What human conditions did Steadman's 1979 apparent temperature model simulate?
Robert G. Steadman's 1979 physiological model simulated a reference 1.7 m (5 ft 7 in), 67 kg (147 lb) adult walking at 1.4 m/s (3.1 mph, 180 W/m²) in shade with a 2.5 m/s (5-knot) breeze against a 1.6 kPa baseline vapor pressure (57°F / 14°C dew point). The heat index was not invented by fitting curves to survey data asking people "how hot do you feel?" Instead, Robert G. Steadman modeled a standard human body as a thermodynamic engine:
- Height & Weight: 5 ft 7 in (1.7 m), 147 lb (67 kg)
- Activity: Walking on level ground at 3.1 mph (1.4 m/s), generating 180 W/m² of metabolic heat
- Environment: Shaded from direct sun, exposed to a 5-knot (2.5 m/s) breeze, sea-level barometric pressure
For any air temperature and humidity pair, Steadman solved for the temperature that would require the exact same physiological cooling effort at a reference vapor pressure of 1.6 kPa (a 57°F / 14°C dew point).
Why did Lans Rothfusz fit a 9-term polynomial to Steadman's table in 1990?
Steadman's coupled differential equations had no simple closed-form algebraic expression. In 1990, NWS Southern Region Technical Attachment SR 90-23 by Lans P. Rothfusz introduced a 9-term polynomial regression in $T$ (°F) and $R$ (% relative humidity) that reproduces Steadman's table within $\pm 1.3^\circ\text{F}$ across normal summer ranges.
When does the NWS Rothfusz polynomial require boundary corrections or fallback?
The official NWS Heat Index algorithm switches to a linear Steadman equation whenever the simple average falls below 80°F (26.7°C), subtracts a dry-air adjustment when T ≥ 80°F with RH < 13%, and adds a humid-air adjustment when 80°F ≤ T ≤ 87°F with RH > 85%.
| Condition | Formula Used by NWS | Why |
|---|---|---|
| Simple average < 80°F | Steadman low-temperature linear equation | The 9-term polynomial diverges below 80°F |
| T ≥ 80°F and RH < 13% | Rothfusz polynomial minus dry-air adjustment | Polynomial overestimates apparent heat in desert-dry air |
| T 80°F–87°F and RH > 85% | Rothfusz polynomial plus high-humidity adjustment | Polynomial underestimates evaporative blockage near saturation |
See the full coefficients and the twelve chart cells where the printed NWS chart differs from the equation in How Heat Index Is Calculated, or run any combination directly in our Heat Index Calculator.