68 



THEORY OF SEAKEEPING 



0.40 0.60 0.80 



f- 1/T [sec-'] 



1.00 



1.20 



Fig. 76 Wave spectrum of irregular waves measured in 



model tank. Dashed curve indicates distortion in true 



wave spectrum due to introduction of artificial linear drift 



in wave record (courtesy David Taylor Model Basin) 



040 0.60 



f-\n [sec-'] 



Fig. 77 Wave spectrum of irregular waves measured in 

 model tank. Dashed curve indicates distortion in true 

 wave spectrum due to introduction of artificial sinusoidal 

 drift in wave record (courtesy David Taylor Model 

 Basin) 



to the apparent infinite period generated by the drift. 

 In order to determine the nature of this misinformation a 

 record of irregular waves, recorded m the Tajdor Model 

 Basin tenth-scale model of their Seakeepuig Facility, was 

 distorted to simulate the type of drift just defined. The 

 effects on the computed spectra are shown in Fig. 76. 

 Except for the huge spike near zero frequency, due to 

 linear drift, there is essentially no change in the spectrum 

 derived from the uncontaminated wave record. There- 

 fore, a spectrum with a spike at zero frequency may be 

 considered not to actually have that spike and it should 

 be ignored. There is one exception to this rule. A 

 shipborne wave recorder which acts as a moving-point 

 source of wave observation may record energy at zero 

 frequency of encounter, for certain wave components, 

 whose speed is equal to the component of ship speed in 



(c) 



10 Seconds 



(d) 



Fig. 78 Filtering a pure tone to eliminate noise: (a) 



No filter; (b) 10-cps filter; (c) 1-cps filter; (</) 0.1-cps 



filter (from Campbell, 1959) 



that direction when both waves and ship travel in the 

 same general direction. Here, the true wave energy is 

 mixed with the energy due to the linear drift of the elec- 

 tronics and separation is a serious problem. 



The Imear-drift problem is not serious. A sinusoidal 

 drift is another matter. Such difficulties may arise 

 from use of an airborne radar altimeter or from the 

 depth-keeping problems of a moving submarine or from 

 an unstable power supply. The problem was investi- 

 gated in the same way as for the linear drift; this time a 

 low-frequency sinusoidal signal was artificially intro- 

 duced into the same Taylor Model Basin wave record. 

 The resultant spectra. Fig. 77, show a distortion not 

 only at the freciuency of the intruding signal (0.2 cps) 

 but at higher harmonics which are integral multiples of 

 the fundamental. It is clear that the additional energy 

 applied to the main portion of the spectrum is not easily 

 separable. In addition, the mam spike may easily be 

 mistaken for a band of swell. Consequently, a wave 

 spectrum, with a spike outside the main energy band, 

 but not at zero frequency, should be treated with great 

 caution. 



A source of error commonly encountered is the intro- 

 duction of "noise" into the system as stated in Section 

 8.2. This may occur either in the transducer or in the 

 recorder or both. It may be an inherent property of the 

 electronics or an artificially induced vibration in the 

 sensing element. Such noise is usually of much higher 

 frequency than is measured in most seakeeping pa- 

 rameters. This noise can be eliminated by passing the 

 signal through a low-pass filter (Campbell, 1959). An 

 example of this appears m Fig. 78 where noise is intro- 

 duced uito the circuitry which generated a nearly pure 

 0.07-cps sine wave. The noise is sufficient to mask com- 

 pletely the .signal (a), and even with the 10 cps cut-off 

 filter (b), the nature of the intended signal is not clear. 

 However, proper filtration does finally produce the de- 

 sired pure tone. Proper filtering should be a key element 

 in any wave and seakeeping instrumentation. In addi- 

 tion to eliminating imwanted elements in the signal, it 

 supplies the cut-off frequency and thereby automatically 

 defines At. 



8.44 Sampling vcriability. The subject of samphng 

 variabihty is relegated to a subsection not because of its 



