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 \(3 \mathrm{mph}\) or $5
\mathrm{~km} / \mathrm{h}$ ). The hypothetical wind-chill temperature (WCT),
called the wind-chill temperature index (WCTI), is an air temperature
equivalent 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 $\left({ }^{\circ} \mathrm{C}\right)=13.12+0.6215 T-11.37
\mathrm{~V}^{0.16}+0.3965 T V^{0.16}$
where \(T\) is the air temperature in \({ }^{\circ} \mathrm{C}\) and \(V\) the wind
speed in \(\mathrm{km} / \mathrm{h}\) at \(10 \mathrm{~m}\) elevation. Show that
this relation can be expressed in English units as
WCTI $\left({ }^{\circ} \mathrm{F}\right)=35.74+0.6215 T-35.75 V^{0.16}+0.4275
T V^{0.16}$
where \(T\) is the air temperature in \({ }^{\circ} \mathrm{F}\) and \(V\) the wind
speed in \(\mathrm{mph}\) at \(33 \mathrm{ft}\) elevation. Also, prepare a table
for WCTI for air temperatures ranging from 10 to \(-60^{\circ} \mathrm{C}\) and
wind speeds ranging from 10 to \(80 \mathrm{~km} / \mathrm{h}\). Comment on the
magnitude of the cooling effect of the wind and the danger of frostbite
