586 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.4 



The coefficients are, in Baker's notation: 



Slip constant X = — — , where A'' is in 



rpm, D in ft, and Fi (= Va) is the speed of 

 advance in kt 

 Diameter constant 



_fl_ r p/D ifi) 



D'Vl 1{P/D) + 21J\bJ' 



where H is the thrust power in horses, Vj the 

 speed of advance in kt, P and D are in ft, and B 

 is a thrust factor for the blade type, actually an 

 arbitrary function of blade-area ratio. The latter 

 is presumably the ratio Ad/Ao . Cross curves of 

 the diameter constant Y and the revolution 

 constant X^Y are plotted on a grid of X, Y, and 

 77(eta). The developed-area ratio A^/Ao of 

 Gawn's series propellers extended up to 1.10. 

 The method of using the R. E. Froude-Gawn 

 charts is explained by W. P. A. van Lammeren in 

 detail in the reference cited. 

 (II) Charts of D. W. Taylor [S and P, 1943, pp. 

 99-102, 109-112, 275-292]. The basic coefficients 



Nd 

 8 (delta) = -:^ , where A'' is in rpm, d is the 



y A 



diameter in ft, and Va is the speed of advance in kt 



NP° 



B, 



VI 



, where P is the propeller power 



in horses. The number of blades is generally 

 added as a subscript to the basic coefficient, such 

 as 5p3 . 



Bu = 



v\ 



, where IJ is the thrust power in 



horses. 



Cross curves of 6 and efficiency e are plotted 

 on a grid of P/D as ordinate and Bp or B^ as 

 abscissas. Other chart forms are used with the 

 coefficients: 



Cv = a 



U 



"^ UOOO/ 



, where a is the pitch ratio 



p/d, U is the thrust power in horses, d is the 

 diameter, and p is the pitch, both the latter in ft 



. lOOOaU , ^, , , 



Av = ,2x^3 — , where the symbols are as de- 

 a y A 



scribed previously for the Taylor charts. 



These coefficients and charts, as given in the 



reference quoted, are for model propellers tested 



in fresh water. Since the coefficients are dimen- 

 sional they do not produce ship-design data for 

 salt water unless a correction is made for the 

 differences in mass density [Kane, J. R., SNAME, 

 1951, pp. 625-626]. D. W. Taylor's statement 

 that "... marine propellers work in water of 

 practically constant density . . ." [S and P, 1943, 

 p. 100] is too sweeping. Many ships operate in 

 fresh water only, and others in water that varies 

 from fully fresh to fully salt. 



A table of values of Va^, for a range of Va in 

 kt from 5 to 50, is given by L. P. Smith [ASNE, 

 Nov 1935, p. 562]. 



(Ill) Charts of K. Schaffran. First published in 

 German in "Systematische Propellerversuche 

 (Systematic Propeller Experiments)," Strauss, 

 Berlin, 1916. Later published in English in what 

 was virtually a treatise on the subject, entitled 

 "The Influence of Propeller Revolutions Upon the 

 Propulsive Efficiency of Merchant Ships," NECI, 

 1923-1924, Vol. XL, pp. 254-320 and Pis. 

 II-XII. Some of these data were published sub- 

 sequently in WRH, 15 Nov 1934, Vol. 15, pp. 

 324-327; see also W. P. A. van Lammeren, 

 RPSS, 1948, pp. 191-196. 



The coefficients are: 



Slip constant C, = 



where n is the 



nD _nD 



Ve ~Va 



rate of rotation in rps, Z) is the diameter, and 

 V E (or V a) is the speed of advance, all in con- 

 sistent units 



'71' 

 where M is the torque 



Revolutions-torque constant C„„ = Uy 



Diameter-torque constant d^ = 



Diameter-thrust constant d = 

 is the thrust 



DVj, 



where & 



Revolution-thrust constant C„ = 



VI 



The basic grids are C. on d and C, on C„ . 

 (IV) Charts of W. Schmidt ["Zusammenfassende 

 Darstellung von Schraubenversuchen (Summar- 

 ized Description of Propeller Experiments);" this 

 is a pamphlet published by Zeit. des Ver. Deutsch 

 Ing., in 1926; copy in TMB Ubrary. See also a 

 paper entitled "Vorausberechnung der Giinstig- 

 sten Schiffsschraube (Calculation of the Most 

 Favorable Ship Propeller)," by H. Volker; ab- 

 stracted by W. Hinterthan in WRH, 1 Dec 1939, 



