Hadler and He eke r 



considerably more scattered. Because this is a two-bladed propeller, the un- 

 steady forces are quite large. At the smaller submergence the thrust will vary 

 from nearly zero to the maximum developable by one blade. 



The results of the cavitation tests in a variable pressure water tunnel on 

 Propeller 3767, Ref. [7], have been presented on the same type of diagram, Fig. 

 22, for purposes of comparison with partially submerged operation. Fig. 21. As 

 may be noted in Fig. 22, the curves change their character with decreasing <j ^ 

 indicating in particular a reduction in the favorable operating range of thrust 

 coefficient. The only region of comparability between cavitating and partially 

 submerged operation is when full ventilation has occurred for the latter. In this 

 region the n and J values are somewhat similar to those of the cavitating pro- 

 peller when operating at low o- values. 



ANALYSIS OF TRANSVERSE FORCES 

 AND THRUST ECCENTRICITY 



The fully submerged propeller, when operating in a uniform flow field, de- 

 velops a net thrust and torque which acts at the axis of rotation. If the propeller 

 operates in an asymmetric flow field, the forces no longer occur at the exact 

 center of rotation nor do they appear as a simple steady force (thrust) and mo- 

 ment (torque). Usually these asymmetries in the flow are not large enough to 

 be of concern as far as the thrust eccentricity and transverse forces are con- 

 cerned. This is no longer possible in the case of the partially submerged pro- 

 peller, which may be viewed as a limiting case of asymmetry in the flow field, 

 i.e., a step-function velocity field which is symmetrical about a vertical plane 

 through the propeller axis. 



Before undertaking an analysis of the results of the measurements of the 

 side force and the thrust eccentricity, it is helpful to examine the force on the 

 propeller as it enters and exits through the air -water interface. There is a 

 modest amount of literature derived from seaplane dynamics and hydroballis- 

 tics on the air-water entry of bodies and more recently on water exit of mis- 

 siles. The most applicable literature is that derived from seaplane dynamics, 

 which is concerned with impact forces of wedgelike bodies. The work was in- 

 tended for the deadrise angle of seaplane floats rather than the knife-edge 

 shapes of propellers; however, extensions have been made using the same as- 

 sumptions as for the larger vertex angles, Ref. [12]. 



There are three phases recognized in the air-water entry of a rigid body, 

 Ref. [13], which might be considered applicable to a propeller blade; sequen- 

 tially these are as follows: 



Shock Phase. This regime covers the initial, extremely brief period of wa- 

 ter contact where compressibility is the important effect. Since this phase lasts 

 only microseconds, and the leading edge of the blade is "sharp," the pressure is 

 localized on an extremely small area; thus, any imposed drag force on the blade 

 is probably negligible. 



Flow -Forming Phase. In this regime the water around the blade is set into 

 motion, and the entry cavity is initiated. It is during this phase that there is a. 



1478 



