The aerodynamic friction between air and sea is an important part of the momentum balance in the development of tropical cyclones. Measurements of the drag coefficient, relating the tangential stress ( frictional drag) between wind and water to the wind speed and air density, have yielded reliable information in wind speeds less than 20 m/s ( about 39 knots). In these moderate conditions it is generally accepted that the drag coefficient ( or equivalently, the "aerodynamic roughness'') increases with the wind speed. Can one merely extrapolate this wind speed tendency to describe the aerodynamic roughness of the ocean in the extreme wind speeds that occur in hurricanes ( wind speeds greater than 30 m/s)? This paper attempts to answer this question, guided by laboratory extreme wind experiments, and concludes that the aerodynamic roughness approaches a limiting value in high winds. A fluid mechanical explanation of this phenomenon is given.