Table III 

 Thrust Loading and Power Coefficient 



n n =<-"Thir 



Lifting Line 



0.690 



1.016 



0.679 



1st Order Lifting Surface 



0.688 



1.013 



0.679 



Second Order: 









Unskewed, 









Loading Only 



0.709 



1.030 



0.688 



Unskewed 









Load & EP thickness 



0.736 



1.089 



0.675 



Skewed 









Load & EP thickness 



0.783 



1.152 



0.680 



Warped 









Load & EP thickness 



0.784 



1.148 



0.683 



Second Order (warped, load and thi 



■kness): 





66 thickness 



0.782 



1.141 



0.685 



Elliptic load. 









EP thickness 



0.782 



1.147 



0.682 



Wake at 



0.790 



1.175 



0.672 



1st Order, Blade at <j> 



0.673 



1.018 



0.661 



Second Order, Blade at <t> 

 Wake at 









0.794 



1.182 



0.672 



As shown by Huang, et al (25), some wake fields have 

 mean axisymmetnc flow velocities with non-zero radial 

 components. In the example body investigated by Huang, 

 a nearly constant value of w R = -0.05 was found. In 

 Table IV, the additive effects of this velocity component 

 are shown. When this w R component is isolated from 

 Equation (22) and the incremental addition to the meanline 

 denoted by AE C , one finds 



AE„ 



N E 



VU-w x ) 2 +(x) 



COS (•fip - 0) 



e(x R ) + 8(x R ) • (x -0.5) 



(115) 



^-.'*C-$ 



COS(^)p-0) 



di T /D d0 s 



2 w R c/D 



cos (<£p - 0) 



x A H,. 



ye r c a — k 



— - = — dx 



c J a x c c 



(1 -x,.) 



(118) 



Thus the e term, due to gradients of the rake and skew of the 

 blaJe, results in an angle-of-attack change, and the 6 term, 

 due to radially variable pitch, results in a parabolic-arc mean- 

 line, with a maximum offset at mid chord of 



= -6/8 (I 19) 



Table IV 



EFFECT OF RADIAL VELOCITY COMPONENT 



ON PITCH AND CAMBER 



(Geometry Similar to NSRDC Model 4498; 



w D =-0 05) 



X R 



vt 'Initial 



w Initial 



e 



5 



Af 



A0 p 



©,.„ 



0.4 

 0.6 

 0.8 



0.0369 

 0.0295 

 0.0188 



1.488 



1.277 

 1.042 



0.0130 

 0.0110 



0.0084 



-0.0008 

 +0.0026 

 +0.0023 



+0.0001 

 -0.0003 

 -0.0003 



-0.746° 

 -0.630° 

 -0.481° 



1.449 

 1.247 

 1.017 



(117) 



*From Table 1, lifting-surface design without effect of Wj.. 



Table IV shows the effect of w R = -0.05 on the 

 pitch and camber ratio for a warped blade similar to NSRDC 

 Model 4498. The change in camber ratio is probably not 

 significant for this case but the change in pitch angle is 

 important, resulting in a few percent change in the final 

 pitch values. Hence this effect should be included in designs 

 operating in a wake having a significant average radial inflow 

 component. 



The present procedure can be improved in several 

 respects: the presence of the hub should be included in the 

 mathematical model, generalized load variations and thick- 

 ness variations should be included, some physically observed 

 phenomena of the shed vortex sheet should be included, 

 consideration of the radially variable inflow (i.e.. free-stream 

 vorticity) should be included, steps to improve the accuracy 

 of computations in the tip region should be undertaken, and 

 program execution time should be shortened. Additionally, 

 similar numerical analysis techniques should be applied to 

 both the performance problem and the determination of 

 unsteady blade response in a non-uniform wake. 



Of particular interest is the physically-observed 

 configuration of the free-vortex sheet. As observed by 

 Nelka (23) and modeled by Cummings (26), for highly-skewed 

 blades, an isolated vortex forms along the leading edge of 

 the blade in the tip region. This vortex will influence the 

 induced velocity field and hence produce changes in the 

 pitch, meanline, pressure distribution and force/moment 

 coefficients relative to the model employed herein. In ad- 

 dition, the trailing vortex will contract and roll up. Present 

 models have a vortex sheet starting at the tip rather than 

 somewhere along the leading edge. 



19 



