ABSTRACT 



This report describes a theoretical and experimental in- 

 vestigation of the pitching motions of a moored, submerged 

 mine. The theoretical predictions are based upon linearized- 

 wave theory as well as the assumptions that the body is 

 slender and axisymmetric and is ballasted to be at equi- 

 librium in the horizontal plane. The mooring cable is 

 assumed to be massless and inelastic; the fluid is assumed 

 to be inviscid. The theory results in an equation of un- 

 damped motion. Parallel experimental results were obtained 

 on a 2-foot long model in wavelengths ranging from 15 to 55 

 feet, and these results confirm the theoretical predictions 

 except in the vicinity of resonance, where viscous damping 

 is important. Full-scale predictions are made for the 

 root -mean -square pitching motions in Sea States 4 through 

 7 for two proposed mine configurations at various depths of 

 submergence. The predicted values are from 1 to 9 degrees 

 in Sea State 4, depending on depth and mine configuration, 

 increasing to greater than 25 degrees in Sea State 7. 



ADMINISTRATIVE INFORMATION 



This work was requested by U.S. Naval Ordnance Lab Itr JM:JR:ich/ 

 3900 Ser 6343 to DATMOBAS dated 8 Sep 1964. 



INTRODUCTION 



In response to a request from the Naval Ordnance Laboratory, an 

 investigation was undertaken to predict the pitching motion in waves of 

 moored mines. The mines are elongated bodies of revolution, about 8 feet 

 long, which are moored with an anchor cable from the nose so as to be in 

 equilibrium at depths of from 50 to 200 feet below the free surface when 

 the axis is horizontal. 



Experimental modeling of the problem is complicated because lab- 

 oratory wavelengths are limited to a maximum of approximately 50 feet, 

 thus implying a scale ratio of at least 1-to-lO between the model and full 

 scale; but a model length of less than 1 foot is impractical, especially 

 when a pitch-measuring gyroscope is incorporated inside the model. In 

 view of this situation it was decided to adopt a scale ratio of l-to-4, 

 test in the resulting short-wavelength domain, and use a slender-body 

 theory for the pitch motion to extrapolate to longer wavelengths. 



