Now since the output was assumed linear, equation (10) can be written 



e = KU R 

 where 



K = constant 

 K>0. 

 The mean (or filtered) value over one wave cycle, e, can be found from 



(11) 



- K 

 e 



-^ f IJ R d(c^t) where \U\ = f(i 2 + U^)'/^ 



2 TT J 



(12) 



The value of R is a known empirical function of p. The value of p is given by 



P = cos" 



tl 



. where U^, = U^ sin G 



(13) 



Using this value for L\., equation (8) for l\, and equation (12) for U, 



(Ui + U^ cos CO?) sin G 



P = cos ^ 



(V^ + L^)' 



(14) 



As a check, let R = cos p. Using equations (12) and (14), where U^, U^, and Q 

 are constants, 



e=-^ / (U^ + U?)'- 



(Ul + L/„ cos cot) sin Q 



fU 2 + L/2)'2 



d wt = 1]^ sin e (15) 



Thus the correct steady-state component along the meter axis is indicated when 

 the response is a cosine function. 



Equation (12) cannot be used at this time for an example of an electro- 

 magnetic meter since an actual direction response is not known. However, to ' 

 illustrate the method, a direction response the same as the Marine Advisers 

 Model Q-8 ducted meter (fig. 7) will be used. This was a noncosine response 

 that would probably be somewhat typical for an electromagnetic meter. The 

 function of R vs p (fig. 7) was approximated by a series of straight lines, connect- 

 ed by points taken at 5-degree intervals. Linear interpolation was used between 

 points. The discontinuity at p = 76 degi'ees was avoided by letting R = 0.356 at 



19 



