used in the Monte ����ROOT � �� Carlo script shown in Table In������ our first round results, we in assumed no as upper andarelower limits for our3.∆𝑣𝑣̅ values.

Theofinputs used the Monte and ∆𝑣𝑣 . In thewesections that uncertainty EDR-based ∆𝑣𝑣��round Carlo scriptonareour shown in Tableestimates 3. In ouroffirst of ��results, assumed no � follow, we explore the issue estimates of EDR ofinaccuracies. probability uncertainty on our EDR-based ∆𝑣𝑣�� and ∆𝑣𝑣Uniform that � . In the sections � distributions usedthe for issue all inputs.

The best-estimate closingfollow, we were explore of EDR inaccuracies. ∆𝑣𝑣𝑣 Uniform probability � ���� and �� minimum and speed were obtained by using theinputs. best-estimate input values.∆𝑣𝑣̅ The distributions were used for all The best-estimate ����� and closingmaximum were obtained directly by input findingvalues. the The endpoints of the speed werevalues obtained by using the best-estimate minimum and resulting output distributions.

The accelerometer-based at the CG is shown in maximum values were obtained directly by finding∆𝑣𝑣𝑣the endpoints of the Table 4. The EDR-based resultsThe are shown in Table 5. The resulting output distributions. accelerometer-based ∆𝑣𝑣̅differences at the CGbetween is shown best-estimate resultsresults and results estimated from 5. theThe accelerometer in Table 4. EDR-based The EDR-based are shown in Table differences are shown best-estimate in Table 6. The average ofresults the differences shown in this table between EDR-based and results estimated from for the both components 0.25 mph. accelerometer areisshown in Table 6. The average of the differences shown in

this table for both components is 0.25 mph.

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Figure 4: Photograph of 1998 Chevy Malibu in its pre-impact configuration (target vehicle).

Figure 5: Photograph of 2002 Buick LeSabre (bullet vehicle).

Summit Instruments accelerometer and rate gyro

“Ride along” EDR (“EDR D”)

“Ride along” EDR

Chevy Figure 7: Photograph showing accelerometer and two "ride along" ACMs inside Chevy Malibu cabin.

Buick

Summit Instruments accelerometer

Figure 8: Close-up view of accelerometer and rate gryo.

Figure 6: Impact configuration Instrument 250G Accel.

250G Accel.

EDR A EDR B EDR C EDR D

X (ft) 0.00 2.83 -7.80 -6.98 -0.67 0.30

Y (ft) 0.00 0.31 -1.50 -1.50 0.00 0.73

Summit Instruments rate gyro

∆vx (mph) 1.29 N/A 5.09 5.09 0.64 0.0

∆vy (mph) -3.94 N/A -24.19 -21.01 -6.37 5.73

Remarks At CGxy position In engine compartment In trunk near impulse In trunk near impulse Just behind CGxy Passenger-front floor pan

Table 1: Location of instruments and cumulative ∆v values.

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The results from Tables 4, 5, and 6 are shown in Figure 17. The red line illustrates the accelerometer-based ∆𝑣𝑣� and ∆𝑣𝑣� estimates. The gray boxes illustrate the uncorrected EDR-based ∆𝑣𝑣� and ∆𝑣𝑣� values. The black dots represent the best-estimate EDR-based ∆𝑣𝑣� and ∆𝑣𝑣� values at the CG. The upper and lower bound corrected EDR values are illustrated by the black lines.

These results illustrate that the correction method properly brackets the accelerometer-based ∆𝑣𝑣� and ∆𝑣𝑣� estimates. Note, the shaded region about the red line indicates the minimum and maximum accelerometer-based ∆𝑣𝑣� and ∆𝑣𝑣� . The upper and lower bound estimates are based on randomly sampling the pre-impact acceleration bias of the accelerometer, which was estimated by examining data during a 10 second window before impact.

Closing-speed Estimates Table 7 shows the EDR-based closing speed estimates for each EDR, along with the corresponding uncertainties obtained using our Monte Carlo script. Table 8 shows the difference between the best-estimate EDR-based value closingspeed and the true value. The average of the differences is approximately -2.7 mph.

Figure 18 illustrates the EDR-based closing-speed estimates versus source of EDR data. The black dots represent the best-estimate. The lines represent the upper and lower-bound estimates. We see in comparison to the true closingspeed, our EDR-based estimates properly bracket the true results.

An example end-to-end calculation is provided in the Appendix 2.

Uncertainty Due to EDR Inaccuracy and the ∆𝑣𝑣 Corridor

In the above presented results, we assumed no uncertainty on EDR-based estimates of ∆𝑣𝑣�� and ∆𝑣𝑣�� ; however, inaccuracies on these input values can have important consequences for one’s minimum and maximum uncertainty range on ∆𝑣𝑣��� and ∆𝑣𝑣��� and closing-speed. This is explored below.

The accuracy of ∆𝑣𝑣 estimates from EDRs has been the subject of numerous studies [5,6,7,8,9,10,11]. Indeed, the authors of reference [12] delineate a helpful checklist of potential error sources which can cause inaccuracies in EDR-reported speed-change data. The reader is strongly encouraged to review this reference. We briefly summarize those error sources here: 1.

2.

3.

4.

5.

6.

Internal acceleration thresholds: Algorithm enable acceleration trigger threshold. Trigger threshold typically in range of 1g to 2g.

Short EDR time-window: EDR time-window for recording ∆𝑣𝑣 too short to capture full acceleration pulse. Can be ruled out by examining if ∆𝑣𝑣 reaches maximum value and possibly decreases prior to end of window.

Long EDR time-window: Recording window may be too long, which may cause post-impact ground-contact tire forces to contribute to ∆𝑣𝑣 over-estimates. This can be ruled out by examining the EDR data for a local ∆𝑣𝑣 maximum, possibly followed by decrease, then an upward drift.

“Clipping”: The true acceleration at the EDR may exceed the EDR accelerometer’s minimum or maximum limit. This can cause a truncation of the true peak acceleration and therefore a corresponding underestimate of ∆𝑣𝑣. This may be discerned by looking for a flattened portion of the EDR’s acceleration curve if possible.

Off-axis: The EDR may be away from the vehicle CG. This is the subject of this paper.

Vehicle crush: The EDR is located in the direct region of crush.

This can cause an overestimate of ∆𝑣𝑣 since the crushed region will undergo accelerations exceeding that of the vehicle CG. This can also result in underestimates if the EDR orientation changes during the collision. For example, material crushing could cause the EDR’s local x-axis to rotate into the vehicle’s x-y plane thereby

7.

Because our formalism to obtain ∆𝑣𝑣��� and ∆𝑣𝑣��� relies on ∆𝑣𝑣�� and ∆𝑣𝑣�� as inputs, EDR errors introduced by sources such as those listed above will naturally propagate to our estimates of ∆𝑣𝑣��� and ∆𝑣𝑣��� , as well as to closingspeed. In some cases, the errors propagated to the final ∆𝑣𝑣��� and ∆𝑣𝑣��� estimates can be quite large due to delicate numerical cancelations between ∆𝑣𝑣��,� and ∆𝑣𝑣��,� and the inverse proportionality to |𝐑𝐑|. This important issue is explored in more detail below.

In order to account for potential sources of error such as those enumerated above, we examined EDR-based versus accelerometer-based ∆𝑣𝑣 values for GM models ranging from 2002 to 2009 production years from references [5,6,7,8,9,10,11]. Using this data, a representative “ ∆𝑣𝑣 corridor” was constructed as a function of EDR ∆𝑣𝑣 (Figure 19 and Figure 20). Ideally, such a corridor is defined based on bench test experiments where the orientation of a given EDR can be precisely controlled, and the input true ∆𝑣𝑣̅ at the accelerometer is known to a high degree of accuracy. Unfortunately, such tests are rare, and therefore our corridor relies on data mostly from staged collisions.

While staged collision data is quite useful for the researcher, using EDR data from staged collisions makes it difficult to disentangle ∆𝑣𝑣 inaccuracies due to physical effects such as vehicle rotation during impact versus inaccuracies due to underlying algorithm design and accelerometer performance characteristics.

Therefore, the corridor depicted in Figure 19 is meant to represent a worst-case potential minimum/maximum range for true ∆𝑣𝑣 as a function of our subject EDR ∆𝑣𝑣.

The corridor is defined as follows. For component j, we have for the lower-bound of the corridor: ∆𝑣𝑣�����,��� � sign�∆𝑣𝑣����� � �1 � 10%��∆𝑣𝑣�����

For the upper-bound, we have the piecewise continuous function: ∆𝑣𝑣�����,���� �

sign�∆𝑣𝑣���� � � �4.4 kph�, for �∆𝑣𝑣���� � � 1.5 kph

sign�∆𝑣𝑣���� � � ��∆𝑣𝑣���� � � 2.9 kph�,

for 1.5 kph � �∆𝑣𝑣���� � �

sign�∆𝑣𝑣���� � � �1 � 17%� � �∆𝑣𝑣���� �, for �∆𝑣𝑣���� � �

2.9 kph 17%

2.9 kph 17%

Thus, for high ∆𝑣𝑣 , the oft quoted �10% uncertainty on ∆𝑣𝑣 , typically attributed to finite accelerometer accuracy [13], becomes a �17% upperbound uncertainty and �10% lower-bound uncertainty. Thus, our uncertainty on ∆𝑣𝑣 is asymmetric.

For low ∆𝑣𝑣, the behavior is more complex due to both threshold effects and offset effects (see Figure 20). The threshold effects cause ∆𝑣𝑣 ��� � 0 for ∆𝑣𝑣 ���� � ∆𝑣𝑣 ��������� , whereas for ∆𝑣𝑣 ���� � ∆𝑣𝑣 ��������� , we have ∆𝑣𝑣 ��� � ∆𝑣𝑣 ���� � ∆𝑣𝑣 ������ . This behavior can be attributed to error type (1) and is explored in great depth in reference [6]. For our ∆𝑣𝑣 corridor, we have ∆𝑣𝑣 ��������� � 4.4 kph and ∆𝑣𝑣 ������ � 2.9 kph. A non-zero ∆𝑣𝑣 ��������� implies, without any other knowledge, that ∆𝑣𝑣 � 0 may actually imply ∆𝑣𝑣 � ∆𝑣𝑣 ��������� in the worst-case. This has important consequences that are explored further below.

With our ∆𝑣𝑣 corridor defined, we can now better understand our uncertainty ranges for ∆𝑣𝑣��� and ∆𝑣𝑣��� . Note, the corridor described above was defined based on tests related to longitudinal ∆𝑣𝑣. A recent bench test study involving 2012 GM EDRs indicates that uncertainty in lateral ∆𝑣𝑣 component may be symmetric about 0 and less than 10% [18]; however, such an experiment is

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causing the EDR to lose sensitivity to longitudinal vehicle acceleration.

EDR power loss: The EDR may lose power before completely recording ∆𝑣𝑣 . This will result in an underestimate of ∆𝑣𝑣.

Depending on model year, the EDR report may indicate if an event’s recording is complete.

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Figure 9: Longitudinal (top) and lateral (middle) acceleration graphs from accelerometer as well as yaw rate (bottom). Black lines illustrate acceleration with CFC60 Butterworth filter applied, while gray shows unfiltered data.

Figure 10: Cumulative longitudinal (top) and lateral (middle) change-in-velocity graphs, as well as change-in-yaw (bottom).

Figure 11: Yaw rate versus time reported by rate gyro. Gray shows unfiltered data and black shows 60CFC Butterworth filter applied.

Figure 12: Positions of EDRs A, B, C, and D.

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Figure 13: Data from EDR A obtained using CDR Tool. Upper graph and table show longitudinal change-in-velocity (in EDR A's frame). The bottom graph and table show lateral change-in-velocity (in EDR A's frame). www.collisionmagazine.com

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Figure 14: Data from EDR B obtained using CDR Tool. Upper graph and table show longitudinal change-in-velocity (in EDR B's frame). The bottom graph and table show lateral change-in-velocity (in EDR B's frame).

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Figure 15: Data from EDR C obtained using CDR Tool. Upper graph and table show longitudinal change-in-velocity (in EDR C's frame). The bottom graph and table show lateral change-in-velocity (in EDR C's frame). www.collisionmagazine.com

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Figure 16: Data from EDR D obtained using CDR Tool. Upper graph and table show longitudinal change-in-velocity (in EDR D's frame). The bottom graph and table show lateral change-in-velocity (in EDR D's frame).

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Figure 17: Longitudinal (top) and lateral (bottom) ∆v displayed for each EDR. In red we show the accelerometer measured ∆v values. Gray dots represent the EDR ∆v values without correction. Black dots represent the best-estimate ∆v values based on correcting EDR data, along with minimum and maximum estimates. Here no uncertainties for EDR ∆v input values are accounted for.

Figure 18: In red we show the true closing-speed for the test. Black dots represent the best-estimate closing-speed values based on correcting EDR data, along with minimum and maximum estimates.

Here no uncertainties for EDR ∆v input values are accounted for. www.collisionmagazine.com

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Table 2: Chevy damage profile hand measurements

Table 3: Inputs to Monte Carlo script.

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Table 4: EDR-based ∆v estimates at Chevy CG (Equations 81 and 82).

Table 5: EDR-based local ∆v estimates at Chevy CG (Equations 81 and 82).

Table 6: Difference between best estimate ∆v and accelerometer value.

Table 7: EDR-based closing-speed estimates.

Table 8: Difference between best EDR-based closing-speed estimates and true value.

Figure 19: ∆v corridor defining the upper and lower true ∆v versus EDR ∆v.

Figure 20: ∆v corridor defining the upper and lower true ∆v versus EDR ∆v. Here we focus on low EDR ∆v values.

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likely less sensitive to clipping effects since the acceleration pulse used by the test apparatus is well controlled without large fluctuations. Another recent study on lateral ∆𝑣𝑣 EDR accuracy using vehicles from 2010 – 2012 model years (including GMs) that were subjected to side-impact tests as a part of the National Highway Safety Administration Side-Impact New Car Assessment Program showed EDRs tended to underestimate lateral ∆𝑣𝑣 [19].

Figure 21 and Figure 22 illustrate ∆𝑣𝑣��� , ∆𝑣𝑣��� , and closing-speed applying the same corridor for both lateral and longitudinal components of the EDR ∆𝑣𝑣 values. For all three values, the uncertainty windows have widened due to accounting for worst-case potential EDR-based ∆𝑣𝑣 inaccuracies. How the analyst can try to reduce the effect of such inaccuracies is discussed below.

Mitigation of Uncertainties Reduction of Input Uncertainties The usefulness of speed and change-in-speed estimates can directly depend on the uncertainty of those estimates. Though the uncertainties illustrated in Figure 21 and Figure 22 appear formidable, they are primarily driven by only a few factors. For the ∆𝑣𝑣� and ∆𝑣𝑣� estimates, the most important contributor to uncertainty is the a priori unknown EDR accuracy. This source of uncertainty can be reduced if one has data from tests conducted on the EDR of same year, make, and model as the subject vehicle. Ideally, the tests would be conducted over a wide spectrum of ∆𝑣𝑣 values.

The second largest contributor to uncertainty is related to the physical location of the accelerometer onboard the ACM EDR circuit board. This can be easily addressed by removing the ACM EDR housing and visually locating and measuring the accelerometer with respect to the ACM EDR’s geometrical center.

Finally, the coefficient of restitution contributes to large uncertainties in closing-speed. Though a large range (from 5% to 25%) was used in this analysis, based on data from staged collisions of similar severity [15,16,17], using reasonable exemplar vehicles could help narrow this range of restitution values.

Use of Additional Constraints Additional evidence collected during scene and vehicle inspections such as crush damage, departure angles, and post-impact trajectory lengths can be used to provide additional constraints on both closing-speed and ∆𝑣𝑣̅ �� . 3D computer simulation applications can be used to quickly simulate post-impact trajectories over scene data. Such simulations can provide further constraints. This is explored in the next section.

Full Virtual CRASH 4 Simulation We performed a simulation of the 2018 IPTM Crash Test 3 using Virtual CRASH 4 [20]. Virtual CRASH 4 is a software application for accident reconstruction which includes the ability to simulate motor vehicle collisions using an impulse-momentum based model. Starting with point cloud data created with the Pix4D application [21] using drone photographs taken after the crash test, the data was automatically aligned using the output .tfw file. A 3D surface mesh was created in Virtual CRASH 4 on top of which the simulated vehicles were placed (Figure 23). The goal of the analysis was to determine if, primarily using knowledge of the post-impact motion of the vehicles and the crush damage on the vehicles, we could use the simulation engine to find estimates for the Buick’s pre-impact ground speed.

Using such an approach, we can place rough upper and lower bounds on |∆𝑣𝑣̅��� | and |∆𝜔𝜔 �� |, which can be included into our Monte Carlo script as selection cuts to eliminate Monte Carlo trials that exceed those bounds. Using this same simulation approach, we can also place constraints on |∆𝜔𝜔 �� | by searching for upper bound values beyond which the Buick’s post-impact heading is directed too far from its documented area of rest. The results of applying these simulation-based selection cuts to our Monte Carlo analysis are illustrated in Figure 24 and Figure 25. The reduction in uncertainty for ∆𝑣𝑣̅��� and closingspeed is evident.

Simulation Optimization of Full Event In addition to using simulation for post-impact motion studies, we also simulated the full collision event. Using the post-impact motion path of the Chevy and point of maximum crush as primary constraints, we obtained a precrash ground speed of 28.9 mph for the Buick, in good agreement with the known pre-impact speed. The resulting simulated change-in-velocity for the �� � �0.74 mph, 5.65 mph�. This is also in good agreement Chevy is 𝑣𝑣𝑣����� with the values obtained from the accelerometer-based estimate. The simulated motion sequence can be seen in Figure 26.

As demonstrated above, the uncertainties on ∆𝑣𝑣 corrections presented above can be sensitive to both EDR position and EDR inaccuracies. In the section below we explore these dependencies in more detail.

Implications of a Singular 𝐑𝐑

Point of Zero Motion

Let’s examine the case where the impulse centroid and accelerometer can be at any arbitrary position within the Chevy (vehicle 1). The condition |𝐑𝐑| � 0 implies: 1�

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(105)

Thus, there is an imaginary line (the 𝑅𝑅� line) along which we cannot solve for a unique ∆𝑣𝑣̅��� given the non-homogenous condition ∆𝑣𝑣̅�� � 0� . We can � : describe the 𝑅𝑅� line as a function of 𝑟𝑟�,� � �� 𝑟𝑟�,�

𝑘𝑘�� 𝑟𝑟�,� � � � � ∙ 𝑟𝑟�,� 𝑟𝑟�,� 𝑟𝑟�,�

(106)

Along the 𝑅𝑅� line, we have for a:

� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � 𝑘𝑘� 𝑟𝑟�,� 𝑘𝑘�� 𝑟𝑟�,� � � 1 � � ∙ �� � � � ∙ 𝑟𝑟�,� � 𝑟𝑟�,� 𝑟𝑟�,� 𝑘𝑘� � 𝑟𝑟�,� ∙ 𝑟𝑟�,� � � 1 � 𝑑𝑑 𝑘𝑘��

(107)

� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � 𝑘𝑘� 𝑟𝑟�,� 𝑘𝑘�� 𝑟𝑟�,� � � � � ∙ �� � � � ∙ 𝑟𝑟�,� � 𝑟𝑟�,� 𝑟𝑟�,� 𝑘𝑘� 𝑟𝑟�,� � ∙ 𝑑𝑑 𝑟𝑟�,�

(108)

� �1�

for b:

���

Focus on Post-Impact Motion In our subject crash, simply focusing on the post-impact trajectory using the Virtual CRASH simulation model can provide useful constraints on the |∆𝑣𝑣̅��� |,|∆𝜔𝜔 �� |, and |∆𝜔𝜔 �� |. Using the real-time feedback given by the Virtual CRASH simulation engine, it is easy to probe, as initial conditions to the �� that simultaneously satisfy simulation, various combinations of ∆𝑣𝑣̅��� and ∆𝜔𝜔 (66) and the correct post-impact motion for the Chevy as loose conditions.

� � 𝑟𝑟�,� ∙ 𝑟𝑟�,� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � �0 𝑘𝑘�� 𝑘𝑘��

and for c:

���

� 𝑟𝑟�,� ∙ 𝑟𝑟�,� � 𝑘𝑘�

(109)

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�

𝑟𝑟�,� ∙ �1 � 𝑑𝑑� 𝑟𝑟�,�

�� � � ∆𝜔𝜔� ∙ 𝑟𝑟�,� �𝑥𝑥� ∆𝑣𝑣̅�� � �∆𝑣𝑣�,� �� � � ∆𝜔𝜔� ∙ 𝑟𝑟�,� �𝑦𝑦� ��∆𝑣𝑣�,�

Therefore, for an accelerometer on the 𝑅𝑅� line, we have: �� � � �1 � 𝑑𝑑� ∙ ∆𝑣𝑣�,� � ∆𝑣𝑣�,�

� � ∆𝑣𝑣�,�

𝑟𝑟�,� �� ∙ 𝑑𝑑 𝑑𝑑𝑑𝑑�,� 𝑟𝑟�,�

𝑟𝑟�,� �� �� ∙ �1 � 𝑑𝑑� ∙ ∆𝑣𝑣�,� � 𝑑𝑑 ∙ ∆𝑣𝑣�,� 𝑟𝑟�,�

�� Using (117) and (118), it is easy to show that 𝐿𝐿�� ∙ ∆𝑣𝑣̅�� � 0 and 𝐿𝐿�� � ∆𝜔𝜔 ∆𝑣𝑣̅�� for any point P. This implies that the 𝑅𝑅� point acts as the effective instantaneous center of rotation in the Earth frame for any point within vehicle 1.

(110)

Uncertainty Near the 𝑅𝑅� Line

which implies the components of ∆𝑣𝑣̅�� must be related by: � 𝑟𝑟�,� ∆𝑣𝑣�,� � � 𝑟𝑟�,� ∆𝑣𝑣�,�

(111)

This interesting result indicates that if an accelerometer happens to sit on the 𝑅𝑅� line, ∆𝑣𝑣̅�� will point either parallel or anti-parallel to the vector pointing from the center-of-gravity to the impulse-centroid. Comparing this to the slope of the 𝑅𝑅� line (equation (106)), the vector ∆𝑣𝑣̅�� must be perpendicular to the 𝑅𝑅� line.

With the condition |𝐑𝐑| � 0, for the homogeneous condition, ∆𝑣𝑣̅�� � 0� , we know we cannot solve for a unique ∆𝑣𝑣̅��� . We can, however, solve for the point along the 𝑅𝑅� line (the 𝑅𝑅� point), which remains in its pre-impact velocity state immediately after impact, by solving: �� � � ∆𝜔𝜔� ∙ 𝑟𝑟�,� ∆𝑣𝑣�,� 0 � � � � �� � � 0 ∆𝑣𝑣�,� � ∆𝜔𝜔� ∙ 𝑟𝑟�,�

(112)

Recall (80) and (81) tell us how to relate the true change-in-velocity at the accelerometer position to the true change-in-velocity at the CG. Let’s assume we have perfect knowledge of our geometry parameters a, b, c, and d with no uncertainties. What effect does EDR measurement uncertainty have on our estimates of change-in-velocity at the center-of-gravity? Suppose our accelerometer-based change-in-velocity estimates at A differ from the true values by a simple scale factor (remember, we do not have access to the “true” value, but only the experimentally determined estimate). To simplify the analysis, let’s suppose the scale factor is the same for both components. That is: � ��� � ���� � 𝑑𝑑 ∙ ∆𝑣𝑣�,� ∆𝑣𝑣�,� � ��� � ���� ∆𝑣𝑣�,� � 𝑑𝑑 ∙ ∆𝑣𝑣�,�

�� �� ∙ 𝑘𝑘�� ∆𝑣𝑣�,� �∆𝑣𝑣�,� � �� �� ∆𝜔𝜔� 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� �� �� � ∆𝑣𝑣 ∆𝑣𝑣 ∙ 𝑘𝑘 � �,� �,� � 𝑟𝑟�,� � � �� �� ∆𝜔𝜔� 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,�

With this, our change-in-velocity estimates at the CG become: �� ��� ∆𝑣𝑣�,� �

(113)

or:

�� ��� ∆𝑣𝑣�,� �

�� � ∆𝑣𝑣�,� 𝑟𝑟�,� �� � � ∆𝑣𝑣�,� 𝑟𝑟�,�

(114)

Therefore the 𝑅𝑅� point must sit on a line going through the center-of-gravity that is also perpendicular to ∆𝑣𝑣̅��� . � in (114), then substituting into (106), we have: Solving for 𝑟𝑟�,� � �� 𝑟𝑟�,�

�� ∆𝑣𝑣�,� 𝑘𝑘�� 𝑟𝑟�,� � � � � ∙ �� �� ∙ 𝑟𝑟�,� � 𝑟𝑟�,� 𝑟𝑟�,� ∆𝑣𝑣�,�

� Solving the above for 𝑟𝑟�,� gives: � � 𝑟𝑟�,�

�� ∙ 𝑘𝑘�� �∆𝑣𝑣�,� �� �� 𝑟𝑟�,� ∙ ∆𝑣𝑣�,� � 𝑟𝑟�,� ∙ ∆𝑣𝑣�,�

� � 𝐿𝐿�� � �𝑟𝑟�,�

∆𝜔𝜔1

� � � 𝑥𝑥� � �𝑟𝑟�,�

∆𝑣𝑣𝐶𝐶𝐶𝐶 1,𝑥𝑥 ∆𝜔𝜔1

(120)

(121)

Thus implying, if our change-in-velocity estimates obtained from our accelerometer differ from the true value by a simple scale factor, we can expect our change-in-velocity estimates at the center-of-gravity to differ by the same scale factor with respect to the true values.

Now suppose instead, our accelerometer-based change-in-velocity values at A differ from the true values by (see reference [6] for examples):

(115)

(122)

where 𝛿𝛿 may be due to an acceleration threshold effect.

In this case, we have:

(116)

� 𝑦𝑦�

1 � ���� � ���� ∙ ��� ∙ 𝑑𝑑 ∙ ∆𝑣𝑣�,� � � ∙ 𝑑𝑑 ∙ ∆𝑣𝑣�,� � |𝑹𝑹|

� ��� � ���� � 𝑑𝑑 ∙ ∆𝑣𝑣�,� � 𝛿𝛿 ∆𝑣𝑣�,� � ��� � ���� � 𝑑𝑑 ∙ ∆𝑣𝑣�,� � 𝛿𝛿 ∆𝑣𝑣�,�

Thus, comparing (116) to (113) confirms that the 𝑅𝑅� point must be a point on the 𝑅𝑅� line. Much like the ground contact point of an ideal (rigid) rolling wheel that is in motion with no slip, the 𝑅𝑅� point can be thought of as the post-impact instantaneous center of rotation for all points within the vehicle. We can confirm this by defining a radial vector, 𝐿𝐿�� , originating from the 𝑅𝑅� point and pointing to some point in the vehicle frame P �𝑟𝑟̅�� �. This vector is given by: ∆𝑣𝑣𝐶𝐶𝐶𝐶 1,𝑦𝑦

1 � ���� � ���� ∙ �𝑑𝑑 ∙ 𝑑𝑑 ∙ ∆𝑣𝑣�,� � � ∙ 𝑑𝑑 ∙ ∆𝑣𝑣�,� � |𝑹𝑹|

�� ��� �� ���� � 𝑑𝑑 ∙ ∆𝑣𝑣�,� ∆𝑣𝑣�,� �� ��� �� ���� ∆𝑣𝑣�,� � 𝑑𝑑 ∙ ∆𝑣𝑣�,�

which implies:

�

(119)

For example, we may have 𝑑𝑑 � 1/�1 � 17%� as shown in the above discussion on the ∆𝑣𝑣 corridor.

� � for 𝑟𝑟�,� and 𝑟𝑟�,� . This gives: � 𝑟𝑟�,� ��

(118)

�� ��� ∆𝑣𝑣�,� �

1 � ��� � ��� ∙ �𝑑𝑑 𝑑𝑑𝑑𝑑�,� � � ∙ ∆𝑣𝑣�,� � |𝑹𝑹|

1 � ���� � ���� ∙ �𝑑𝑑 𝑑 𝑑𝑑 𝑑𝑑𝑑𝑑�,� � � ∙ 𝑑𝑑 ∙ ∆𝑣𝑣�,� � |𝑹𝑹| 1 � ∙ �𝑑𝑑 ∙ 𝛿𝛿 � � ∙ 𝛿𝛿� |𝑹𝑹| 1 �� ���� � 𝛿𝛿 ∙ ∙ �𝑑𝑑 � �� � 𝑑𝑑 ∙ ∆𝑣𝑣�,� |𝑹𝑹| �

(123)

and

(117)

The change in velocity at this point is given by:

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Figure 23: 3D simulation environment created in Virtual CRASH 4 using point cloud data.

Figure 21: Longitudinal (top) and lateral (bottom) ∆v displayed for each EDR. In red we show the accelerometer measured ∆v values. Gray dots represent the EDR ∆v values without correction.

Black dots represent the best-estimate ∆v values based on correcting EDR data, along with minimum and maximum estimates. Here we apply the same ∆v corridor to both lateral and longitudinal components.

Figure 24: Longitudinal (top) and lateral (bottom) ∆v displayed for each EDR. In red we show the accelerometer measured ∆v values. Gray dots represent the EDR ∆v values without correction.

Black dots represent the best-estimate ∆v values based on correcting EDR data, along with minimum and maximum estimates. Here we apply the same ∆v corridor to both lateral and longiFigure 22: In red we show the true closing-speed tudinal components. Monte Carlo selection cuts for the test. Black dots represent the best-estimate based on post-impact motion studies conducted closing-speed values based on correcting EDR data, with Virtual CRASH 4 are used to reduce the along with minimum and maximum estimates. uncertainty range.

Here no uncertainties for EDR ∆v input values are accounted for. Here we apply the same ∆v corridor to both lateral and longitudinal components.

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Figure 25: In red we show the true closingspeed for the test. Black dots represent the best-estimate closing-speed values based on correcting EDR data, along with minimum and maximum estimates. Here no uncertainties for EDR ∆v input values are accounted for. Here we apply the same ∆v corridor to both lateral and longitudinal components. Monte Carlo selection cuts based on post-impact motion studies conducted with Virtual CRASH 4 are used to reduce the uncertainty range.

Figure 26: Diagram showing Virtual CRASH 4 simulation sequence.

No adjustments with no correction

Figure 27: (Top) Estimated ∆vx at the center-of gravity as a function of EDR position, assuming no thresholds or corrections are applied. (Bottom) Estimated ∆vy at the center-of gravity as a function of EDR position, assuming no thresholds or corrections are applied. Note, view is from below vehicle looking up. www.collisionmagazine.com

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�� ��� ∆𝑣𝑣�,� 1 � ��� � ��� � ∙ ��� ∙ ∆𝑣𝑣�,� � � ∙ ∆𝑣𝑣�,� � |𝑹𝑹| 1 � ���� � ���� � ∙ ��� ∙ � ∙ ∆𝑣𝑣�,� � � ∙ � ∙ ∆𝑣𝑣�,� � |𝑹𝑹| 1 � ∙ ��� ∙ � � � ∙ �� |𝑹𝑹| 1 �� ���� � � ∙ ∆𝑣𝑣�,� ��∙ ∙ �� � �� |𝑹𝑹|

Within this corridor, ∆𝑣𝑣��,���� � 0 for any 𝑟𝑟��,� .

Figure 28 illustrates zero corridors using the upper-bound ∆𝑣𝑣 corridor line condition where ∆𝑣𝑣 ��������� � 4.4 kph.

(124)

�� ��� �� ��� Thus, here we see the ∆𝑣𝑣�,� and ∆𝑣𝑣�,� values will differ from the true values by terms dependent on 1/|𝑹𝑹|. This can have important consequences for one’s uncertainty analysis. That is, if our accelerometer is moved closer to the 𝑅𝑅� line, we can expect our uncertainty on ∆𝑣𝑣̅��� to increase if ∆𝑣𝑣̅�� differs from the true value by a linear constant. This means, when conducting an error analysis, we should expect to see larger error bars for EDRs near the 𝑅𝑅� line. This is indeed what we see in our data. For our subject crash, we estimate the 𝑅𝑅� line to intersect with the center-line of the Chevy about 9 inches behind the front axle.

In our results presented above, it is observed that the uncertainty range in �� increases as the EDR position gets closer to the front axle. Since ∆𝑣𝑣̅����� �� closing-speed is directly proportional to the magnitude of ∆𝑣𝑣̅����� , this same pattern is observed in our closing-speed results.

Threshold Effects We can gain more insight into the effects of the 𝑅𝑅� line and 𝑅𝑅� point using a forward evaluation calculation C++ script written for ROOT. In this script, we tested all possible EDR (x,y) positions within the Chevy. With the script, we can assume a known ∆𝑣𝑣̅��� ���� , as well as impulse centroid location. With the known (true) impulse as an input, we can then use equations (75) and (76) to � ���� � ���� simulate the exact ∆𝑣𝑣�,� and ∆𝑣𝑣�,� values expected at a given point � ���� � ���� and ∆𝑣𝑣�,� , we within the vehicle. Starting with these expected true ∆𝑣𝑣�,� can probe the effects introduced by EDR measurement error by modifying � ���� � ��� � ���� � ��� them such that ∆𝑣𝑣�,� → ∆𝑣𝑣�,� and ∆𝑣𝑣�,� → ∆𝑣𝑣�,� , where our modifications are based on behavior observed in staged collision data (see Figure � ��� � ��� and ∆𝑣𝑣�,� values can then be used to calculate ∆𝑣𝑣̅��� ��� .

19). The ∆𝑣𝑣�,� This is done for each point within the vehicle. Using this framework, we can � ��� � ��� and ∆𝑣𝑣�,� to also study the effect of adding corrections back to ∆𝑣𝑣�,� account for thresholding effects and offsets. After adding corrections, we can �� ��� and then apply equations (80) and (81) to obtain our estimates for ∆𝑣𝑣�,� �� ��� as a function of EDR position. The results introduced below assume: ∆𝑣𝑣�,� �� ���� �� ���� ∆𝑣𝑣�,� � 1.04 mph and ∆𝑣𝑣�,� � �6.3 mph.

�� ��� �� ��� Figure 27 shows ∆𝑣𝑣�,� and ∆𝑣𝑣�,� assuming no modifications to ∆𝑣𝑣̅�� and �� ��� �� ��� with no corrections applied. As expected, the ∆𝑣𝑣�,� and ∆𝑣𝑣�,� values are � ��� � constant and independent of position, except at the 𝑅𝑅� point where ∆𝑣𝑣�,� � ��� 0 and ∆𝑣𝑣�,� � 0. Note, the impulse centroid (“IC”) and impulse unit vector are also depicted in the figure.

In low-speed tests of EDR performance, it has been demonstrated that for a � ���� value, ∆𝑣𝑣 ��������� , below which we given EDR, there is a minimum ∆𝑣𝑣�,� � ��� expect ∆𝑣𝑣�,� → 0 for component j. ∆𝑣𝑣 ��������� is both EDR dependent as well as dependent on peak acceleration and pulse width [4]. The upper-bound ∆𝑣𝑣 corridor line shown in Figure 19 is constructed assuming a worst-case scenario ∆𝑣𝑣 ��������� � 4.4 kph. It is easy to solve for “zero-corridors” within � ��� � ��� the x-y plane where either ∆𝑣𝑣�,� or ∆𝑣𝑣�,� will always equal 0 (assuming the � ��� worst-case scenario in both lateral and longitudinal directions). The ∆𝑣𝑣�,� zero-corridor is defined along the x-axis by: �� ���� �� ���� �𝑣𝑣�,� � ∆𝑣𝑣 ��������� �∆𝑣𝑣�,� � ∆𝑣𝑣 ��������� � � 𝑟𝑟�,� � ∆𝜔𝜔� ∆𝜔𝜔�

� ��� � Within this corridor, ∆𝑣𝑣�,� � 0 for any 𝑟𝑟�,� . Similarly, the ∆𝑣𝑣�� ��� zerocorridor is given by: �� ���� 𝑣𝑣�,� � ∆𝑣𝑣 ��������� ∆𝑣𝑣 �� ���� � ∆𝑣𝑣 ��������� � � 𝑟𝑟�,� � �,� ∆𝜔𝜔� ∆𝜔𝜔�

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The intersection of these two zero-corridors defines a “zero box” whose sides are given by 2 ∙ ∆𝑣𝑣𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 /∆𝜔𝜔1 . Within this box, we are guaranteed to have both ∆𝑣𝑣��,���� � 0 and ∆𝑣𝑣��,���� � 0 which implies our calculations must yield ∆𝑣𝑣�,��� ��� � 0 and ∆𝑣𝑣�,��� ��� � 0 for EDRs within this box.

Figure 29 shows ∆𝑣𝑣��� ��� and ∆𝑣𝑣��� ��� assuming the ∆𝑣𝑣��,���� and ∆𝑣𝑣��,���� values were adjusted to follow the upper bound of the ∆𝑣𝑣 corridor (∆𝑣𝑣 ��������� � 4.4 kph) and no corrections applied. Because of the threshold, the ∆𝑣𝑣��� ��� and ∆𝑣𝑣��� ��� values are dependent on position. All points within the white box, including the 𝑅𝑅� point, have ∆𝑣𝑣�� ��� � 0 and ∆𝑣𝑣�� ��� � 0; this yields the trivial solution: ∆𝑣𝑣��� ��� � 0 and ∆𝑣𝑣��� ��� � 0. For this plot, we assume ∆𝑣𝑣�,��� ���� � 1.31 mph and ∆𝑣𝑣�,��� ���� � �6.14 mph.

Figure 30 shows ∆𝑣𝑣��� ��� and ∆𝑣𝑣��� ��� assuming the ∆𝑣𝑣��,���� and ∆𝑣𝑣��,���� values were adjusted to follow the upper bound of the ∆𝑣𝑣 corridor (∆𝑣𝑣 ��������� � 4.4 kph) and corrections applied. Because ∆𝑣𝑣�� ��� → 0 and ∆𝑣𝑣�� ��� → 0 for values below 4.4 kph, the correction applied in this region takes 0 kph → 2.9 kph.

It is evident from Figure 27, Figure 29, and Figure 30 that near the 𝑅𝑅� line, ∆𝑣𝑣̅�� ��� is extremely sensitive to measurement inaccuracies of ∆𝑣𝑣̅ � ��� introduced by the measuring device. Even in cases where the exact correction is known, threshold effects, which cause low ∆𝑣𝑣�� ��� → 0 and low ∆𝑣𝑣�� ��� → 0, when corrected for, will still yield problematic regions near the 𝑅𝑅� line where |∆𝑣𝑣̅ �� ��� | can tend toward extremely large values, and thus will greatly increase estimate uncertainties. This is an irreducible effect that the analyst should be aware of.

In a recent study on combined EDR lateral and longitudinal ∆𝑣𝑣 accuracy, it was demonstrated that for the 2012 EDRs tested, lateral ∆𝑣𝑣 error was symmetric about 0 and less than 10% [18]. Figure 31 illustrates the combined effect of reducing longitudinal ∆𝑣𝑣 (using our corridor) while leaving lateral ∆𝑣𝑣 unchanged.

Finally, to illustrate the dependence on PDOF, Figure 32 illustrates the changing behavior of ∆𝑣𝑣��� ��� and ∆𝑣𝑣��� ��� versus various PDOFs assuming |∆𝑣𝑣̅ | = 5 mph.

Conclusions

Using a 2D rigid-body dynamics approach, we have created a mathematical model which allows one to transform change-in-velocity estimates at any position within a vehicle to the center-of-gravity equivalent value. We have demonstrated the method by reproducing experimentally measured change-invelocity values from a staged collision. We have also demonstrated the possibility of reconstructing pre-impact ground speeds with the Virtual CRASH simulation.

About the Authors Bob Scurlock, Ph.D., ACTAR, is a Research Associate at the University of Florida, Department of Physics. He is also the owner Momentum Forensics, LLC (MomentumForensics.com), an accident reconstruction consulting firm based out of Newberry, Florida, USA. He is also the CEO of Virtual CRASH, LLC (vcrashusa.com). He can be reached at Bob.Scurlock@MomentumForensics.com.

Andrew Rich, BSME, ACTAR, ASE is the owner of Rich Consulting LLC (www.rich-llc.com), an accident reconstruction consulting and training firm based out of Fairlawn, Ohio, USA. He can be reached at: andy@rich-llc.com.

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Figure 28: Zero-corridors shown in yellow highlighted areas for ∆v1,xA Est (top) and ∆v1,yA Est (bottom) assuming ∆vThreshold=4.4 kph. Note, view is from below vehicle looking up.

Adjustment applied with ∆vThreshold=4.4 kph, no correction

Figure 29: (Top) Estimated ∆vx at the center-of gravity as a function of EDR position. (Bottom) Estimated ∆vy at the center-of gravity as a function of EDR position. In both cases, ∆vxA Est and A Est ∆vy were adjusted values following upper limit of the ∆v corridor. No corrections were applied.

An EDR within the white box will result in ∆vxA Est=0 and ∆vyA Est=0. Note, view is from below vehicle looking up. www.collisionmagazine.com

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Adjustment applied with ∆vThreshold=4.4 kph, with correction

Figure 30: (Top) Estimated ∆vx at the center-of gravity as a function of EDR position. (Bottom) Estimated ∆vy at the center-of gravity as a function of EDR position. In both cases, ∆vxA Est and A Est ∆vy were adjusted values following upper limit of the ∆v corridor. Corrections were applied. An EDR within the white box will result in ∆vxA Est=2.9 kph and ∆vyA Est=2.9 kph. Note, view is from below vehicle looking up.

(a)

(b)

Figure 31: Estimated ∆vx and ∆vy at the center-of gravity as a function of EDR position given: (a) longitudinal ∆v reduced using corridor and unmodified lateral ∆v, (b) longitudinal ∆v reduced using corridor followed by inverse correction and unmodified lateral ∆v.

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(a)

(b)

(c)

(d)

Figure 32: Estimated ∆vx and ∆vy at the center-of-gravity as a function of EDR position given for |∆v| = 5 mph: (a) impulse at -90 degrees, unmodified longitudinal ∆v and unmodified lateral ∆v, (b) impulse at -90 degrees, longitudinal ∆v reduced using corridor and unmodified lateral ∆v, (c) impulse at -135 degrees, longitudinal ∆v reduced using corridor and unmodified lateral ∆v, (d) impulse at -45 degrees, longitudinal ∆v reduced using corridor and unmodified lateral ∆v.

Using a 2D rigid-body dynamics approach, we have created a mathematical model which allows one to transform change-in-velocity estimates at any position within a vehicle to the center-of-gravity equivalent value. www.collisionmagazine.com

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Kyle Poe is an undergraduate research assistant in Physics at the University of Florida.

Acknowledgements The authors thank the 2018 IPTM crash team for their hard work putting together this crash test. They would also like to thank Jeremy Daily, Ph.D. for the use of his instrumentation.

References [1] R. Bundorf, “Analysis and Calculation of Delta-V from Crash Test Data”, Society of Automotive Engineers, 960899.

[2] M. Marine and S. Werner, “Delta-V Analysis from Crash Test Data for Vehicles with Post-Impact Yaw Motion”, Society of Automotive Engineers, 980219.

[3] J. Marion and S. Thornton, “Classical Dynamics of Particles and Systems, Fifth Edition”, Harcourt College Publishers, New York, New York, 1995.

[4] B. Scurlock, “Use of ROOT in Vehicular Accident Reconstruction”, Accident Reconstruction Journal, Vol. 21, No. 3, 2011, Cornell University Library arXiv:1102.2422.

[16] M. Bailey et al., “Data from Five Staged Car to Car Collisions and Comparisons with Simulations”, Society of Automotive Engineers, 2000-010849.

[17] W. Cliff and A. Moser, “Reconstruction of Twenty Staged Collisions with PC-Crash’s Optimizer”, Society of Automotive Engineers, 2001-01-0507.

[18] L. Carr et al, “EDR Pulse Component Vector Analysis”, Society of Automotive Engineers, 2015-01-1448.

[19] A. Tsoi, N. Johnson, and H. Gabler, “Validation of Event Data Recorders in Side-Impact Crash Test”, Society of Automotive Engineers, 2014-01-0503.

[20] vcrashusa.com [21] Pix4d.com Endnotes I.

For a thorough derivation of these equations, see chapter 10 of reference [3].

II.

Note, typically this vector points from the vehicle CG to accelerometer (or EDR), which in general can have a non-zero zcomponent. To use the formalism presented in the rest of this work, simply ignore the z component, using only the projection on the vehicle’s local x-y plane to define this vector.

[5] W. Bortles et al., “A Compendium of Passenger Vehicle Event Data Recorder Literature and Analysis of Validation Studies”, Society of Automotive Engineers, 2016-01-1497.

[6] C. Wilkinson et al., “The Accuracy and Sensitivity of 2003 and 2004 General Motors Event Data Recorders in Low-Speed Barrier and Vehicle Collisions”, Society of Automotive Engineers, 2005-01-1190.

[7] A. Tsoi et al., “Validation of Event Data Recorders in High Severity FullFrontal Crash Tests”, Society of Automotive Engineers, 2013-01-1265.

[8] C. Gabler, C. Thor, and J. Hinch, “Preliminary Evaluation of Advanced Air Bag Field Performance Using Event Data Recorders”, NHTSA Report No. DOT HS 811 015, August, 2008.

[9] P. Niehoff et al., “Evaluation of Event Data Recorders in Full Systems Crash Tests”, NHTSA Paper No. 05-0271, 2005.

[10] J. Comeau, A. German, and D. Dalmotas, “Crash Pulse Data from Event Data Recorders in Rigid Barrier Tests”, NHTSA Paper No. 11-0395; Proc.

22nd ESV Conference, Washington, DC, June 2011.

III. Note, Note,ininthis thismodel, model,where we define restitution as the point of contact is approximately aligned with the negativeofratio of separation-velocity to as closing-velocity vector negadirection crush, we define restitution the point of contact ^ CG axis. In other rigid body components directed along theto∆v 1 tive ratio of separation-velocity vector components _ CG closing-velocity is cases represented in a normal “crush axis” impactalong models, 1 In directed the where ∆v axis. where frictional effects are nonand tangent basis, may be defined as the negligible, one“friction may wishaxis” to use therestitution more generally applicable formalpoint of contact negative ratio of to closingism, where is represented in separation-velocity a normal “crush axis” and tangent velocityaxis” vector components directed alongisthe normal “friction basis, and where restitution defined asaxis. the point of contact negative ratio of separation-velocity to closing-velocity vecIV. torSee Appendix 1directed for discussion onnormal solvingaxis for (see pre-impact ground components along the for example, R. speeds.planar impact mechanics). This topic will be considered in a Brach’s future article.

PLANNING A 2022 RETURN!!

[11] J. Wilkinson, J. Lawrence, and D. King, “The Accuracy of General Motors Event Data Recorders in NHTSA Crash Tests”, Collision Magazine 2(1): 7176, 2007.

[12] N. Rose, W. Bortles, and N. Carter, “Motorcycle Accident Reconstruction: Applicable Error Rates for Struck Vehicle EDR-Reported Delta-V”, Collision Magazine Volume 12, Issue 1, 2019.

[13] A. Childester et al., “Recording Automotive Crash Event Data”, International Symposium on Transportation Recorders, Arlington VA, 1999.

[14] D. MacInnis, W. Cliff, and K. Ising, “A Comparison of Moment of Inertia Estimation Techniques for Vehicle Dynamics Simulation”, Society of Automotive Engineers, 970951.

If you would like to present a topic at the 2022 EDR Summit, please submit your topic and abstract to: sbaker@crashdatagroup.com

[15] B. Scurlock, “Reconstruction of 60-degree Front-to-Side Staged Collisions with the Virtual CRASH Software Application”, VC White Paper, vcrashusa.com/s/VirtualCRASH_RICSAC_60deg.pdf.

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Appendix 1 The closing-velocity ambiguity problem Typically, the analyst would like to use EDR ∆𝑣𝑣 to arrive at some estimates of pre-impact ground speeds for the interacting vehicles; however, our key result, given by (100), does not yield ground speeds, but rather the projection of the closing-velocity vector onto the axis given by the impulse vector for vehicle 1, thus leaving the component tangent to the vehicle 1 impulse vector axis undetermined. It is possible, in some cases, to resolve this ambiguity problem by either using more information, such as departure angles, or using a simplified system where one vehicle is initially at rest. Resolving the ambiguity problem is explored in this appendix. Note, in the presentation below, it is assumed that the orientations at impact are known for the vehicles. Impact orientation is needed in order to use much of the formalism presented in this paper.

are initially in motion, the ambiguity can be solved if a departure angle is known for one of the vehicles.

From the law of sines, we know:

and

III

Starting with (99): � ��1 � �� ∙ �𝑣𝑣𝑣���,� ∙ ∆𝑣𝑣���� � �

From this we have:

� �𝑣𝑣̅���,� ∙ ∆𝑣𝑣���� �

Next, we distribute dot product:

�∆𝑣𝑣̅��� � �∆𝑣𝑣̅��� � � 𝛾𝛾� 𝛾𝛾�

where,

�� �� � �𝑣𝑣̅�,� |∆𝑣𝑣̅��� | �𝑣𝑣̅�,� � � � |sin�𝜃𝜃�� �| |sin�𝛼𝛼�� �| |sin�𝛽𝛽�� �|

�� �� � �𝑣𝑣̅�,� |∆𝑣𝑣̅��� | �𝑣𝑣̅�,� � � � |sin�𝜃𝜃�� �| |sin�𝛼𝛼�� �| |sin�𝛽𝛽�� �| �� �� 𝜃𝜃�� � cos�� �𝑣𝑣��,� ∙ 𝑣𝑣��,� � �� �� 𝛼𝛼�� � cos �𝑣𝑣��,� ∙ ∆𝑣𝑣���� � �� ∙ ∆𝑣𝑣���� � 𝛽𝛽�� � cos�� �𝑣𝑣��,�

and

|∆𝑣𝑣̅��� | |∆𝑣𝑣̅��� | 1 ∙� � � 1�� 𝛾𝛾� 𝛾𝛾�

�� �� ∙ 𝑣𝑣��,� � 𝜃𝜃�� � cos�� �𝑣𝑣��,� �� ∙ ∆𝑣𝑣���� � 𝛼𝛼�� � cos�� �𝑣𝑣��,� �� ∙ ∆𝑣𝑣���� � 𝛽𝛽�� � cos�� �𝑣𝑣��,�

�� Note, in the special case where, at the moment of impact, 𝑣𝑣��,� is aligned with �� vehicle 1’s local x axis and 𝑣𝑣��,� is aligned with vehicle 2’s local x axis, 𝛼𝛼�� and 𝛼𝛼�� are equivalent to each vehicle’s principal direction of force (PDOF).

� � ��𝑣𝑣̅�,� � 𝑣𝑣̅�,� � ∙ ∆𝑣𝑣���� � � ∙ ∆𝑣𝑣���� � 𝑣𝑣̅�,� ∙ ∆𝑣𝑣���� � �𝑣𝑣̅�,� |∆𝑣𝑣̅��� | |∆𝑣𝑣̅��� | 1 ∙� � � � 𝛾𝛾� 𝛾𝛾� 1��

Again, we assume the vehicle orientations at impact are known. This implies that 𝛼𝛼�� and 𝛼𝛼�� are known. We are now ready to examine some special cases that help resolve the closing-velocity ambiguity problem.

� � ∙ ∆𝑣𝑣���� � 𝑣𝑣̅�,� ∙ ∆𝑣𝑣���� �𝑣𝑣̅�,� � � � � ∙ ∆𝑣𝑣���� � ∙ �𝑣𝑣̅�,� � � �𝑣𝑣��,� ∙ ∆𝑣𝑣���� � ∙ �𝑣𝑣̅�,� � � ��𝑣𝑣��,�

�� , we then also have 𝜃𝜃�� With known vehicle 1 departure angle, thus giving 𝑣𝑣��,� �� �� � using the law of and 𝛽𝛽�� . This implies we can solve for both �𝑣𝑣̅�,� � and �𝑣𝑣̅�,� sines above. With this, x is given by:

Known vehicle departure angle

� � Factoring out the magnitude of 𝑣𝑣𝑣�,� and 𝑣𝑣𝑣�,� gives:

Therefore, we have:

� � � � ∙ ∆𝑣𝑣���� � ∙ �𝑣𝑣̅�,� � � �𝑣𝑣��,� ∙ ∆𝑣𝑣���� � ∙ �𝑣𝑣̅�,� �� ��𝑣𝑣��,�

|∆𝑣𝑣̅��� | |∆𝑣𝑣̅��� | 1 ∙� � � 1�� 𝛾𝛾� 𝛾𝛾�

Let us assume the special case that for each vehicle, the initial velocity vector at the effective point of contact, P, is the same as at the CG. Therefore:

where A, B, and C are known:

Thus, we can now easily solve for 𝑦𝑦:

�� 𝑦𝑦 � �𝑣𝑣̅�,� ��

𝐶𝐶 𝐴𝐴 � 𝑥𝑥 𝐵𝐵 𝐵𝐵

�� � � |∆𝑣𝑣̅��� | ∙ 𝑦𝑦 � �𝑣𝑣̅�,�

𝐴𝐴𝑥𝑥 � 𝐵𝐵𝑦𝑦 � 𝐶𝐶

Thus, we can now easily solve for 𝑥𝑥:

�� 𝑥𝑥 � �𝑣𝑣̅�,� ��

|sin�𝛽𝛽�� �| |sin�𝜃𝜃�� �|

𝐶𝐶 𝐵𝐵 � 𝑦𝑦 𝐴𝐴 𝐴𝐴

�� �� ∙ ∆𝑣𝑣���� � 𝑣𝑣��,� ∙ ∆𝑣𝑣���� 𝐴𝐴 � �𝑣𝑣��,�

Solving for non-zero initial speed when other vehicle is initially at rest

|∆𝑣𝑣̅��� | |∆𝑣𝑣̅��� | 1 ∙� � 𝐶𝐶 � � 𝛾𝛾� 𝛾𝛾� 1��

If one vehicle is initially at rest, no departure angles are needed to resolve the closing-velocity ambiguity problem. Suppose we know vehicle 2 is initially at rest. With 𝑦𝑦 � 0, in this case, our above equation reduces to:

�� �� ∙ ∆𝑣𝑣���� � �𝑣𝑣��,� ∙ ∆𝑣𝑣���� 𝐵𝐵 � 𝑣𝑣��,�

and x and y are unknown:

�� � 𝑥𝑥 � �𝑣𝑣̅�,� �� 𝑦𝑦 � �𝑣𝑣̅�,� �

�� �� 𝑥𝑥 � �𝑣𝑣̅�,�

� . This Here, 𝑥𝑥 and 𝑦𝑦 are free parameters, thus causing an ambiguity in 𝑣𝑣𝑣���,� ambiguity can be solved if one vehicle is initially at rest; however, if both vehicles

𝐶𝐶 𝐴𝐴

If, on the other hand, vehicle 1 is initially at rest, we have 𝑥𝑥 � 0, and

�� therefore: 𝑦𝑦 � �𝑣𝑣̅�,� ��

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|sin�𝛽𝛽�� �| |sin�𝜃𝜃�� �|

If, on the other hand, the vehicle 2 departure angle is known, this implies we �� have 𝑣𝑣��,� , and therefore 𝜃𝜃�� and 𝛽𝛽�� . In this case, we know y:

�� �� �� �� ∙ ∆𝑣𝑣���� � ∙ �𝑣𝑣̅�,� � � �𝑣𝑣��,� ∙ ∆𝑣𝑣���� � ∙ �𝑣𝑣̅�,� � ��𝑣𝑣��,� �� �� |∆𝑣𝑣̅� | |∆𝑣𝑣̅� | 1 ∙� � � � 𝛾𝛾� 𝛾𝛾� 1��

The above is in the form:

�� � � |∆𝑣𝑣̅��� | ∙ 𝑥𝑥 � �𝑣𝑣̅�,�

�

�

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Appendix 2 Example calculation using data from EDR A.

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Aftermarket ECU’s for Crash Reconstruction in a growing David Carr UTV market Impact Collision Forensics

C

rash/Event Data Recorder (CDR/EDR) technology has become an integral part of modern traffic crash reconstruction. Many non-automobiles that are involved in on-road and off-road crashes do not come equipped with stock or OEM electronic recording capability. However, the discovery process described in this case study ultimately revealed that recording capabilities can be an aftermarket addition for vehicles such as UTV’s, ATV’s, Motorcycles, Street Racing Imports, and even boats. These aftermarket components are becoming affordable and easier to program without specialized equipment and training.

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I would also argue this data is just as useful, if not more useful than, automobile CDR/EDR data we have traditionally seen for crash reconstruction.

Motorcycles and street racing have remained popular, but Utility Terrain Vehicle (UTV) sales have exploded in recent years. People have been interested in powersports recently, due to its ability to offer affordable and fun outdoor recreation. In 2018 the powersport industry has trended upward and is not showing any signs that it will stop. There were Eleven Billion dollars in UTV sales in 2018.

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With the COVID 19 restrictions sales have spiked even higher. People are spending their money on UTV’s and outdoor equipment instead of going on cruises and travelling vacations.

With UTV sales spiking, combined with the “Do It Yourself ” (DIY) movement, there has been solutions for consumers seeking custom options and creating high performance vehicles on a family budget.

The ECU Master Black and ADU Display (Figure 1) adds recording capabilities in a UTV which exist even without any dashboard displays or other visible clues. This can make an investigators job very difficult because it doesn’t look like the vehicle has been modified.

ECU Master Black and the Advanced Display Unit (ADU) displays shown on Figure 1- above, offer affordable and easy to program CAN bus solutions for modern spark control engines. It offers access to and control over several analog and digital inputs. The ADU display alone has GPS and CAN connections that may contain data, and often are overlooked during inspections (they look like a typical digital speedometer). The GPS and CAN connections are in the rear of the ADU and can only be seen if the unit is removed from the dashboard. Owners with these setups are now able to control wheel speeds and creating ABS or traction control for vehicles not equipped from the factory with these options. You can

control and monitor pressures, temperatures and more. Customers are now fully customizing these vehicles for their specific applications. Many available accessories and control panels allow for a customizable experience and full tuning control. All programming needs are available on the manufacturer’s website. You can download a free software, read the manual, and watch “YouTube” videos to set up the system from start to finish.

Another popular use for ECU Master is data logging and track positions. This is also an advantage over typical EDR Data stored in vehicles after an event that causes a record to be stored. This data logging is live and constant for the entire trip of the vehicle. The ADU can use a CAN connection and may be equipped with a GPS connection. The EMU is using a CAN connection with installed inputs. These systems record data that includes speed, acceleration, throttle position (%), gear position, engine pressures, RPM, and angular rates on three planes. These systems record each at their own specific rates, I have found them to typically be from 5 HZ to 25 HZ. The upper sampling limit of the system is set at 500 samples per second. The plug and play adapters allow this unit to connect to a variety of manufactured motors and vehicles on and off the road.

These units may even be installed in the next Domestic or Import motor vehicles you inspect after a collision on the road. You might not know they exist under the damaged hood of the next Honda or Muscle car you inspect.

Figure 1: ECU Master Black, EMU and ADU www.collisionmagazine.com

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Case Study

ment unit and several custom modifications. The UTV’s Engine was modified to produce more power. The suspenFigure 2 above is actual surveillance video of the collision. sion was modified, and center of gravity was raised from its The UTV with driver and passenger is captured as it left manufactured height. The wheels were changed and there the roadway. The UTV violently rolled and the driver had were off-road tires in the rear and narrower street tires in not fully bolted the seats or installed the seatbelts yet. The the front. A turbo charger was installed, and the vehicle passengers are seen being ejected and dynamics of the UTV was tuned using the ECU Master Black (Figure 3-below) flipping and rolling to its final rest at the chain link fence. using manufacturer’s software and a laptop computer.

At the time of the collision, the single vehicle involved was These were all completed by the owner who also owned a turbo charged Yamaha 1000R side by side UTV. This a shop specializing in those type of modifications. These UTV was found to have an aftermarket engine manage- types of modifications can also be done in your garage with some time, tools, and a laptop.

Figure 2: Surveillance video of actual collision

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During my investigation I discovered that the ECU Master (ADU) display, as shown earlier in Figure 2, could be just as valuable with data logging. I was not aware of these affordable options, until the middle of the investigation of this collision. While measuring the scene, I discovered a detached USB thumb drive nearby in the dirt and it looked out of place. I seized it as evidence which was valuable once back in the office. The EMU was discovered due to it being dislodged from the rollover and a USB port was clearly visible. I googled the ECU Master Black and saw what the device was capable of.

Back at the office, the thumb drive was found to have saved files that were later imported into ECU Master software. The complications started and I wasn’t seeing any data and finally discovered that the file had custom labels.

A separate file of custom labels was found and imported.

After these custom labels were used, I finally had the entire

2 1/2-minute trip recorded on a graph. I turned on all the inputs and could see the data as shown in Figure 4.

After completing a traditional reconstruction to determine the speed of the UTV, I analyzed the data using ECU Master’s free and easy to use software. The speed from the reconstruction and EMU data overlapped nicely. I located and confirmed the speed of the vehicle prior to yawing, running off the roadway, and rolling. Having all this electronic data logging at high sample rates, I was able to go a step further to analyze and graph the throttle positions plus time it took to accelerate through the gears. See figure 5 for details.

This reckless acceleration was captured as the UTV was accelerated at 100% throttle leading to losing control of the UTV. Ultimately this caused an ejection and death of a passenger riding within the UTV.

Figure 4: ECU Master, file from collision

Figure 5: Table of acceleration leading to crash www.collisionmagazine.com

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One challenge was identifying where the speed of the UTV became accurate as the operator over-accelerated through the gears. The hard acceleration caused the tires to break traction in each gear. Thus, the displayed speeds were over reported where the hard acceleration was occurring. This could be a common theme with operators testing the upper limits of their modified high-performance vehicles. It wasn’t until the operator released pressure on the throttle, allowing the wheel speeds to settle down and report speeds more accurately. Using the tri-axial accelerometers and gyroscopic data as shown in Figure 6, I was able to match the data with the collision sequence.

We could now see where the UTV tripped, what speed he was travelling, and the rate at which it rolled. With all this evidence sitting in front of me, I could verify the data stored by the ECU Master Black was true, accurate, and definitively from this crash sequence. In this particular collision, the actual speeds, although significantly over the speed limit, were perhaps not as important as the operator’s 100% throttle application to demonstrate recklessness. This information came from the aftermarket recording capability found in the UTV.

Even though what was found wasn’t a native or OEM crash data recorder, it proved to be more detailed and contain more valuable data than many traditional automobile EDR’s.

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Figure 6: ECU Master, Acceleration and Gyroscopic labels Conclusion In the case study outlined above, we had sufficient roadway and surveillance video evidence to establish a pre-collision speed. However, the data from the aftermarket recording capability that had been installed in the UTV provided a far more comprehensive record of the circumstances and the operator’s reckless behavior that resulted in this fatal single vehicle collision.

Even though what was found wasn’t a native or OEM crash data recorder, it proved to be more detailed and contain more valuable data than many traditional automobile EDR’s.

This case study should serve as a reminder to investigators that when owners make modifications to improve engine power and performance, such modifications may include adding components that have aftermarket recording capability. Those modifications could prove to be a valuable part of a situationally complete collision analysis.

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An Overview of the Subaru Eyesight Advanced Driver Assistance System

I

ntroduction What reconstructionist wouldn’t want a set of dual color cameras in the front seat of the collision they are investigating? With the development in the North American market of a stereo camera Advanced Driver Assistance System (ADAS) known as EyeSight in 2013, Subaru has officially piqued the datahungry curiosity of the accident reconstruction community. The main question vexing reconstructionists: is there any data contained within this camera-based Subaru EyeSight system that can be accessed and analyzed by investigators?

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Shawn Harrington Forensic Rock

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Along with determining the ultimate answer to this question, this article will investigate the history of the Subaru EyeSight system, present testing analyzing automatic cruise control, establish gap definitions, and evaluate the automatic emergency braking functionality of the system.

In addition, a novel approach to develop a more costeffective (i.e. DIY “cheaper”) methodology for creating a build-your-own ADAS vehicle separation system will be presented.

History and Explanation of Subaru EyeSight in North America The first-generation Subaru EyeSight system was introduced in Subaru’s home country of Japan in 2008. After the success of the system in Japan, Subaru introduced the EyeSight system into the Australian market in December 2011.

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This was followed by the debut of EyeSight in the North American market as an optional feature in 2013 Subaru Legacy and Outback models.1 The technology debuted on the all-new SJ Forester platform as an option in the 2014 model year.

The first-generation EyeSight system was advertised with four main ADAS capabilities:

There have been three generations of Subaru EyeSight systems since the technology debuted in Japan in 2008 on the Legacy B4, Legacy Touring Wagon, and Legacy Outback. To be consistent with the North American marketing materials and the introduction of the technology to the North American market, this article will reference first and second generations of the EyeSight technology. EyeSight technology in the North American market, which is known and marketed as generation one (G1) and two (G2) in the United States, would be considered versions two and three in the international market, respectively.

3. Lane departure and sway warning; and,

Thus, information about the first-generation (G1) North American EyeSight system was based on information from Subaru of America’s (SOA) press release from March of 2012 introducing the technology 2: EyeSight uses two charge-coupled device (CCD) cameras developed by Subaru. EyeSight is mounted inside the car on the upper edge of the windshield, thus reducing the potential for damage that could occur in bumper-mounted systems, such as radar. The EyeSight system processes stereo images to identify the vehicles traveling in front, as well as obstacles, traffic lanes and other items. The video information is relayed to the EyeSight computer, which is also networked with the car's braking system and electronic throttle control. Below speeds of approximately 19 mph, EyeSight is capable of detecting pedestrians in the vehicle's path and can activate in order to mitigate or even avoid the collision. Under certain circumstances, EyeSight is able to bring the car to a complete stop, thus avoiding a collision.

1. Pre-collision braking; 2. Pedestrian detection; 4. Adaptive Cruise Control.

The initial technical information that SOA provided relative to the system outlined a 19 mph (30.6 kph) relative speed detection threshold. This was highlighted in SOA’s explanation of their pre-collision braking control and mitigation technology, which advertised that the system could either slow the vehicle or bring the vehicle to a full stop at relative speeds under 19 mph. SOA advertises the ability to detect pedestrians below a 19 mph threshold as well.

The next generation of the Subaru EyeSight system, i.e. the second-generation technology (G2), was introduced in North America in model year 2015 Subaru Legacy and Outback vehicles. The G2 EyeSight system was introduced mid-platform into the Forester in model year 2017. For model year 2018, EyeSight was available as an option on all Subaru models (expect the joint Toyota venture BRZ model). And, for the first time for a Subaru model, the all-new 2019 Subaru Ascent debuted G2 EyeSight technology as standard on all trim levels sold. The G2 EyeSight technology became standard on more Subaru models in model year 2020.

The G2 EyeSight system introduced the following new and/or improved technologies versus the G1 system: 1. Rear cross traffic alert; 2. Blind spot monitoring;

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3. Increased detection and speed ranges for collision mitigation relative to G1; 4. Brake light detection; and, 5. Improved pedestrian and obstacle detection.

Overview of Testing Testing evaluating the G1 EyeSight ADAS in a 2014 Subaru Forester and a G2 EyeSight ADAS in a 2019 Subaru Ascent was conducted in January and February of 2020.

The testing was designed to evaluate the following areas of the G1 and G2 EyeSight ADAS:

hicles were accelerated up to pre-determined target test speeds between idle and 55 mph into the fabricated 4’ x 8’ vinyl target breakaway “barrier” by a test driver. As the EyeSight system is a purely camera-based ADAS, no radar reflectors or other “handshake” measures that are required to test other ADAS were necessary to redundantly verify the signature of an actual vehicle. The aforementioned onboard VBOX video HD2 data acquisition system was used to measure three stages of collision mitigation by the two EyeSight-equipped vehicles: 1. Warn mode via an audio beeping and dashboard visual warning;

•

Automatic Emergency Braking (AEB);

2. First-stage braking mode;

•

Automatic Cruise Control (ACC);

3. Second-stage braking mode.

•

•

Gap Definitions;

Automatic Cruise Control Testing

•

Detection Range; and,

For both the G1 and G2 EyeSight systems, there were three following distances that could be selected by the driver with respect to the automatic cruise control system. Subaru denotes these as “FAR”, “MEDIUM”, and “CLOSE” settings. Testing to evaluate what following distances were established by the vehicle was conducted using the G1 EyeSight system for these three settings. This testing involved equipping both the “lead” vehicle and the “following” G1 EyeSight-equipped vehicle with a Racelogic VBOX system. Depending on the test, the three following settings, FAR, MEDIUM, and CLOSE were selected and set on the G1 EyeSight-equipped vehicle.

Pedestrian Detection System (PDS).

Different equipment was used depending on the testing that was being conducted. Overall, testing utilized some combination of a Video VBOX HD2 two-camera system, VBOX Sport, Sony a7RIV video camera, GoPro Hero8 and GoPro Hero7 action camera, DJI Mavic 2 Pro drone, and DJI Mavic Mini drone. In this article, an overview of the AEB and ACC testing that was conducted will be presented.

Automatic Emergency Braking Testing For the automatic emergency braking testing, a custom test rig was fabricated to mount a magnetic breakaway 4’ x 8’ vinyl banner of an image of the rear of a four-door passenger sedan. The G1 and G2 EyeSight-equipped ve-

For the ACC testing, a cost-effective methodology to determine the following distance between two VBOX-equipped vehicles in motion was developed using two VBOX data acquisition systems. Upon consultation with Racelogic in Farmington Hills, Michigan, the following protocol was

Figure 2: 2019 Subaru Ascent with 4’ x 8’ vinyl banner and breakaway test rig at the testing site.

[February 2020].

Figure 3: View from Sony A7Riv video camera showing location of some of the testing equipment [February 2020].

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developed to calculate the following distance between two vehicles equipped with VBOX data acquisition systems: •

Run testing with a lead vehicle and following vehicle. Both vehicles need to be equipped with VBOX data acquisition systems that are running and collecting data at the same time;

•

Retrieve the two .VBO files from the two respective VBOX systems that were generated from the testing;

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Download VBOX File Processor from the VBOX website;

•

Open the VBOX File Processor software and select the ‘ADAS’ menu;

•

Double click on the ‘Vehicle Separation’ link in the blue column;

•

Click on the ‘Load Input File’ button near the top of the menu and load the following vehicle (i.e. the bullet vehicle) .VBO file;

Figure 4: Setting utilized in VBOX File Processor under the ‘Target Vehicle Data” menu.

•

Click on the ‘Load Target Vehicle File’ button and load the lead vehicle (i.e. the target vehicle) .VBO file;

•

Adjust the ‘Subject Vehicle Offset’ and ‘Target Vehicle Offset’ based on the location of your respective GPS receivers on the VBOX systems (make sure to measure where the GPS receiver is located on your testing vehicles!);

•

•

Adjust the ‘Target Vehicle Data’ fields (See Figure below for suggestions that were successful for this author);

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Leave all ‘Channels’ checked to acquire all potential data from the processor;

•

Click the ‘Process Output File’ button at the bottom of the software;

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Open the folder where the new modified .VBO has been created. This file will have “_Processed” after the file name. Open the .VBO file in VBOX Test Suite;

•

There are now new Channels available for analysis that are located under ‘Dashboard’ -> ‘Add Gauge’ ->‘Channels’ in the VBOX Test Suite;

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Utilizing channel ‘LngRsv-tg1’ will provide the dynamic following distance between the two VBOXequipped vehicles. (Closing speed between the vehicles and speed of the target vehicle are also available channels)

It must be noted that the overall tolerance of this methodology is higher compared to the VBOX system sold by Racelogic that was specifically designed for this ADAS testing purpose. Thus, further validation testing needs to be conducted to determine the ultimate precision of this approach.

It must be noted that the overall tolerance of this methodology is higher compared to the VBOX system sold by Racelogic that was specifically designed for this ADAS testing purpose. Further validation testing needs to be conducted to determine the ultimate tolerance of this approach, but the methodology thus far has yielded accurate and reliable results.

Results Automatic Emergency Braking Testing Both the G1 and G2 EyeSight-equipped Subaru’s reliably and repeatedly detected the vinyl 4’ x 8’ “barrier” during

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testing. As stated previously, three phases were evaluated for both the G1 and G2 EyeSight-equipped test vehicles.

These three phases were an audio “beeping” warn mode with a visual red flashing indicator on the dashboard, a first-stage braking response by the EyeSight system, and a second-stage braking response by the EyeSight system.

These three stages are known as ‘Warn’, ‘S1’, and ‘S2’ in the presented data. Acceleration was measured and calculated from the onset of the braking phase to the next phase of the data. For a Warn/S1-only phase with no S2 activation – due to a low idling target test speed, for example – the average deceleration would be calculated from the onset of the braking pulse to a zero or near-zero (less than 0.5 mph) speed. For a full Warn/S1/S2 activation – for a 30 mph

target test speed for the G2 EyeSight-equipped system, for example – the braking pulse for the S1 phase was either obtained through a clear delineation in braking threshold levels in the data or from listening to the audio of the braking system obtained using the Video VBOX HD2 system.

A clear second stage activation could be heard when S2 was activated versus the initial S1 braking.

Automatic Cruise Control Testing The results from the testing of the G1 EyeSight-equipped 2014 Subaru Forester consistently fell within the approximate ranges provided in the owner’s manual.

Figure 5: Results from G1 EyeSight-equipped 2014 Subaru Forster [Test Date – February 14, 2020]

Figure 6: Results from G2 EyeSight-equipped 2019 Subaru Ascent [Test Date – February 28, 2020] www.collisionmagazine.com

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Figure 7: ACC range defined in the 2014 Subaru Forester owner’s manual.

The following presents examples of individual data from the ACC testing. For example, at the ‘Far’ setting and at a speed of 42 mph, the following distance was determined to be approximately 135 feet using the aforementioned VBOX-to-VBOX processing methodology. This provides a following distance time of 2.25 seconds. At the ‘Medium’ setting and at a speed of 46 mph, the following distance was determined to be approximately 100 feet which provided a following time of 1.5 seconds. At the ‘Close’ setting and at a speed of 37 mph, the following distance was approximately 63 feet. This provides a following time of 1.1 seconds.

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mine where in a curve the lead vehicle was lost by the ACC system. In the following figures, the white box represents the location of the G1 EyeSight-equipped Subaru and the red box represents the target lead vehicle when the Eyesight system “lost” sight of the lead vehicle.

Discussion The 19 mph detection threshold for the G1 system was a reliable upper bound for consistency of the system in AEB testing. The same was determined for the G2 system which performed consistently up until the 30 mph threshold. However, both the G1 and G2 EyeSight systems contacted the barrier below these 19 and 30 mph detection thresholds, respectively. The G1 system had a 90% success rate at testing differentials below 19 mph, contacting the

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Figure 8: Video VBOX with Processed ADAS vehicle separation data for the ‘Close’ setting.

Curve 1

Figure 9 (above left): G1 EyeSight-equipped view of right curve at the point the lead vehicle in the red box was lost by the Eyesight system.

Figure 10 (above right): Nearmap aerial perspective of the approximate location of the G1 EyeSightequipped vehicle [white box] and lead vehicle [red box] at the point when the lead vehicle was lost by the G1 EyeSight system. barrier in only one out of the ten tests conducted. The G2 system had an 81% success rate at testing differentials below 30 mph, contacting the barrier on only four out of the twenty-one tests conducted. The speed utilized as the “official speed” of the test was the speed of the EyeSightequipped vehicle when the audio and visual warning was first detected (Speed @ Warn in the data).

The detection range of the G2 EyeSight-equipped system was indeed a significant improvement over the G1 system.

The two tests in the Figure below highlight the increased detection range and improved collision mitigation system of the G2 system versus the G1 system. At a speed of approximately 26 mph, the G2 2019 Ascent first detected and warned the driver of an impending collision at a time

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Curve 2

Figure 11 (above left): G1 EyeSight-equipped view of right curve at the point the lead vehicle in the red box was lost.

Figure 12 (above right): Nearmap aerial perspective of the approximate location of the G1 EyeSightequipped vehicle [white box] and lead vehicle [red box] at the point when the lead vehicle was lost by the G1 EyeSight system.

Figure 12: Comparison of successful G2 avoidance test versus G1 contact with barrier test at a similar speed of 26 mph. to collision (TTC) of 2.3 seconds and at a distance of 88 feet to the stationary target. At the same speed, the G1 2014 Forester first detected the stationary target at a distance of 56 feet and a TTC of 1.5 seconds.

What Data is Available to Reconstructionists after a Collision?

One of the goals of this research was to determine what information from the EyeSight system was available for imaging after a collision event. After a dialogue with executives at Subaru of America in the first quarter of 2020, it was determined that there is no current nor reliable protocol for downloading or imaging any data from EyeSight systems in the North American market. Subaru of America is currently forwarding law enforcement requests – with warrants only – to Subaru of Japan. Based on the knowledge of this author, those requests are effectively being ignored by Subaru of Japan.

Although the system to connect to the EyeSight system appears to only be a simple modification to the Subaru Select Monitor 4 software (SSM4), there are no current dealers or Subaru technicians in the United States who have the software to image information from EyeSight-equipped vehicles. The exception to obtaining data from EyeSight 54 Collision Magazine - Volum 15 Issue 1

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systems in the North American market, however, involves litigation with a product liability component against Subaru. Even in this scenario, it has been reported to the author that a technician from Subaru of Japan was required to image the data.

The vexing component of this situation is the known data that is being stored in the EyeSight system. In 2018, Oga et al. published an article in the Society of Automotive Engineers that outlined testing and the available data in the Version 3 EyeSight system (G2 in the NA market). 3 The authors, who work in Japan, partnered with Subaru of Japan to run testing evaluating the EyeSight system. After each test, Subaru engineers would connect to the EyeSight system to image freeze-frame data from the ADAS. This freeze-frame information included one data point on steering angle, vehicle speed, accelerator throttle position, estimated distance to the target, relative speed of the target, lateral lap rate, and a single monochrome photograph from the system at activation of the respective phase of the EyeSight system. (A monochrome photograph from a color stereo system?) In addition, the system has multiple storage slots to store data from more than one event. The system stores data in a first-in/first-out hierarchy. Thus, the potential for data from these systems is real. The un-

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resolved issue is the ability to image this information from the EyeSight system in North America.

Final Thoughts Additional work remains to define the accuracy of the VBOX vehicle separation methodology. Further work will also include plotting the following distance of the EyeSight system during different ACC speeds and following distance settings. Evaluations of the system in different weather conditions was also completed; this data needs to be processed and analyzed. Furthermore, the lane keeping ability of the G2 EyeSight system was evaluated; further post-test processing also needs to be completed. Overall, the camera-only EyeSight system displayed an admirable ability to recognize a hazard and stop the vehicle below the stated upper bound thresholds of the system. Further testing of other manufacturers’ ADAS is ongoing, including commercial vehicle systems.

Shawn Harrington is the principal accident reconstructionist with Forensic Rock. He can be reached at sharrington@forensicrock.com or (215) 620-1288.

Acknowledgments The author would like to thank Bill Ward of Forensic Rock for his help with testing and the fabrication of the test-

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ing rig in January and February 2020. Acknowledgment and deep gratitude are also given to Alan Moore for his consultation (and the banner image) and Shawn Gyorke of Crash Data Services for his consultation. The author would like to thank Scott Baker, and Dan Walker of Crash Data Group and Rusty Haight of Collision Safety Institute for their help and assistance. In addition, the author would like to especially thank Mary Harrington from Subaru of America for her assistance.

References [1] Subaru Press Information. “FHI to Introduce the “EyeSight” to North America – The Second Overseas Launch of Subaru’s Unique Driving Assist System,” March 16, 2012, Tokyo, Japan.

[2] Subaru U.S. Media Center. “Subaru Debuts New EyeSightTM System,” March 15, 2012, Cherry Hill, New Jersey.

[3] Oga, R., Takubo, N., Kato, K., Terashima, T. et al., "Accident Reconstruction with Data Recorded by Electronic Control Units in Vehicles with a Pre-crash Safety System," SAE Technical Paper 2018-01-1440, 2018, https://doi.org/10.4271/2018-01-1440.

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crash·ol·o·gy THE SCIENCE OF CRASHES Wesley Vandiver

Robert Anderson

Collision Forensics, Inc.

Biomechanics Analysis

Validation of Ford SG3v1 Speeds Acquired and Derived with Berla iVe

F

or collision reconstructionists, the ability to retrieve digital evidence of vehicle speed around the time of particular incident can yield key evidence in an investigation. The acquisition of vehicle speed data from Event Data Recorders (EDRs) has become commonplace and is a routine item on the checklist for those investigating vehicular incidents. Much has been written about the accuracy of EDR data from a multitude of vehicle tests involving actual crashes, simulated crashes, hard acceleration, hard braking, etc. In summary, nearly all experts agree that EDR data is tremendously valuable, but should always be considered alongside the other physical evidence and a properly-done analysis of that evidence as part of a situationally complete reconstruction.

the data acquired and derived from the SG3v1 module under these conditions.

During this testing, the Mustang was driven on a closed highway in Tampa, Florida and subjected to high speeds, hard acceleration, and hard braking. The purpose of this testing was to assess the accuracy of

eled between the points and the time interval. For the purposes of the distance measurement, the iVe software uses the Great Circle Methodology, which is used to calculate the distance between two points

The testing of data from EDRs goes back approximately 20 years. In this time, the collision reconstruction industry has had the opportunity to observe and learn about the limitations of EDR data, including issues such as 1) relationship of impact time to Time Zero values or Time -1 second values, and 2) the effects of wheel slip or yaw on the accuracy of recorded speeds.

The SG3v1 module examined in this research records vehicle speed at 10 Hz, which is sourced from the vehicle CAN bus. This is similar to the way in which a typical EDR sources its speed values. However, the difference lies in the time associated with the speed More recently available to the reconstructionist than readings. A typical EDR assigns a time value to each EDR data is Vehicle System data acquired using Berla recorded speed that is approximately the time before iVe. The focus of this research is Vehicle System data an impact/event. The CAN bus speed recordings in acquired and derived from a Ford SYNC Generation the SG3v1 module are timestamped with the local 3 Version 1 (SG3v1) module in a 2018 Ford Mustang system time and displayed in a Velocity Log within GT that was subjected to instrumented testing. The the iVe software, as seen in Figure 2.

SG3v1 module, referred to as the Accessory Protocol The second type of speed data available from this Interface Module (APIM) by Ford, is part of the Mus- system is actually derived from the recording of GPS tang’s infotainment/telematics system and only one track points. The SG3v1 system records the location of the many Electronic Control Units (ECUs) in the of the vehicle at 1 Hz intervals. Therefore, GPS coMustang that has recording capability. This research ordinates are recorded for the vehicle location every is limited to the speed data acquired and derived from one second. With this data, the average vehicle speed the SG3v1 module. An example of an SG3v1 module between track points is derived (calculated) within is depicted in Figure 1. the Berla iVe software based upon the distance trav-

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termined and verified, which is valuable in hit-and-run investigations.

Among the numerous ECUs from various manufacturers that are supported by Berla iVe, the SG3v1 is, thus far, unique in that it records CAN bus speed data. Many ECUs record GPS data from which speed can be derived. But, to date, only the SG3v1 module is known to record GPS data alongside CAN bus speed data. This provided an opportunity in this research to compare both GPS-derived speeds and recorded CAN-bus speeds to instrumentation data.

Figure 1: Ford SYNC Generation 3, Version 1 Module on the surface of a sphere. An example of the track point organization within the iVe software is depicted in Figure 3. As can been in Figure 3, derived speeds are listed with their associated timestamps and GPS coordinates.

The iVe software can display the recorded track points on various map views. The track points depicted in Figure 4 are for the test data examined in this research with all before-and-after track points hidden from view.

These two sources of speed data can provide valuable evidence to an investigator. These may be used to corroborate other speed data from an EDR or results of a traditional evidence-based collision analysis. Furthermore, this data could be the only available evidence of the vehicle location and/or speed if the incident did not involve an impact or did involve an impact that failed to reach the required threshold for recording an EDR event. This phenomenon is now commonplace in collisions involving pedestrians and cyclists. Given that the GPS data is timestamped, the historical whereabouts of the vehicle can also be de-

The testing model for this case was taken from SAE International Technical Paper 2018-01-1442. Included in this publication was a testing protocol for assessing the accuracy of speed data from Ford SYNC Generation 2 and Generation 3 systems acquired by the Berla iVe System.

For the testing in this case, the same instrumentation was used. The reference instrument used to collect GPS data was the Racelogic VBOX Sport.

The specifications for the VBOX Sport are as follows: •

•

• •

Velocity • Accuracy: 0.1 kph (averaged over 4 samples) • Update rate: 20 Hz • Minimum velocity: 0.1 kph • Maximum velocity: 1800 kph • Resolution: 0.01 kph Acceleration • Accuracy: 0.5 % • Maximum: 4 G • Resolution: 0.01 G Heading • Resolution: 0.01° s • Accuracy: ±0.2° s Position • 2D Position: ±5m 95% CEP * • Height: 5 Metres 95% CEP * *95% CEP (Circle of Error Probable) means 95% of the time the position readings will fall within a circle of the stated radius

Figure 2: The Velocity Log for the CAN bus speeds reported in the SG3v1 module

The test data examined in this paper includes approximately 5 minutes of driving involving continually-changing speeds. The speed range examined is between zero MPH up to approximately 118 MPH with several periods of hard acceleration and hard braking. The analysis was done by comparing each speed recording/calculation by way of its timestamp. The VBOX instrumentation data utilized timestamps based upon Coordinated Universal Time (UTC). For

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Figure 3: Example Track Log display from Berla iVe software

Figure 4: Map of Track Points included in this research as shown in the mapping function of the Berla iVe software

this analysis, all other timestamps were converted to UTC and translated to “seconds after midnight” values. The VBOX collected data at 20 HZ. The GPS-derived speeds were reported at 1 Hz. The CAN bus speed recordings were reported at 10 Hz. The method of comparison in this analysis was to compare at 1-second intervals, using the closest to on-second values from each source.

Time (seconds) 30526 30539 30542 30550 30575 30590 30619 30628 30662 30672 30691 30696 30702 30711 30721 30746 30791 30816 30822

A tabular summary of the testing to include approximate acceleration and deceleration values is included in Table 1.

The results of the data analysis are depicted graphically in Figure 5.

As can be seen in Figure 5, there was a very strong correlation between the recorded CAN bus speeds and the VBOX instrumentation. The derived GPS average speeds also correlated well to the instrumentation speed data, but not as tightly as the CAN bus data. A numerical analysis of the CAN bus speed data and derived GPS speed values in comparison to the instrumentation data is contained in Table 2. The accuracy of the reported speeds was assessed using R-squared and RMSE values. Whereas R-squared is a relative measure of fit, RMSE is an absolute measure of fit. As the square root of a variance, RMSE can be interpreted as the standard deviation of the unexplained variance and has the useful property of being in the same units as the response variable. Lower values of RMSE indicate better fit. This testing provided a rare opportunity to examine the accuracy of vehicle speed data under high-speed conditions that included both hard braking at hard accel58 Collision Magazine - Volum 15 Issue 1

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Speed (MPH) 72.0 83.9 81.2 96.7 60.7 118.7 61.1 115.0 56.0 110.1 77.6 102.4 0.0 9.0 3.0 98.7 44.4 110.6 0.0

Acceleration (G) +0.04 -0.04 +0.09 -0.06 +0.19 -0.09 +0.27 -0.08 +0.25 -0.08 +0.23 -0.78 +0.05 -0.03 +0.17 -0.05 +0.12 -0.83

Table 1: Time, speed, and acceleration values for the entire test run

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Figure 5: Graphical representation of data comparison between VBOX instrumentation speeds, Berla iVe GPS derived speeds, and recorded CAN bus speeds from the SG3v1 module Source CAN bus GPS-derived

R-squared 0.998 0.984

RMSE (MPH) 1.27 2.38

Table 2. Comparison of CAN bus recorded speeds and GPS-derived speeds to VBOX instrumentation data eration events. The results of this testing are consistent with other analyses based upon Berla iVe acquisitions of Ford SYNC data, notably SAE Technical Paper 2018-011442, Accuracy of Speed Data Acquired from Ford Sync Generation 2 and Generation 3 Modules Utilizing the Berla iVe System, and SAE Technical Paper 2021-01-0903, Analysis of Vehicle GPS and Derived Speed Data from Ford SYNC Generation 3, Version 2 Systems Acquired with Berla iVe. References 1. Vandiver, W., and Anderson, R., “Analysis of Berla iVe Acquisitions of Vehicle Speed Data from Ford SYNC Systems,” SAE Int. J. Trans. Safety 6(3):257-274, 2018

2. Vandiver, W. and Anderson, R., “Analysis of Vehicle GPS and Derived Speed Data from Ford SYNC Generation 3, Version 2 Systems Acquired with Berla iVe,” SAE Technical Paper 2021-01-0903, 2021 3. Vandiver, W., and Anderson, R., “Analysis of Vehicle GPS and Derived Speed Data from BMW NBT Evo Systems Acquired with Berla iVe,” SAE Technical Paper 2021-01-0906, 2021 4. Analysis of Berla iVe Acquisitions of Vehicle Speed Data from Ford SYNC Systems,” SAE 5. Bortles, W., McDonough, S., Smith, C., and Stogsdill, M., “An Introduction to the Forensic Acquisition of Passenger Vehicle Infotainment and Telematics Systems Data,” SAE Technical Paper 2017-01-1437, 2017 6. Berla iVe User Guide, version 3.1, Berla Corporation

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Legal Challenges Regarding EDR Data in Testimony James Norris, P.E.

Parham Engineering Consultants, Inc

David A. Chapman, Esq. Lewis Thomason, P.C.

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EDR Summit 2020: The Expert Deposition From David Chapman As part of the 2020 EDR User's Summit in Houston, Texas, accident reconstruction expert James Norris and I conducted a mock deposition in which we presented a series of attorney questions and witness responses based on several different scenarios involving EDR data. The transcript of the mock deposition forms the basis for this article. Unlike physicians, accident reconstruction experts are not immune from subpoenas requiring live testimony at trial in most states. This means that in most circumstances, the expert will testify in a “discovery” deposition before he or she takes the witness stand at trial. A discovery deposition is so named because, in theory, it is the opportunity for attorneys for the other parties in a case to “discover” the opinions held by the expert. Discovery depositions are therefore designed to simply prevent a party from being “ambushed” at trial with the previously undisclosed or unexplored opinions of an expert.

In practice; however, the discovery deposition of an expert is more often used by an opposing attorney to “test” the expert and to experiment with different types of examination questions to see which ones may prove most effective at trial. Thus, if an attorney discovers that the expert handles questions regarding certain issues effectively, it is unlikely that he or she will give the expert the opportunity to duplicate that success in front of a judge or jury “when it counts.” See In re NC Swine Farm Nuisance Litig., No. 5:15-CV-00013-BR, 2016 U.S. Dist. LEXIS 89074, *159 (E.D.N.C. July 7, 2016) (citing Polozie v. United States, 835 F. Supp, 68, 72 (D. Conn. 1993) (noting distinction between an attorney's questioning of an expert for discovery purposes versus crossexamination at trial; "Attorneys presumably know what the purpose of a trial deposition is, and they will be mindful of the fact that they will not have another chance to develop fully the testimony of the witness. In cases www.collisionmagazine.com

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involving expert testimony this is particularly the case, and the Court must bear in mind that after taking a discovery deposition the attorney fully expects to examine the expert witness again at trial.").

Accordingly, discovery depositions of experts often do not entail actual disagreements regarding the content or meaning of EDR data or numerous other elements of an accident reconstruction analysis. Instead, the deposition often focuses on the attorney’s attempt to make the expert’s methodology appear incomplete or imprecise, and thus, unreliable.

Such were the questions posed to James Norris at the 2020 EDR Summit. Readers should keep in mind that the deposition was presented to a live audience, and thus there were multiple instances in which James and I addressed the audience outside the context of the deposition to pass on tips for effective testimony. The “exhibits” to the deposition were a series of slides that accompanied the presentation and that played during the examination.

From James Norris: David and I greatly appreciated the opportunity to conduct this mock deposition at the 2020 EDR Summit. The mock deposition expounded upon our presentation titled “Legal Challenges Regarding EDR Data” from the 2018 EDR Summit. As with that presentation, our goal was to get attendees thinking about the potential areas and issues regarding EDR data that they could be confronted with during testimony. Many times, those areas can be addressed with proper training, documentation, and policies/procedures. As an expert witness, testimony is the culmination of our work throughout the lifetime of a case. My personal belief is that we begin preparing for that testimony from Day 1 of a case. We must think comprehensively about our data collection, analysis, and opinions and how to support and defend them in the future. As David mentioned, the deposing attorney will be testing the expert, so we should prepare as such. We hope you enjoy our examples and that it may help in your own development.

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James E. Norris, II, P.E., ACTAR March 9, 2020 1

3 1

INDEX

2

PAGE

3

MOCK DEPOSITION

4

Appearances...........................................2

5

General remarks.......................................4

6

Scenario #1 Examination by Mr. Chapman...............12

7

Scenario #2 Examination by Mr. Chapman...............19

8

Scenario #3 Examination by Mr. Chapman...............28

MOCK DEPOSITION OF

9

Scenario #4 Examination by Mr. Chapman...............38

JAMES E. NORRIS, II, P.E., ACTAR

10

Witness Corrections and Signature....................44

MARCH 9, 2020

11

Reporter's Certificate...............................46

*******************************************************

12 *******************************************************

13 14 15 16

MOCK DEPOSITION OF JAMES E. NORRIS, II, P.E.,

17

ACTAR, taken via machine shorthand on the 9th of March,

18

2020, at Hilton Houston North - Raphael Ballrooms A &

19

B, 12400 Greenspoint Drive, in the City of Houston,

20

County of Harris, State of Texas, before Rachel

21

Hendrix, a Notary in and for the State of Texas.

22 23 24 25

2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

4 1

APPEARANCES

P R O C E E D I N G S

2

Mr. David Chapman Lewis, Thomason, King, Krieg & Waldrop, P.C. 620 Market Street, 5th Floor Knoxville, TN 37902 Mr. James E. Norris, II, P.E., ACTAR Parham Engineering Consultants, Inc. P.O. Box 6215 Knoxville, TN 37914 (865) 329-0007

MR. NORRIS:

One thing I think is

3

really important is doing your homework on who is

4

deposing you.

5

about it a little bit himself.

6

you're working for has had some previous experience

7

with the opposing attorney that's going to be deposing

8

you, I think it's always good to discuss with him what

9

kind of questions they have, what kind of demeanor they

10

have, how they have maybe attacked expert testimony in

11

the past, just to kind of get a good idea.

12

I think David will echo this and talk If your attorney that

If not, if that's not the case, maybe you can find

13

another expert.

14

proceedings are open; you might be able to get a copy

15

of a transcript to get a little bit of information

16

about that.

17

Or a lot of, you know, court

And then, of course, during the actual deposition

18

itself -- I think David will also recommend this --

19

don't be afraid to take your time.

20

times we get in a rush to answer a question.

21

already anticipating the answer before the attorney

22

even finishes his question.

I think too many We're

23

And so it's easy to kind of get stuck in that trap

24

or caught in that trap to -- oh, I know where this is

25

going -- you've got the answer on the tip of your

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James E. Norris, II, P.E., ACTAR March 9, 2020 5 1

tongue.

2

a report, flip back to a CDR, confirm something.

3

It's never bad to take your time, flip back to

It's much easier to do that up front than to try

laden with acronyms that no one can follow it.

So, if

2

you're an expert on one of my cases, you get to pick

3

your three favorites, and everything else you've got to

4

say it all the way out, spell it out, every single time.

4

to correct that in an errata sheet later.

5

course, never be afraid to take a break -- of course,

5

6

bathroom breaks, need water, stuff like that.

6

It just makes it simpler, it makes it easier to

7

sometimes during the middle of it, as the questioning

7

digest for the folks who are trying to digest what is

8

goes along, it can get a little overwhelming, it can

8

more than likely months, if not years, of analysis in

9

get a little taxing.

9

just a couple of hours.

10

started -- James has been my expert in a lot of cases.

10

And then, of

7 1

But just

Don't be afraid to say, hey, I just need to take a

11

break.

12

know, remember -- these aren't marathons, they're not

12

cases.

13

endurance matches.

They're scheduled times, there is

13

cases in which he testifies for me, his analysis is

14

plenty of time, so taking a five-minute break here or

14

spot on.

15

there is not going to cause any issues.

15

every single time -- it's weird how that works.

16

Each person is a little bit different, but, you

So, with that being said, I'm going to turn it

17

over to David.

18

from his side.

19

He's going to share a few perspectives

MR. CHAPMAN:

Okay, that handsome

I'm David Chapman.

I'm with the

11

I'll say this before we get

He's also been on the other side of me in some It's a super weird coincidence, but on the

When he's on the other side, it goes wrong

16

Uh, but I'll say this, too, because it leads into

17

what the real thrust of this exercise is going to be --

18

the lawyers don't understand this stuff.

Lawyers like

19

me like pretending we do, but we don't.

So you're

20

devil is me.

20

going to get -- there's no lawyer in the whole wide

21

Knoxville, Tennessee, office of Lewis, Thomason.

I'm

21

world who's going to sit down and go toe-to-toe with

22

with our transportation group and do primarily defense

22

you on the actual data or on your analysis.

23

work for mid-size and larger motor carriers.

23

It's all going to be about things that to a lay

24

And we're kind of doing the tips here at the

24

person might appear as though you're skipping a step or

25

beginning just to kind of, I guess, lay some context

25

that your process is somehow flawed.

On the off chance

6 1

for what we're doing.

1

that you have, you know, a report that has some data

2

are excerpts based on civil cases, some actual cases,

2

that, Heaven help us, the lawyer can interpret --

3

all actual cases actually.

3

that's going to be one of our scenarios here -- that's

4

about as close as you're going to get.

4

What we're doing is -- these all

8

The principles that we're talking about, though,

5

are equally applicable to certainly being cross-

5

Conventional wisdom -- a lot of times people think

6

examined as an expert at a criminal trial.

6

when they give depositions, the goal is to somehow, you

7

what James says in terms of my kind of quick tips.

7

know, use a minimal amount of words and to answer as

8

Before an expert testifies for me in a case, we spend

8

many questions with "yes" and "no" as you possibly can.

9

so much time getting ready for it that if the expert

9

I'm here to say, that's not right.

10

can survive my preparation work, then the deposition

10

The questions that you're going to get from a

11

itself is probably going to seem pretty easy.

11

lawyer who doesn't like what you have to say are going

I will echo

12

But, one of the things that I always emphasize

12

to be designed to have you answer "yes" or "no" and

13

with the experts is -- don't be afraid to take a pause

13

just leave it at that.

14

before you answer a question.

To you it seems like

14

reason that they're phrased the way that they are.

15

it's forever, but to everybody else in the room they

15

So, what I would encourage you to do is what I

16

won't even notice.

16

encourage experts in my cases to do -- which is to

That's the point.

That's the

17

Most people, when they're engaged in something

17

don't be afraid of "yes, but;" "no, but;" "yes, and;"

18

that is intellectually taxing like testifying in a

18

"no, and."

19

case, can take a pause.

19

will be fine.

20

that at all.

20

Because as soon as you say "no, and" or "yes,

21

testify in my cases, no matter what their field of

21

but," then you've taken the thrust out of the question

22

expertise, is you get to pick your three favorite

22

that the lawyer put in there, you know, a week before

23

acronyms and that's it.

23

you testified.

There's nothing wrong with

One of my rules of thumb for experts who

If you can remember that, then everything

Last, but not least, I will say be

24

There's nothing worse than a transcript or, even

24

super, super cognizant of your prior testimony, both at

25

worse, live testimony in front of a jury that is so

25

trial and during deposition.

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James E. Norris, II, P.E., ACTAR March 9, 2020 9 1

The first thing that we do when we get a

11 1

We're talking about consent for data imaging as

2

disclosure from -- I do all the defense work, so when

2

well as my expert training and imaging process.

3

we get the plaintiff's expert disclosures, the very

3

of the scenario on this one -- John owned a vehicle

Kind

4

first thing we do is we go and find everything that

4

that was involved in a collision in which he rear-ended

5

that expert has ever written, everything that that

5

another vehicle waiting to make a left turn.

6

expert has ever testified to in a deposition or in a

6

7

trial or otherwise, and that stuff is really easy to

7

but they didn't function properly.

8

get so long as you can, you know, make a couple of

8

that before; right?

9

phone calls to the court clerk.

9

actually retained to investigate the accident on behalf

Now Mr. Smith claims that he applied the brakes, We've all heard

Resulting in the collision.

I was

10

The reason that matters is -- I don't expect that

10

of Mr. Smith's insurance company because they were

11

any expert worth his or her salt is going to analyze a

11

concerned about this braking defect or issue and

12

particular data set differently from case to case.

But

12

thought they may have a potential products issue.

13

what I'm after is your phraseology.

What I'm after is

13

John also claims that he did not ever give any

14

the way that you as the expert characterize certain

14

permission for the EDR of his vehicle to be imaged, and

15

data elements, certain phenomena, certain things that

15

his attorney, therefore, argues that it was not

16

are going to happen over and over and over again, and

16

obtained properly.

17

I'm going to use your own phrases against you if I

17

did it actually show?

18

don't like the way that's going to go.

18

Now in terms of the EDR data, what

Well, it showed that the brakes were working.

19

When you -- there's nothing more unsettling if

19

Surprise, surprise -- the brakes were working.

20

you're a witness, I would think -- but I've never given

20

However, if you don't put them on until about the

21

a deposition before -- but I would think to be sitting

21

second before the collision, then they're probably not

22

there and to hear your own phrase turned on you in the

22

going to work too well.

23

course of a different case.

23

So, in fact, this one was just too late to avoid

24

the collision, and we had a supplemental mechanical

25

inspection that was performed, and that actually

24 25

So, be aware of what you've testified to in the past.

That's our tips.

We're going to go into our

10

12

1

first scenario now, which I will let Mr. Norris

1

verified the condition of the brakes to not be an

2

introduce.

2

issue.

3

MR. NORRIS:

All right.

Thanks,

So with that, we're going to jump into the actual

4

David.

5

out there.

6

about preparation in the very beginning.

The other

6

7

thing I would like to stress is that preparing for a

7

8

deposition or courtroom testimony doesn't start weeks

8

9

or days before.

9

the date of this accident this vehicle was owned by my

10

client, John?

10

And actually I do want to throw one more tip

3

I meant to speak about it when I talked

It starts day one when you pick up the phone call.

4

deposition testimony.

5

SCENARIO NUMBER ONE EXAMINATION

BY MR. CHAPMAN: Q.

All right, Mr. Norris.

Isn't it true that on

11

And I've even mentioned this a few years ago when we

11

12

did the presentation on the EDR issues.

12

13

do, a step along the way, think about down the road a

13

14

year or two, how am I going to answer this question?

14

15

Whatever I chose to do to repower a vehicle or et

15

A.

I would agree with that.

16

cetera during the process, or how I analyze a certain

16

Q.

That means all the parts on the vehicle are

17

piece of data.

17

18

answer a question for that down the road.

And I think

18

A.

I would agree with that.

19

if you keep that in mind as the case progresses, it'll

19

Q.

Well, are you -- you didn't ask my client if

20

really help you be more prepared in the future.

20

21

Everything you

Just think about how you'll have to

So with that being said, we're going to jump right This is one that kind of

A.

Yes, according to the accident report, that

was Mr. Smith's vehicle.

Q.

All right.

That means that everything in the

vehicle is his; right?

his?

you could go download this data, did you?

21

A.

No, I did not.

22

Q.

Well, are you aware that federal law says

22

into the first scenario.

23

combines two topics.

23

that you can't conduct this download without the

24

helped me contribute quite a bit to this one, so thank

24

owner's permission?

25

you, Dirk, for this.

25

Thanks to Dirk.

I think Dirk

A.

Well, I am aware of that.

I assume that what

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Scenario: John owned a vehicle that was involved in a collision in which he rear-ended a vehicle that was stopped ahead of him, waiting to make a left turn. John claims that he applied the brakes, but they did not work properly, resulting in the collision. I was retained to investigate the collision by the John’s insurance company.

John also claims that he did not ever give permission for the EDR of his vehicle to be imaged; his attorney therefore argues that it was not obtained properly.

March 9-11, 2020

Slide 5

What did the EDR Data show?

• Brakes were working • Brake application was too late to avoid collision • Mechanical inspection verified condition of brakes March 9-11, 2020

Slide 6

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Consent/Authority to Access Data • Driver Privacy Act of 2015 – EDR data is the property of the owner of lessee of the vehicle in which the recorder is installed. Access requires: • Court Order/Warrant • Owner/Lessee Consent • NTSB or DOT investigation • Retrieval for appropriate medical response to crash • Traffic safety research (with personably identifiable info not disclosed)

• Consent was given by John’s insurance company, which was the owner of the vehicle when the data was collected

March 9-11, 2020

Slide 7

Expert’s Training & Imaging Process • Training/courses related to EDR data collection and analysis • Bosch CDR system is “read-only” • The raw data file (.cdrx) is preserved and available for review • Documentation of imaging • Photographs • Video – screen recording

March 9-11, 2020

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James E. Norris, II, P.E., ACTAR March 9, 2020 13

15

1

you're referring to is the Driver Privacy Act of 2015.

1

that documentation that I discussed earlier.

2

I'm aware that that requires consent of the owner, but

2

would see in the photographs from the inspection --

3

in this matter we were actually retained by the

3

I've got photographs of several identifying features of

4

insurance company.

4

the vehicle such as the VIN, the license tag, the

5

vehicle itself.

5

They called us about two weeks after the incident,

So you

6

and it looks like we scheduled an inspection and got

6

Then I've also got the same pictures that show my

7

the vehicle about a week after that, so we're about

7

equipment and laptop hooked up to the vehicle, and also

8

three weeks out.

However, at that time the insurance

8

have the screen recording we referred to earlier.

9

company had actually settled with your client and had

9

10

assumed ownership of the vehicle, so I've got an email

10

isn't it true, Mr. Norris, that because you were by

11

here that actually specifies that from the insurance

11

yourself and have had access to this data alone for all

12

adjustor, and she provided consent for our company to

12

this time, you could have simply changed this to make

13

image that data as a part of our investigation.

13

my client look bad, whenever you wanted?

Q.

Okay, well.

Numbers and all that aside,

As you can imagine,

14

15

this adjuster and I are not getting along too well.

15

that was utilized for this vehicle was the Bosch Crash

16

Let me ask you this -- nobody watched you conduct this

16

Data Retrieval software.

17

download; right?

17

used one because it covers the majority of vehicles.

18

And now this Bosch system is a read-only type of

19

system, it doesn't have a capability for me to alter or

20

erase any of the data, and during the download process,

21

I would refer to the screen recording again that I

14

18

A.

19

this.

20

Q.

21

Well, let me see that.

Q.

That's correct.

I was by myself when I did

You didn't have anybody else out there to

verify that you were conducting this correctly?

A.

No, no, that was not the case.

The software

That is the most commonly

22

A.

Uh, no, again, I was alone.

22

mentioned, because in that video you can see that once

23

Q.

So what qualifies you to get out there by

23

the data has been imaged, it immediately shows the

24

report on the screen, and at that time I flipped

25

through the document for several seconds showing each

page as well as the PDF that was created.

24

yourself and make this up?

25

A.

Well, to step back before your previous

14

16

1

question, I will acknowledge that I was by myself.

1

2

However, I did document the process in multiple ways.

2

3

I took several photographs as well as a screenshot

3

4

recording or a screen recording of my laptop during the

4

5

download process, and I actually have copies of that

5

part of the Bosch downloading process, a raw data file

6

that you can look at.

6

is created, and that raw data file can be reopened at

7

any point down the road.

8

that file does not change, and so that can be reopened by your expert.

7

That screen recorder was going during the entire

8

process.

Now, in terms of your question about

Q.

All right.

Well, what if my client wants to

get his own fancy expert?

A.

That would be fine, because actually as a

The data that's contained in

9

qualifications, I initially received some training from

9

10

the Institute for Police Technology and Management.

10

11

That was a course called EDR Use in Traffic Crash

11

12

Reconstruction.

12

course, we talked about the consent for imaging.

13

all know, it is important to obtain the proper consent

13 14

That was taught by Mr. Rick Ruth.

Q.

Who's that?

I don't care who that is.

A.

Well, Mr. Ruth is a nationally certified

Q.

He can look at it if he wants to.

All right.

There you go.

MR. NORRIS:

So just to recap, of As we

14

that you would need and to retain the documentation.

15

instructor in that field, and his course covered the

15

It's not just good enough to get it and then lose it.

16

data imaging process as well as the analysis of the

16

You need to definitely get it and preferably not

17

data that is collected.

17

just get it -- from my understanding, it really needs

18

under Mr. Ruth, I have conducted a little over 200

18

to be in a written format, though.

19

downloads, and also I get yearly continuing education

19

little iffy at times.

20

training at the EDR Center put on by --

20

writing.

Q.

Verbal consent is a

I would much rather have it in

How do we know -- assume all that

21

Now, of course, outside of the Privacy Act of

22

whatever you said is true -- how do we know that this

22

2015, we've also got to keep in mind -- and we talked

23

data set that you brought here today is from my

23

about this in the presentation a few years ago -- there

24

client's vehicle?

24

are a lot of states that have their own specific law.

25

Arkansas is one that has a pretty quirky law.

21

25

A.

All right.

Now, since taking my training

Well, again, it would primarily be related to

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James E. Norris, II, P.E., ACTAR March 9, 2020 17

19

1

There are a few others that you will recall.

So

1

2

just make sure that you abide by any state-specific

2

3

rules that you might be dealing with.

3

4

course, commonly you're going to get attacked on your

4

5

training and your background, so it's definitely

5

Q.

Lawyer number one really didn't know what an

6

important to obtain and maintain your proper training,

6

EDR was.

Lawyer number two knows just enough to be

7

keep up with your continuing education, retain any raw

7

dangerous.

8

data files, and, of course, document the imaging

8

even close to the time of this accident, did you?

And then, of

So now we'll jump into the deposition.

SCENARIO NUMBER TWO EXAMINATION

BY MR. CHAPMAN:

Mr. Norris, you didn't download this ECM

9

process thoroughly, whether it's photos -- I definitely

9

A.

10

recommend some sort of video screen recorder that would

10

weeks after.

11

eliminate a lot of these questions.

11

12

MR. CHAPMAN:

12

As it relates to this

Q.

Uh, well, that's correct.

Weeks after.

Yes, it was a few

You downloaded this ECM weeks

after the accident?

13

first little bit here, the lawyer who doesn't like the

13

14

report, number one, wants to try and establish that you

14

accident report indicates a time or a date of May 31st,

A.

15

didn't have permission to get the data in the first

15

2018.

16

place; and, number two, wants to try and establish that

16

ECM on June 26th, 2018, so, yeah, a little short of a

17

you can change it -- which you can't, but he doesn't

17

month.

18

know that.

18

Q.

Yes, that's correct.

It looks like the

We inspected the vehicle and did our download

In the interim isn't it true that XYZ

19

And a lot of these steps that we're talking about

19

Transport never even cared enough to take this tractor

20

in terms of saving imagery, et cetera, in the course of

20

out of service?

21

the initial investigation -- a lot of this seems

21

A.

22

redundant and a lot of it seems superfluous, but it's

22

issue.

23

not.

Well, I can't really speculate into that I can only address issues and items that I know

23

of since I was retained.

24

Because imagine how much different this line of

24

retained a few weeks after the incident, I did

And actually when I was

25

questioning goes if James' answer were, "well, I mean,

25

recommend for the vehicle to be placed out of service,

18 1

I didn't change it."

1

and we scheduled an inspection at the next available

2

all of these initial steps have a purpose, and it's

2

opportunity.

3

anticipation of being questioned by someone who doesn't

3

4

know what they're talking about.

4

impounded or held by the police at the scene.

So we'll move to the next

5

was not badly damaged, it was mostly cosmetic damage in

This is one primarily concerning heavy vehicle

5

That's another hour at least.

MR. NORRIS:

So

20

However, I can state that the vehicle was not Also it

6

topic.

6

this incident, so the driver continued with his

7

EDR data, which we all know have some clock and time

7

delivery and subsequent delivery routes assigned by the

8

stamp issues that are inherent with those.

8

company until we actually got it taken off the road.

9

scenario we had XYZ Transport.

10

In this

9

Their unit was involved in a collision reported to

10

And in my years of experience I've found this to actually be a common occurrence.

Q.

Okay, well, let's get into the numbers a

11

occur on May 31st of 2018 at approximately 1:04 a.m.

11

12

The data for their unit was imaged a few weeks after

12

little bit here.

13

the collision, but the unit had remained in service for

13

time of the accident was 50,739.4 miles; right?

14

a while during that time.

14

15

There was a last stop record from the collision,

15

16

but that was overwritten due to the vehicle being moved

16

17

or driven, and hard brake record number two was from an

17

18

old event in April of 2018.

18

19

that we do have some data from this collision.

20

Of course, I'm claiming

19

It's hard brake record number one, but it's from Of course,

A.

The odometer on this truck at the

Yes, that is correct.

At the time of hard

brake record number one, that was the mileage.

Q.

Okay, but the odometer at the time that you

conducted this download was 54,090.9 miles; right?

A.

Yes, that's correct.

On the day of the

download, that's what the current odometer reading was.

20

Q.

21

that right?

That's a difference of 3,351 miles; isn't

21

the day before, which is May 30th of 2018.

22

we've got here the documentation of the ECM clock at

22

A.

Yeah, that sounds about right.

23

the time of the download, and that shows that it's

23

Q.

You would agree with me -- that's a long way?

24

approximately six hours behind the actual time, and,

24

A.

No, not really.

25

additionally, we had Daylight Savings Time in effect.

25

I mean, to you or I that

would seem like a long distance, but for some of these

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Scenario: XYZ Transport’s tractor-trailer was involved in a collision that was reported to have occurred on May 31, 2018 at approximately 1:04 am. The ECM data for their unit was imaged a few weeks after the collision, but the unit had remained in service during that time. The Last Stop Record from the collision sequence was overwritten due to the vehicle being driven, and Hard Brake Record #2 was from an older event (April 7, 2018). The engineer claims that Hard Brake Record #1 is related to the collision, but it is from the day before (May 30, 2018).

March 9-11, 2020

Slide 11

ECM Clock Documentation • Documentation of the ECM clock shows that there is clock drift present; the ECM time at imaging was approximately six hours behind the actual time.

• Additionally, Daylight Savings Time was in effect at the time of the collision March 9-11, 2020

Slide 12

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Event Data

March 9-11, 2020

Slide 13

Correlation of Event Time to Actual Time

March 9-11, 2020

Slide 15

Event & Mileage Assessment • Utilizing Driver Log Books and Company records, we were able to account for the difference between Odometer vs. Incident Odometer (~3,350 miles) • There were no more events recorded since the event in question, so no events have been overwritten.

• Event data is consistent with physical data and details of the incident

March 9-11, 2020

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James E. Norris, II, P.E., ACTAR March 9, 2020 21

23

1

long haul truckers, they could easily cover that kind

1

2

of distance in a week or so.

2

3

actually go back and look at the driver logbooks and

3

you've mentioned.

4

the company records, and for the time that the vehicle

4

to this accident says it's from May 30th, 2018, at

5

was on the road from the time of the accident to when

5

6:02 p.m.; right?

6

we had it taken out of service, we were able to

6

7

actually account for that mileage with the logbooks and

7

record one and the DDEC reports, that's the reported

8

the company records.

8

time.

Q.

9

Now, we were able to

Well, suffice to say, wouldn't it be possible

a hard brake record from the incident.

Q.

Well, let's talk about that record that

A.

Q.

9

Yes, that is correct.

for something else to happen that would record data

10

11

somewhere on this ECM sometime during those 3,351 miles

11

A.

12

that the truck drove after this accident?

12

the time.

A.

actually occurred on May the 31st at 1:04 a.m.; right?

Q.

Yes, according to the police report, that's

So how can you say that the data could have

I would first state

13

14

that the last record, as I indicated, was overwritten

14

been related to the accident if the ECM itself says

15

from the first time it was driven, and every time it

15

it's from the day before?

16

was subsequently driven after that, that's going to

16

17

overwrite and produce a new one.

17

an issue or phenomenon known as clock drift with ECMs,

18

Well, yes, absolutely.

From the hard brake

But this accident that we're here about today

10

13

The data set that you say is related

Now, in terms of hard brake events, this ECM can

A.

Well, first I've got to explain that there is

18

and in that the clocks can actually drift from the

19

record up to two hard brake events and keep those

19

original value over time.

20

stored.

20

tracking time, and in that instance these clock drifts

21

accident, yes, it is possible that we could have

21

are common occurrences and they have been well

22

multiple occurrences of hard brake incidents that would

22

documented in a lot of research and studies, but that's

23

occur and be recorded, and those would overwrite the

23

why it's very important to document the clock, as I

24

ones recorded in the collision.

24

mentioned earlier.

25

Now, if the truck is driven after the

However, that's not the case that we're dealing

However, the clock is still

25

I showed a screenshot that had a difference of

1

approximately six hours that showed that there was a

22 As I indicated before, we've got the hard

24

1

with here.

2

brake data from record one that is from the time of the

2

documented drift between the clock at the time of the

3

accident, and then we had another hard brake that was

3

download versus what the ECM said.

4

actually from April 7th, 2018, which is prior to the

4

information and some adjustments we can actually

5

accident by a month or more.

5

correlate that to the data.

6

So now we know that there have not been any new

6

7

hard brake record events recorded on this ECM since the

7

8

time of the accident.

8

Q.

9

You mentioned a last stop record.

This ECM

Q.

Now, with that

What adjustments are you adding to the data

to change it?

A.

Well, first of all, I would refer to some

9

calculations that I have here.

So, as we see at the

10

would have recorded a last stop record after the

10

top, I've got the time as documented from the ECM as

11

accident; right?

11

well as what it was on my laptop at the time, which was

12

A.

Yes, that's correct.

12

a difference of a little over six hours -- six hours

13

Q.

And that's long gone now; right?

13

two minutes and 29 seconds.

14

A.

Yes, that is correct.

14

Now, once we add that to the reported time of the

As I mentioned, that

15

was replaced with a new last stop record as soon as the

15

hard brake record, which was 6:02, that actually takes

16

vehicle was moved from the scene, and then each time

16

us up to a little after midnight, 12:04 a.m.

17

it's driven it does the same process.

17

ECM was set in the Eastern time zone, as was my laptop,

18

so we didn't have to make any kind of time zone

19

adjustment; however, Daylight Savings Time was in

I would agree that the last stop record was

20

effect at the time of this accident.

21

not preserved, but there has been other data that has

21

And so that would also require an adjustment

22

been preserved.

22

because the ECM clock does not account for Daylight

23

Savings Time.

24

that was documented from the difference as well as that

25

Daylight Savings Time, that puts our time right at

Q.

18 19 20

A.

Q.

23 24

Well, you would agree with me then that the

data on this ECM was not properly preserved?

But the same thing happened to the rest of it

that happened to the last stop record.

25

A.

No, no.

That's not correct.

Again, we have

Now, this

So, once we have added the six hours

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James E. Norris, II, P.E., ACTAR March 9, 2020 25

27

1

1:04 a.m., which again is consistent with the time of

1

2

the incident for the accident report.

2

Q.

3

So your testimony in this case, is that the

talking about earlier.

Try to get a lot of information.

If you've got a

3

non-deployment event that's at a certain ignition cycle

4

times don't match, the dates don't match, and the

4

or odometer reading and you're trying to figure out

5

odometer doesn't match, but this is still the data set

5

whether that came from the vehicle in question, having

6

from the accident?

6

information about the vehicle usage is going to be key.

Yes, I acknowledge that the date and times on

7

You have anything to add on that?

8

the hard brake incident are different from the reported

8

MR. CHAPMAN:

I agree.

9

time of the accident; however, there is a legitimate

9

MR. NORRIS:

All right.

10

documented clock drift on this unit, and it matches

10

want to thank Rusty for some of his help with this and

11

once you actually account for that documented drift as

11

feedback.

12

well as the Daylight Savings Time.

12

talk about and some actually, I think, maybe even some

7

A.

This one -- I

He gave us some good examples on this one to

13

And, additionally, I would say that analyzing the

13

real-life scenario questions that he's going to ask,

14

hard brake data is also -- because the hard brake data

14

and that helped to develop this one.

15

that we have in here is very consistent with the

15

16

physical evidence of this crash.

16

Chevy Camaro ZL1, and if you know anything about these

Q.

This one is a fun one.

This one involved a 2016

Here's my question, as an increasingly

17

cars, they are extremely fast.

18

frustrated attorney -- does this drifting clock

18

bottom, 650 horsepower, 0 to 60 in about 3.6 seconds,

19

business happen all the time, or just when you want it

19

something you'd basically give your teenager on their

20

to?

20

16th birthday; right?

17

21

A.

As you see there at the

Well, again, I would acknowledge that the

21

But, we've got the driver of this Camaro, he got

22

clock drift issue is very prevalent and happens on

22

on it and subsequently lost control of the vehicle and

23

quite a bit of ECMs, and that's why it's common

23

caused it to rotate in a counter-clockwise manner.

24

doctrine to actually do this documentation as a part of

24

vehicle entered the oncoming lanes, where it was

25

the download.

25

actually struck by an SUV.

26 1 2

MR. CHAPMAN: you get that question.

3

Yep, y'all laugh until

It'll happen.

MR. NORRIS:

So, yeah, as we got on

The

28 1

Now, as you can see, the imaging was originally

2

conducted back in May of 2017, and the version of the

3

software at that time was 17.3, and we've got some

4

the recap, I mean, I'm sure if you've dealt with trucks

4

other information down here on the bottom.

5

for any length of time and the ECM data that you get,

5

that, I'm going to jump into the deposition testimony.

6

this is not a new issue.

It pops up fairly often.

6

7

This one was probably a little bit more of an odder

7

8

issue, considering the way the time worked out -- it

8

9

actually pushed us into a day before that.

So with

SCENARIO NUMBER THREE EXAMINATION

BY MR. CHAPMAN: Q.

9

Okay.

This CDR software that you used in

10

But again, you're going to run into that with

10

this case, Mr. Norris, it updates all the time, doesn't

11

vehicles that not only have a clock drift, but may be

11

it?

12

set in, you know, Mountain Time, involving an accident

12

13

on Eastern Time.

13

I wouldn't say that it's -- it's not on a weekly or

14

accounting for all the different differences and, of

14

even a monthly basis.

15

course, keep your PC clock updated.

15

be identified or they add some new vehicle coverage.

So, just make sure that you're

A.

Q.

Well, there are updates that are issued, but

It's basically when an issue may

Suffice to say that you -- you downloaded

16

You know, when you're doing your periodic updates,

16

17

it's always great before you go out to do an inspection

17

18

to verify that your clock setting is good, and even do

18

19

an automatic adjustment.

And then, of course, if you

19

and that would have been the current version at the

20

have issues where something like this is going to come

20

time of the imaging.

21

up, talk to your folks at the company and try to

21

22

account for any kind of additional mileage or something

22

report comes out, we're already on version 19.0 by that

23

like that that would help correlating and -- you know,

23

time, aren't we?

24

we didn't do this as a specific example, but this

24

25

extends to ignition cycles kind of like what Kent was

25

this module using version 17.3; right?

A.

Q.

A.

Uh, yes, according to my report, yes, 17.3,

But if we move ahead two years to when your

Yes, that is correct.

By that point we had

moved up a few versions.

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Scenario This incident involved a 2016 Chevy Camaro ZL1. The driver of the Camaro “got on it” and subsequently lost control of the vehicle, causing it to rotate in a counterclockwise manner. The vehicle entered the oncoming lanes where it was struck by an SUV. • 6.2 L Supercharged V8 • 650 HP • 0 to 60 – approx. 3.6 seconds

March 9-11, 2020

Slide 18

CDR Versions throughout case • Imaging conducted on 5/8/2017 (Version 17.3)

• Report issued July 10, 2019 (Version 19.0) • Deposition (Version 19.3) March 9-11, 2020

Slide 19

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Using the Current Version • At the top of each CDR Report…

• Occasionally, Bosch and/or manufacturers identify potential errors in translation of raw data and correct them • Sometimes it may just be formatting or cosmetic changes March 9-11, 2020

Slide 20

The Event Data • Heavy Acceleration then braking

• Large changes in speed that defy physics March 9-11, 2020

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Evidence/Analysis • Unrealistically high accelerations/decelerations

• Vehicle tires spinning relative to ground March 9-11, 2020

Slide 22

Evidence/Analysis • Pre-impact tire marks consistent with rotation and sliding

• Video analysis placed speed mid to upper 40’s just prior to loss of control and ground speed in mid-50’s prior to impact March 9-11, 2020

Slide 23

Assessment of Data • Source of Data – speed sensor • Vehicle speed calculated from wheel speed data • Reported Vehicle Speed ≠ Ground Speed • Pre-crash speeds in this incident are greatly over-reported

March 9-11, 2020

Slide 24

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James E. Norris, II, P.E., ACTAR March 9, 2020 29 Q.

1 2

And as we sit here today, we're on version

1

19.3, aren't we?

3

A.

31

Well, that's correct up until recently.

there either.

2

Q.

3

itself.

All right.

Well, let's look at the data

Let's assume you're right and that this

4

There was a patch, and technically we're on 19.3.1.

4

data set is accurate.

5

But you are correct, yes.

5

this report says that five seconds before this crash,

Q.

6

this driver had the pedal to the floor and got up to 82

7

You can see that at the very top of this report it

7

miles an hour.

8

says, "Important notice, Robert Bosch, LLC, and the

8

9

manufacturers whose vehicles are accessible using the

9

heavy accelerator input in between negative-five and

10

CDR system urge end users to use the latest production

10

negative-three seconds and, yes, there is a recorded

11

release of the crash data retrieval system software

11

vehicle speed of 82 miles per hour at that negative-

12

when viewing, printing, or exporting any retrieved data

12

three-and-a-half seconds.

13

from within the CDR program."

13

14

on here?

6

Okay.

Go to 20.

I'll show you this exhibit.

You would agree with me that

Why would they put this

A.

Q.

Well, I would agree that we did have very

So you would also agree with me that,

14

according to this report that you downloaded, this says

15

this driver got all the way up to 91 miles an hour

16

Bosch or the manufacturer may discover an issue with

16

before he crashed into another vehicle?

17

the way that the software is translating or displaying

17

18

some of the data.

18

displayed speed on here is 91 miles an hour

19

newfound data, but when these issues are identified,

19

approximately three seconds prior to the event.

20

they will correct it and release an update.

20

However, I want to acknowledge that I believe that this is a misreported value.

15

A.

Well, again, as I mentioned before, sometimes

There's not really magically

A.

Well, I would agree that the recorded or

21

This notice is basically acknowledging to the

21

22

users that you should keep your software up to date for

22

23

that reason.

23

this report says he was at 51 miles an hour before he even tried to get on the brake.

Well, but let me ask you this -- if you are

24

25

urged to do something by the manufacturer, you should

Q.

25

1

probably do it, shouldn't you?

24

Q.

A.

You would also agree with me, though, that

Again, I would agree that that is what the

30

32 1

reported speed was with the same caveat that I do not believe it to be the actual speed of the vehicle.

2

A.

Yes, I would agree with that.

2

3

Q.

And you wouldn't disagree with me that Bosch

3

4

says it is important -- that's their word, not mine --

4

5

important -- to use the latest version of the software,

5

6

wouldn't you?

6

speed relative to other vehicles and/or the speed limit

7

could be dangerous.

7

A.

8

that.

Q.

9

That's correct.

I wouldn't disagree with

Q.

A.

8 So how can the data that you pulled from this

Will you at least agree with me that 91 miles

an hour on a standard highway is reckless?

9

Well, I would state that driving at a high

I would agree with that.

Q.

The report says what it says, doesn't it?

A.

Well, that's correct.

The airbag module is

10

vehicle be accurate if you used a software version

10

collecting and storing data to the events that it

11

that's obsolete?

11

experiences.

12

from other sources in the vehicle such as the power train control module.

12

A.

Well, first I would note that the software

And much of this data, though, is coming

13

was not obsolete.

The version of the software that I

13

14

had at the time was the most current version, and that

14

Now, due to the way that the vehicle actually

15

data is stored in a raw data file, a CDRX file, and

15

calculates the speed that gets displayed in this report

16

that was retained by my file.

16

or your speedometer, I believe that the data for this

17

And you can actually open that with newer versions

17

vehicle's speed is actually getting misreported

18

and verify whether or not the data has changed in any

18

relative to the real speed of the vehicle.

19

way.

As a matter of fact, I've got another printout

19

20

here from 19.0, which would have been around the time

20

and the jury and everybody in this room that this

21

of the report, and you can put that side by side to the

21

report doesn't mean what it actually says.

22

original and see that there's not any changes.

22

Q.

A.

So you're trying to convince me and the judge

Well, first I've got to explain how the

23

And then this one was actually printed yesterday

23

system actually gets this data.

24

while I was going through my file, and it's 19.3.1, and

24

any vehicle really doesn't know how fast it's going.

See, your vehicle or

25

you can also see that there are really no changes in

25

It's taking information such as the wheel speeds and

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James E. Norris, II, P.E., ACTAR March 9, 2020 33

35

1

the tire sizes, and it's calculating a speed based upon

1

Now, looking at that data in conjunction with the

2

those parameters.

2

physical evidence, that just goes to further show that

3

3

the data that's getting reported in here is being over-

4

module as well as displayed on your speedometer.

That's then the speed that gets reported to our Now,

4

reported in relation to the actual ground speed of the

5

if there's some sort of issue where the wheels either

5

vehicle.

6

lock or spin in some manner, then the wheel speed

6

7

sensors are going to cause the data to be misreported

7

this was kind of a long one, so thanks for bearing with

8

in terms of the actual vehicle speed.

8

us on this one.

9

Rusty mentioned this several times earlier, is to keep

9

Now, this could be occurring in a variety of We could have a vehicle that goes airborne,

MR. NORRIS:

So, to recap this one,

But, of course, the big takeaways, and

10

instances.

10

the software up to date, make sure you've got the most

11

and that causes the tires to spin.

We could also have

11

current version, but also making sure you're using the

12

a vehicle that is sliding on ice, or any kind of heavy

12

most current data translation when you look at the

13

braking with wheel lock-up or ABS.

13

data.

14

Next, I would actually refer to the data itself.

14

So, it's always important to go back and recheck

15

When we look at the data, I've parsed out and kind of

15

that raw data file, which you've got anyway, with newer

16

calculated the speed changes and the accelerations and

16

versions as the case progresses.

17

decelerations, and what we see are values that are just

17

18

really unrealistic.

18

Number one, were this an actual deposition, there is

MR. CHAPMAN:

Two things on this one.

19

Now, of course, I'll acknowledge that this is a

19

absolutely no way I would let an expert talk that long

20

very fast car, but these values are even more than that

20

in response to a question.

21

vehicle is capable of, not even in the acceleration,

21

knock over a glass of water or something.

22

but also in the deceleration and braking portions.

22

23

Now, finally, we've got evidence from the crash itself.

23

recall our note at the very beginning where we're

24

We've got physical evidence and tire marks that

24

talking about "no, and;" "yes, and;" "yes, but;" "no,

25

are consistent with the vehicle rotating and sliding

25

but."

I would interrupt him or

Again, you laugh -- just wait.

Secondly, you

James' answer to the question, "Wouldn't you

34

36

1

prior to impact, and in the timeframe of what we've got

1

agree with me that 91 miles an hour on a standard

2

prior to the crash, we've got time when the tires would

2

highway is reckless?" -- that's not accidental.

3

be spinning and then side slipping as the vehicle was

3

4

rotating.

4

"recklessness" is one of the four criteria for the

I'm using the word "reckless" because in Tennessee

5

In that timeframe that's where we're seeing some

5

assessment of punitive damages.

So that word has a

6

of this data that wouldn't actually match the ground

6

very real legal significance.

It means something to

7

speed of the vehicle.

So in the data we actually see

7

the lawyers.

8

large jumps in the time where the vehicle tires would

8

9

have been spinning because of the hard acceleration

9

but."

10

from the driver, but then we've also got some issues

10

with you about your inarguable point except that that's

11

here in the decelerated part, where we've got large

11

not applicable to this case.

12

drops in speed where it begins to rotate and slide

12

important -- that's why that's an important distinction

13

prior to the impact.

13

to make, because if you're zoned in to, "I should just

14

answer the question asked with a yes or no if

14

Now, I would also note that we also were able to

But he answered the question with basically "yes, The answer is, yeah, I'm not going to disagree

And that's why that's an

15

get some video footage from a security camera of a

15

possible," then you're left on a transcript with the

16

nearby business.

16

word "yes."

17

some analysis on the ground speed of the vehicle

17

18

itself.

18

printed out for trial.

19

board. jury.

19

With that we were able to actually do

The ground speed just prior to the loss of control

And that's the sound bite that's going to get That's what's going on the big

It's going to go on the tripod in front of the

20

is in the mid to upper 40s, which is consistent

20

21

actually with the beginning of the pre-crash data of

21

22

what we see here.

22

of the last part of the scenario -- I'm sure everybody

23

into a slide and sideways, and at the timeframe just

23

has dealt with this -- and as you've taken courses

24

before impact, we've got a ground speed that's really

24

either with Rick or with Rusty's group, learning to

25

more like the mid 50s just prior to impact.

25

explain where the data comes from is a huge part of

However, then we see the vehicle go

MR. NORRIS:

Right, and to recap kind

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James E. Norris, II, P.E., ACTAR March 9, 2020 37 1

this.

39 1

going on his cruise control and had it set a few miles

2

Because, again, you've got to not only be able to

2

below the speed limit.

3

explain it to a jury, but you've got to put it out in

3

4

terms that they can understand.

And I think most can

4

5

understand the wheel speed sensor concept, and if you

5

6

use some of those analogies, like the spinning tires on

6

7

the airborne or ice or some real examples, people can

7

8

kind of relate to that.

8

deposition where he said -- surprise, surprise -- he

9

wasn't speeding prior to this impact, didn't you?

9

And that really goes to showing why these issues,

Q.

Right, right.

So the dump truck is obviously

braking before the impact; right?

A.

Yes, that is correct.

The skids that we have

here are prior to impact.

Q.

But you also read the dump truck driver's

10

you know, can occur, and really just being able to

10

11

explain them is the key thing.

You can have tons of

11

that he had his cruise control on and it was below the

12

technical knowledge, but if you can't put it into the

12

speed limit.

13

right words, it really is not going to be effective.

13

14

The last topic that we've got here is in regard to

Q.

Again, that's correct.

I recall him stating

And you would agree with me that the best way

14

for me to find out if that dump truck driver is telling

15

the truth would be to look at the data from the ECM on

16

the dump truck?

15

some data anomalies and issues.

16

near and dear to David and I's heart.

17

case that we actually worked on together, and it has to

17

18

do with some V-MAC data.

18

to verify his statement, if there was an event

19

recorded, but we can also estimate his speed using the

20

tire marks and the impact dynamics.

19

So, we go hauling.

This is one that's

A.

It came from a

Their dump truck was involved The truck was

A.

Well, I would acknowledge that that's one way

20

in a collision on March 3rd, 2018.

21

driven after the collision, resulting in the last stop

21

22

record being overwritten.

22

23

trigger event, but it's from May 26th, 2006, so there's

23

24

quite a bit of time difference.

24

and it does record one hard brake or one acceleration

25

trigger event and one last stop record.

We do have an acceleration

Q.

But you're telling me here today that,

despite the usefulness of this data, it doesn't exist?

A.

Yes, that is correct.

This was a MAC ECM,

The last stop

25

Despite evidence of heavy braking from the dump

1

truck, there's no data related to the event, and you

1

record was overwritten at the scene because the vehicle

2

can imaging that he is just biting at the bit to get to

2

was moved at the request of the police officers.

3

me about that.

3

And there was an acceleration triggered event,

4

but, as I would refer to on the page here, it was from

38

4

MR. CHAPMAN:

And it is worth noting

40

5

by way of further background, the injuries in this case

5

May 26th of 2006.

6

are extremely serious.

6

data itself.

This is a big one.

Now, there are some issues with that

When we look at the data, it looks odd.

7

SCENARIO NUMBER FOUR

7

Of course, we've got some times just before the

8

EXAMINATION

8

incident was reported to have occurred.

9

BY MR. CHAPMAN: Q.

10

9

All right, Mr. Norris.

You would agree with

We've got low speeds of two, one, zero miles per

10

hour.

That just doesn't fit at all with anything

11

me that this dump truck left basically over 200 feet of

11

related to this case.

12

tire marks in the roadway before the impact with my

12

acknowledge is that this vehicle was a V-MAC III step

13

client's vehicle?

13

12A.

14 15

A.

Yes, it was actually a little over 200 feet.

You're right.

Q.

16

We look at these pictures that we've looked

17

at all day today.

18

see that in the photographs; right?

19

A.

We look at these pictures and we can

That's correct.

14

Now, one thing I will also

And for those particular items, they had some

15

special issues in the step 12, 12A, and 12B.

16

that issue, the first log, which was the acceleration

And in

17

triggered event, would often be from the actual build

18

date at the factory.

There are some pre-impact

19

And once that was recorded, it would be locked,

20

skid marks, and then they continue on from impact to

20

and the ECU would not actually record any new events

21

final rest.

21

since then.

22

Q.

22

MAC, we can see that the transfer to sales date was actually on that same day of May 26th of 2006.

Okay, well, you read the dump truck driver's

23

deposition where he said under oath that he braked

23

24

before this impact?

24

25

A.

Yes, I do recall that he stated that he was

25

Now, if we look at the data that came from

And, additionally to that, we have a shipment date of June 7th, 2006.

So, all this was well before this

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Scenario: WeGo Hauling’s dump truck was involved in a collision on March 3, 2018. The truck was driven after the collision, resulting in the Last Stop Record being overwritten. There is an Acceleration-Triggered Event, but it is from May 26, 2006. Despite evidence of heavy braking from the dump truck, there is no data related to this event.

2007 Mack CV713 V-MAC III Engine

March 9-11, 2020

Slide 27

Event Data • Only recorded event is from a long time ago

March 9-11, 2020

Slide 28

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Event Data • Additionally, data around trigger is odd…

March 9-11, 2020

Slide 29

Vehicle Data from Mack • V-MAC III, Step 12, 12a, & 12b have special issues • Log 1 (Acceleration-Triggered Event) will often be around the initial build date at the factory and the unit will not record any new AccelerationTriggered Events).

March 9-11, 2020

Slide 30

Vehicle Data from Mack

March 9-11, 2020

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James E. Norris, II, P.E., ACTAR March 9, 2020 41 1

vehicle could even have gotten to the owner, my client.

43 1

and being able to explain the instances where EDRs may

Well, I mean, it could be all that, I guess,

2

not have recorded data or might have incomplete data.

3

or it could be the dump truck company turning off the

3

4

recording capability so we'll never find out how fast

4

deal with issues where maybe there was a power

5

their drivers are going.

5

interruption and that caused an event to not be

6

recorded or only part of the data to be recorded.

Q.

2

6

A.

No, no.

So there are some settings to

So, for heavy vehicles, trucks, a lot of times we

7

disable the recordings; however, those settings and

7

We've got issues where events just don't reach the hard

8

parameters have not been changed in this ECM.

8

brake threshold because the vehicle was going at such a

9

recorder is still enabled.

However, due to the issues

9

low speed or it came to more of a controlled stop.

10

that I mentioned earlier, it's just able to overwrite

10

And then, of course, in passenger vehicles we've

11

and record new event data.

11

also got power loss potential issues, we've got data

12

clipping, if you recall that to be an issue, and we've

13

also got low delta V speed collisions where we don't

14

reach that 8K or five-mile-an-hour delta V, and we just

15

don't get a recording, although we may have damage and injuries.

12

Q.

13

did you?

14

A.

The

You didn't even download this ECM yourself,

No, that is correct.

The MAC ECMs can only

15

be accessed by an actual designated affiliate.

16

to remove the modules from the vehicle and actually

16

17

send them to one of the affiliates, Matthew --.

17

Q.

18 19

I had

Who are these people and how do I know they

know what they're doing?

20

A.

that.

19

to kind of do is go back to the recap slides, and what

Now, as we go into questions, what we're going

20

I'd like to do is just start at the first, and so if

21

access these modules, and he's with one of them.

21

you've got questions about topic one and two, we'll go

22

However, I'm sure if you'd like to pay him for his

22

through that, then the three and so forth rather than

23

time, we can probably get him to come on down here and

23

bouncing around from topic to topic.

24

answer some questions.

24

25

Well, MAC only has four affiliates that can

So, again, it's important to stay on top for all

18

MR. CHAPMAN:

Right, right.

You can

(Off the record at 4:45 p.m.)

25

42

44

1

imagine the reaction from plaintiff's counsel when we

1

WITNESS CORRECTIONS AND SIGNATURE

2

really did have -- not with James himself,

2

Please indicate changes on this sheet of paper, giving

3

unfortunately -- I had to have this conversation by

3

the change, page number, line number and reason for the

4

myself -- when I had to tell him that this was, in

4

change.

5

fact, the scenario we were dealing with.

5

PAGE/LINE

6

_______________________________________________________

6

That this is just one of those anomalies in which

Please sign each page of changes.

CORRECTION

REASON FOR CHANGE

7

there was no event recorded.

7

_______________________________________________________

8

MR. NORRIS:

Absolutely.

8

_______________________________________________________

9

MR. CHAPMAN:

Yep.

9

_______________________________________________________

10

MR. NORRIS:

So, of course, to recap

10

_______________________________________________________

11

on this one, training and continuing education is your

11

_______________________________________________________

12

best tool when you come up against these kinds of

12

_______________________________________________________

13

anomaly issues, because they're being discovered as we

13

_______________________________________________________

14

go, and especially with the trucking anomalies -- Tim

14

_______________________________________________________

15

Teague, John Steiner, Dave Plant -- those guys are very

15

_______________________________________________________

16

active in teaching the SAE course and some of the other

16

_______________________________________________________

17

courses, and they're really good at helping identifying

17

_______________________________________________________

18

these issues and doing testing.

18

_______________________________________________________

19

_______________________________________________________

19

So, your best tool is to stay up to date on that

20

and, of course, getting your documentation.

You know,

20

_______________________________________________________

21

once these issues have been discovered, a lot of times

21

_______________________________________________________

22

they're getting published in SAE papers or journal

22

_______________________________________________________

23

articles, so having that documentation of those issues

23

_______________________________________________________

24

is definitely going to be a key; and then, again, as we

24

_________________________

25

stated in the last topic, just being able to understand

25

James Norris

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Crash-Induced Yaw Motion Effects on Airbag Control Module Delta-V Micky Marine P.E.

Steve Werner, Ph.D. P.E.

SSi, Phoenix Inc.

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ntroduction If one were to examine the velocity change data plot and table of the Crash Data Retrieval (CDR) report shown in Figure 1, without additional knowledge of the event in which the vehicle was involved, it might seem that the event was a very minor one. This would certainly seem to be the case as far as the longitudinal component is concerned as the recorded longitudinal change in velocity (delta-V) is of small amplitude and duration.

I

Alternatively, if one were to examine the velocity change data plot and table of the CDR report shown in Figure 2, without additional knowledge of the event, it would seem reasonable to consider it to be something more than a minor event and that the delta-V monotonically increased over the 300 millisecond recording time might seem curious. Interest might be piqued regarding the accident mode that resulted in such an exceptionally long pulse duration; one in which a significant delta-V has developed but not yet reached a maximum after 300 milliseconds.

Despite the substantial differences between the CDR reports of Figures 1 and 2, they were both imaged from the airbag control modules (ACMs) of the struck (target) vehicle of two very similar two-moving-vehicle impacts.

The general impact configuration of these two collisions is depicted in Figure 3. These collisions were eccentric impacts that induced large target vehicle yaw rates. The differences that exist between the CDR reports of Figures 1 and 2 occur because, in collisions that result in significant vehicle yaw rate and heading angle change, the location of the ACM within the vehicle is an eminently important factor. The reason for this is that the response measured by an accelerometer strongly depends on its location within the rotating vehicle. To gain further understanding of this effect, we will review the kinematic equations that govern the response of an accelerometer at a given position in an automobile.

Acceleration of a Point on a Rigid Body The kinematic equations that describe the absolute velocity and acceleration at a point of interest on a rigid body are developed through a general analysis of the motion of that point relative to a reference system that is translating and rotating relative to a space-fixed reference system. In Figure 4 the position of a point P on the body is defined with vectors rP (position of point P relative to fixed system), rB (position of a base point B on the body relative to fixed system), and rP/B (position of point P relative to the translating and rotating coordinate system at point B) [throughout this article boldface type will indicate a vector quantity]. www.collisionmagazine.com

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Figure 1: Velocity change plot and table Through vector addition, the position of point P can be defined as follows, (1) The absolute velocity and acceleration of point P are found by determining the first and second time derivatives of the vector rP. The time derivatives of rB, are straight forward and are simply the velocity (vB) and acceleration (aB) of point B relative to the space-fixed reference system. However, the time derivatives of rP/B, a vector describing relative motion in a translating and rotating reference system, are not so straightforward. The time derivatives of rP/B are derived in any number of dynamics textbooks (one of which is included as reference 1) and will not be re-derived here.

Instead, we simply proceed to the resulting well-known ki84 Collision Magazine - Volum 15 Issue 1

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nematic equations that describe the absolute velocity (v) and acceleration (a) of a point on a body that is both translating and rotating with angular acceleration and angular velocity.

(2)

(3)

The terms in Equations 2 and 3 with the subscript “rel” indicate that the acceleration and velocity components

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Figure 2: Velocity change plot and table

Figure 3: Example impact configuration

Figure 4: Position vectors defining a point on a translating and rotating body

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represented by these terms reflect relative motion of point P with respect to an observer that is both translating and rotating with the body-fixed reference system at point B. For rigid body considerations, there is, by definition, no relative motion between points P and B and the “rel” terms are thus zero.

lar rate sensor was installed at the right rocker panel near the A-pillar. With this array of sensors, and their known locations within the vehicle, all elements of Equations 6 and 7 can be determined. The acquisition and post-test processing of this data followed the Society of Automotive Engineers (SAE) Recommended Practice J211 2.

Both test vehicles were equipped with ACM modules that record velocity change data in the front-to-rear vehicle longitudinal direction only. The as-designed installation locations for these modules were under the right front seats (position C in Figure 5). Figure 6 depicts the measured yaw rate of the target vehicle and Figures 7 and 8 depict the longitudinal acceleration data measured at the ACM location and the calculated longitudinal acceleration at the c.g. (using Equations 6 and 7) of the target vehicle of this crash test, respectively. Also included in Figures 7 and 8 are the results of a direct integration of the accelerometer (4) data (i.e. numerical integration of the as-measured and as-filtered acceleration data). During the early portion of the crash pulse, the velocity change calculated by direct (5) integration of the data is of a very low level and is similar in that regard to the data depicted in Figure 1. As stated For the purposes of this study, we consider only yaw-plane above, the ACM models used in the test vehicles do not remotion (i.e. no significant vertical, pitch, or roll motion cord velocity changes directed from rear-to-front (positive of the vehicle) and need only consider the vehicle longi- x-direction) and thus, the data in Figure 1 does not contudinal and lateral axes, and the yaw (heading) angle. The tinue to resemble that of Figure 7 beyond approximately longitudinal and lateral components of equation 5 then 60 milliseconds. In Figure 8 we see that the delta-V data reduce to, for the c.g. is quite different from that at the ACM location - a direct result of the effect of yaw motion.

(6) The event from which the report of Figure 2 was imaged was also a two-moving-vehicle crash test (second test – T2) in which the bullet vehicle was traveling 58.8 mph at impact and the target vehicle was traveling 20.0 mph at (7) impact. The target vehicle in this crash test was not instru-

In the development of the above kinematic equations there has been no constraint imposed on the selection of the base point B. There is no inherent necessity that the reference point be located at either the center-of-gravity (c.g.) of the body or at a so-called “center of rotation.” In practice, the base point is often chosen for the sake of convenience or of particular interest; in accident reconstruction analyses the c.g. is often a point of interest and we will herein adopt that as our reference point. Equations 2 and 3 therefore reduce to,

As we can see from Equations 6 and 7, the acceleration at a point P on a vehicle differs from that at the c.g. by factors associated with the location of point P within the vehicle, as well as the vehicle yaw acceleration and yaw velocity.

Application to Crash Test Data The event from which the CDR report of Figure 1 was imaged was a two-moving-vehicle crash test in which the bullet vehicle was traveling 60.3 mph and the target vehicle was traveling 20.5 mph. As depicted in Figure 5, instrumentation installed on the target vehicle included a triaxial accelerometer set on the ACM, a triaxial accelerometer set at the rocker panel adjacent to the right A-pillar, and a triaxial accelerometer set in the rear cargo area adjacent to the right wheel. Additionally, a solid-state triaxial angu86 Collision Magazine - Volum 15 Issue 1

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Figure 5: Instrumentation setup for crash test target vehicle

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Figure 6: Measured yaw rate of target vehicle

mented so we are unable to make a direct comparison to the information depicted in Figure 2. Notwithstanding this inconvenience, we can instead use the data from the target vehicle of the first crash test (herein referred to as T1) to gain some insight as the impact-induced motion of the vehicles in the respective tests is quite similar (see Figure 9). The location of the OE ACM in the T2 target vehicle is forward of the driver position and underneath the instrument/dash panel. Using the data from the T1 target vehicle and employing Equation 6 to determine the longitudinal acceleration at a similar location in the T1 target vehicle to the ACM location in the T2 target vehicle, we get the data shown in Figure 10.

As can be observed in Figure 10, the direct integration of the acceleration data is very similar to the delta-V data shown in Figure 2 – i.e. a monotonically increasing delta-V over the 300-millisecond duration, and, incidentally, of roughly the same magnitude as that imaged from the T2 target ACM. Integration of Accelerometer Data and the Effect of Yaw Rate

Figure 7: Measured longitudinal acceleration and integrated acceleration at ACM location of target vehicle

For impacts that result in vehicle yaw motion, direct integration of accelerometer data recorded anywhere on a vehicle that experienced high yaw rates, with concomitant heading angle change, does not produce accurate delta-V information. That this is the case was explained in reference 3 and will be briefly reviewed.

The absolute velocity vector of any point P on a vehicle can be expressed as the following, (8) In Equation 8, ex and ey are unit vectors aligned with the vehicle longitudinal and lateral axes, respectively and rotate with the vehicle (a vehiclefixed reference frame). The corresponding acceleration at point P is, by definition, the time derivative of the absolute velocity vector and is expressed as follows, (9)

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For a vehicle experiencing yaw motion, the time derivatives of the unit vectors ex and ey in Equation 9 are non-zero as they are rotating relative to an inertial reference frame. For motion limited to the Collision Magazine - Volume 15 Issue 1 87

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yaw rate time history (via a yaw rate gyro or an appropriate combination of accelerometers); the velocity components of Equations 12a and 12b can then be found through numerical integration.

Figure 10: Longitudinal acceleration and integrated acceleration for T2 target vehicle ACM location on the T2 target vehicle. yaw-plane, the unit vector time derivatives are defined in Equations 10a and 10b [1], (10a) (10b) Substitution of these unit vector time derivatives back into the Equation 9 yields,

It is important to note that the integration of Equations 12a and 12b will yield accurate time histories for the vehicle-fixed velocity components but care must be taken to determine accurate delta-V component time histories as a simple subtraction of the initial u- or v-velocity component from the u- or v velocity component at some later time is not, generally speaking, a proper calculation of the delta-V. The calculation of delta-V is a vector subtraction operation that requires the respective vectors be expressed in a consistent coordinate system. Consequently, to properly determine the delta-V component time histories relative to the rotating vehicle-fixed system, the initial velocity vector must be transformed to the current vehicle-fixed coordinate system (which has changed orientation relative to the space-fixed coordinate system) at each time step. Thus, the longitudinal and lateral delta-V components expressed in the vehicle-fixed system are the following, (13a)

(11) Expressing Equation 11 in component form and rearranging terms yields the time derivative of the vehicle-fixed velocity components, (12a) (12b) Properly functioning accelerometers mounted at any location on a vehicle will appropriately sense the acceleration experienced at that location (the aPx and aPy terms in Equations 12). A direct integration of the measured accelerometer data (the components of Equation 11), however, will yield incorrect vehicle-fixed velocity components because of the presence of coupled translational and yaw velocity terms. To correctly determine the velocity component time histories from the accelerometer data one must also have knowledge of the www.collisionmagazine.com

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(13b) An alternative to this method is to transform the measured acceleration components to a spacefixed coordinate system and directly integrate these transformed acceleration components to determine the space-fixed delta-V components.

The vehicle-fixed delta-V components can then be found by a transformation of the space-fixed delta-V components back to the vehicle-fixed reference frame at each time step.

To demonstrate the effect that yaw rate has on the calculation of velocity change components, the directly integrated longitudinal velocity change data of Figures 7, 8, and 10 along with the corrected longitudinal velocity change (Equations 13a and 13b) are presented in Figures 11, 12, and 13, respectively.

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Figure 11: Direct integration and corrected longitudinal velocity change at ACM location of the T1 target vehicle

Figure 12: Direct integration and corrected longitudinal velocity change at c.g. location of the T1 target vehicle

We can see from these figures that the corrected delta-V data is quite different from that of the directly-integrated data. For instance, at the OE ACM location under the right front seat of the T1 target vehicle, the directly-integrated longitudinal delta-V data remains essentially zero until about 60 milliseconds where it then becomes positive (rear-to-front) growing to a peak magnitude of about 4 mph, whereas the corrected velocity change is rearward-directed reaching a peak magnitude of about 10 mph (Figure 11). At the vehicle c.g., the maximum directly-integrated delta-V is just below 5 mph but is about 17 mph when corrected (Figure 12). For the replicated T2 target ACM location over the presented time range, while the magnitude of the longitudinal velocity change is roughly the same for the directly-integrated data and the corrected data, the time-histories of these data are notably different (Figure 13). The corrected data reaches a peak at about 205 milliseconds and begins to diminish after that, whereas the directly-integrated data is ever increasing and has not yet reached a peak at 300 milliseconds.

Thus far, as the ACMs of our crash test vehicles record only longitudinal axis data, we have considered just the longitudinal components of acceleration and velocity change. Many ACMs, of course, also record lateral acceleration and velocity change data. Using our crash test data, we plot the vehicle lateral components of acceleration, directly-integrated velocity change, and corrected velocity change for our three reference locations in Figures 14, 15, and 16.

As can be observed in Figures 14 through 16, the directly-integrated and corrected velocity data are initially very similar in each of our three locations of interest - through approximately 120 milliseconds for the OE ACM location, approximately 70 milliseconds for the c.g. location, and approximately 50 milliseconds at the replicated T2 target ACM location on the T1 target vehicle.

After these times the directly-integrated data and the corrected data begin to diverge, and significant differences develop as a result of yaw motion effects.

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Yaw Rate and the Notion of a Principal Direction of Force For vehicles experiencing solely translational motion, the concept of a principle direction of

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force (PDOF) is easily understood and has two practical applications: (1) in interpreting the orientation in which the collision impulse acts on the vehicle, and (2) in assessing the direction an occupant tends to travel within the vehicle interior as a result of that impulse. In instances of predominately translational motion, data from an ACM that provides both longitudinal and lateral information may be used to determine the PDOF in the usual manner (i.e. through an inverse tangent function). As our discussion above has demonstrated, however, caution must be employed when using ACM data from vehicles that have experienced significant yaw motion during the collision.

In Figure 17 the corrected velocity and delta-V vectors at the T1 target vehicle c.g. are depicted at 100 milliseconds after initial contact. Similar vector constructions were made for the T1 target vehicle delta-V vectors at the OE ACM location, and the replicated T2 target ACM location at 100 milliseconds after initial contact for both the directly-integrated data and the corrected data. These three vector constructions are shown in Figure 18. In this figure, green arrows represent the corrected delta-V vectors, and the cyan arrows represent the directly integrated delta-V vectors. We can see that, at each location, there is an appreciable difference between them with the angle of the corrected delta V vector oriented at a greater angle (more rearward) than the directly-integrated delta-V vector. Furthermore, and because of the effects of yaw motion, differences exist when comparing the angle of the delta-V vectors of one location with another. Because the delta-V angle varies from one location to the next in a yawing vehicle, a description of the accident using only a single angle and calling it a "PDOF "is insufficient in understanding occupant motion within the vehicle at various seating locations. For this reason, and the fact that the delta-V angles at a given position can change significantly over the duration of the impact, a free-particle analysis of the type discussed in references 4 and 5 may be more appropriate in assessing potential occupant kinematics.

Figure 14: Lateral acceleration and velocity change at the T1 target vehicle ACM location

Figure 15: Lateral acceleration and velocity change at the T1 target vehicle c.g. location

Conclusions •

Properly functioning accelerometers mounted at any location on a vehicle will appropriately sense accelerations experienced at that location.

Figure 16: Lateral acceleration and velocity change for replicated T2 target ACM location on the T1 target vehicle. www.collisionmagazine.com

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Figure 17: Velocity and delta-V vectors for the T1 target vehicle at 100 milliseconds after initial contact

•

[yellow arrow = initial velocity; red arrow = velocity at 100 ms; green arrow = delta-V • at 100 ms] [green arrow = corrected delta-V vectors; cyan arrow = directly integrated delta-V vectors]

•

•

Accelerations measured at different locations within a vehicle experiencing crash-induced yaw motion may vary significantly. The variance is strongly dependent on the location at which an accelerometer is installed within the vehicle.

Though the acceleration experienced at a given ACM installation location will be accurately measured, and a direct-integration technique properly performed, inaccurate delta-V components can be produced if the vehicle has undergone significant impact-induced yaw motion.

These inaccuracies occur because the vehicle (and therefore the ACM) rotation relative to a space-fixed coordinate system is not accounted for with a direct integration of the accelerometer data.

An accident analyst attempting to interpret ACM data from a vehicle that has experienced crash-induced yaw motion should take care in assessing the delta-V components indicated by the ACM and in using this information for occupant kinematics purposes.

References

1. Greenwood, D., “Principles of Dynamics, 2nd Edition”, Prentice-Hall, Inc., 1988.

2. Society of Automotive Engineers Surface Vehicle Recommended Practice J211-1, “Instrumentation for Impact Test – Part I – Electronic Instrumentation,” Revised July 2007.

3. Marine, M., and Werner, S., “Delta-V Analysis from Crash Test Data for Vehicles with Post-Impact Yaw Motion,” Society of Automotive Engineers, Paper 980219, 1998.

4. Wirth, J., Marine, M., and Thomas, T., “An Analysis of a Staged Two-Vehicle Impact,” Society of Automotive EngiFigure 18: Differing delta-V vectors for the neers, Paper 2000-01-0464, 2000.

T1 target vehicle at 100 milliseconds after 5. Bready, J., Nordhagen, R., Perl, T., and James, M., “Methods impact (green arrow = corrected delta-V vecof Occupant Kinematics Analysis in Automobile Crashes,” Sotors; cyan arrow = directly integrated delta-V ciety of Automotive Engineers, Paper 2002-01-0536, 2002. vectors) 92 Collision Magazine - Volum 15 Issue 1

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Accident Reconstruction ACTAR Accredited Biomechanics CDR / EDR Crush Analysis Drones Forensic Mapping Human Factors Motorcycles Vehicle Systems Visibility The Crash Hub is the leading online Accident

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Reconstruction Expert Directory. Crash Experts vary by experience, rate and specialties.

When evaluating the right expert for your case, make sure you search, review and connect with the expert that best matches your case needs.

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Comparison of occupant stress in frontal collisions with varying degrees of seat belt use Dipl.-Phys. Annika Kortmann

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T

he biomechanical stress on an occupant in a head-on collision is not only linked to the cabin acceleration of the passenger compartment.

Where an airbag is activated, the seat belt and the airbag work together to reduce the relative forward motion of the occupants in the vehicle and minimize the risk of an impact with the vehicle interior. What stress such an impact has on the head, chest, and hips of a passenger and to what extent the improper use of the seat belt affects the biomechanical stress has not yet been tested and examined by accident reconstruction experts. For this reason, a series of experiments were conducted in which a Ford Focus traveling at 50 kph had a head-on collision with a tree and the acceleration sequence of the driver upon collision was measured using a biofidelic dummy fitted with measurement instruments. A total of three tests were performed, in the first test the dummy was not wearing a seat belt, in the second test the chest strap was worn just under the left shoulder and in the final test the three-point safety belt was used correctly. The results obtained are discussed and compared depending on the degree of use of the seat belt.

Introduction

A common issue in the reconstruction of accidents is the determination of the biomechanical stress on occupants during a vehicle collision. Known studies (see for example 1,2,3,4,5,6, carried out in cooperation with medical experts showed a connection between the cabin acceleration or change in velocity of the passenger compartment as a result of the collision and the biomechanical stress on the passengers. Tests on volunteers were used to test low-impact rear, front and side collisions. In practice, the load on the occupants was determined by technical experts, who calculated, for example, the vehicle’s average cabin acceleration or the corresponding change in velocity upon collision so that medical experts could use this information to interpret the risk of injury.

The actual acceleration of the head, chest, or hips of the occupant is not taken into account in most cases as the rate of cabin acceleration was determined from the vehicle damage. In the case of low-impact collisions, the average cabin acceleration was then correlated with the injuries suffered by the passengers involved in the voluntary tests.

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those that activate the airbag, as the risk of injury is too high. It has only recently become possible to use biofidelic dummies in accident reconstruction, which, in addition to their humanoid physiognomy and comparable movements, can also be equipped with measurement instruments. The acceleration is recorded through triaxial accelerometers in the head, chest and hips, which record at 20,000 Hz (Figure 1). A separate accelerator compares the cabin acceleration of the passenger compartment and records these values synchronously with those of the sensors in the dummy.

Was the passenger wearing the seat belt properly?

In high-impact frontal collisions (e.g., impact with a tree at 50 kph), the question regularly arises, especially before the courts, as to whether the occupant was wearing their seat belt correctly and, if not, which injuries still would have been suffered had the occupant been wearing their seat belt properly.

If experts have access to photos of the vehicle involved in the accident, they may be already able to make a statement about the occupant’s seat belt usage from the position of the seat belt or the deformation of the steering wheel. A seat belt that is firmly locked on the B pillar might indicate that the seat belt was not on at the time of impact and the seat belt pretensioner had locked the seat belt to the B pillar when the ignition was turned. According to Walter 7, an investigation of the seat belt itself in combination with the change in velocity determined to have resulted from the collision also offers an indication of whether the seat belt was used.

If such photos are not available or if they are inconclusive, medical experts would have to evaluate the severity of passenger injuries to determine whether the seat belt was used. From a technical perspective, it would therefore be beneficial to have some publicly available test results comparing head-on collisions that occur under the same conditions (collision speed, type of vehicle, impact configuration, etc.) where the only difference on the movement of the occupants and the resulting stress was the use of the seat belt (seat belt used/seat belt not used). This would make it possible to directly compare the effect of a collision on an occupant who was wearing a seat belt and one who was not.

Unfortunately, no such tests were available.

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Figure 1: Positioning of the triaxial accelerometers in the PRIMUS

Figure 2: Collision configuration for the series of tests with a head-on collision with a tree accounting for 40% coverage of the vehicle (left) and the PRIMUS dummy used for the tests, positioned in the vehicle (right)

Figure 3: Degree of seat belt use for the tests: not wearing a seat belt (left), the chest strap worn under the left shoulder (middle), and the seat belt worn correctly (right) 96 Collision Magazine - Volum 15 Issue 1

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Structure of the series of experiments A research project with the company crashtest-service.com GmbH (CTS) on the validation of the biofidelic PRIMUS 8 made it possible for the first time to carry out an investigation into the above topic, in cooperation with the engineering firm Schimmelpfennig + Becke.

Three tests were carried out in which a Ford Focus traveling at approximately 50 kph was driven head on into a tree accounting for 40% coverage of the vehicle. The collision configuration can be seen in Figure 2. In all three tests, a PRIMUS dummy equipped with instruments was placed in the driver’s seat to determine the head, chest and hip acceleration throughout the course of the collision. The acceleration of the passenger compartment was measured using an additional accelerometer between the front seats in the center console, at the height of the center of gravity and the results were correlated with the data measured by the dummy.

For the tests, only the level of seat belt usage of the dummy varied. All other parameters remained the same. The differences in seat belt use of the dummy are depicted in Figure 3: not wearing a seat belt, seat belt worn under the left shoulder, and seat belt fitted properly. The test with the seat belt worn under the shoulder is designed to test the effect of a seat belt worn “poorly or in-correctly” on the passenger stress.

Implementation and analysis Figure 4 shows a side view of the motion sequences of the dummies in a collision at the same points in time. In the red vehicle, the dummy is unbelted; in the silver vehicle, the dummy is wearing the seat belt under the shoulder (hereinafter referred to as “poorly belted”); and in the blue vehicle, the seat belt is being worn correctly (hereinafter referred to as “properly belted”).

A clear difference can be identified in the occupant movement in the case of the unbelted dummy (red vehicle). Unrestrained, the dummy’s chest collided with the steering wheel and before its head struck the roof edge and then windshield. Optically, there is almost no difference between the poorly belted dummy and the one with the seat belt worn properly (silver and blue vehicles respectively).

The upper body of both occupants is obviously restrained by the seat belt. The locking mechanism of the hips of the dummies and the lap strap cause the upper bodies of both dummies to rotate forwards and downwards so that both dummies hit the opening airbag with their head.

The comparison of the acceleration sequence of the passenger compartment in the x-direction for all three tests

as depicted in the diagram in Figure 5 shows that all three crash tests can be directly compared to one another. In all three tests, the passenger compartment shows a change in velocity of around 55 kph as a result of the collision. The damage to the vehicles also corresponds optically to one another (Figure 6). The following diagrams are filtered by CFC60 (Channel Frequency Class). The customary filtering by CFC1000 for head acceleration does not provide any additional relevant information for this test so that the CFC60 filter was used instead for illustration.

As the acceleration sensors in the dummy and the passenger compartment are measured via the same module, it is possible to synchronize each acceleration in time with one another. The resulting acceleration sequences for the three tests are juxtaposed against one another in Figure 7. This sets out the passenger compartment acceleration (gray) in relation to the head (red), chest (blue) and hip acceleration (green). The acceleration is given in g (g = 9.81 m/s2).

From this juxtaposition, it is immediately clear that in the case of an occupant who is not wearing a seat belt or one who is not wearing it properly, there is a higher head acceleration (or to be precise, excessively high deceleration) (red graph), which does not occur in the case of an occupant with a seat belt worn properly. The deceleration of the occupant is delayed compared to the deceleration of the passenger compartment. The occupant is only connected to the vehicle through the seat belt. The delay of approximately 0.02 s before the deceleration of the occupants in the case of occupants who are wearing a seat belt can be explained by the slack in the seat belt. The tighter the seat belt, the earlier it will force the occupant to change movement in line with the movement of the passenger compartment.

In the case of the unbelted occupant, it is the collision of the occupant’s head with the steering wheel or the roof liner after approximately 0.06 s that first causes the body to decelerate.

After further analysis of the acceleration sequences, it seemed sensible to look at the acceleration of each part of the body separately and to compare these depending on the level of seat belt use.

Evaluation of the head acceleration To compare the resulting acceleration sequences of the heads of the differently retrained occupants, the effect of the acceleration on the head is depicted in x-, y- and zdirections for each test and then correlated with the movement of the occupants based on each frame.

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Figure 4: Motion sequence for unbelted (top), poorly belted (bottom) and properly belted PRIMUS (next page)

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Figure 4 (cont.): Properly belted PRIMUS

Figure 5: Acceleration sequences of the passenger compartment of the crash vehicles in the x-direction

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Figure 6: Comparison of the damage to the vehicles used for the crash tests

Figure 7: Comparison of the resulting acceleration of the head (red), chest (blue), hips (green), and the passenger cell (gray) for the varying degrees of seat belt use by the occupants 100 Collision Magazine - Volum 15 Issue 1

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Figure 7 (cont.): Comparison of the resulting acceleration of the head (red), chest (blue), hips (green), and the passenger cell (gray) for the varying degrees of seat belt use by the occupants

Figure 8: Head acceleration of the unbelted occupant in x-, y- and z-directions www.collisionmagazine.com

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Figure 9: Multiple impacts of the head of the unbelted occupant with the roof edge (1), the windshield (2) and the roof liner (3) Figure 8 graphically plots the acceleration sequence of the head of the unbelted occupant in x-, y- and z-directions against time. In the x-direction (red graph), three marked peaks can be identified, which have been numbered consecutively. The peaks can be allocated to the movement of the occupants based on time (Figure 9). The first peak is the impact of the occupant’s forehead with the roof edge.

With an impact time of 0.023 s, an average deacceleration of 46.36 g (454.79 m/s2) can be derived from the graphs.

The integration of the acceleration over the extremely short impact time results in a change of velocity of the head upon collision of 36 kph. All further measurements of the collision time t, maximum and average acceleration (amax and aavg), and the change in velocity resulting from the collision Δv are summarized as an overview in Table 1 at the end of the article.

The head subsequently snaps backwards so that the occupant hits the windshield with their face (second peak). In

this phase, during a collision time again of 0.23 s, the average acceleration was 23.14 g (227.00 m/s2), which equates to a change in velocity of 18.72 kph caused by the collision.

After hitting the windshield, the occupant bounces back into the vehicle interior and hits their head on the roof liner from below at around 0.25 s after the start of the collision (third peak).

Figure 10 depicts a similar analysis assigning the acceleration peaks with the occupant’s movement for the occupant who is wearing their seat belt incorrectly, while the related occupant movement is depicted in Figure 11. The first peak arises when the movement of the head decelerates after 0.1 s due to the airbag. A further 0.02 s later, the head is severely slowed. The head still hits the steering wheel although the airbag activated and although the occupant was using the lap strap fully and the chest strap partially.

Figure 10: Head acceleration of the poorly belted occupant in x-, y- and z-directions 102 Collision Magazine - Volum 15 Issue 1

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Figure 11: Impact of the poorly belted occupant with the airbag (1) and the steering wheel (2)

Figure 12: Head acceleration of the properly belted occupant in x-, y- and z-directions The average acceleration is approximately one-third of the acceleration of the unbelted occupant when they hit the roof edge with their head (14.27 g/139 m/s2), see Figure 8.

the occupant who was not wearing their seat belt correctly.

However, the longer duration results in a lower average deceleration of 11.87 g (116.44 m/s2).

If one depicts the acceleration sequence of the head for the occupant with the seat belt worn properly (Figure 12), there are none of the brief, strong peaks in acceleration as are noted for the occupants who were not wearing a seat belt or not wearing it properly. Instead, the head merely experiences a deceleration of up to 32 g. The head also decelerates over a comparatively long time of 0.12 s. This longer deceleration time is achieved through the combination of the airbag and the chest strap. The change in velocity of 50.15 kph caused by the collision is comparable to the impact of the head on the steering wheel of

The comparison of the resulting deceleration of the head depending on the seat belt use is shown in Figure 13. The airbag alone is not sufficient to “softly” decelerate the head.

If the upper body is not sufficiently restrained by the chest strap, the head will hit the steering wheel despite the activated airbag. Figure 14 shows an enlarged excerpt of the deceleration since the start of the collision (enlarged to 0.2 s).

The acceleration sequences of the head of an occupant who is poorly belted (blue) and whose seat belt is worn properly (green) are in close approximation for up to 0.1 s after the collision. After that, the chest strap of the occupant who

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Figure 13: Comparison of the resulting head acceleration depending on the degree of seat belt usage

Figure 14: Enlarged excerpt of Figure 13 104 Collision Magazine - Volum 15 Issue 1

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is poorly belted slips further away from the left shoulder so that the seat belt no longer sufficiently restrains the upper body (indicated in magenta). While the head of the properly belted dummy only decelerated slightly quicker, the airbag collapses in the case of the poorly belted dummy because the airbag could not effectively stop the head and the chest at the same time. As a result, the head impacts with the steering wheel.

If one evaluates the change in velocity of the head as a result of the collision for the poorly belted occupant and the

occupant with a seat belt worn properly, it shows that the head experiences a loss in velocity of 105±3.5 kph in both cases as a result of the collision. However, the maximum deceleration amax for the occupant who is not wearing the seat belt properly is around four times larger, while the average deceleration aavg is approximately twice as large.

Head rotation when immersing in the airbag The diagram in Figure 12 shows that, despite the frontal collision, the occupant also experiences deceleration in y- and z-directions, which can be quite significant. This is

Figure 15: Significant rotation of the head when immersing in the airbag (properly belted) www.collisionmagazine.com

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because of the head movement of the occupant, which was recorded using an onboard camera in the case of the occupant with the seat belt worn properly (Figure 15).

As the head immerses in the airbag, it rotates significantly.

Individual images show that the left shoulder of the occupant is restrained by the seat belt. The right shoulder swings forward, resulting, among other things, in the rotation of the upper body. The head follows this rotation, so that airbag no longer slows the head just from the front but from the right side of the head, too.

Evaluation of the chest acceleration The diagram in Figure 16 applies the resulting acceleration sequence of the chest depending on seat belt usage.

There is almost no difference in the acceleration sequence of a poorly belted dummy (blue) compared to the dummy with the seat belt worn properly (green). The occupants are essentially held by the lap strap and the upper body cannot reach the steering wheel, regard-less of how the chest strap is sitting. The maximum deceleration in the range of 35 to 44 g occur. With an exposure time of 0.14 or 0.17 s, this results in a loss of velocity from the collision of 76.64 or 84.41 kph, with an average deceleration of 15.50 or 13.74 g respectively.

Where the occupant is not wearing a seat belt, the occupant moves forward freely within the vehicle. For that reason, the deceleration of the upper body is clearly delayed compared to the occupants who were wearing a seat belt.

The acceleration sequence of the chest of the unbelted occupant is shown for each direction in Figure 17. In the x-direction (red graph), there are two characteristic deceleration peaks. The impact with the airbag accounts for first peak (Figure 18). A short time later, the airbag collapses and the chest collides with the steering wheel (second peak). When colliding with the steering wheel, the occupant experiences a change in velocity of 76.74 kph (Figure 16) as a result of the collision. The change in velocity is therefore comparable to the change in velocity in the case of an occupant who was wearing a seat belt. However, in the case of an impact with the steering wheel, the maximum delay is approximately two times larger and the deceleration time is accordingly low.

Evaluation of the hip acceleration As expected, there is also no noteworthy difference in the resulting hip acceleration of the dummies depending on the position of the chest strap (Figure 19 blue/green graph) as both dummies are restrained by the lap strap in the same way. At 71.34 and 65.90 kph respectively, the change in velocity of the hips as a result of the collision is close to the change in velocity of the passenger compartment (78.75 and 63.75 kph) because the hips are directly attached to the vehicle through the lap strap, apart from a small amount of slack in the seat belt.

In the case of the unbelted occupant, the deceleration of the hips is delayed because the lap strap does not decelerate the hips directly; instead, it is the impact of the chest

Figure 16: Comparison of the resulting chest acceleration depending on the degree of seat belt usage 106 Collision Magazine - Volum 15 Issue 1

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Figure 17: Chest acceleration of the unbelted occupant in x-, y- and z-directions

Figure 18: Chest impact of the unbelted occupant with the airbag (1) and the steering wheel (2) first with the airbag and then with the steering wheel that results in the deceleration. As the dummy’s hips do not impact directly with the vehicle in this case, the resulting change in velocity of the hips is only 36.38 kph.

Comparison of the injuries The biofidelic sensors of the PRIMUS dummy which was used not only made it possible to record the acceleration sequences of each area of the body, but they also allowed for an “autopsy” of the dummy to be conducted after the test to reveal the injuries of the occupants.

The autopsy showed that the unbelted occupant suffered massive hyperextension of the cervical vertebrae and a break in some thoracic vertebrae (Figure 20). The hyperextension resulted from the motion sequences outlined above (Figures 4 and 9). In comparison, the dummy that was not wearing the seat belt properly suffered two broken ribs on the left side, an injury to the elbow joint on the right, and ligament sprains in both knees (Figure 21).

A comparison of the injuries suffered by the unbelted dummy and the poorly belted dummy shows that the amount of the stress incurred is not the only significant element. Although the duration and the level of acceleration

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Figure 19: Comparison of the resulting hip acceleration depending on the degree of seat belt usage

Table 1: Summary of the measured values and the resulting change in velocity for the series of tests 108 Collision Magazine - Volum 15 Issue 1

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Figure 20: Injuries to the unbelted PRIMUS dummy

Figure 21: Injuries to the poorly belted PRIMUS dummy differed significantly, the resulting change in velocity of the head arising from the collision was similar in both tests.

However, the direction of the forces acting on the head resulted in the hyperextension of the cervical vertebrae in the unbelted dummy, while the poorly belted dummy hit the airbag front on with the head and then hit the steering

wheel, with-out any significant hyperflexion or hyperextension of the cervical vertebrae.

The injuries of the PRIMUS dummy that was wearing a seat belt properly are depicted in Figure 22. The collision resulted in two broken ribs on the left side and a fracture of the sternum.

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Figure 22: Injuries to the properly belted PRIMUS dummy Summary The use of PRIMUS dummies outfitted with biofidelic sensors and instruments now makes it possible for accident reconstruction experts to reproduce even severe collisions and to record the stress impacting directly on the occupants, even in scenarios where it is no longer safe to use volunteers for the tests. In addition, the subsequent “autopsy” of the dummy allows the injuries suffered in the

ing the stress suffered by the occupants. If the seat belt is not worn properly over the shoulder and slips during the collision, the airbag will no longer be able to sufficiently stop the head. The occupant will still hit the steering wheel with their head despite the deployment of the airbag. Where the seat belt is worn correctly, the upper body is restrained to the point that the head will be stopped over a longer period and at a lower level of deceleration.

The resulting change in the velocity of the head caused by

The use of PRIMUS dummies outfitted with biofidelic sensors and instruments now makes it possible for accident reconstruction experts to reproduce even severe collisions and to record the stress impacting directly on the occupants, even in scenarios where it is no longer safe to use volunteers for the tests. form of broken bones, ligament sprains, etc., to be documented in a way that even non-specialists can understand.

The series of tests carried out involving a head-on collision of a Ford Focus traveling at 50 kph showed that the proper use of the chest strap has a considerable impact on reduc110 Collision Magazine - Volum 15 Issue 1

Volume 15 Issue 1.indd 110

the collision in the case of the impact of the head with the steering wheel and the deceleration through the airbag is comparable at 105±3.5 kph. However, the differences in the duration and speed of the deceleration are significant.

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A comparison of the injuries suffered by the unbelted dummy the poorly belted dummy shows that the amount of the stress incurred is not the only significant factor. Although the duration and the level of deceleration differed significantly, the resulting change in velocity of the head caused by the collisions was similar in both tests. However, the direction of the forces acting on the head resulted in the hyperextension of the cervical vertebrae in the dummy who was not wearing a seat belt, while the dummy that was not wearing the seat belt properly hit the airbag front on with the head and then hit the steering wheel, without any significant hyperflexion or hyperextension of the cervical vertebrae.

The evaluation showed that despite the fact that it was a frontal collision, there were also comparatively significant acceleration forces acting on the head area of the occupants in the y- and z-directions. This can be explained from the head movement of the occupant with the seat belt worn properly so that the left shoulder was restrained by the chest strap.

As expected, the change in velocities of the hips resulting from the collisions was almost equivalent to those of the passenger compartments, as the occupants who were wearing a seat belt were connected to the vehicle, apart from a small amount of slack in the seat belt.

Outlook When evaluating the biomechanical stress on an occupant in a head-on collision, the collision can sometimes cause the front airbag to activate. At present, there are no comparable measurements available to show the extent to which an airbag reduces the stress on the head in the case of a frontal collision. Until now, experts were limited to using the collision-related change in velocity of the passenger compartment based on the damage to the vehicle in order to determine the biomechanical stress on the occupants.

In the future, the instrumented PRIMUS dummy will make it possible, for example, to test the effect of the partial activation of front airbags in a crash test involving a frontal collision and thereby ascertain the level of influence of the airbag on biomechanical stress.

sanalyse und Bewertung des Verletzungsrisikos von Insassen bei Seitenkolli-sionen – Erkenntnisse aus Crashtests beim fahrenden Pkw (Movement Analysis and the Evaluation of the Risk of Injury to Occupants in Side-on Collisions), VKU 11/2015 2. S. Meyer, I. Mazzotti, M. Becke, HWS-Belastungen beim Heckanstoß – Erkenntnisse zur Schutzhaltung für Pkw-Insassen (Cervical Vertebrae Stress in a Rear Collision – Findings on the Safety Position for Passenger Car Occupants), VKU 01/2018 3. B. Walter, M. Winninghoff, M. Becke, Gurtschlitten – aktualisierte Untersuchung der biomechanischen Belastung (Seat Belt Slide – Updated Investigation into Biomechanical Stress), VKU 03/2007 4. M. Becke, Heckkollision – Ist delta v out? (Rear Collision – Is Delta-v Out?), UREKO Spiegel (03) 2002 5. S. Meyer, M. Weber, W. Kalthoff, M. Schilgen, W. H. M. Castro, Freiwilligen-Versuche zur Belastung der Halswirbelsäule durch Pkw-Heckanstöße (Voluntary Tests of the Stress of Rear Collisions Involving Passenger Cars on the Cervical Vertebrae), VKU 01/1999 6. S. Meyer, Experimentelle Untersuchung des Zusammenhangs zwischen technischen Kollisionsparametern und der Bewegungskinematik von Insassen im Hinblick auf leichte HWS-Schleudertraumen (Experimental Investigation of the Connection between Technical Collision Parameters and the Motion Kinematics of Occupants with regard to Mild Whiplash Injuries of the Cervical Vertebrae), Diploma Thesis, Universität Hannover, 1993 7. B. Walter, Belastungsspuren an Sicherheitsgurten (Signs of Strain in Seat Belts), VKU 04/2008 8. The name crashtest-service.com GmbH gave the biofidelic dummy.

I would like to thank crashtest-service.com GmbH for the excellent cooperation and Dr. Dobberstein in particularly for his comprehensive and quick evaluation of the various measurements.

Sources 1. C. J. G. Castro, M. F. Hein, W. Kalthoff, M. Becke, L. Gorny, H. Wagner, W. H. M. Castro, Bewegungwww.collisionmagazine.com

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