No new episode of Mythbusters this week, unfortunately, but in its absence I get to write about Car vs. Rain, the episode originally aired three weeks ago. It focuses on a fantastic physics-based myth: when driving a convertible in the rain, does less rain get in the car if you step on the gas, as opposed to pulling over and putting the top up?

This one is actually pretty easy to analyze theoretically. Let’s say the rain is falling straight down. Obviously, if your car is parked on the side of the road, you’ll see the rain falling straight down. But if you’re driving forward, it’s going to look to you like the rain is slanted backwards. This phenomenon is called aberration. To see it in action, just take a look at the side window next time you’re in a car moving through rain, and you’ll see the slanted streaks left by raindrops; the faster the car, the greater the slant angle. The effect of all this is that driving through rain, if the rain is falling straight down, is pretty much equivalent to the car sitting still and the rain falling at an angle.

The size of the angle, \(\theta\), is determined by two things: the downward velocity of the rain and the forward velocity of the car.

According to the Physics Factbook, a typical speed for a falling raindrop is about \(\unit{10}{\frac{\meter}{\second}}\), or \(\unit{22}{\mileperhour}\) (as long as it falls from a height of more than \(\unit{5}{\meter}\), which was certainly the case in the show). So even in the Mythbusters’ slowest test run, at \(\unit{25}{\mileperhour}\), the slant angle is greater than 45 degrees, meaning that from Jamie’s perspective in the car, the rain was already closer to horizontal than vertical! In the \(\unit{70}{\mileperhour}\) test run, which is probably more believable if you hit the gas as the myth tells you to, the slant angle works out to \(\theta = 72^{\circ}\) — only a measly 18 degrees (1/20 of a full circle) short of being purely horizontal. No wonder they barely got the seat tops wet with that one.

So far I’ve been looking at this situation from an entirely different angle (no pun intended) from Adam and Jamie. Their focus during the show was on the plume of water that flies off the windshield and over the seats of the convertible. Why do I ignore that? Well, to keep the analysis simple, I just assumed that many of the raindrops that miss the windshield will also pass right through the plume as if it weren’t there. Plus, any raindrops that do interact with the plume will only be slowed down — remember that that plume is just water that’s been launched upwards off the windshield (which acts as a ramp), and when an upward-moving raindrop collides with a downward-moving raindrop, they both slow down. The point is that raindrops which do collide with the plume aren’t going to fall on parts of the car that unhindered raindrops won’t. So if, by ignoring the plume, we can calculate that the car seats won’t be getting wet — they won’t be getting wet. Car 1, rain 0.