H = ( A + B * sqrt(S) + C * S ) dT where: H == Heat Loss, kg cals/m²/hr dT == temperature difference (°C), between assumed skin temperature (33°C) and ambient temperature S == windspeed, m/s and the constants, A, B, and C are: Siple Court A 10.45 9.00 B 10.00 10.90 C -1.00 -1.00In a practical sense, with the following definitions, use the following formulas for calculating windchill (Siple's and Court's formulas, rearranging terms and substituting for unit conversions):
For °C and m/s (baseline conditions of 33°C and 1.8 m/s):
Siple: Twc = 33 + ( T - 33 ) ( .474 + .454 sqrt(S) - .0454 S ) Court: Twc = 33 + ( T - 33 ) ( .550 + .417 sqrt(S) - .0454 S ) for S >= 1.79 m/s T < 33 °C
For °F and mph (baseline conditions of 91.4°F and 4 mph):
Siple: Twc = 91.4 + ( T - 91.4 ) ( .474 + .304 sqrt(S) - .0203 S ) Court: Twc = 91.4 + ( T - 91.4 ) ( .550 + .279 sqrt(S) - .0203 S ) for S >= 4 mph T < 91.4 °F Test (Siple): S=20mph, T=20 °F ---> Twc = -10.5 °F
And finally, for folks who prefer °F and knots (baseline conditions of 91.4°F and 3.47 knots):
Siple: Twc = 91.4 + ( T - 91.4 ) ( .474 + .326 sqrt(S) - .0234 S ) Court: Twc = 91.4 + ( T - 91.4 ) ( .550 + .299 sqrt(S) - .0234 S ) for S >= ~3.5 knots (note: 1 mph = .869 knots) T < 91.4 °F
There's some uncertainty concerning the "baseline" values to be used. However, the stated values are likely close enough, and since windchill is only a crude estimate, ...
Court, A., 1948: Windchill. Bull. Amer. Meteor. Soc., 29, 487-493.
Siple, P.A., and C.F. Passel, 1945: Measurements of dry atmospheric cooling in subfreezing temperatures. Proc. Amer. Phil. Soc., 89, 177-199.
Steadman, R.G., 1971: Indices of windchill of clothed persons. J. Appl. Meteor., 10, 674-683.