TM No. 377 



Directional Response of the Wave Meter - The final effect of instrument 

 bias to be considered is the deviation of the orthogonal sensors from the ideal 

 cosine law. This is, indeed, a most complicated matter. Referring to the 

 discussion of instrument response in chapter II for any factual evidence of 

 response characteristics, let us again consider the possible effects of biasing 

 of the amplitudes and of the phase relation. 



The magnitude of the vector component was shown to be a function of the 

 angle of attack © between the current vector and the cylinder axis. This function 

 was approximately sinusoidal except at very large angles (0 approaching 90°). 



The magnitude of flow velocity calculated from the response of two orthogo- 

 nally mounted meters was about 10-15 percent larger than the true velocity in the 

 tow tests. A like positive error in the amplitude of both velocity components 

 would produce a covariance 25 percent too large. Corrections were thus used on 

 the orthogonal velocity data (see chapter II). The main weakness in this method 

 is that true ocean waves were not used in the calibration. Because of the nature 

 of the turbulent medium of ocean waves, the errors in the individual components 

 may well be greater than 10-15 percent; however, it seems unlikely that they 

 should be larger by more than a factor of two. In other words, the biasing of 

 the covariance function caused by magnitude distortion should be much less than 

 a factor of four. 



The possibility of introducing an artificial phase lag through distortion of 

 the wave flow caused by the geometry of the ducted meters is a most complicated 

 question. One effect that can be readily examined is the biasing associated with 

 the physical separation of the orthogonally mounted impellers. The axes of the 

 coupled impellers (mounted as shown in figure II-16) have a separation of 11 cm. 

 When the OMDUM system is aligned properly to detect wind waves, the line of axes 

 separation _£ is parallel to the wave crests (see figure V-50). If the u meter 

 axis subtends an angle © with respect to the mean direction of wave propagations 

 -£ makes an equivalent angle © with the y axis. In this position, the projection 

 of Ji upon the x axis is defined as: 



&X -JLTVG . (v-55) 



Since the two orthogonal sensors are mutually displaced with respect to the 

 direction of wave propagation (defined as the +x axis), a constant phase 

 difference occurs between the two sensors. This is given by: 



A<f = — ' > (v-56) 



L. 



where L is the wavelength. The phase angle &<f may be considered identical to 

 that appearing in equations (V-h^>) . 



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