Bounds on thickness and loading noise of rotating blades and the favorable effect of blade sweep on noise reduction

The maxima of amplitudes of thickness and loading noise harmonics are established when the radial distribution of blade chord, thickness ratio, and lift coefficient is specified. It is first shown that only airfoils with thickness distribution and chordwise loading distributions which are symmetric with respect to midchord need be considered for finding the absolute maxima of thickness and loading noise. The resulting chordwise thickness and load distributions for these maximum noise conditions require infinite slope at some points along the chord but otherwise are uniform. It is shown that sweeping the blades reduces the thickness and loading noise, but there is no optimum sweep which generates the lowest noise.