The first harmonic pressure coefficient is approximated by, 



^"Vjmax (P-^Jmin 



J pl 



l/2p[V 2 +(2TTrn) 2 ] 



This information produces a lagging cosine series phase angle <(>.. , as defined by 

 Equation (1), of 270 deg if C . is negative, and 90 deg if C - is positive. Sub- 

 stituting into the previous equations, C 1 can be represented as 



~ pjmin 



pi ~ 2 



V 2 +(27Trn+V ril ) 2 

 c T 



V 2 +(2TTrn) 2 

 c 



"pJmax 



V 2 +(27Trn-V T ) 2 

 c 1 



V +(2irrn) 



The first harmonic pressure coefficient C 1 , can be seen to depend upon two effects. 



One is the local variation in J producing the C T . and C T terms. The other is 



pjmm pJmax 



the speed correction of those terms due to the local variation in speed V,,, repre- 

 sented by the ratios inside the brackets. Term C T . will always be increased by 

 ' pjmin J J 



the speed correction by a constant ratio, dependent upon radial position for a given 

 operating condition. In a similar manner, C will always be decreased. 



From this result, trends can be observed in the predicted quasi-steady first 

 harmonic pressure coefficients. Figure 27 demonstrates typical quasi-steady calcu- 

 lations on the suction and pressure sides of the propeller blade. Note that the 

 magnitude of the slopes of the C versus J plots for the suction side and pressure 

 side of the blade are roughly similar, but the pressure side has a negative slope 

 while the suction side has a positive slope. This slope polarity difference will 

 produce an opposite effect of the quasi-steady speed correction in calculating the 

 first harmonic pressure coefficients. The speed correction will tend to decrease 

 the first harmonic pressure coefficient on the pressure side of the blade, and 

 increase it on the suction side. This trend is due to only the difference in local 



velocities at J , and J . , and the signs of slopes of the C versus J curves, 

 max mm p 



34 



