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<br />tower and other stationary elements of the wind machine also emit <br />sound, the power of which varies with the sixth power of the <br />windspeed. <br /> <br />The noise generated by an aerodynamic dipole is: <br />2 6 <br />W - ApL u n <br />- 3 <br />c <br /> <br />w = <br />A = <br /> <br />p = <br />L = <br /> <br />noise power, W <br />constant characterizing the geometry of the blade <br /> <br />density of air, kg.m-3 <br />a characteristic length of the blade, m <br /> <br />airspeed relative to blade, lTI.s-1 <br />-1 <br />speed of sound, m.S <br />number of blades <br /> <br />u = <br /> <br />c = <br />n = <br /> <br />This may be <br />W <br />2p u 3L 2 <br /> <br />rewritten in dimensionless form as: <br />M3 <br /> <br />ex: <br /> <br />M = Mach number <br /> <br />For any wind machine then, the noise \Olill be emitted almost <br />entirely from the fastest moving part, and noise from other parts <br />may generally be neglected. For a horizontal-axis wind machinE!, <br />this is the blade tips. For a vertical-axis machine it is the <br />center portion of the blades. For any windspeed below cut-in or <br />above cut-out, the relative airspeed is simply the windspeed. <br /> <br />Considering first a horizontal-axis machine in operation, the <br />relative airspeed at the blade tip may be obtained from the <br />relationship <br /> <br />u6 = [( r Q )2 + y2]3 <br /> <br />r = blade radius, m <br />n = blade rotation rate, rad.s-1 <br /> <br />y = windspeed <br /> <br />If we take the first two terms of the binomial expansion, we <br />have <br /> <br />u6 = (m)6 <br /> <br />[1 + 3 (r~ r ] <br /> <br />7 <br />