This is crazy. Look at this crash test between two similar Nissan models. The video shows a silver 2016 Nissan Versa (made for the US market) vs. a red 2015 Nissan Tsura sold in Mexico. Which car would you pick to drive?

### Video Analysis

The great thing about these crash test videos is that they give a great shot of the collision in slow motion. On top of that, there are also these very nice markers on the vehicles so I can track their motion during the collision. From the description, these two cars have a closing speed of 80 mph (35.8 m/s). But I don’t actually know the time scale (it’s in slow motion) and I don’t know the distance scale.

After a quick Google search, I found that a 2016 Versa has a wheelbase of 102.4 inches. From this, I can measure the size of the distance markers on top of the car. My value was close enough to 24 inches that I’m pretty sure it should be exactly 24 inches. Also, since I know the closing speed of the cars each car should be moving at about half that value. With this I can get an approximate frame rate.

Now for some data. First, here is a plot showing both cars’ motion in the x-direction (the original direction of motion) as a function of time.

The top curve represents the Tsuru and the bottom is the Versa. I was surprised to find that their initial velocities were a little bit different—but I guess that’s OK. What I really care about is the acceleration during impact. Because both cars are deformed during impact, there isn’t just *one* acceleration: Different parts of the car will have different accelerations. However, I want a measure of the acceleration inside the cabin of the car, so I chose to look at a point further back on both cars that are outside of the crumple zone.

Let’s look at the Versa first. Here is a plot of the position vs. time.

Notice that the Versa doesn’t actually stop. It just slows down and then continues moving with a nearly constant velocity after the collision. I can find the average acceleration (in the x-direction) with the following definition.

I can get the velocity before and after the collision by looking at the two slopes of this data. From that I get an initial speed of 19.42 m/s and a final of 5.50 m/s. For the time interval, I am just going to get an approximate value for when the collision started and then when the vehicle stopped changing speeds. From this, I get a Δt of about 0.025 seconds. Putting this together, the car has an average acceleration of about 557 m/s^{2} or 57 g’s.

Now for the Tsuru.

Perhaps you can see a difference in this car’s motion. First, the Tsuru almost comes to a stop instead of continuing to move on like the Versa. Second, it seems to take a much longer time to accelerate. In fact, I can find the acceleration of this vehicle (the back of it at least) by fitting a quadratic equation to the data. The term in front of t^{2} is half the acceleration (because of kinematics). This gives the Tsuru an acceleration of about 134 m/s^{2} or just 13.7 g’s.

You should also notice that both cars accelerate in the y-direction (perpendicular to the original path). I’m just ignoring that for now, but you can find the y-acceleration as homework.

### What Does It Mean?

If you just look at the video of the crash, it seems like the Versa came away with less damage, but the Tsuru clearly has a lower acceleration. In this case, the safety of a human inside either car is complicated. However, we can focus on two important aspects of crashing.

**Acceleration.**If you fall off a building, it’s not the fall that kills you—it’s the acceleration from when you hit the ground. Don’t worry, NASA has data on surviving the highest g forces. 57 g’s would be pretty bad.**Human Protection.**Who cares if you have a small acceleration but are crushed in the process. A car needs to also include a container that provides a safe space around the human.

The Tsuru might have a smaller acceleration, but in this crash, it still crushes the test dummy—and I doubt the acceleration of the *dummy* is lower for the Tsuru. Creating a lower acceleration is all about increasing the time over which the human (or dummy) stops. You can do this with a car by creating crumple zones where the car compresses as it stops and increases the stopping time. For the Versa, the stopping time of the human is further increased by having an airbag inside the car—just because the car stops, that doesn’t mean the human inside has the same acceleration.

### Homework

Yes—there is homework. There is always homework. Embrace the homework.

- Find the vector values for acceleration for both cars (in two dimensions).
- Find the mass of both cars. Is momentum conserved in this collision?
- Using the mass and initial velocities, estimate the total kinetic energy before and after the collision. How much energy went into deforming the cars?
- Look at the head of the two dummies inside each car. See if you can estimate the head acceleration for the two.