Sec. 70.46 



SCREW-PROPELLER DESIGN 



637 



For a complex shape of trailing edge, as in the 

 figure, the eftective thickness is both difficult to 

 estimate and to confirm. A means of making a 

 tentative prediction is given by F. Kito [Zosen 

 Kokai, Japan, May 1948, No. 277; also Abstract 

 Notes and Data for 6th ICSTS, 1951, pp. 41-42 

 (in English)]. 

 From Sec. 2.22 the Strouhal number is 



S„ = =^ , or / = ,S„(|) = S„ ^ (70.XX) 



Here / is the vibration frequency, lying within the 

 audible range to produce singing, generally above 

 10 per sec and below 10,000 or 12,000 per sec. 

 Practically, the highest audible frequency of a 

 singing propeller is about 700 to 1,200 cycles per 

 sec. The velocity U is the blade velocity Feude , 

 obtained by combining vectorially the rotational 

 velocity 2-KnR with the advance velocity V a ■ The 

 blade velocity varies with radius R, with rate 

 of propeller rotation n, and with ship speed V. 

 The maximum occurs at or near the tip at full 

 designed speed; the minimum at some smaller 

 combination of the three variables. As a low 

 limit it should be satisfactory to use R = 0.4/?Ma:c , 

 n = 0.5nMai , and V = O.ST^Max • 



The blade-section Reynolds numbers R„ are 

 calculated for these two extremes, and from the 

 graph at the left in Fig. 46. G the corresponding 



Hmiting values of S„ are found. The value of t 

 for the limiting radii is then estimated and from 

 Eq. (70. xx) the frequency / is calculated. If / 

 lies within the audible range, objectionable singing 

 is possible. An example illustrating this procedure 

 is worked out in Sec. 46.9. 



If singing is thought probable, or if it is actually 

 occurring, it is almost invariably prevented or 

 eliminated by the use of the so-called chisel edge, 

 sketched in heavy Unes in Fig. 70. P. Provided 

 there is no large slope well ahead of the trailing 

 edge where separation might begin, the two 

 corners thus formed comprise two definite and 

 fixed separation points at the upstream end of a 

 narrow separation zone between them. The eddy 

 pattern in this zone remains sensibly steady, to 

 the extent that any eddy pattern can do so. At 

 least, the circulation around the blade does not 

 vary periodically, with a frequency in the audible 

 range, nor does it fluctuate in magnitude at any 

 such frequency. 



Other methods of providing fixed separation 

 points along the trailing edges of propeller blades, 

 to prevent singing, are shown by J. A. van Aken 

 [European Shipbldg., 1955, Vol. 4, Fig. 3, p. 31]. 



The singing propeller is discussed briefly by 

 F. M. Lewis [ME, 1944, Vol. II, p. 131]. A partial 

 list of references relating to singing propellers is 

 given in Sec. 46.10. 



