Propeller -Induced Appendage Forces 

 Zero Appendage Attack Angle 



The first case considered is that of the four-bladed propeller. Figure 13 

 illustrates the influence of blade thickness on the induced appendage forces for 

 the first, second, and third harmonics of the blade rate for a symmetrical ap- 

 pendage. From this figure it can be noted that blade thickness is an important 

 factor in determining the magnitude of the axial induced appendage force. How- 

 ever appendage asymmetry has little effect, as is shown in Fig. 14. In this same 

 figure, blade-rate (or first-harmonic) data are presented for two propeller blade 

 thicknesses and three appendage asymmetries. This plot reinforces the obser- 

 vation that the blade thickness has the dominant effect and appendage asymmetry 

 has minimal effect. The minimal effect of appendage asymmetry is also shown 

 in Fig. 15, where the unsteady axial induced appendage forces associated with the 

 first, second, and third harmonics of the blade rate are shown for a four-bladed 

 propeller having double- thickness blades. This figure shows that the induced 

 appendage forces associated with the first harmonic of the blade rate are 30 to 

 40 times as large as those associated with the second and third harmonics of the 

 blade rate. 



For transverse induced appendage forces and operations with a three-bladed 

 propeller and a symmetrical appendage. Fig. 16 illustrates the effect of propeller 

 blade thickness on the induced appendage forces for the first, second, and third 

 harmonics of the blade rate. In this case, as for the case of the axial induced 

 unsteady appendage forces, blade thickness is an important factor in determining 

 the magnitude of the forces associated with the first harmonic of the blade rate, 

 but the second and third harmonics of the blade rate are not as strongly influenced 

 by propeller blade thickness as for the case with axial induced appendage forces. 



Appendage asymmetry has a much more dominant effect on the transverse 

 induced appendage forces than on the axial induced forces. Figure 17 illustrates 

 the first harmonic data for both of the propeller blade thicknesses and three 

 cases of appendage arrangement. Compare this figure with Fig. 14 to note the 

 different effect appendage asymmetry has on the magnitude of induced axial and 

 transverse appendage forces. The effect of appendage asymmetry on the un- 

 steady induced appendage forces associated with the first, second, and third 

 harmonics of the blade rate are shown in Fig. 18. It is shown that the effect of 

 appendage asymmetry and the propeller blade rate harmonic condition both have 

 a strong influence on the transverse induced appendage forces. 



Single-Bladed Propeller Tests 



During this series of investigations, data were obtained with a two-bladed 

 propeller as well as with three- and four-bladed units. The information obtained 

 with the two-bladed propeller, coupled with that obtained with the three- and four- 

 bladed units, was then used to verify a test technique developed during these 

 studies which establishes a basic relationship between the unsteady induced ap- 

 pendage force and the propeller thrust. This technique involves testing a par- 

 ticular propeller as a single- bladed unit and from this information then deter- 

 mining the induced appendage forces for a multibladed propeller. Using this 

 technique, it was found that the unsteady force induced on an appendage by a ' 



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