borne load, speed, and trim do not change appreciably for the short interval influenced 

 by the bottom clearance, or that the product of the length-beam ratio times the lift 

 coefficient is constant. The plots against the clearance parameter z/b for various trim 

 angles indicate a large reduction in wetted-length-beam ratio and increase in moment 

 coefficient as the clearance approaches zero. The hydrodynamic center of pressure 

 actually moves aft with the decrease in wetted length. The lift coefficient increases 

 because the hydrodynamic lift is constant. At high angles, the L/D remains the 

 same, but at low trims it increases sharply because of the decreased wetted area and 

 frictional resistance. These effects are relatively unimportant for transition to and 

 from the ramp, as has been demonstrated by operation with light ski airplanes and 

 dynamic model tests of jet airplanes with high ramp speeds, because of the very shallow 

 depths at which they appear. 



Self-excited vibration. — A tendency for flat planing surfaces to vibrate in a 

 vertical plane at high speeds and short wetted lengths has been encountered as shown 

 in Figure 14. The oscillations are self -starting in smooth water, have high fundamental 

 frequencies, and can be very violent. The speed for inception is a function of the 

 trim angle and load (wetted length-beam ratio) as indicated, and the inception condi- 

 tions are the same for both the systems diagrammed. The phenomenon is thus not 

 explainable on the basis of coupling between trim and vertical motions since it occurs 

 without freedom in trim (ref. [24]). 



It can be seen that the inception moves to higher speeds with decrease in trim 

 or increase in load, both of which are in the direction to increase wetted length. The 

 vibration can be reduced or eliminated by the use of V plan forms or cross sections, 

 which limit the wetted aspect ratio to low values. It can also be minimized or avoided 

 by stiffening the planing surface itself, or restraining the vertical motion by reduction 

 in overhang or the use of auxiliary struts. 



The evidence so far shows that the problem is not inherent and where it exists, 

 may be reproduced in the towing tank with a Froude model. The basic mechanism 

 involved however, is not well understood, and theoretical means to predict its occur- 

 rence in practical cases are not yet at hand. 



,/////// 



///// //y / / // /// 



2. 



2: 



FREE -TO-TRIM 



FIXED TRIM 



LOAD 



TRIM 25° 20° 15' 



NO 



VIBRATION 



TRIM 



VIBRATION 



LOAD, 

 LB 10 30 60 



NO 

 VIBRATION 



VIBRATION 



SPEED SPEED 



BOUNDARIES FOR INCEPTION 



Figure 14. Self-excited vibration of planing surface. 



197 



