Fig. k. 



Apparatus for producing simulated step 

 function response in a wind tunnel. 



in wind speed as soon as the puck loses contact 

 with the anemometer cap. 



This procedure was carried out for several 

 values of mean wind, for increasing and decreasing 

 step functions of various amplitudes . The sur- 

 prising result was that the response character- 

 istics were uniform for all wind speeds from 

 2 m/sec to 10 m/sec for both increasing and 

 decreasing step functions. The observed response 

 was, in fact, an exponential function with a 

 time constant identical to the RC time constant 

 of the integrating circuit, which is 0.27 sec. 

 This result holds true, even at the extreme con- 

 dition, for a mean wind of 2 m/sec with a 

 12 m/sec step function. 



This result is both encouraging and disap- 

 pointing. If the pulse output had been recorded 

 as well as the integrated output much more could 

 have been learned about the cups themselves. 

 The requirement for a smoothed voltage into the 

 telemetry" system forced the inclusion of the 

 integrating circuit in the anemometer. While 

 the integrator has masked the response of the 

 cups themselves this is not entirely without 

 virtue since the observed dynamic response of 

 the anemometer is uniform over a wide range of 

 mean wind speeds. Hence, within the limits 

 imposed by this relatively slow response, the 

 instrument has a single and simple dynamic 

 response. The only question remaining is whether 



or not the response is adequate for investigation 

 of turbulent wind. 



FREQUENCY RESPONSE 



As mentioned earlier, one of the more useful 

 means of presenting turbulent wind data is the 

 power spectrum. The reason for desiring to use 

 a frequency scale in preference to a time scale 

 for data presentation is that certain manipula- 

 tions of the data are easier to perform in the 

 frequency domain and frequency data are almost 

 always easier to interpret. The time constant 

 when transformed into the frequency domain 

 becomes the frequency response function. If then, 

 the time constant can be experimentally deter- 

 mined and if the response to a step function is 

 (approximately) exponential the frequency response 

 function w(f) may be written 



W(f) = ^2. = [l+(27Tfk) 2 f l/2 

 U 



(1) 



where f is the component frequency in cycles per 

 second of the turbulent wind, U is the observed 

 amplitude at frequency f, U is the "true" ampli- 

 tude at frequency f and k is the time constant. 

 This shows that the amplitude, U, is attenuated 

 proportionally to l/kf so that at higher fre- 

 quencies the observed amplitude, U Q , becomes 

 smaller. For power spectra the quantity of 

 interest is w2(f ) and this function may be used 

 to correct the observed power spectrum for the 

 attenuation due to the instrument's time con- 

 stant by the formula 



U(f) = 



u 2 (f) 

 w 2 (f) 



(2) 



Fig. 5 shows a plot of W 2 (f) for k = 0.27 

 superimposed on a portion of a typical power 

 spectrum U (f) calculated from observation of 

 wind over Buzzards Bay, Mass. Wind velocity was 

 measured with one of the anemometers described 

 here over a period of about 10 minutes. The 

 velocity signal was sampled 5 times per second so 

 that the highest frequency computed in the power 

 spectrum is 2-5 cps (only a portion of which is 

 shown in Fig. 5). Since the observed power spec- 

 trum attenuates very much more rapidly than the 

 frequency response curve it can be assumed that 

 the frequency response of the anemometer is high 

 enough so that important high frequency components 

 in the wind are not cut off. However, if the 

 observed spectrum is corrected for the effect of 

 the time constant according to Eqn. (2)some modifi- 

 cation of the spectrum does occur with the possi- 

 bility of a secondary peak occurring near 

 f = . k cps . Whether or not such a peak has real 

 meaning can only be determined by careful con- 

 sideration of the statistical reliability of the 

 power spectrum reinforced by the experimenter's 

 own prejudices and preconceived notions as to 

 what he is looking for. 



152 



