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with s defined by Equation (5.50).

The form of the resulting normalized cross-correlation function, pu(r1, r2, t) = K0u(r1, r2, t)/ou, is illustrated in Figure 5.18 for the case considered in Example 5.2, taking ri = i0 m and r2 = 20 m. In Figure 5.2i, the rotationally sampled cross spectrum for this case is compared with the rotationally sampled single point spectra or 'autospectra' at these radii. It can be seen that the form of the cross spectrum curve is similar to that of the autospectra with a pronounced peak at the rotational frequency roughly midway between the peaks of the two autospectra. At higher frequencies, however, the cross spectrum falls away much more rapidly.

The evaluation of the the power spectrum of the blade root bending moment is, in practice, carried out using summations to approximate to the integrals in Equation (5.49), as follows:

Sm(n) = (ipQ dC) X X SI(rj, rk, n)c(r;)c(rk)rjtft*r)2 (5.52)

Integral length scale, L = 73.5 m Mean wind speed = 8 m/s Speed of rotation = 30 r.p.m.

Integral length scale, L = 73.5 m Mean wind speed = 8 m/s Speed of rotation = 30 r.p.m.

0.1 1 Frequency, n (Hz, logarithmic scale)

Figure 5.21 Rotationally Sampled Cross Spectrum of Longitudinal Wind Speed Fluctuations at 10 m and 20 m Radii Compared with Auto Spectra: log-log Plot

0.1 1 Frequency, n (Hz, logarithmic scale)

Figure 5.21 Rotationally Sampled Cross Spectrum of Longitudinal Wind Speed Fluctuations at 10 m and 20 m Radii Compared with Auto Spectra: log-log Plot

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