TM No. 377 



If both meters are biased toward higher positive or negative values, then 

 contribution to the covariance does occur. This is easily seen, since the inte- 

 gration would be made in intervals of quarter periods (in lieu of half periods) 

 for equation (V-52) . These integrals do not vanish (vis. «5»M TT/1. —I ). 



It should be noted in passing that if both ducted meters have calibrations 

 which are linear (as was experimentally shown in chapter II) , but which differ 

 slightly, this alone produces no effect on the covariance except that, if it is 

 non-zero, its magnitude (but not sign) is altered slightly. 



It was noted in chapter II that for both the OMDUM II and OMDUM III systems, 

 the forward and backward calibrations of the respective instruments proved identical 

 within the limits of the accuracy of the determinations. 



Instrumentation Time Lag - Time lag may be mechanically or electronically 

 induced in the record pairs, u(t) and w(t), by either the sensors or the recording 

 system. 



Suppose the instrument has an inherent difference in frequency or time 

 response between its two sensors so that the recording at the instant of time t 

 is actually of the variables u'(t), w*(:£ + ifc), or correspondingly, from equation 

 (V-U5), 



A* sin <rt t Acu cos(<rt + $£277) 



Cv-53) 



4Z 



T 



. F< 



lag of 2° is equivalent to 



AT 



The time lag ^-277*-^$ is the instrumental phase lag of the u' sensor over 



the w l sensor. For example, for a wave period of k.O seconds, an angular phase 



^"t s — K^SEC = 22 milliseconds. 



3&0 



Figure V-^5 shows that a relatively small time shift (or phase shift) can 

 produce relatively large covariances. 



Let us examine possible phase lag induced by the recording or sensor systems, 

 The recording systems described in chapter II were two-channel, general purpose 

 recorders (model 320 and 322, manufactured by the Sanborn Co., Waltham, Mass.). 

 The response time (reported in the Sanborn Co. catalogue S-15m-U-6U) is 5 milli- 

 seconds for a 0-90 percent rise for a step input in voltage. By the definition 

 given in appendix A, this is an equivalent response time T r of about 2.5 milli- 

 seconds. This value is at least an order of magnitude less than the response 

 time of the impellers (as discussed in chapter II). Therefore, the amplifier 

 and recording system can produce no sensible time lags, and hence can cause no 



151 



