Airborne Doppler Radar by M. Schetzen

By M. Schetzen

The e-book starts with a easy dialogue of the Doppler impression and its quite a few purposes, 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 besides illustrations and discussions to assist the reader achieve an intuitive realizing of the approximation and its boundaries. A precis of the mathematical suggestions required for improvement of an actual idea is then provided utilizing the case of a slender beam antenna. this can be by way of the improvement of the precise conception for the final case, that's graphically illustrated and in comparison with the quasi-static approximation. common stipulations for which the quasi-static approximation mistakes will be over the top – in particular as utilized to laser Doppler radars and low-flying airplane – are presented.
- facts and knowledge showing during this publication are for informational reasons purely. AIAA and the writer will not be chargeable for any damage or harm because of use or reliance, nor do AIAA and the writer warrant that use or reliance could be unfastened from privately owned rights..

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QUASI-STATIC APPROXIMATION OF THE DOPPLER SPECTRUM 43 We’ll present illustrative graphs of dqs and sqs versus various antenna parameters for the case in which the terrain is a diffuse surface. A diffuse surface is one for which the backscatter follows the Lambert law, which is b sin b in which b is the angle between the incident wave and the plane of the terrain. A surface for which this is a good model is a smooth sandy ocean beach. In Fig. 1, b is the angle between the x –y plane and the line from the antenna to the point P.

3:4) AIRCRAFT DOPPLER STABILIZATION AND NAVIGATION 33 in which cr is the range angle and ca is the azimuth angle. Substituting this result in Eq. 3), we obtain dr ¼ Àv sin cr cos ca dt (3:5) The Doppler shift thus is d¼À 2v0 dr 2v0 ¼ v sin cr cos ca c dt c rad=s (3:6) Because, c ¼ lf0 , this expression also can be written in terms of the wavelength of the radiated wave l as d ¼ 2p 2v sin cr cos ca l rad=s (3:7) Because v ¼ 2pf in which f is in hertz, we also have d¼ 2v sin cr cos ca l hertz (3:8) The aircraft navigation and control will be obtained by determining the Doppler shift d at various range and elevation angles.

The Doppler shifts in hertz thus are: 1) For the fore antenna beam, df ¼ 2v sin (ue þ f p ) cos (fd ) l hertz (3:9a) 2) For the aft antenna beam, 2v sin (Àue þ f p ) cos (fd ) l 2v ¼ À sin (ue À f p ) cos (fd ) l da ¼ hertz (3:9b) 3) For the starboard antenna beam, p  2v sin (ua þ fr ) cos þ fd l 2 2v ¼ À sin (ua þ fr ) sin (fd ) hertz l dS ¼ (3:9c) 4) For the port antenna beam,  p  2v sin (ua À fr ) cos À þ fd l 2 2v ¼ sin (ua À fr ) sin (fd ) hertz l dp ¼ (3:9d) Using standard trigonometric identities we then obtain 4v cos fd sin f p cos ue l 4v d f À da ¼ cos fd cos f p sin ue l 4v d p þ dS ¼ À sin fd sin fr cos ua l 4v d p À dS ¼ sin fd cos fr sin ua l d f þ da ¼ (3:10a) (3:10b) (3:10c) (3:10d) We then obtain by dividing one equation by another tan f p ¼ d f þ da tan ue d f À da (3:11a) 36 AIRBORNE DOPPLER RADAR tan fr ¼ À d p þ ds tan ua d p À ds (3:11b) tan fd ¼ À d p þ ds cos ue sin f p d f þ da cos ua sin fr (3:11c) We now can determine the pitch angle fp from Eq.

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