Check Out This Awesome Crash Test. Now, Let’s Run the Physics

This is the ETI Roller System. It uses rolling drums to absorb the impact of a vehicle collision, turning a serious impact into a glancing blow and, presumably, reducing the risk of injury. That may be, but I’m more interested in using this video to measure the acceleration during the impact.

To do that, I need position-time data for the car during a collision. This video presents an almost perfect case for video analysis because the camera remains stationary and mostly perpendicular to the motion. However, I don’t know the distance scale or the video frame rate. For the scale, I’ll assume the distance markers on the silver car are 1 meter apart. For the frame rate, I’ll refer to a video of a similar system from KSI Global Safety that shows cars traveling 100 km/hr (27.8 m/s). I will assume the same initial velocity and adjust the frame rate to produce that speed.

Now for some data (using Tracker Video Analysis). Here is the horizontal position-time data for the silver car (I am calling this the x-direction).

The slope of this plot reveals a horizontal velocity of about 26.1 m/s. Notice that the x-velocity doesn’t change even though the car hit the barrier. I suspect that as the car collides, the rolling drums exert very little force in the x-direction. Without an x-force, there can be no change in x-velocity.

Now, the y-position of the car before and after the collision.

From the slope of the plot before the collision, I can peg the initial velocity in the y-direction at -10.5 m/s. I can do the same thing after the collision to find the final y-velocity of 3.30 m/s. Determining the time of the collision is trickier because the car is not a point object, making when and where it collided not so cut-and-dried. If I go with the time it first touched the barrier until it left, I get a time of 0.181 seconds.

But what does this y-motion reveal? Since there is a change in the y-velocity, there also is an acceleration in the y-direction. I can calculate this with the estimated time interval.

Yes, I have the initial and final y-velocities—but there is one small trick. It’s important to remember that direction matters. If I call “away from the wall” the positive y-direction, then the initial y-velocity is negative and the final y-velocity is positive. This means I will see an even greater change in velocity since the two velocities have opposite signs. Using the values above, I calculate an average acceleration of 76.2 m/s².

It turns out that acceleration provides a great indicator of human damage. The greater the acceleration, the greater the risk of bad things happening to you. Here is a nice plot showing the maximum tolerance an average human body can withstand. Notice that the units for accelerations are in “g’s” where 1 g = 9.8 m/s². This means the y-acceleration in this collision would be 7.8 g’s. Another important point is that the g-force tolerance depends on time. Humans can take a larger acceleration is the time interval is small. But for this 0.18 second interval, a lateral acceleration of about 13 g’s seems like the max (which is greater than the calculated 7.8 g’s). However, it should be noted that I have calculated the average acceleration over the time interval. It is entirely possible that the acceleration actually peaks at much greater value.

The real question is: Did the roller barrier work? Here are some final thoughts.

The roller barrier reduces friction along the axis of the barrier. In a collision with a conventional barrier, a force pushes in the opposite direction of the motion of the car to slow it down. This is good or bad, depending upon what you want to happen. If you want to stop the car, this roller barrier doesn’t do that.
Rebounding is usually bad. Imagine if the car crashed into the wall but the final y-velocity was zero. This would probably result in a lower y-acceleration (this depends on the time interval too).
Speaking of accelerations, I used just one point on the car to calculate the acceleration. In fact, different parts of the car would see different accelerations because the car rotates and deforms. If you like, you can calculate the acceleration for different points.
Do the rotating drums absorb kinetic energy? That’s not how I would describe it—but from one point of view they do. As the car collides with the rollers, they increase in rotational energy. The car must provide this energy. But because the x-velocity of the car doesn’t change much, I don’t think there is a huge change in energy. If the rollers were filled with some heavy material, they would have more rotational energy but they would also slow the car down more. Again, I’m not sure what is best for the car or the people.
I guess I will leave you with one homework question. What is the change in kinetic energy of the car? Try to estimate how much energy goes into deformation of the barrier and the car and how much goes into rotational energy.