2r>. ^ Lehman and Kaplan 



The millivolt value recorded from the wave analyzer was converted into 

 pounds of induced force in the following manner. The initial value was adjusted 

 for the influence of the "flow background" by taking the square root of the differ- 

 ence of the squares, a procedure implying an uncorrelated test condition. As 

 noted in Fig. 10 the flow background was extremely small and resulted in a 

 meaningful change in the adjusted millivolt value in very few cases. The ad- 

 justed millivolt value was converted into pounds of force by dividing this value 

 by the millivolts-per-pound calibration value existing for that particular fre- 

 quency and the particular arrangement undergoing test. The final data form was 

 obtained by dividing the "true" induced force by the net propeller thrust value, 

 and this ratio is employed for most of the data presented. 



DATA PRESENTATION AND DISCUSSION 



Before discussion of the propeller induced appendage forces which existed 

 at specific blade rate harmonics, it is perhaps of value to clarify two points 

 which are raised most often after presenting unsteady appendage data. 



The first clarification is to demonstrate that propeller induced appendage 

 forces exist only at the blade rate and its harmonics. During a test the entire 

 frequency range encompassed by the blade rate harmonics is scanned to insure 

 that the induced appendage forces occurring at specific frequencies (correspond- 

 ing to certain blade rate harmonics) are larger than any force values measured 

 at other frequencies. However, only those values occurring at blade-rate fre- 

 quencies are normally recorded. Figure 11 illustrates that this contention is 

 true. This figure is a plot of the measured force level ratio as a function of fre- 

 quency. The data on this figure present the axial induced appendage forces asso- 

 ciated with a four-bladed propeller (double- thickness blades) when operating be- 

 hind a symmetrical appendage. Data taken over the entire frequency range of 

 interest are shown. The information is presented for two spacing ratios. From 

 this figure it can be noted that the induced appendage forces do exist only at fre- 

 quencies corresponding to specific blade-rate harmonics and that the induced 

 force magnitudes decrease rapidly with an increase in spacing ratio (this latter 

 observation will be illustrated more fully in other figures). 



The second point of clarification concerns the relationship between the num- 

 ber of blades on a propeller and the nature of the induced appendage forces. 

 Theory (5) states that a propeller with an even number of blades should induce 

 only axial unsteady forces and that a propeller with an odd number of blades 

 should induce only transverse unsteady forces. All experimental data verify 

 this contention except at extremely close appendage- propeller spacing ratios. 

 For close spacing ratios a propeller with an even number of blades induces some 

 transverse force on the appendage and a propeller with an odd number of blades 

 induces some axial force. An investigation of the effect that the appendage at- 

 tack angle has on the unsteady propeller induced appendage forces supplied a 

 clue as to the reason for this apparent inconsistency between experiment and 

 theory. 



During an investigation involving appendage attack angle (11) it was observed 

 that the appendage attack angle has a significant effect on the nature of the in- 

 duced appendage forces. Very slight appendage attack angles resulted in the 



180 



