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X-. FRACTION OF CHORD 



Fig. 8 Meanline shape for three blades 



blade similar to NSRDC Model 4498. Both changes in 

 chordwise variables lead to increased suction near mid-chord 

 and reduced suction near the leading edge on the suction 

 side of the blade. An engineering approximation is that 

 cavitation will occur when the minimum pressure on a body 

 equals the vapor pressure of the liquid. Hence at the design 

 point, back bubble cavitation may be degraded by these 

 chordwise variations relative to the conditions of Figure 7 

 but off-design leading-edge sheet cavitation on the suction 

 side may be improved by these changes in chordwise vari- 

 ables. This conjecture is based on assumed equal incremental 

 changes to the pressure due to off-design operation. Leading 

 edge pressure-side cavitation may be degraded at off-design 

 operation with the elliptic load distribution because of the 

 peak near the leading edge in Figure 9. Meanline shapes are 

 different for these chordwise variations as shown in Figure 9. 



Thrust loading and power coefficients (computed 

 from Equations 80 and 81 with C D = 0.0085) are shown 

 in Table 111 lor the various overall geometries and chordwise 



modifications. The performance coefficients computed 

 according to the lifting-line model and first-order linear 

 lifting-surface model (E = in Equations (76) and (78) and 

 ACp from Equation (74)) are nearly identical. The non-linear 

 performance coefficients (E *= in Equations (76) and (80) 

 and Cp from Equation (66)) for a blade with only loading 

 (Ex = 0) are increased a few percent relative to the lifting-line 

 values. The addition of thickness and skew or warp changes the 

 pressure distribution and meanline slope, and increases the 

 values by another few percent each, eventually producing 

 values of C Th and C p which are more than ten percent greater 

 than predicted by the lifting-line model. In both the pressure 

 distribution and force calculations, non-linear, second-order 

 effects have been included in an intrinsically first-order 

 theory. It is not known if the calculated trends with these 

 second-order effects included are valid or not. Experimental 

 evaluation is required to confirm the predictions. Predictions 

 given in Table III should be interpreted as possible trends in 

 the actual performance. The present lifting-line model 

 employed in propeller design (3, 4) assumes a straight radial 

 line with vanistung chordlength to represent the blade arid 

 can hardly be expected to be an acceptable model of wide- 

 bladed lifting surfaces, especially ones with skewed or warped 

 blades. Fortunately, the majority of applications to date have 

 generally performed within a few percent of predictions with 

 this simple model but some significant differences have also 

 occurred. Hence both a curved lifting-line and increased- 

 accuracy lifting-surface performance predictions should be 

 developed and evaluated. 



MODEL 44M GEOMETRY 



NACA M (MODI THICKNEB 



LOAD BIMILAR TO NACA a - OM 

 ELLIPTIC CHORDXItE LOAD. EP THKKNEn 



. FRACTION OF CHORD 



Fig. 9 Pressure distribution and meanline shape 

 for variation of chordwise load and thickness 



18 



