Wind chill Factors
The information on this page was provided by Canada/U.S. METAR--Mutations of the International Standards and Gene Nygaard.
Wind chill factors are supposed to measure the effect of the combination of temperature and wind speed on
human
comfort. It is important to remember that these do not have the same effect on inanimate objects, or even on other
animals or on plants. Nor is this effect felt by humans who are sheltered from the wind.
Wind chill factors can be expressed as an equivalent temperature on either the Celsius or Fahrenheit scale, or
in units
of power per unit area. In Canada, wind chill factors are often reported as heat loss in watts per square metre.
Wind chill factors are often published as tables. There are many such published tables here in the U.S., and
most of
them don't agree exactly on all the equivalents.
Calculations
The variations in various tables that have been published may be the result of use of different formulas for heat
loss or
different assumptions for skin temperature or calm wind speed, though many are round-off errors from conversions
among the various units used along the way. As near as I can figure out, both the U.S. and Canada us an old wind
chill
formula developed by Paul Siple in the 1930s.
Start with a formula for heat loss, given the air temperature and wind speed. This is Siple's formula:
H = (10.45 + 10×sqrt(v) - v)×(33 - t)
where H is in kilocalories per square metre-hour (kcal/(m²·h), and t is air
temperature in degrees Celsius and wind
speed v is in metres per second, and the 33 °C factor is based on human skin temperature. To convert
this to the
modern units of watts per square metre, which are used in Canada, multiply the result by 4184 J/kcal and 1 h/3600
s
and 1 W s/J. (Note that 4184/3600 is about 1.162, and you can multiply by this number; the above shows where
this
number comes from.) Or, using the same units for t and v, change the formula to:
H (in W/m²) = (12.1452 + 11.6222×sqrt(v) -1.16222×v)×(33 -
t)
[NOTE: constants change if other units used for t or v]
To get the equivalent temperature that is usually used in the U.S., the heat loss at the given temperature and
wind
speed is calculated, and then the temperature is calculated which would give the same heat loss at a low (but not
zero)
wind speed. In the U.S. and Canada the speed used for this is 4 statute miles per hour (1.78816 m/s). A formula
that
will do this is the following, where s equals the skin temperature, either 33 °C or the same
temperature on the
Fahrenheit scale, 91.4 °F, with the result in the same type of degrees:
equivalent temp. = s - (s - t)×(0.474266 +
b×sqrt(v) + c×v)
where the constants b and c depend on the units in which the wind speed
v is measured:
units b c
m/s 0.453843 -0.0453843
km/h 0.239196 -0.0126067
kt 0.325518 -0.0233477
mi/h 0.303444 -0.0202886
I have carried my factors to 6 significant digits, which probably isn't really necessary, except to provide
consistent
results no matter what units are used for t, v, or H. These will most likely
be used in a program or a spreadsheet
anyway, so all the numbers won't have to be entered for each calculation. If you want to round the results to a
whole
number of degrees using an INT function, be careful how that function works with negative numbers; some round
to
the next lower number and some to the number closer to zero. For example, to calculate equivalent temperature in
the
degrees used for t and for t in °C and v in km/h, use:
teq = 33 - (33 - t)×(0.474266+0.239196×sqrt(v) -
0.0126067×v)
for t in °F and v in knots, use:
teq = 91.4 - (91.4 - t)×(0.474266 + 0.325518×sqrt(v) -
0.0233477× v)
IMPORTANT NOTE: These wind chill formulas are not valid at all for wind speeds outside the
range from
1.78816 m/s to 25 m/s (90 km/h, 55.9 mi/h, 48.6 kt). If you write a program to calculate wind chills,
change all speeds higher than 25 m/s to 25 m/s
and all speeds lower than 4 mi/h to 4 mi/h.
To convert between heat loss in watts per square metre and equivalent temperatures, use these formulas:
H = 1300.3 - 14.227 teqF
teqF = 91.4 - 0.0703 H
H = 845.1 - 25.608 teqC
teqC = 33 - 0.03905 H
The formula the National Weather Service uses to compute wind chill is:
T(wc) = 0.0817(3.71V**0.5 + 5.81 -0.25V)(T - 91.4) + 91.4
T(wc) is the wind chill, V is in the wind speed in statute miles per hour and T is the temperature in degrees
Fahrenheit.
The formula to calculate a Celsius wind chill using V as the wind speed in kilometers per hour and T in
degrees Celsius
is:
T(wc) = 0.045(5.27V**0.5 + 10.45 - 0.28V) (T - 33) + 33
These two formulas don't quite agree with each other. For the Fahrenheit-miles per hour formula, the 0.0817 is
the
reciprocal of the heat loss (in the obsolete kcal/(m²·h)) per degree Fahrenheit for a wind speed of 4 mi/h. Doing it
this
way, rounding off this number and each of the other three variables to 3 significant digits each, introduces more
roundoff error than my formulas above which only round off after what is rounded off to 0.0817 by NWS is
multiplied
by the other numbers. I haven't checked for sure, but I think that this simpler version would be truer to the original
formula than the one listed by USA Today: (following their order of elements and notation here)
T(wc) = (0.3V**0.5 + 0.474 - 0.02V)(T - 91.4) + 91.4
