Cylindrical array radiator
BACKGROUND OF THE INVENTION 
     The present invention relates to cylindrical array radiators, and more particularly to a cylindrical array radiator with staggered vertical staves. 
     There are two conventional techniques for reducing the undesirable vertical side lobes created by unphased cylindrical arrays. The first method is to baffle the array in the vertical direction. In many applications the baffle is limited in size, and thus effectiveness, due to installation requirements. Often the acoustic properties of the baffle depend on pressure, thereby limiting the general usefulness of this technique for underwater acoustic arrays. 
     Cylindrical arrays are often constructed by placing vertical staves on the face of a cylinder. The second conventional techniques of reducing undesirable vertical side lobes is to design each stave to have very low vertical side lobe levels. In many applications this technique involves relatively complicated design of the individual staves and adds to the complexity of the associated electrical wiring. This problem is compounded by the fact that the vertical side lobe levels of the entire array are generally significantly higher than the vertical side lobe levels of each individual stave. This causes a vertical side lobe level of the entire array which is greater than the vertical side lobe level of an individual stave. 
     The major disadvantage of both techniques is that they add to the size and complexity of the cylindrical array radiator. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention provides a cylindrical array radiator having vertical staves on the circumference of a cylinder. The staves are staggered alternately in the vertical direction by an amount Δz so that every stave is either Δz higher or Δz lower than the two adjacent staves. Δz is chosen such that Δz sin θ=λ/2, where θ is the angle of an undesirable side lobe and λ is the wavelength of the radiated energy. The result is cancellation of the undesirable side lobe. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 is a perspective view of the radiation pattern from a prior art cylindrical array radiator; 
     FIG. 2 is the plot of the vertical beam pattern of a prior art cylindrical array radiator; 
     FIG. 3 is a perspective view of a prior art cylindrical array radiator; 
     FIG. 4 is a perspective view of a staggered stave cylindrical array radiator according to the present invention; and 
     FIG. 5 is a plot of the vertical beam pattern of a staggered stave cylindrical array radiator according to the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     For a cylindrical array radiator the desirable radiation is along the major radiation axis in the horizontal plane as indicated in FIG. 1. However, undesirable radiation occurs along the vertical axis due to the additive effects of the vertical side lobes of each individual stave of the array. FIG. 2 shows a typical vertical beam pattern of such a cylindrical array radiator. 
     Referring now to FIG. 3, a prior art cylindrical array radiator has a housing 10 upon the circumference of which are mounted a plurality of vertical staves 12. Consider an observation point, Q a , on the major radiation axis, the distance from the point, Q a , to each of the end staves is greater than the distance from Q a  to the center stave. The relative distance is given by: 
     
         Δ1.sub.a =R(1-cos φ/2) 
    
     where R is the radius of the cylinder and φ is the active angular aperture of the array. If this distance is as large as several wavelengths, then the energy contributions from different staves will not in general have the same phase. This is because relative phase is determined by relative travel time, which is determined by relative distance to the observation point. Since the total amplitude at any point is the sum of the contributions from each stave, the total amplitude at Q a  is reduced because all of the staves do not contribute in phase. It should be noted that this reduction is necessary in order to create a uniform amplitude over a broad azimuthal angle. 
     Now consider the observation point, Q b , near the vertical axis. The distance from this point to an end stave is greater than the distance to the center stave by an amount ##EQU1## even though Δ1 a  might be greater than many wavelengths, Δ1 b  will be less than a quarter wavelength for values of θ near 90°, and the energy contribution from all the staves will be in phase at Q b . The fact that the individual energy contributions add with equal phases at angles near 90°, and add with unequal phases in the horizontal plane, causes the vertical side lobe levels of the entire array to be significantly greater than the corresponding side lobe levels for each individual stave. 
     FIG. 4 illustrates a cylindrical array radiator which will eliminate these undesirable vertical side lobes. A plurality of staves 40 on the face of the cylindrical housing 41 are staggered in the vertical direction by an amount Δz. This causes the distance from each stave to Q b  &#39; to be unequal to the distance from the adjacent stave to Q b  &#39;. The difference, Δ1 c  in distances from a pair of adjacent staves to Q b  &#39; is: 
     
         Δ1.sub.c =Δz sin θ&#39;. 
    
     If each individual stave has an undesirable side lobe at the angle θ&#39;, then Δz is chosen such that: 
     
         Δz sin θ&#39;=Δ1.sub.c =λ/ 2, 
    
     where λ is the wavelength of the radiated energy. If Δz is chosen such that Δ1 c  =λ/2, then the relative distance from the point Q b  &#39; to adjacent staves is a half wavelength. Consequently, the energy contributions from any two adjacent staves will be 180° out of phase at Q b  &#39; and will exactly cancel. This cancellation will eliminate the undesirable vertical side lobe. 
     A simple example will illustrate how the array of FIG. 4 is built. Suppose that a single test stave is constructed, and its vertical radiation pattern is measured. Further suppose that the single stave vertical radiation pattern exhibits an undesirable vertical side lobe centered at θ=90°. For θ=90°, Δz=λ/2. If every other stave is staggered by a half wavelength, then the energy contributions from each pair of adjacent staves will be 180° out of phase at θ=90°, and the total pressure field will be zero at this angle. 
     FIG. 5 illustrates the measured vertical radiation pattern of a cylindrical acoustic array in which the staves were staggered by a half wavelength. The active angular aperture, φ, was 133° and the radius of the cylinder was 14 wavelengths. Comparing FIG. 5 with FIG. 2 the improvement in vertical side lobe reduction is quite noticeable. 
     In some applications it might be useful to stagger the staves by an amount that changes from stave to stave. Suppose the individual stave radiation pattern exhibits undesirable side lobes at two angles, θ 1  and θ 2 . Then half of the pairs of staves can be staggered by Δz 1  and the other half by Δz 2 . The staggering distances Δz 1  and Δz 2  are given by: 
     
         Δz.sub.1 =λ/2 sin θ.sub.1 
    
     
         Δz.sub.2 =λ/2 sin θ.sub.2 
    
     This technique can be generalized to eliminate all undesirable vertical side lobes if the total number of staves is large enough. 
     The same technique can be used if it is desirable that the cylindrical array radiator operate at more than one frequency. If λ 1  and λ 2  are the wavelengths corresponding to two frequencies of operation, then half the pairs of staves can be staggered by 
     
         Δz.sub.1 =λ/2 sin θ&#39;, 
    
     and the other half staggered by 
     
         Δz.sub.2 =λ.sub.2 /2 sin θ&#39;. Again this technique can be generalized to allow operation over a broad range of frequencies. 
    
     The major advantages of the staggered vertical stave cylindrical array radiator are its simplicity of construction and its increased effectiveness. This radiator does not require a bulky and unpredictable baffle or large staves with complicated drive electronics. Furthermore, the present invention is a much more effective method of reducing energy radiated in the vertical direction.