There are two things you need to consider: temperature and wind speed. Just as a convection oven can cook things faster by moving hot air around food, a strong wind will chill your body faster by exposing your body to more cold air. When planning for exposure to the elements, you need to look at the wind chill index: This is what the cold feels like to your body, and is an accurate measurement for determining how fast your body will freeze.
The formula for calculating wind chill is a bit complicated, but you can use the National Weather Service's calculator here:
Note that this is the North American Wind Chill Index, formulated in 2001 to simulate effects of weather on human skin. There are other systems, but for determining the chance of frostbite this method is the most accurate.
Let's put this into perspective:
A wind chill below 0 degrees Fahrenheit (-18 Celsius) will freeze exposed skin in about five minutes. Hawaii is on average the warmest state in the country, but their record lowest temperature is still only 12 degrees Fahrenheit. With only a five MPH wind, the wind chill would be -4.
A wind chill below -20 F (-29 C) will freeze exposed skin in a minute or less. At a temperature of 0 degrees, the wind would only need to be blowing at 20 miles an hour to reach a wind chill of -22. Over half of the U.S. experience these conditions at least once during the winter.
A wind chill below -70 F (-57 C) will freeze skin in under 30 seconds. Thirty-five of the fifty states have experienced record low temperatures that combined with wind of 35mph or less have reached this category.
Posted 2879 day ago