Example mean Doppler shift data fitted with 3rd order polynomial curve ͑ y ͒ . Line indicates true CW frequency; ‘P’ indicates crossover point. Data taken from ‘horizontal’ rotor ensonification at 0.5 m. 

Contexts in source publication

Context 1

... the fan was turned off ͑ and it was verified that it therefore contributed no appre- ciable noise to recordings ͒ and measurements taken over a period of 3 s, during which time the rotor could be consid- ered to be rotating with a constant angular velocity. The Doppler shift signatures made by moving blades at a distance of 0.5 m were assessed using a Continuous Wave, Constant Frequency ͑ CW CF ͒ source tone of 40.7 kHz. This was emitted via a MA40B8R ͑ Murata Manufacturing Co., Ltd., Kyoto, Japan ͒ transducer, through a tone generator, situated opposite the turbine. Transducer beam angle was 50°, similar to the beam angle of some bat species ͓ e.g., the FM bat Eptesicus fuscus at 40° ͑ Wotton and Jenison, 1997 ͔͒ , giving a beam diameter of approximately 0.4 m at 0.5 m distance. The transducer was placed in horizontal juxtaposition with a cali- 1 brated, flat response 40BF microphone and 26AC preamp- 4 Љ lifier with 12AK power module ͑ GRAS Sound & Vibration, Holte, Denmark ͒ ͑ frequency range 2 Hz–100 kHz ͒ and a high speed A602fc ͑ Basler AG, Ahrensburg, Germany ͒ video camera set to capture at a rate of 60 frames per second. The camera was positioned to capture roughly the same area of rotor as was ensonified by the transducer. The turbine rotor was then ensonified during operation at one of the following angles to the source: ͑ a ͒ ‘horizontal’, ͑ b ͒ ‘lateral top’, ͑ c ͒ ‘lateral mid’, or ͑ d ͒ ‘lateral bottom’ ͑ Fig. 1 ͒ , accurately aligned with the assistance of a low power laser. The reflected echo was recorded and time-synchronized with the motion capture via a USB-6251 ͑ National Instruments Corporation, TX, USA ͒ DAQ card sampling at a rate of 1250 kS s −1 at 16-bit resolution, over a 3 s period, which enabled exact blade movements and positions to be corre- lated with any Doppler shift patterns returned to source. The operational rotor itself was verified not to contribute to the ambient sound in the ultrasonic frequency band. All recorded data were saved directly to a PC in uncompressed .wav file format and were processed using AUDITION 1.0 ͑ Adobe Systems, Inc., CA, USA ͒ and analyzed using MATLAB 2009b ͑ The MathWorks, Inc., MA, USA ͒ . Moving turbine blades were found to produce Doppler shift signatures that varied according to the angle of rotor ensonification and blade position at the point of reflection. Figure 2 describes the Doppler shift signatures for all angles ensonified, indicating the blade positions resulting in shift portions for each blade sweep. In Fig. 2, Doppler shift portions have been segmented ͑ A, B, C, etc. ͒ and the nature of blade movement resulting in these portions detailed beneath the corresponding signature sonogram. For example, segment ‘A’ of the horizontal shift corresponds to movement of the blade’s leading edge from a position above the source to a position parallel with the source; segment ‘B’ corresponds to the blade becoming parallel with the source; segment ‘C’ corresponds with movement of the blade’s trailing edge from the parallel position to one below the source. The extent of the Doppler shift deviation from the mean shift varied between angles; ‘horizontal’ shift ranged between Ϯ 25 Hz, ‘lateral top’ shift ranged between Ϯ 595 Hz, ‘lateral mid’ shift ranged between Ϯ 785 Hz and ‘lateral bottom’ shift ranged between Ϯ 730 Hz. Overall, sound reflected from the operational rotor from the horizontal aspect demonstrated slight negative Doppler shift, from the lateral top aspect demonstrated negative shift, from the lateral mid aspect demonstrated slight positive shift and from the lateral bottom aspect demonstrated positive shift. Since an incoming bat-like echolocation pulse approximately 2–6 ms ͒ is much shorter than the blade sweep pass period for this turbine model at low wind speed ͑ approximately 100 ms ͒ , an approaching bat would receive only short samples of the Doppler shift produced by the moving blades. As the extent of the shift observed in these short echoes would depend on the exact blade position at the point of echo reflection it is useful to simulate random sampling of the rotor Doppler shift pattern using a Monte Carlo method. This would allow an estimation of the number of pulse echoes an approaching bat would need to receive in order to determine the true nature of blade movement. To do this, five single blade sweep signatures were extracted from the CW echo data set and had the true CW frequency removed by applying a second order Butterworth band stop filter. Each single signature was divided into ten equal 10 ms segments around a common point, which was taken as the position that the shift sweep crossed the true CW frequency ͑ see Fig. 3 ͒ . A fast Fourier transform ͑ FFT ͒ was then applied to each segment and the frequency of peak energy obtained. The series of ten values for frequency of peak energy was then averaged over five blade sweeps and to this mean shift data a polynomial ͑ 3rd order ͒ curve was fitted, as shown in Fig. 3. To simulate CF sampling, the curve function was applied to sample the frequencies at random time intervals over the course of a single blade sweep generated using MAT- LAB’s random number generator function. Sampled frequencies were generated in increasingly greater numbers ͑ i.e., more echoes per blade sweep ͒ and the mean frequency extracted until the sample size was sufficient for the resulting mean to converge to the mean shift of the signature ͑ within an error margin of Ϯ 10 Hz ͒ . However, some bat species employ a Frequency Modulated ͑ FM ͒ echolocation strategy. For FM simulations, an additional random shift of between Ϯ 200 Hz was combined in order to take into account the more broadband nature of the FM pulse and hence the greater potential for variation in frequency of peak energy. All Monte Carlo simulations were run 20 times to obtain an average number of samples required to converge. Simulation results revealed that, for CF bat-like echoes, the number of samples required to converge to the mean shift per blade pass was 320 Ϯ 121 for ‘horizontal’ ensonification, 150 Ϯ 105 for ‘lateral mid’, 55 Ϯ 16 for ‘lateral top’ and 100 Ϯ 78 for ‘lateral bottom’. For FM simulations, the number of samples required to converge to the mean shift per blade pass was 330 Ϯ 123 for ‘horizontal’ ensonification, 200 Ϯ 91 for ‘lateral mid’, 190 Ϯ 143 for ‘lateral top’ and 150 Ϯ 78 for ‘lateral bottom’. Nearly all cases showed a high degree of variance in the number of samples required for convergence. As bats employ a set duration ultrasonic pulse to ‘sample’ an operational rotor, it is useful to experimentally measure the information contained in such echoes reflected from turbine blades in order to compare with simulation predictions. In order to produce consistent, accurately replicable pulses for analysis, an artificial bat echolocation pulse was simulated, modeled on the FM pulse of a common pipistrelle bat ͑ Pipistrellus pipistrellus ͒ ͑ see Fig. 5 ͒ . The equation used to create this pulse, Y , over time t , is defined as: Y ͑ t ͒ = A ͑ t ͒ · ␭ ͑ t ͒ . ͑ 1 ͒ Time t is divided into four segments, t 0 : t 1 ; t 1 : t 2 ; t 2 : t 3 and t 3 : t end . The amplitude modulation of the pulse, A ͑ t ͒ , is varied over three portions of the pulse and is defined ...

Context 2

... to rotate freely up to a speed of 10.5 rad s −1 , measured by stroboscope, consistent with low wind speeds of 4.1 m s −1 ͑ previous research has found bat mortality to be highest on nights of wind speed less than 6 m s Arnett et al. , 2008; Horn et al. , 2008 measured by anemometer. At this point the fan was turned off ͑ and it was verified that it therefore contributed no appre- ciable noise to recordings ͒ and measurements taken over a period of 3 s, during which time the rotor could be consid- ered to be rotating with a constant angular velocity. The Doppler shift signatures made by moving blades at a distance of 0.5 m were assessed using a Continuous Wave, Constant Frequency ͑ CW CF ͒ source tone of 40.7 kHz. This was emitted via a MA40B8R ͑ Murata Manufacturing Co., Ltd., Kyoto, Japan ͒ transducer, through a tone generator, situated opposite the turbine. Transducer beam angle was 50°, similar to the beam angle of some bat species ͓ e.g., the FM bat Eptesicus fuscus at 40° ͑ Wotton and Jenison, 1997 ͔͒ , giving a beam diameter of approximately 0.4 m at 0.5 m distance. The transducer was placed in horizontal juxtaposition with a cali- 1 brated, flat response 40BF microphone and 26AC preamp- 4 Љ lifier with 12AK power module ͑ GRAS Sound & Vibration, Holte, Denmark ͒ ͑ frequency range 2 Hz–100 kHz ͒ and a high speed A602fc ͑ Basler AG, Ahrensburg, Germany ͒ video camera set to capture at a rate of 60 frames per second. The camera was positioned to capture roughly the same area of rotor as was ensonified by the transducer. The turbine rotor was then ensonified during operation at one of the following angles to the source: ͑ a ͒ ‘horizontal’, ͑ b ͒ ‘lateral top’, ͑ c ͒ ‘lateral mid’, or ͑ d ͒ ‘lateral bottom’ ͑ Fig. 1 ͒ , accurately aligned with the assistance of a low power laser. The reflected echo was recorded and time-synchronized with the motion capture via a USB-6251 ͑ National Instruments Corporation, TX, USA ͒ DAQ card sampling at a rate of 1250 kS s −1 at 16-bit resolution, over a 3 s period, which enabled exact blade movements and positions to be corre- lated with any Doppler shift patterns returned to source. The operational rotor itself was verified not to contribute to the ambient sound in the ultrasonic frequency band. All recorded data were saved directly to a PC in uncompressed .wav file format and were processed using AUDITION 1.0 ͑ Adobe Systems, Inc., CA, USA ͒ and analyzed using MATLAB 2009b ͑ The MathWorks, Inc., MA, USA ͒ . Moving turbine blades were found to produce Doppler shift signatures that varied according to the angle of rotor ensonification and blade position at the point of reflection. Figure 2 describes the Doppler shift signatures for all angles ensonified, indicating the blade positions resulting in shift portions for each blade sweep. In Fig. 2, Doppler shift portions have been segmented ͑ A, B, C, etc. ͒ and the nature of blade movement resulting in these portions detailed beneath the corresponding signature sonogram. For example, segment ‘A’ of the horizontal shift corresponds to movement of the blade’s leading edge from a position above the source to a position parallel with the source; segment ‘B’ corresponds to the blade becoming parallel with the source; segment ‘C’ corresponds with movement of the blade’s trailing edge from the parallel position to one below the source. The extent of the Doppler shift deviation from the mean shift varied between angles; ‘horizontal’ shift ranged between Ϯ 25 Hz, ‘lateral top’ shift ranged between Ϯ 595 Hz, ‘lateral mid’ shift ranged between Ϯ 785 Hz and ‘lateral bottom’ shift ranged between Ϯ 730 Hz. Overall, sound reflected from the operational rotor from the horizontal aspect demonstrated slight negative Doppler shift, from the lateral top aspect demonstrated negative shift, from the lateral mid aspect demonstrated slight positive shift and from the lateral bottom aspect demonstrated positive shift. Since an incoming bat-like echolocation pulse approximately 2–6 ms ͒ is much shorter than the blade sweep pass period for this turbine model at low wind speed ͑ approximately 100 ms ͒ , an approaching bat would receive only short samples of the Doppler shift produced by the moving blades. As the extent of the shift observed in these short echoes would depend on the exact blade position at the point of echo reflection it is useful to simulate random sampling of the rotor Doppler shift pattern using a Monte Carlo method. This would allow an estimation of the number of pulse echoes an approaching bat would need to receive in order to determine the true nature of blade movement. To do this, five single blade sweep signatures were extracted from the CW echo data set and had the true CW frequency removed by applying a second order Butterworth band stop filter. Each single signature was divided into ten equal 10 ms segments around a common point, which was taken as the position that the shift sweep crossed the true CW frequency ͑ see Fig. 3 ͒ . A fast Fourier transform ͑ FFT ͒ was then applied to each segment and the frequency of peak energy obtained. The series of ten values for frequency of peak energy was then averaged over five blade sweeps and to this mean shift data a polynomial ͑ 3rd order ͒ curve was fitted, as shown in Fig. 3. To simulate CF sampling, the curve function was applied to sample the frequencies at random time intervals over the course of a single blade sweep generated using MAT- LAB’s random number generator function. Sampled frequencies were generated in increasingly greater numbers ͑ i.e., more echoes per blade sweep ͒ and the mean frequency extracted until the sample size was sufficient for the resulting mean to converge to the mean shift of the signature ͑ within an error margin of Ϯ 10 Hz ͒ . However, some bat species employ a Frequency Modulated ͑ FM ͒ echolocation strategy. For FM simulations, an additional random shift of between Ϯ 200 Hz was combined in order to take into account the more broadband nature of the FM pulse and hence the greater potential for variation in frequency of peak energy. All Monte Carlo simulations were run 20 times to obtain an average number of samples required to converge. Simulation results revealed that, for CF bat-like echoes, the number of samples required to converge to the mean shift per blade pass was 320 Ϯ 121 for ‘horizontal’ ensonification, 150 Ϯ 105 for ‘lateral mid’, 55 Ϯ 16 for ‘lateral top’ and 100 Ϯ 78 for ‘lateral bottom’. For FM simulations, the number of samples required to converge to the mean shift per blade pass was 330 Ϯ 123 for ‘horizontal’ ensonification, 200 Ϯ 91 for ‘lateral mid’, 190 Ϯ 143 for ‘lateral top’ and 150 Ϯ 78 for ‘lateral bottom’. Nearly all cases showed a high degree of variance in the number of samples required for convergence. As bats employ a set duration ultrasonic pulse to ‘sample’ an operational rotor, it is useful to experimentally measure the information contained in such echoes reflected from turbine blades in order to compare with simulation predictions. In order to produce consistent, accurately replicable pulses for analysis, an artificial bat echolocation pulse was simulated, modeled on the FM pulse of a common pipistrelle bat ͑ Pipistrellus pipistrellus ͒ ͑ see Fig. 5 ͒ . The equation used to create this pulse, Y , over time t , is defined as: Y ͑ t ͒ = A ͑ t ͒ · ␭ ͑ t ͒ . ͑ 1 ͒ Time t is divided into four segments, t 0 : t 1 ; t 1 : t 2 ; t 2 : t 3 and t 3 : t end . The amplitude modulation of the pulse, A ͑ t ͒ , is varied over three portions of the pulse and is defined ...