Table I 

 tiffed of Parameters on Pitch, Camber and Computer Run Time 



COMPUTATIONAL. PROCEDURE 





91 x 10 



181 xlO 



181 x 13 



91 x 19 



181 xl9 



91 x 19 



181 x 19 



Kerwin Computation (7) 



X R 



Direct 



Direct 



Direct 



Direct 



Direct 



Approx + Diff 



Approx + Diff 



A0 = 2°,M = 52 



A8 = 2°,M = 70 













PITCH/DIAMETER 









0.25 



_ 



- 





- 



- 



_ 



_ 



1.580 



1.603 



0.254 



1.495 



1.495 



1.517 



1.537 



1.538 



1.539 



1.540 



1.576 





0.4 



1.466 



1.466 



1.477 



1.487 



1.487 



1.487 



1.488 



1.511 



1.523 



0.6 



1.264 



1.264 



1.271 



1.277 



1.277 



1.277 



1.277 



1.292 



1.296 



0.669 



1.184 



1.184 



1.189 



1.194 



1.193 



1.193 



1.193 



1.213 





0.8 



1.038 



1,038 



1.040 



1.043 



1.042 



1.042 



1.042 



1.065 



1.070 



0.946 



0.883 



0.882 



0.882 



0.884 



0.883 



0.883 



0.883 



0.894 



_ 



0.95 



_ 



- 



- 



- 



- 



- 



- 



0.890 



0.885 













CAMBER/CHORD 









0.25 



- 





- 



- 



_ 



_ 





0.0266 



0.0259 



0.254 



0.0305 



0.0305 



0.03 1 5 



0.0320 



0.0322 



0.0323 



0.0324 



0.0268 



_ 



0.4 



0.0365 



0.0365 



0.0367 



0.0368 



0.0368 



0.0369 



0.0369 



0.035C 



0.0351 



0.6 



0.0291 



0.0291 



0.0293 



0.0295 



0.0295 



0.0295 



0.0295 



0.0301 



0.0294 



0.669 



0.0255 



0.0255 



0.0257 



0.0257 



0.0258 



0.0254 



0.0257 



0.0257 



_ 



0.8 



0.0189 



0.0189 



0.0189 



0.0188 



0.0189 



0.0188 



0.0188 



0.0181 



0.0180 



0.946 



0.0124 



0.0124 



0.0122 



0.0122 



0.0123 



0.0123 



0.0122 



0.0122 



_ 



0.95 



- 







- 



- 



- 





0.0120 



0.0113 



CPU Time 



, 310 



420 



600 



735 



1085 



785 



1135 



N/A 



N/A 



Seconds 





















Fig. 3 Helical velocity component, v • e-, /V 



DISCUSSION OF EXAMPLE COMPUTATIONS 



In this section, the consequences of choices the 

 designer might make both for overall geometry and for the 

 chordwise variation of the thickness distribution and loading 

 distribution are examined. Some common variations in the 

 location of the blade mid-chord line are investigated to deter- 

 mine the effects of overall geometry on pitch, camber, 

 pressure distribution, and second-order performance coeffi- 

 cients. The variations are unskewed, skewed and warped (23) 

 blades with other input specifications the same. Skewed 

 blades have blade-sections displaced along the pitch helix 

 and warped blades have blade sections displaced circum- 

 ferentially in the plane at x = 0. 



Input quantities and selected output are shown in 

 Table II for a warped blade similar to NSRDC Model 4498 

 (and one similar to the example of Reference 7). For an 

 unskewed blade, the column labeled TETS, the skew angle 

 S , would be zero, and for a skewed blade the column 

 labeled RAKT/D, the total rake ij /D, would be equal to 

 P • s /(27rD). In Figure 4, the computed pitch and 

 camber ratios are shown for these various overall geometries 

 with all other input the same as in Table II. In Figure 5, 

 the effects of the chordwise load distribution and chordwise 

 thickness function on pitch and camber are shown. The 

 effect of rake and skew on pitch and camber follows known 

 trends (7, 24). The effect of thickness distribution on pitch 

 and camber is negligible and the effect of elliptic loading is 

 to reduce the pitch and increase the camber, as would be the 

 case in two dimensional flow at the ideal angle for a given 

 lift coefficient. In Figure 6, the pitch and camber change is 

 shown for another modification of the waiped blade. Since 

 a large change occurs in the pitch from the input specifica- 

 tion (Table II) to the computed values (Figure 4), computa- 

 tions were performed with the singularities distributed on 

 the blade reference surface at a pitch taken from Figure 4. 

 This change in pitch places the singularities nearer the final 

 blade surface. To have uniformity in the calculations, the 

 pitch angle of the shed vortex sheet was taken as (3, the 

 advance angle of the shed vortex sheet. (In Figure 4, the 

 shed vortex sheet was taken to be at the input pitch, which 

 is /3j, the pitch angle derived from the solution of a straight 

 radial lifting-line representing each blade.) The change in 

 pitch angle of the shed vortex wake from 0, to produces 

 a slight increase of pitch near the hub (compare data in 

 Figures 4 and 6). A change in the pitch of the blade reference 

 surface to the values shown by the dashed curve in Figure 4 

 produces a significant reduction in computed pitch and a 

 compensating increase in camber near the root, with negli- 

 gible change in either pitch or camber from about xr = 0.5 

 to the tip. Hence the orientation of the free vortex sheet 

 and blade reference surface have significant effects on the 

 pitch and camber values only near the hub. 



14 



