732 AIRBORNE NAVIGATION AND GROUND SURVEILLANCE 



2. The measurement of the horizontal velocity components is highly- 

 insensitive to errors in the vertical reference used. 



3. Measurement of the vertical velocity component (rate of climb and 

 descent) is possible, whereas it is not possible in the 2-beam (non- 

 Janus) case. In fact, in the non-Janus case, it is necessary to 

 furnish rate of climb and descent information from an external 

 source, such as a barometric device, as a correction signal. 



In a Janus system, the doppler shift obtained with a forward beam is 

 effectively added to the doppler shift obtained with the rearward beam. 

 For the condition of no pitch and roll (so that the forward and rearward 

 doppler shifts are equal) Equation 14-1 for the total doppler shift from two 

 beams takes the form: 



/. = ^cos7 (14-3) 



where the symbols are the same as those defined earlier. 



The particular beam configuration shown in Fig. 14-7 has been called 

 X-configuration. It is perhaps the most general beam configuration for 

 fixed-wing aircraft. Since it is a three-beam Janus system, all three compo- 

 nents of aircraft velocity — the along-heading, cross-heading, and vertical 

 components of velocity — can be obtained with it. For the condition of 

 no aircraft pitch or roll, the mathematical expressions for the computation 

 of the three velocity components are: 



'' 4X cose cos /3 ^ ^ 



-^^ = %^ ("-^) 



where ^h = along-heading velocity component 



^D = cross-heading (drift) velocity component 



^v = vertical velocity component 



fdn = doppler shift of beam n 



6 — depression angle of antenna beams 



(8 = azimuth angle of antenna beams (smallest angle between 

 projections of longitudinal axis of aircraft and antenna beam 

 on the ground plane). 



