Let's talk about wind chill

It's that time of year again where - depending on where you live - it sometimes gets kind of cold outside.  Sometimes it gets really cold.  Sometimes it's windy.

This leads to a lot of news about the cold, and specifically about the wind.

I overheard a conversation the other day that went more of less like this:

Person A: "Did you hear?  It's supposed to be like -40 degrees tomorrow"
Person B: (skeptically) "Really?"
Person A: "Well, you know, wind chill"

You may have taken part in conversations like this yourself.  I've certainly heard my share of them.

For those of you who understand how the wind chill works, you're maybe wondering why people don't get it.  Well, part of it may be that this is how it's calculated:

Where the variables to be entered are ambient temperature and wind velocity (speed).

The result is just a number that is expressed in a different scale that people widely understand (temperature). It's very easy to just take a wind chill number at face value and interpret it as a raw temperature.

In fact, wind chill is somewhat designed to do just that.  It is meant to be a perceptual scale, to give an idea of how cold the air feels to a human.  It's a harder measurement problem than it might first appear.

Let's take a step back.  If you've ever taken a class on meteorology (I'd highly recommend it, if you have the opportunity), you might have encountered the following question in some form or another:

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Bob and Sally live in the Rocky Mountains near a particular canyon that - especially in the winter - has the effect of producing exceptionally strong winds.  One day during winter break Bob and Sally have run out of things to do, and are staring out the window at some light snow flurries that have just started to fall.  The TV is on, and they hear the local weatherman reporting the current temperatures.

"The current air temperature is 34 degrees, but the current temperature with wind chill is only 15 degrees."

Bob suddenly has an idea to cure their boredom.  "Let's put a glass of water out on the porch and then watch it freeze!"

Sally looks at the thermometer mounted to the porch and confirms what she's just heard from the weatherman - the air temperature is 34 degrees.  The wind, however, is quite strong, and she has no problem believing that the temperature with wind chill might only be 15 degrees.  "That won't work, water doesn't freeze above 32 degrees!"

A argument ensues.  Which child is correct?
>>

Think about it for a while, because it's a fun thought experiment.  I ask this question of people occasionally every winter, and far and away people tend to agree with Bob.  Interestingly enough, Sally is the one who is correct.  We'll come back to it.

Temperature is a fairly complex idea, but it's also pretty easy to measure objectively (the hard part was all the early work in establishing scales, etc, that is).  The problem is that a person can be standing in an open field in 20 degree weather and no wind and have a completely different experience than someone standing in the same field at the same temperature with 50mph winds.

Those of you who have never been around Chicago during the winter months might only have a vague idea of why it's really called the Windy City.  I've often said that I'd take much colder temperatures without wind than less cold temperatures with wind, any day.  I almost just typed it without thinking it, because it's something that you just learn to say in a knee-jerk sort of way:

"The wind is great at just ripping the heat right out of you."

Does anyone out there have a freezer with, like, a glass door?  I kind of want one now, but it seems like they wouldn't be great except for things like this.  Put a glass of room temperature water in it and then pull up a chair.

The water isn't going to freeze right away, but it will freeze eventually.  Anyone waiting for a tray of ice cubes to set knows this well.

Now, watch a few episodes of any random Food Network cooking challenge show and you'll likely see someone use a blast chiller.  You put stuff in, and bam! it's frozen pretty quick.  It's not instant, but certainly faster than your freezer at home.  What's the difference?

Well, it's in the name.  A blast chiller is just a freezer (sure, temperature can vary with different units, but temperature could be held constant across devices and the blast chiller would still work quicker), but instead of just making something cold by looking at it really hard for a while (like my freezer), it blasts cold air over the thing being chilled.

The wind chill in a freezer is non-existent, because there is no wind.  The wind chill in a blast chiller is, well, more extreme than that.

The reason why people aren't going out to spend more money on blast chillers instead of freezers is because we're usually fine with waiting an hour or two for our ice cubes.  Time isn't a huge factor, and a freezer will eventually get the job done.

What's happening when you put some water cubes in the freezer?  You might say, "well, the freezer is making them cold."

More accurately, the heat in the water is being lost to the cold air of the freezer.

Most accurately, the freezer-water system is tending toward equilibrium.

Two things in a system at different temperatures means that the warmer thing will give up heat to the cooler thing until they're the same temperature.  So, your freezer will get a little warmer, and the water cubes will (eventually) turn into ice cubes.

Now, as a thought experiment, what would happen if you made a big pot of chili, and put some of the warm leftovers (in a freezer safe container) into your freezer. Or put all the chili in there.  Make some water cubes at the same time.  Make all the water cubes you can.  Make them with boiling water.  If you put that much warm stuff in there, the system should equalize on the warm side of the freezing line, right?

Now we're getting somewhere.  It should not be a surprise that if you come back a day or so later, the water cubes and the chili will all be frozen.  Take that, warm stuff, says your freezer.  Install some glass in the door so next time you can watch me pwn all these water cubes.

Your freezer might have had to work a little harder than normal, but the reason this worked is that your freezer isn't just a cold box (give it some thought, though - a century ago, an ice box would not have been talking to you about the l33t pwnage it just unleashed on those water cubes, as it probably would have succumbed to the heat).  Your freezer has a motor, and can magically make the air inside it cooler (okay, enough asides, but most of you probably have no idea how your freezer actually works to make air colder, at which point you're viewing it as magic - it's a hard problem that you should try to understand, there's a reason that boiling water was one of the first things we were capable of doing as a species but that freezing water artificially took us until the last century).

Because your freezer has a motor, it can regulate temperature.  As long as it is plugged in and has power it can work its magic against pretty much anything.  Give it time and it will get things to a certain temperature.

Magic aside, this should make sense to you.  You do this all the time, and probably take it for granted.

If you understand this (and maybe even if you don't), you should see why humans are able to go outside when it's 50 degrees without dying.

You see, your body has a temperature range it wants to stay at, just like your freezer.  Put a whole bunch of boiling water in your freezer and it will bring it to the temperature it's set at.  Eat a whole bunch of ice cream and your stomach won't freeze, your body will simply regulate itself and keep your temperature where it wants it to be (upper 90s, etc).

When you stand outside in a 20 degree field with no wind, the air around you is acting like the freezer.  It's trying to freeze you, and bring you to 20 degrees.  Your body, in the upper 90s, is going to lose some heat, and that heat is going to warm up the air around you.  The process of you heating up the air around you and that air heating up the air around it and so on and so on is a slow one, just like your freezer trying to freeze some water cubes.

At the same time, your body is expending energy to produce heat to keep you warm.  It's fighting the heat loss, and if it can produce heat faster than you're losing it, then you're perfectly fine.  You're technically losing heat all the time on a 70 degree day, but you're probably not too worried about it.

Heat is lost through exposure with the air, which is why it's a good idea to a) wear clothes and b) minimize skin contact with the air.  Gloves, hats, etc.  Think about it, though, what do coats actually do for you?  You know this, you've probably just never said it in these terms.  Coats don't produce heat (well, awesome ones might), they just trap the heat that your body is producing and slow the loss of it to the air around you.

So you're standing around in a field having a heat fight with nature.  Good for you.  Nature is a lot like the freezer, even on a day with no wind.  It has a lot more reserve of cold air than you have heat, and unless the temperature rises nature is probably going to win.  The result?  Human cubes.  Ice human?  Take your pick.

The point is, though, that it will probably take a little bit of time.  You can hang out for a bit fighting the air with your heat, but at some point you'll probably realize you're losing and go inside for a cup of hot chocolate.

Now let's imagine the same situation, but with a bit of wind.  Remember that pocket of air that you're warming with your body that then has to warm the air around it?  That slow process?  Well, that pocket of warmer air just got swept away by some wind, and replaced by air that is just as cold as the air before you started warming it.  Oh, you'll just warm that, too?  Oh wait, it's gone.

Standing outside fighting the cold with your body heat on a windy day is not like being in a freezer - it's like being in a blast chiller.  Nature can cool you down a lot quicker with wind, because that wind is constantly replenishing the cold air around you and pulling away any air that you might have heated.

But how much can nature cool you down?  Now we're back to Bob and Sally's argument.

Temperature, and particularly heating and cooling, is all about equilibrium.  If we turned your refrigerator into a blast refrigerator it wouldn't start freezing your food (unless you turned down the temperature, or put stuff in the waaaay back), it would just get them to the temperature your fridge was set at, faster.

Imagine that while fighting nature the first time you decide against going in to get that cup of hot chocolate.  Days later, your body is found frozen, fist still held defiantly against the cold as if in mid-shake.  What temperature is it at?  Well, whatever ambient is - 20 degrees in this example.

How about the second fight, with wind?  Your body, found frozen days later will be what temperature?  Ambient.  20 degrees.  It just got there faster.

In the same way, a glass of room temperature water placed outside will eventually get to ambient temperature.  It has no magic motor or circulatory system, so it's not really going to put up a fight.  The question of how fast it will freeze (holding starting temperature constant) is really only up to a few factors. The main factors?  Ambient air temperature, and wind speed.

A higher wind speed can cool (or heat) a thing faster, but it can't cool (or heat) a thing beyond the temperature of the air around it.  It is simply a tool of the equilibrium.

Wind chill, then, is trying to paint a picture of how fast your body will be brought down to equilibrium. What's the equilibrium temperature, you ask?  Well, if you're talking about wind chill (wind chill only works as a calculation below 50 degrees) it's probably below 98.6, so...low enough to kill you (with time).

Your body isn't completely defenseless, though.  Well before nature kills you, your body will start to sacrifice parts for the whole.  Do you know what needs to keep working to stop you from dying?  The stuff in your torso.  Do you know what doesn't need to keep working to stop you from dying?  Well, pretty much everything else.

When your body stops pumping heat (via blood) out to your extremities, you've probably made some poor decisions.  You're in the danger zone, and that danger is frostbite.  How fast will frostbite set in?  Well, that depends on two things, ambient air temperature and wind speed.

Wind chill is based on those same two factors because both of these things are tapping the same underlying quantity: how quickly is nature going to kill you.  Give nature enough time and it always will.

Because this one quantity (wind chill) is based on two others (ambient and wind), we can also make a pretty cool graph of it.  Thankfully, though, we don't have to, because the NOAA already did, and it's public domain.  So, here you go:

Now stay warm.