Friday, June 13, 2014

Fermi Problem Friday: Cars and Lightning

To hear Al and Betty Perry tell it, they were lucky to survive the direct hit from a lightning bolt that struck their pickup. It's true that it provided for one heck of a dramatic video.

 How much danger were they really facing?

Judging by the video below, things could have been much worse had Al and Betty chosen to walk or bike (and ended up at the same place at the exact same time, which would have been pretty unlikely of course). Keep an eye in the tree at the very far right to see a graphic example of lightning's power.

So why weren't Al and Betty, or their truck, blown to bits? There's certainly enough energy in a lightning bolt to obliterate two people. Here's a little Fermi problem style calculation to explain the potential ferocity of a lighting strike:

Lightning bolts typically release about 5 billion joules of energy. So what would that do if it was all deposited in two people?

To begin with, let's estimate that the average couple weigh a combined 150 kilograms.

So if all the energy in a lightning bolt were deposited in a pair of people, that would provide

5 billion joules/150,000 grams= 333,000 joules per gram

Now humans are mostly water, and for every 4.2 joules of energy put in a gram of water, the temperature rises by one degree Celsius.  That means the energy in lightning could potentially raise the body temperature in Al and Betty by

333,000 joules/4.2 joules per degree = 79, 000 degrees (roughly)

That's plenty hot to totally vaporize the two of them. Of course, even people who are directly hit by lightning while standing in the open are not vaporized, primarily because most of the energy passes around a person even in the case of a direct hit. Still, even a tiny fraction of the energy in a lightning bolt is more than enough to cause severe damage and often death.

And yet, despite a vicious hit to their truck, Al and Betty were only dazed. How can a vehicle provide such protection? The short answer is that the conductive metal of the vehicle frame and panels directed the lightning strike around them.

But a vehicle like a truck or car isn't a sealed metal container. Most vehicles have large, non-metallic portions in the form of windshields and side windows. Why wouldn't the lightning pass through the windshield and door glass? Would it matter if a window were open?

Obviously, some electromagnetic energy certainly can pass through your car windows. That's why you can use a cell phone or GPS device from inside your car. There are many differences between lightning and cell signals. But the important difference, as far as life and death goes anyway, is in the wavelength.

Cell phones transmit and receive microwave signals, which have frequencies between one and three gigahertz. "Giga" is the prefix for a billion, so one gigahertz is the same as one billion hertz. The wavelength of a one gigahertz signal can be calculated from the equation

v = f  * l, where v is the velocity of a wave, f is the frequency, and l is the wavelength.

In this case, v is the velocity of light (microwaves are essentially an invisible form of light, or more correctly, microwaves and light are just electromagnetic waves of different wavelengths - any electromagnetic waves we can see is called light), and that's about 300,000,000 meters per second.

The longest wavelength of a cell phone signal is about

 l = v/f = 300,000,000 meters per second/1,000,000,000 waves per second = 0.3 meters = 30 centimeters

Most car windows are much larger than that, and windshields in particular are usually over a meter across. It's oversimplifying a bit, but the reason you can use a cell phone in your car is because the wavelength of cell signal can fit easily through the window.

Lightning is a complicated phenomenon, so you can't assign a single frequency or wavelength to a bolt, but people have often measured the spectrum of frequencies in lightning strikes, and they range from a few kilohertz (thousands of waves per second) to tens of megahertz (tens of millions of waves per second). The highest frequencies have the shortest waves - but are they short enough to squeeze through a car window?

A ten megahertz signal has a wavelength of

l =  300,000,000 meters per second / 10,000,000 waves per second = 30 meters

That's much larger than the opening in a car window or windshield, and most of the energy in a lightning strike is at even lower frequencies (and therefore longer wavelengths).

In short, you're safe from lightning in your car because the waves that make up a lightning bolt are simply too big to fit through the windows.

(Radio stations broadcast in about the same range of frequencies as contained in lighting. You need an antenna on the outside of your car because broadcast radio signals are also too big to fit through car windows.)

While Al and Betty were dazed and temporarily deafened by the blast, the effects probably had nothing to do with the electricity itself, but instead were likely the result of the brilliant flash and accompanying thunder clap, as well as the detonation of their air bags.

The electronics that control their truck (and the air bags) didn't fare so well. That's probably because cars are very good, but not perfect lightning shields. Although the portion bolt that made it through is too small to hurt a person, electronics are much more sensitive than we are. In fact, artificial lightning bolts (typically called electromagnetic pulses or EMPs) are occasionally proposed as a way to disable cars without hurting occupants.

So, the next time you're at an outdoor event when a thunderstorm rolls in, just head for your car or truck. You'll be perfectly safe, even if your vehicle's electronics might not.

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