Wind Chill

 HS #43 2019.2.14

Wind Chill

Whether bragging or complaining, wind chill adds sensationalism to the forecast, just as does its summer equivalent – the dreaded heat index. As a youngster, the Twin Cities weather forecaster simply said, “Tomorrow the high temperature will be 0 degrees with a 20 mile/hour northwest wind.  That’s all we needed. We could take it from there. Didn’t need a meteorologist instructing us how to dress, when to stock up on groceries, or whether to venture out. We embraced Emerson’s “Self-Reliance” essay without having read it. Heck, Minnesotans don’t need a New Englander telling them how to live. 

Now with melodramatic air, forecasters provide ostensibly crucial new information:  the wind chill will be . What good is that?   Who in Michigan has felt , so what value is the comparison?  

I, on the other hand, as a proud ex-Minnesotan, DO know what feels like.  As a teenager, I occasionally stood out on the front sidewalk in my shirtsleeves just to experience it. Not even a hint of breeze when it’s that cold – the very wind is frozen.  The sky is deep deep blue – bluer than ever a summer sky can be.  The sun pierces through the blue and you can feel it in your eyes in its futile attempt to warm you.  Low in the sky, on each side of the sun, there are two bright spots – sundogs, they are called – the winter equivalent of rainbows, as sunlight reflects off the ice crystals in the air.  

Each inhaled breath – and you breath very slowly – tingles the nostrils. You blink often to keep your eyeballs from freezing. Each step sounds like you are walking on broken glass as you crunch the brittle snow.  Several blocks away two men are talking, and (due to downward-bending of sound waves by the warmer air above) you can hear them as if they are standing beside you.  Another quick glance at the sundogs and then back inside, being careful not to touch the metal doorknob with your bare hands. 

Why the rich experience of cold? After all, the cold we acutely feel is just the absence of heat energy - our ears don’t acutely hear the absence of sound energy.  What we actually feel is the rate at which the body loses (or gains) heat energy. That is why you can safely touch a wooden object in a hot oven, but not a metal one. They are both the same temperature, but metal transfers thermal energy more readily so it feels hotter. 

Isaac Newton was the first to explain how thermal energy moves.   “Newton’s Law of Cooling” states that the rate an object loses heat is proportional to thedifferencein temperature between the object and the surrounding medium. That’s why a pan hot from the oven will quickly cool to warm, but takes a while cooling all the way to room temperature. 

When expressed succinctly and precisely in mathematical symbols, Newton’s discovery is called a differential equation. These describe how something changes with time. My former Hope College colleague, John Van Iwaarden, wrote a textbook explaining them. It’s no stretch to say that differential equations are the single most important way that mathematics is used to describe and predict natural phenomena. Meteorologists give us advanced warning of weather because of differential equations. 

So, now we can better understand wind chill.   Consider standing outside in still air at . Because of the larger difference in temperature between your body and the  air, heat will leave your body faster than in the air, so it feels colder. However, if there is no wind, then that lost body heat warms the air surrounding your body. Since the difference in temperature between your body and the surrounding air is now not quite so extreme, the rate of cooling decreases.  But wind removes that warm blanket of air, so the full difference in temperature is back in effect, and hence the body cools faster. 

So, if the air temperature is  and the wind chill is , then, like your body, a hot car engine will cool faster because of the wind, but it still will never go below the actual air temperature.  Also, wind chill is more pronounced for someone in shirtsleeves or with bare skin than bundled up. (So there are multiple formulas for calculating wind chill.)

Everything make sense? Good. Then on a cold day why will a bowl of boiling water freeze faster than a bowl of lukewarm water?   Try it – it does.