^TRANSDUCER 



NOMINAL 

 BEAMWIDTH 



SURFACE MEASURED BY EARLIEST RETURN 

 SEA SURFACE 



100- 



SURFACE MEASURED BY AVERAGE RETURN 



Fig. k. Effect of excessive beamwidth on height error. 

 -a = 30° 



5 10 15 20 25 



INCLINATION IN DEGREES 



30 



Fig. 5- Error in height due to beam width 

 wave slopes. 



and 



on sidelobe reflections or, alternatively, loss 

 of signal when the wave slope is greater than 

 one-half the beamwidth. 



It is apparent from Fig. 5 that very narrow 

 heamwidths would minimize the errors due to 

 wave slopes but a compromise must be made if loss 

 of signal is to be kept within allowable bounds. 

 Such loss occurs when the slope of the entire 

 surface in the area encompassed by the beam 

 exceeds one-half the beamwidth. Furtunately, 

 large slopes are statistically improbable under 

 conditions of light wind and smooth surfaces. 

 Moreover, the presence of wind roughens the sur- 

 face and diffuses the return reflection thereby 

 causing an effective increase in beamwidth 

 without an attendant loss of accuracy. 



Statistical measurements of the slopes of 

 waves have been made. '^ The distributions are 

 approximately Gaussian with parameters shown in 

 Table I. Since the measurements were made from 

 photographs taken at substantial altitude com- 

 pared with wavelength, the slopes represent the 

 superposition of ripples and chop on the larger 



Table I. Distribution of inclinations of 

 reflecting facets. 



Direction Crosswind Upwind-Downwind 

 Wind velocity, knots 10 20 10 20 

 Bias, degrees -0.5 -1.0 



Standard deviation, 

 degrees 



7-5 7 



10 



waves . From Table I it is apparent that a slope 

 of -20°, corresponding to sinusoidal waves of 

 length-to-height ratio of 9:1 or greater, would 

 include all the statistically significant cases. 

 However, a half beamwidth of 20° would produce a 

 range error of about 6"jo. 



In practice it is feasible to operate at a 

 frequency of 38 Kcps and reduce the beamwidth 

 to -8 between nulls, a value which can be obtained 

 with commercially available transducers of 5 inches 

 diameter. The RCA hydrofoil ultrasonic height 

 sensor has undergone many hours of successful 

 testing with such transducers . Sea conditions 

 ranged from glassy calm to white caps with waves 

 up to 5 feet . Relative winds from zero to 50 

 knots were encountered. Although receipt of 80$ 

 of return pulses is sufficient for proper opera- 

 tion, usually more than 90$> a nd often more than 

 98$ were received. 



SELECTION OF TYPE OF MODULATION 



Of the types of modulation applicable to dis- 

 tance measurement two of the simplest are short 

 pulse and sinusoidally modulated CW. The mea- 

 sures of range are respectively the time interval 

 between transmission and reception and phase 

 shift of the sinusoidal envelope. For a maximum 

 range of kO feet the total transit time is about 



Superior numbers refer to similarly numbered references at the end of this paper. 



103 



