14-2] BASIC PRINCIPLES OF DOPPLER RADAR NAVIGATION 729 



doppler shift and if we know the frequency of transmission, the velocity of 

 light, and the direction of radiation, we can determine the only unknown 

 quantity, the ground speed of the aircraft. The velocity can then be 

 integrated to measure the miles traveled along the ground and combined 

 with heading information to compute present position. 



A doppler navigation radar^ then, is an airborne radar which transmits 

 electromagnetic energy toward the earth's surface and utilizes the doppler 

 shift of the received energy to determine two or three of the velocity 

 components of the aircraft. This is illustrated schematically in Fig. 14-4. 



Fig. 14-4 Basic Doppler Beam Configuration. 



The basic output of a doppler radar is a frequency, which is the observed 

 doppler shift, given by the basic doppler equation 



IVf IV 



fd = — ^ COST = ^ COST (14-1) 



C A 



where/d is the doppler shift, ^is the velocity of the aircraft, c is the velocity 

 of light, T is the angle between the velocity vector and the direction of 

 propagation, and X is the wavelength of transmission. 



Since the antenna beam has a finite width and since the scattering from 

 the earth is randomlike, the information received from the ground is not a 

 single frequency, but rather is in the form of a noiselike frequency spectrum 

 as shown in Fig. 14-5. A certain amount of smoothing time is therefore 

 required to determine the quasi-instantaneous velocity to a given accuracy. 

 A velocity smoothing time constant of about 1 second is usually chosen; 

 this value is limited by the need for compatibility with the dynamics of 

 typical aircraft. However, the effective smoothing time for navigational 

 distance measurement is the total time flown and, for typical systems, it 

 turns out that the so-called JIuctuation error is completely overshadowed by 

 certain other instrumentation errors after approximately 10 miles of flight. 



