You’re driving along, minding your own business, and—TING! Something smacks your windshield. You didn’t see it coming, but the glass is cracked. Where the heck did it come from, and why did it hit your windshield?
As I always say, you don’t understand something unless you can model it. So let’s try a little thought experiment. We’ll start with a basic scenario, where someone ahead of you drops an object in the road, and then see what we need to make it work.
Follow the Bouncing Ball
OK, imagine a car is driving in front of you at 30 miles per hour. A child in the back seat takes a bouncy ball and drops it out of the window. Why would they do this? Who knows why children do things. This is what it would look like to someone on the side of the road:
Is that what you expected? The ball bounces up, but it continues to move along with the car. This is because when the ball is released, it’s horizontal velocity is the same as the car’s. The only change is in its vertical velocity: The gravitational force causes it to move down until it hits the ground, at which point, it rebounds upwards. As you can see, it won’t hit the car behind.
Oh, but what about air drag? It’s true, as the ball moves through the air, it collides with air molecules. This produces a force in the opposite direction. The magnitude of this drag force depends on the speed of the moving ball and its size. Plugging in some reasonable values, its motion now looks like this.
Now the ball behaves more like you would expect. Its horizontal velocity decreases so that it falls behind the original car. But it’s still not going to hit your windshield. With air drag and loss of energy on impact with the ground, each bounce is a little lower than the one before. You should be fine.
Rock Out
Now say that kid drops a rock out the window. Kids! Or maybe there’s a truck carrying gravel, and some of it slips through a crack. When the rock hits the road, its motion can change in a few ways. First, there’s a frictional force between the rock and the road, which will reduce the rock’s horizontal velocity. As we saw above, slower is bad.
Second—and this can seem weird—because a rock is irregularly shaped, it’s possible that it spins and hits the pavement in a way that makes it skip up higher than it started.
Hold on! Isn’t that a violation of the law? You know, the law of conservation of energy? Nope, it’s an energy transfer. A rotating and moving rock has both rotational and translational (linear) kinetic energy. Some collisions can convert rotational energy to translational energy, which makes the rock bounce higher. Higher is bad.
Here’s what that might look like:
So you’re cruising along the highway at, say, 70 miles an hour—and there’s a rock up in the air at the top of its path. It’s momentarily at rest, but you aren’t. Let the court take note: The rock didn’t hit you. You hit the rock. But the effect is the same. Either way, you need a new windshield.
Rock and Roll
That’s a plausible scenario, but what if there is no truck in front of you? Actually, a more common cause of windshield damage is a rock lying in the road that gets kicked up by another vehicle. You might think it gets shot back at the car behind, but that’s not quite right. The rock still doesn’t move backward.
Picture this: a wheel is rolling along the road and a rock gets wedged between the tire treads. When the rock comes in contact with the ground, it’s at rest. Here’s what that would look like:
What if the rock falls off at the exact moment when it is in contact with the ground? Well, at that point the velocity of the rock with respect to the ground is zero. It would just be another dumb rock on the road. No big deal.
But wait! What if the rock sticks to the tire just a bit longer and then gets released, maybe due to the flexing of the rubber. In this case the rock could have a significant upward velocity. Here, let me show you. This is a faster-rolling wheel so I’ve slowed down the animation a little:
This is bad. Now we have this rock moving upward with very little horizontal velocity. That means it’s just going to be sitting there in midair waiting for the next car to slam into it. Now it’s true, a rock is more likely to get jammed in the treads of a big truck tire. But that’s why big trucks have mud flaps—those rubber flaps that hang down behind the wheel.
I know, having to replace your windshield sucks. but just remember, your car probably collided with the rock, so it’s not really the rock’s fault. You want to avoid flying rocks? It’s pretty simple, really: Move back! Stop following so close.
