Math in the Natural Sciences

Math in Meteorology

What is the new formula used for calculating wind chill?

Most people know about wind chill: the temperature your body feels when it is exposed to a certain air temperature combined with a particular wind speed. The higher the wind speed, the “colder” the wind chill temperature and the faster the exposed areas of a person’s body will lose heat (a process known as transpo-evaporation; when moisture evaporates, the surface from which it evaporates loses some heat).

The newest wind chill chart—called the Wind Chill Temperature Index—took over from the old chart (developed in 1945) in the 2001-2002 winter season. The reason for the change was simple: The original wind chill index revolved around heat loss, with a standard set at the chill experienced while standing outside in air moving 4 miles (2 kilometers) per hour. Based purely on temperature and wind—and on how water freezes in plastic containers—the charts were developed in Antarctica by Paul Siple and his fellow explorer, P. F. Passel, back in 1939, partly with the intention of being used in World War II battlefield planning.

Not everyone was thrilled with this simplistic, two-factor interpretation, however. There were pieces missing from the wind chill puzzle, such as the fact that humans constantly generate heat to the lack of wind measurements above 40 and below 5 miles per hour (64 and 5 kilometers per hour). Passel and Siple’s wind speeds were also taken about 33 feet (10 meters) above the ground, making the chart more valuable for a third-floor office than ground level. But the biggest problem overall was that the old wind chill chart could not accurately predict how humans perceive temperature.

Thus, the new wind chill index was created. This chart includes such changes as wind speeds calculated at the average height of a human head (about 5 feet [1.52 meters] above the ground); it is based on a human face model and sundry other more “modern” considerations. The actual general formula for the wind chill has now changed to the following: Wind chill in degrees Fahrenheit = 35.74 + 0.6215T -35.75(V0.16) + 0.4275(V0.16), in which T is the air temperature (in degrees Fahrenheit), and V is the wind speed (in miles per hour).

The biggest difference between the old and new indexes is that the new index usually registers warmer temperatures than the old index. Still, no matter what the equation or chart, when temperatures are icy cold and winds are high, everyone should be careful and bundle up.


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