It is well-known that at the same outdoor air temperature a person is cooled at a faster rate under windy conditions than under calm conditions due to the higher convection heat transfer coefficients associated with windy air. The phrase wind chill is used to relate the rate of heat loss from people under windy conditions to an equivalent air temperature for calm conditions (considered to be a wind or walking speed of 3 mph or 5 km/h). The hypothetical wind chill temperature (WCT), called the wind chill temperature index (WCTI), is an equivalent air temperature equal to the air temperature needed to produce the same cooling effect under calm conditions. A 2003 report on wind chill temperature by the U.S. National Weather Service gives the WCTI in metric units as
WCTI (°C) = 13.12 + 0.6215T – 11.37V0.16 + 0.3965TV0.16
where T is the air temperature in °C and V the wind speed in km/h at 10 m elevation. Show that this relation can be expressed in English units as
WCTI (°F) = 35.74 + 0.6215T – 35.75V0.16 + 0.4275TV0.16
where T is the air temperature in °F and V the wind speed in mph at 33 ft elevation. Also, prepare a table for WCTI for air temperatures ranging from 10 to 260°C and wind speeds ranging from 10 to 80 km/h. Comment on the magnitude of the cooling effect of the wind and the danger of frostbite.
