Sec. 47.6 



SHIP AND PROPELLER CAVITATION 



151 



distribution across the — Ap side for some repre- 

 sentative angle of attack, so much the better. 



Taking a representative case, assume a hydro- 

 foil similar to that diagrammed in Fig. 47. C to 

 be running in salt water at a depth of 8 ft below 

 the surface and at a speed of advance of 30 kt, or 

 50.67 ft per sec. The hydrostatic pressure is, from 

 Tables 41.e or X3.a, 8(0.4447) = 3.56 psi. 

 Assuming a value of Pa of 14.7 lb per in", a vapor 

 pressure of 0.4 lb per in' and a mass density p 

 of 1.9905 slugs per ft^, the cavitation index works 

 out as 



V^-e _ [(3.56 + 14.7) - 0.4]144 

 q ~ 0.99525(50.67)' 



1.006. 



From the lower diagram of Fig. 47. C it is to be 

 noted that at this cavitation parameter the 

 hydrofoil will cavitate on the face or on the back 

 at angles of attack greater numerically than 

 — 2.7 or +4.5 deg, respectively. 



"0 0.01 O.oa 0.03 0.04 0.05 0.06 0.07 



Ratio of Leadinq-Edae Radius R^e to Chord Lenoth c. 



Fig. 47.D Cavitation, Lift-Coefficient, and 

 Angle-of-Attack Data for a Stmmetrical Hydrofoil 



Fig. 47. D, adapted from a set of graphs given 

 by P. Mandel [SNAME, 1953, Fig. 7, p. 471], 

 gives the average pressure coefficient E„ , at the 

 point of minimum absolute pressure, for a large 

 number of 2-diml symmetrical hydrofoils at four 

 different angles of attack. The £^„-values are 



plotted on a basis of the 0-diml ratio of the nose 

 radius Rle to the chord length c. 



If the cavitation number a in the adjacent 

 liquid is smaller numerically than the pressure 

 coefficient £'„ at the point of minimum absolute 

 pressure on the hydrofoil, cavitation occurs there, 

 hence the pressure coefficient at the lowest- 

 pressure point equals numerically the critical 

 cavitation number acR ■ 



As an example of the manner in which the 

 diagrams of Fig. 47. D may be used, consider the 

 situation at the leading edge of a symmetrical 

 streamlined balanced rudder with an all-movable 

 blade. The rudder lies abaft a portion of the upper 

 blade of a screw propeller where the rotational- 

 or tangential-flow component is such as to cause 

 the water in the inflow jet to meet the leading 

 edge of the rudder at a given waterline at an 

 angle of 10 deg. Assume a nose radius of 0.25 ft, 

 a chord length of 10 ft, a nominal depth of sub- 

 mergence /i of 15 ft, and a ship speed of 18 kt 

 (actually, the local velocity in the outflow jet 

 may be greater than this). Then from the nomo- 

 gram of Fig. 47. B the cavitation number a is 

 about 3.3 if cavitation is to begin at 18 kt. The 

 ratio of nose radius Rle to chord length c is 

 0.25/10 = 0.025. From the curve for a 10-deg 

 angle of attack in Fig. 47. D the pressure coefficient 

 E^ at the point of lowest absolute pressure, where 

 cavitation will first appear, is about —3.2. Then 

 <jcB is 3.2, and the differential pressure available 

 to create a gradient which will cause the water to 

 follow the rudder section closely is represented by 

 a cavitation number of only 3.3. The "lee" or 

 — Ap side of the rudder section in question is, 

 therefore, just on the verge of cavitation at the 

 given speed. 



Contours for pressure minima in terms of 

 (1) Ap/q, (2) thickness ratio, and (3) lift coefficient, 

 for ogival and airfoil sections, respectively, are 

 given by K. E. Schoenherr [SNAME, 1934, Figs. 

 19-20, pp. 109-112]. These sections are suitable 

 for use on propeller blades. 



47.6 Cavitation Data for Bodies of Revolution 

 and Other Bodies. Cavitation may take place 

 on many parts of a ship and its appendages which 

 do not even remotely resemble the hydrofoils 

 discussed in the preceding section. A considerable 

 number of these parts have the forms of bodies 

 of revolution, or they can be simulated by 3-diml 

 axisymmetric forms, such as certain types of 

 bulbs incorporated into the forefoot. 



Cavitation data are available for a great 



