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14 Approx. Spiral Angle (a) (b) Figure 1. Notional 90-element circular spiral array with 15 spokes of 6 elements each and inner and outer radii of 19.7 and 47.6 in. (0.5 m and 1.2 m), respectively: (a) array pattern, (b) directivity pattern of array projected on x,y plane parallel to array plane and situated 20 ft (6 m) in front of it. In Figure 5, the spot width is illustrated for the major and 3.2.3 Balance Between Array Aperture minor axes of the alternative arrays shown in Figure 2 [i.e., and Spherical Spreading Loss Ellipse 1, Ellipse 2, and the 7 ft (2.1 m) circular array] as a ref- erence. Given the design requirement of constant area for all As the truck sources pass by the microphone array, there is arrays, the degradation in horizontal beam width for the ben- a sound level change at the array microphones that is simply efit of vertical discrimination is clearly seen. due to the spherical spreading loss resulting from the varying D= 7 ft A= 9.1 ft B= 5.37 ft A= 11.8 ft B= 4.1 ft (a) Circular (b) Ellipse 1 (c) Ellipse 2 Figure 2. Patterns for various arrays of 70 elements distributed around 14 spokes of 5 elements each: (a) circular spiral, (b) Ellipse 1, (c) Ellipse 2. A is the major axis, B is the minor axis. The spiral angle is 0.5 degrees.
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15 (a) Circular (b) Ellipse 1 (c) Ellipse 2 Figure 3. Directivity pattern projections on the parallel x,y plane 20 ft (6 m) in front of the array plane shown in Figure 2 at 1000 Hz. 100 Array Length or Diameter La=4 ft La=6 ft La=8 ft 10 La=10 ft Spot Width, ft La=12 ft 1 0.1 100 1000 1000 0 Frequency, Hz Figure 4. Width of the focus spot of arrays of various lengths or diameters as function of frequency at range of 20 ft (6 m).
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16 100 Circular Ellipse 1:Major Ellipse 1:Minor Ellipse 2:Major 10 Ellipse 2:Minor Spot Width, (-6dB), ft 1 0.1 100 1 000 10000 Frequency, Hz Figure 5. Total width of the -6 dB-down focus spots for major and minor axes of arrays shown in Figure 2. distance. Ignoring possible effects of source directivity, which profile can be estimated. Figures 7 and 8 provide these approx- are probably of little concern in the 250 Hz region of interest, imate profiles for Ellipses 1 and 2. In all cases, the closest point this variation in the sound level provides some localization of approach (CPA) is 20 ft (6 m). along the truck. Figure 6 illustrates this effect. The -6 dB-down These sketches show that spreading loss provides added dis- points for the passby are indicated along with the -6 dB-down crimination as the horizontal directivity is reduced to provide points (at 250 Hz) for the three arrays that are shown in Fig- for an increased vertical dimension of the array. One cannot ure 2. Although the combined effect of spreading loss and arbitrarily increase the horizontal dimension because this directivity gain has not been calculated, the approximate sound would result in degradation of the side lobe structure. 5 Variation in SPL, dB 0 -5 Range - Limited Ellipse 2 -10 Ellipse 1 Circle -15 -80 -60 -40 -20 0 20 40 60 80 Cross-Range, ft Figure 6. Horizontal profile of sound pressure level (SPL) due to passby of simple source at 20 ft (6 m) from array compared with cross-range apertures of array alternatives at 250 Hz.