Blog | Occupant Kinematics
The study of motion and of physical concepts such as force and mass is called dynamics. The part of dynamics that describes motion without regard to its causes is called kinematics [1]. Occupant kinematics is the study of kinematics as it applies to occupants within a motor vehicle. Broadly speaking, in accident reconstruction, one uses concepts of occupant kinematics to understand mechanisms of injury causation by identifying potential points of contact between an occupant’s body and the occupant cabin itself. Another typical use of occupant kinematics is to understand potential ejection portals through which the occupant may travel during a complex event. In either of these cases, an occupant kinematics study can be achieved by simply applying Newton’s First Law of motion; that is, the analyst aims to understand the way in which the human body moves with respect to the moving vehicle reference frame in response to some change-in-state of the vehicle. Newton’s First Law tells us, an occupant will continue moving in its pre-impact state until acted upon by some external force which changes the occupant’s state. The external force is generally provided by some component of the occupant cabin. By studying how an occupant moves with respect to the occupant cabin, one can develop a better understanding of potential points of contact between the occupant’s body and the cabin, as well as potential ejection portals.
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Many methods to study occupant kinematics have been presented over the years. In the article “Methods of Occupant Kinematics Analysis in Automobile Crashes” [2], Bready et al recommend a generalized graphical “free-body analysis” approach in which one first diagrams the motion of the occupant and vehicle in the Earth-fixed frame, assuming that the occupant acts as free-body traveling unobstructed as the post-impact motion of the vehicle evolves. Using such a diagram, the position of the occupant with respect to the occupant cabin can be understood. A new diagram can then be drawn depicting the position of the occupant at fixed times with respect to the vehicle’s reference frame. Below we review this procedure and show how the corresponding Virtual CRASH simulation compares to the expected behavior from free-body analysis diagramming technique. We first focus on the example given in Figure 3 of reference [2].
Example with significant change-in-yaw
Below we have a t-bone crash simulation where the target pickup truck (red) has a pre-impact speed of 34.091 mph and the bullet sedan (gray) has a pre-impact speed of 56.250 mph.
Next, we want to display the pickup truck’s position every 100 milliseconds. We can do this by left-clicking on our truck, then going to the interpositions menu in the left-side control panel. Next, make sure “show” is enabled, set the criteria to time (rather than distance), and enable “step”. Enabling the step option will draw the vehicle at each interposition rather than simply showing a bounding box. Note, enabling “sequence” here will draw the vehicle (rather than a bounding box) at the location where a sequence entry has been initiated.
Going to the 2D vehicles tab in the gallery browser, we drag and drop into our scene a 2D image of our pickup truck and position it at the simulated truck’s position at 300 msecs. When using the interpositions to study object positions as a function of time, it is often helpful to freeze the object so that the snap-to-time function of the interpositions is disabled. The time slider should be set to 0 seconds to ensure that the 100 msec increments that are drawn start at time=0 seconds.
Now, we clone the 2D image to also mark the truck’s position at 0 seconds, 100 msecs, and 200 msecs.
Hiding our simulated truck model and adding some text labels, we have the below diagram:
Using the axes tool we draw our axes with the origin at the pre-impact location of our driver’s head. Points are placed on the tool’s x-axis every 5 feet to indicate the positions we expect to find an unrestrained occupant (every 100 milliseconds) that is traveling at a uniform speed of 50 ft/s (34.091 mph). Circles are placed at each point on the x-axis to mark the driver’s head position. Arrows are also placed at each position to indicate the head’s pre-impact orientation.
In the above diagram, we see the expected head position and vehicle position with respect to the Earth-frame. We can graphically transform this diagram to the truck’s frame of reference by cloning each set of circle, arrow, and truck figures, and re-orienting them so that each truck overlaps. First we select the set at 0 ms, clone, and drag them to another area in our environment. Next, we clone and re-orient the three other sets, deleting the truck image each time, leaving only the first image visible. This is illustrated in the video below:
Note, when multiple objects are selected, then translated and/or rotated, the relative orientation of the objects is preserved when the “Use Selection Center” option is enabled (this is enabled by default). If “Use Pivot Center” is enabled instead, the select objects will rotate individually about their own pivot points.
Here we see our final diagram, illustrating that the right side of the driver’s head will likely make contact with the dash or front windshield sometime between 200 ms and 300 ms.
Next, we want to simulate the occupant’s motion in Virtual CRASH and compare the results with our expectations based on the graphical method illustrated above.
First, we place a multibody (with driver pose) into the truck (see the User’s Guide (VC5 | VC4 | VC3) to review placing multibodies into vehicles). We are careful to ensure that the multibody’s segments are not penetrating into any portion of the truck’s interior polygons – this will help prevent snags which can happen with the default-auto collision model when polygons are overlapping at the start of a simulation. The multibody is given the same initial velocity as the truck. Note, the multibody’s x-axis is aligned with the truck’s x-axis, both with yaw and pitch equal to 0. Therefore, the velocity vectors are parallel at time=0 seconds.
Switching the polygon selection mode, we lasso the truck’s roof polygons and change the material type to glass so that the polygons become transparent.
Next, we attach a camera to the truck’s reference frame, and position it above the truck looking down.
Below we see the final video.
Note, the simulation indicates the right side of the occupant’s head makes contact with the windshield prior to time = 300 msecs, but otherwise, the simulated behavior agrees extremely well with our expectations from the free-body analysis.
Switching to elements selection mode, we can remove the front windshield, dash, and steering wheel to fully compare the simulated motion of our occupant with our free-body analysis. Switching to polygon face selection mode, we remove all other polygons from our truck which the multibody could impact. This allows us to compare the full unimpeded (free-body) motion of our simulated occupant to our expectation from our free-body analysis. In the video below, we see at each marked circle, our simulated multibody’s head arrives in with the predicted orientation at the predicted time. There is a slight delay at 300 msecs, but this is expected, as the simulated occupant is not truly a free-body, but is undergoing frictional forces due to contact with the seat as well as the feet. Overall we see excellent agreement.
Graphing head position
Using the data report, the head's position with respect to the occupant cabin can be easily graphed. The result is seen below:
Because the truck's z-axis did not deviate too far from the Earth's z-axis, it's a straight-forward process to estimate the head's position inside of the truck by performing a simple coordinate transformation using a 2x2 rotation matrix. This is shown in the video below. Note, with significant pitch and roll, we would need to perform the generalized transformation using a 3x3 matrix rotation since the vehicle's local x-y plane would no longer be parallel with the Earth's x-y plane.
Below we see a 360 degree view from inside the pickup:
References
[1] College Physics, 7th Edition, Volume 1, Serway, Faughn, Vuille, and Bennett, ISBN: 0-495-11374-3.
[2] "Methods of Occupant Kinematics Analysis in Automobile Crashes," SAE 2002-01-0536, Bready et al.