Airborne Doppler Radar by M. Schetzen

By M. Schetzen

The publication starts off with a simple dialogue of the Doppler impression and its a number of functions, and the way Doppler radar can be utilized for the stabilization and navigation of airplane. A quasi-static approximation of the Doppler spectrum is gifted in addition to illustrations and discussions to assist the reader achieve an intuitive realizing of the approximation and its boundaries. A precis of the mathematical innovations required for improvement of a precise conception is then offered utilizing the case of a slender beam antenna. this can be through the advance of the precise conception for the final case, that is graphically illustrated and in comparison with the quasi-static approximation. basic stipulations for which the quasi-static approximation blunders will be over the top – in particular as utilized to laser Doppler radars and low-flying plane – are presented.
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48 AIRBORNE DOPPLER RADAR Fig. 8 Normalized quasi-static Doppler bandwidth versus the azimuth angle. azimuth angle ua ¼ 0, 25, 50, and 75 degrees. 8 is a graph of the normalized quasi-static Doppler bandwidth versus the azimuth angle ua for the elevation angle ue ¼ 5, 30, 55, and 80 degrees. For both graphs, the antenna pattern has a circular cross section with s1 ¼ s2¼1 degree. To understand these graphs, note from Fig. 3 and Fig. 4 that dqs decreases for increasing ua and the rate of increase decreases for increasing ue; also dqs increases for increasing ue and the rate of increase increases for increasing ua.

2:7) 24 AIRBORNE DOPPLER RADAR in which a is the angle shown in Fig. 1. With the use of Eq. 4), the ratio of the Doppler shift to the emitted frequency thus is d n ¼ À sin a v0 c (2:8) Now, the approximate velocity of an electromagnetic wave in the atmosphere is c ¼ 3 Â 108 meters/s. 2 is a graph of the Doppler shift as a percentage of the frequency radiated from the star versus the angle a. Note that there is no Doppler shift when the star’s velocity is perpendicular to the earth (for which x ¼ 0) because the radial velocity of the star is zero at that point.

4 Normalized quasi-static Doppler frequency versus the azimuth angle. 46 AIRBORNE DOPPLER RADAR Note that s is not the 3-dB beamwidth. Because S(cr , ca ) is a two-way antenna pattern, the 3-dB beamwidth is the angle at which S(cr , ca ) ¼ 1=2. Now S(cr , ca ) in Eq. 18) is a p normal 3-dB ffiffiffiffiffiffiffiffiffiffiffi function so that for f ¼ 0,pthe ffiffiffiffiffiffiffiffiffiffi ffi width along the s1 axis is ce ¼ s1 2 ln 2 ¼ 1:17741s1 and is ca ¼ s2 2 ln 2 ¼ 1:7741s2 along the s2 axis. 53 degrees. 1 degrees with the rotation angle f ¼ 0, the azimuth angle ua ¼ 60 degrees, and the elevation angle ue ¼ 30 degrees.

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