Str^m-Tejsen and Chislett 



significant standing waves which completely preclude the possibility of making 

 useful measurements. 



The frequencies at which tank resonance occurs are solely dependent on 

 tank dimensions (12) and governed by the relation 



277 



period = — 



where 



o-^ = gk tanh kh 



277/k = wavelength = 2b, b, (2/3)b, (2/4)b, etc. 



h * depth of tank water 



b = breadth of tank 



g = acceleration due to gravity. 



For the HyA towing tank, when b= 2h, the first four resonant standing-wave 

 systems, according to these relationships, have periods of 4.07, 2.78, 2.26, and 

 1.98 seconds. The corresponding revolutions of the HyA planar-motion mecha- 

 nism at which tank resonance may be expected are then 14,8, 20.5, 26.5, and 30.3 

 revolutions per minute. 



"Pure sway" tests and "pure yaw" tests were made with a 6-m model of 

 the Mariner class of vessels, for revolution of the planar-motion mechanism 

 covering the range from to 35 rpm. The object of the tests was to find the 

 low-frequency area in which the measured forces ceased to be frequency de- 

 pendent. The model used in the tests was the same as that described in Ref. 5, 

 and the tests were made predominantly at 15 knots ship speed and with 65 mm 

 amplitude at the scotch yokes. The raw forces measured at the Y gauges in the 

 "pure sway" tests are shown plotted in Fig. 33. Above about 12 rpm the forces 

 measured during a run down the tank varied in a manner akin to the "beating" 

 phenomenon resulting from the interference of two wave trains having nearly 

 equal frequencies. The ranges of variation of forces measured during a run 

 down the tank are shown by heavy lines, and when the forces were repeatable, 

 the values are indicated by single points in the usual manner. 



It is evident that resonant standing waves occurred at about 15, 20, and 30 

 rpm exactly as predicted by theory. 



At the higher frequencies, standing waves were clearly visible, and in an 

 additional test at zero speed, they built up to alarming proportions, the whole 

 water surface in the portion of the tank adjacent to the model being set into 

 violent motion. 



Below 12 rpm, however, no standing waves were observable, and it can be 

 said that if they did exist, then the wave height was less than 1 mm. This was 

 ascertained by close examination of the water level on the tank side when the 

 model was oscillating. 



376 



