The formula used in the U.S. and Canada to express the combined effect of wind and low temperature on how cold it feels was changed in November 2001. Many had felt that the old formula for equivalent temperature, derived in the 1960s from Siple and Passel's flawed but quite useful Wind Chill Index, unnecessarily exaggerated the severity of the weather. The new formula is based on a mathematical model of heat flow from the upwind side of a head-sized cylinder moving at walking speed into the wind. The paper details the assumptions that were made in generating the new wind chill charts. It also points out weaknesses in the concept of wind chill equivalent temperature, including its steady-state character and a seemingly paradoxical effect of the internal thermal resistance of the cylinder on comfort and equivalent temperature. Some improvements and alternatives are suggested.