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.
- info and knowledge showing during this publication are for informational reasons purely. AIAA and the writer are usually not answerable for any harm or harm due to use or reliance, nor do AIAA and the writer warrant that use or reliance might be unfastened from privately owned rights..
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Additional info for Airborne Doppler Radar
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.