Hadler and He eke r 



The vertical force coefficient for the base-vented regime is dependent upon 

 both test speed and submergences. The force is upward, implying that the im- 

 pact forces are significant and that more blade lift is developed during the entry 

 half of the revolution than during the exit half. This is consistent with the thrust - 

 eccentricity measurements. 



The vertical force coefficient for the fully vented condition, just as for the 

 horizontal force coefficient, appears to be independent of test speed. It also 

 appears to be independent of depth of submergence. In this regime the net 

 force is downward, implying that more blade lift is being developed on the exit 

 half of the revolution and that this net force is greater than the impact force 

 upon entry. This again is consistent with the thrust-eccentricity measurements, 

 where the center of thrust is located in the exit half of the propeller disk. 



The generation of the spray upon blade entry and exit represents a loss of 

 energy to the system. It would be expected that this would have a significant 

 effect upon the efficiency of the propeller. It is probable that these losses ac- 

 count, in the case of Propeller 3768, for the gains made in the L/D ratio when 

 operating in a base-vented as compared to the fully wetted condition; hence the 

 reason for the comparable efficiencies when being operated as either a fully 

 wetted or a partially submerged propeller. 



SCALING 



The dominant scaling problem is associated with maintaining the proper 

 value on the propeller blade sections to ensure achieving similarity of flow. 

 Since the cavities are vented to the atmosphere at all times, with the possible 

 exception of a small leading-edge vapor cavity just before transition from base- 

 vented to fully vented flow, the static pressure is equal to the atmospheric 

 pressure. The pressure differential is 



l\p - -yh , 



where y is the density of water, and h is the depth of water at the propeller 

 blade section; thus 



A/3 yh 



1,1, 



2 ^ 2 



iw^ 



where u is the inflow velocity to the propeller-blade section. This relationship 

 can also be expressed in terms of a depth Froude number: 



2 



h 



where Fj^ = u/gh . Since cry^ is a function of Froude number, the condition for 

 similarity of flow is that the speed of advance of the model and full-scale pro- 

 pellers should be in accordance with the Froude law of comparison; thus 



1480 



