342 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 59.12 



One such feature applies to the element of a 

 screw-propeller blade on which the instantaneous 

 incident-A'elocity vector impinges in a plane not 

 normal to the blade axis, corresponding to the 

 non-axial flow situation described in Sec. 17.7 

 and depicted in diagram 1 of Fig. 17. D. It is 

 again emphasized that for this case the effective 

 velocity across the blade is the incident velocity 

 U R times the sine of the angle which that velocity 

 vector makes with the blade axis, as projected 

 on a plane passing through the base chord of the 

 blade element and the blade axis. The situation 

 here corresponds to that of the flow over an 

 airplane wing with sweep-back. The effective 

 velocity of the air stream, for generating lift, is 

 the component of the speed vector l3'ing normal 

 to the blade axis, in a plane generally parallel to 

 the wing. This is equal to the stream velocity 

 times the cosine of the angle of sweepback [Collar, 

 A. R., "Aeroelastic Problems at High Speed," 

 Jour. Roy. Aero. Soc, Jan 1947, pp. 15-16]. 



Theoretically, this situation should apply also 

 to a screw-propeller blade with skew-back, and 

 to the converging flow of an inlet jet when 

 approaching the propeller disc. In the former 

 case, throughout most of the length of the blade, 

 the local blade-axis direction is not normal to 

 the tangent plane of the local incident flow. 

 However, since the effect and the magnitude of 

 sweep-back have not as yet (1955) been incor- 

 porated in any of the analysis or design phases for 



screw propellers, the effective velocity is assumed 

 the same as the nominal incident velocity. 



In the latter case, diagram 1 of Fig. 59. G of 

 Sec. 59.13 indicates that for a thrust-load factor 

 Ctl of 24, rarely reached in any kind of ship 

 service, the convergence angle of the inflow jet, 

 at the propeller tip, is about 19 deg. The cosine 

 of this angle is 0.9455, but it must be remembered 

 that the lift and the thrust for any blade element 

 of thickness dR vary as the square of the incident 

 velocity. The effective thrust on the tip blade 

 element therefore appears to be reduced by the 

 factor (1 — cos' B), where 5(theta) is the conver- 

 gence angle. For the case mentioned this is 

 [1 - (0.9455)'] or about 0.106. 



Applying also to Fig. 59.G of Sec. 59.13, the 

 graphs of Fig. 59. F indicate the ratios of the 

 inflow-jet and outflow-jet diameters to the diam- 

 eter of an imaginary actuator-disc propeller, for 

 a range of thrust-load coefficient values up to 6.0. 

 The data given are for positions 3D ahead of and 

 2iD abaft the disc position, respectively. 



Only in the case of systematic variations in 

 inflow, occurring over most of the disc area, is it 

 possible to predict their effect on propeller per- 

 formance. For instance, general prerotation in 

 the inflow jet, in a direction opposite to that of 

 the propeller, results in a slower rate of rotation, 

 a reduction in power absorbed, and (usually) an 

 increase in efficiency for the generation of a given 

 propeller thrust. 



Thrust-Load Coefficient C^l 

 2.0 2.4 2,8 3.2 3.£ A.O 



0-7 1=1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I M I I I I I I I I I I I I I I I I I I I I I 11 I I I 1^ 07 



0.0 0.4 0.& ).2 1.6 2D 2.4 Z.8 3.2 3.G 4.0 4.4 A.& 5.2 5.G G.O 



Thrubt-Load Coefficient Ctl 



Fig. 59. F Graphs Indicating Ratios of Inflow- and Outflow-Jet Diameters to Disc Diameter of an Ideal 



Screw Propeller 



