10-9] RADOMES 531 



This represents two current standing waves in space and time quadrature. 

 That is to say, the first has two current maximums on opposite sides of the 

 radiating circle, and the second has current maximums where the first wave 

 is zero. Further, the first standing wave achieves its maximum value in 

 time when the second is at zero. The four current maximums at each 

 quadrature of the circle may now be considered an array of four elementary 

 dipole radiators. This convenient mathematical model of the spiral antenna 

 radiates in a manner similar to the antenna itself, and thus its use has been 

 justified experimentally. Using the four-element array set in a ground 

 plane, the normalized radiation pattern will be found to be^^ 



p = \ cos2 ^[1 + cos (sin Q)Y (10-17) 



to a circularly polarized detector. For a linearly polarized detector, 

 however, 



p = cos2 ^[cos (sin Q)Y (10-18) 



when the pattern is measured perpendicular to the plane of the polarization 

 of the detector and 



p = cos^^ (10-19) 



when the pattern is measured in the plane of the detector polarization. 

 These patterns give beamwidths of 77°, 68°, and 90° respectively. A some- 

 what improved model of the spiral may be had by replacing the short dipole 

 radiator elements by half-wave dipole radiators. The effect is to reduce the 

 90° beamwidth of Equation 10-19 to 78°, which is closer to the actual 

 measurements on the spirals. 



Application. Electrical characteristics such as these find application 

 to antennas for direction finding or possibly for semiactive missile guidance. 

 As a specific example, a cluster of four nonmoving geometric spiral antennas 

 could be used in the nose of a small semiactive, homing missile giving 

 steering information in up-down, left-right coordinates. With a typical 

 beamwidth of 70° and with rigidly mounted antennas, low-accuracy steering 

 information is available from the antennas over plus or minus 70° of 

 azimuth and elevation for proportional navigation, etc. Information from 

 the antennas may be collected by standard monopulse or sequential lobing 

 techniques. 



10-9 RADOMES 



One of the most limiting components in radars for high-speed aircraft 

 has been the radio transparent window or radome. The system may suffer 

 a loss in useful range because of a poor radome; equally important, the 



I'lM. S. Wheeler, "An Electrically Scanned Spiral Antenna," Fifth East Coast Conference on 

 Aeronautical and Navigational Electronics, p. 55. 



