14-6] MODIFYING THE RADAR RANGE EQUATION 749 



then, are the resulting water bias errors for typical modern doppler systems 

 equipped with land-sea switches. 



The second error mentioned above is caused by the motion of the water 

 surface droplets (and hence scatterers) incident to the action of the surface 

 wind. Workers in the United States (primarily at the Naval Research 

 Laboratory) and in Great Britain have experimentally determined this 

 error to be somewhere between 8 and 16 per cent of the surface wind speed. 

 It should be remembered, however, that this error (unlike the bias error) is 

 proportional to the prevailing wind speed and hence becomes smaller and 

 smaller, percentagewise, as the speed of the aircraft increases. 



The third and final water error mentioned is that incident to current 

 motion (tidal currents. Gulf Stream, etc.). Since in this case the scattering 

 surface below the aircraft is moving with a given rate, this rate appears as 

 a direct error in the ground speed measurement. If this rate is known, 

 however, as is often the case for water currents, then it is possible to correct 

 for it by preflight calibration. In general such currents are known to move 

 at speeds of no greater than 1 to 2 knots. And again, as in the case of the 

 surface droplet motion error, the error decreases percentagewise as aircraft 

 speeds increase. 



It might be mentioned at this point that water "wave motion" as such 

 produces no doppler error, since water mass is not actually transported or 

 moved forward in the wave action. 



In summary it can be said that, while water motion errors are appreciable 

 at lower aircraft speeds and short distances, these errors become less 

 significant for the higher aircraft speeds and for the longer distances. This 

 is the case since the absolute velocity errors tend to be a small percentage of 

 the total aircraft speed and because such errors are likely to occur in 

 different directions and hence will tend to average out over long distances. 

 Also, correction for a portion of these errors before or during the flight 

 appears possible. The water bias error, on the other hand, can be reduced 

 considerably through the use of a land-sea switch, and for typical doppler 

 radars should amount to less than 0.25 to 0.7 per cent peak error in velocity. 

 New automatic techniques have recently been developed which are designed 

 to further reduce the over-water bias error. 



14-6 MODIFYING THE RADAR RANGE EQUATION FOR 

 THE DOPPLER NAVIGATION PROBLEM 



The standard radar range equation (see Paragraph 3-2) may be expressed 

 in the following form which is more convenient for the doppler radar 

 problem: 



m _ Pa,,GoWnFEM)\^FjA .J4 13) 



\nU NFkTAfd{4-jrhy sec' ^ 



